pyscf.dft package#
Subpackages#
Submodules#
pyscf.dft.LebedevGrid module#
pyscf.dft.dft_parser module#
unified dft parser for coordinating dft protocols with 1. xc functionals 2. dispersion corrections / nonlocal correction 3. GTO basis (TODO) 4. geometrical counterpoise (gCP) correction (TODO)
pyscf.dft.dks module#
4-component Dirac-Kohn-Sham
- class pyscf.dft.dks.DKS(mol, xc='LDA,VWN')[source]#
Bases:
KohnShamDFT,DHFKramers unrestricted Dirac-Kohn-Sham
- CasidaTDDFT = None#
- TDA(*args, **kwargs)#
Tamm-Dancoff approximation
- Attributes:
- conv_tolfloat
Diagonalization convergence tolerance. Default is 1e-9.
- nstatesint
Number of TD states to be computed. Default is 3.
Saved results:
- convergedbool
Diagonalization converged or not
- e1D array
excitation energy for each excited state.
- xyA list of two 2D arrays
The two 2D arrays are Excitation coefficients X (shape [nocc,nvir]) and de-excitation coefficients Y (shape [nocc,nvir]) for each excited state. (X,Y) are normalized to 1/2 in RHF/RKS methods and normalized to 1 for UHF/UKS methods. In the TDA calculation, Y = 0.
- TDDFT(*args, **kwargs)#
- TDHF = None#
- to_gpu(out=None)#
Convert a method to its corresponding GPU variant, and recursively converts all attributes of a method to cupy objects or gpu4pyscf objects.
- x2c()#
- class pyscf.dft.dks.KohnShamDFT(xc='LDA,VWN')[source]#
Bases:
KohnShamDFT- property collinear#
- energy_elec(dm=None, h1e=None, vhf=None)#
Electronic part of RKS energy.
Note this function has side effects which cause mf.scf_summary updated.
- Args:
ks : an instance of DFT class
- dm2D ndarray
one-particle density matrix
- h1e2D ndarray
Core hamiltonian
- Returns:
RKS electronic energy and the 2-electron contribution
- get_veff(mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1)#
Coulomb + XC functional
Note
This function will change the ks object.
- Args:
- ksan instance of
RKS XC functional are controlled by ks.xc attribute. Attribute ks.grids might be initialized.
- dmndarray or list of ndarrays
A density matrix or a list of density matrices
- ksan instance of
- Kwargs:
- dm_lastndarray or a list of ndarrays or 0
The density matrix baseline. If not 0, this function computes the increment of HF potential w.r.t. the reference HF potential matrix.
- vhf_lastndarray or a list of ndarrays or 0
The reference Vxc potential matrix.
- hermiint
Whether J, K matrix is hermitian
0 : no hermitian or symmetric1 : hermitian2 : anti-hermitian
- Returns:
matrix Veff = J + Vxc. Veff can be a list matrices, if the input dm is a list of density matrices.
- property spin_samples#
- to_dhf()[source]#
Convert the input mean-field object to a DHF object.
Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.
- to_ghf()[source]#
Convert the input mean-field object to a GHF object.
Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.
- to_gks(xc=None)[source]#
Convert the input mean-field object to a GKS object.
Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.
- to_hf()#
Convert the input mean-field object to a DHF object.
Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.
- to_ks(xc=None)#
- to_rhf()[source]#
Convert the input mean-field object to a RHF/ROHF object.
Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.
- to_rks(xc=None)[source]#
Convert the input mean-field object to a RKS/ROKS object.
Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.
- class pyscf.dft.dks.RDKS(mol, xc='LDA,VWN')[source]#
-
Kramers restricted Dirac-Kohn-Sham
- CasidaTDDFT = None#
- TDA(*args, **kwargs)#
Tamm-Dancoff approximation
- Attributes:
- conv_tolfloat
Diagonalization convergence tolerance. Default is 1e-9.
- nstatesint
Number of TD states to be computed. Default is 3.
Saved results:
- convergedbool
Diagonalization converged or not
- e1D array
excitation energy for each excited state.
- xyA list of two 2D arrays
The two 2D arrays are Excitation coefficients X (shape [nocc,nvir]) and de-excitation coefficients Y (shape [nocc,nvir]) for each excited state. (X,Y) are normalized to 1/2 in RHF/RKS methods and normalized to 1 for UHF/UKS methods. In the TDA calculation, Y = 0.
- TDDFT(*args, **kwargs)#
- TDHF = None#
- to_dhf()[source]#
Convert the input mean-field object to a DHF object.
Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.
- x2c()#
- pyscf.dft.dks.energy_elec(ks, dm=None, h1e=None, vhf=None)[source]#
Electronic part of DKS energy.
Note this function has side effects which cause mf.scf_summary updated.
- Args:
ks : an instance of DFT class
- dm2D ndarray
one-particle density matrix
- h1e2D ndarray
Core hamiltonian
- Returns:
DKS electronic energy and the 2-electron contribution
- pyscf.dft.dks.get_veff(ks, mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1)[source]#
Coulomb + XC functional
Note
This function will change the ks object.
- Args:
- ksan instance of
RKS XC functional are controlled by ks.xc attribute. Attribute ks.grids might be initialized.
- dmndarray or list of ndarrays
A density matrix or a list of density matrices
- ksan instance of
- Kwargs:
- dm_lastndarray or a list of ndarrays or 0
The density matrix baseline. If not 0, this function computes the increment of HF potential w.r.t. the reference HF potential matrix.
- vhf_lastndarray or a list of ndarrays or 0
The reference Vxc potential matrix.
- hermiint
Whether J, K matrix is hermitian
0 : no hermitian or symmetric1 : hermitian2 : anti-hermitian
- Returns:
matrix Veff = J + Vxc. Veff can be a list matrices, if the input dm is a list of density matrices.
pyscf.dft.gen_grid module#
Generate DFT grids and weights, based on the code provided by Gerald Knizia <>
- Reference for Lebedev-Laikov grid:
V. I. Lebedev, and D. N. Laikov “A quadrature formula for the sphere of the 131st algebraic order of accuracy”, Doklady Mathematics, 59, 477-481 (1999)
- class pyscf.dft.gen_grid.Grids(mol)[source]#
Bases:
StreamObjectDFT mesh grids
- Attributes for Grids:
- levelint
To control the number of radial and angular grids. Large number leads to large mesh grids. The default level 3 corresponds to (50,302) for H, He; (75,302) for second row; (80~105,434) for rest.
Grids settings at other levels can be found in pyscf.dft.gen_grid.RAD_GRIDS and pyscf.dft.gen_grid.ANG_ORDER
- atomic_radii1D array
- radi.BRAGG_RADII (default)radi.COVALENT_RADIINone : to switch off atomic radii adjustment
- radii_adjustfunction(mol, atomic_radii) => (function(atom_id, atom_id, g) => array_like_g)
Function to adjust atomic radii, can be one of | radi.treutler_atomic_radii_adjust | radi.becke_atomic_radii_adjust | None : to switch off atomic radii adjustment
- radi_methodfunction(n) => (rad_grids, rad_weights)
scheme for radial grids, can be one of | radi.treutler (default) | radi.delley | radi.mura_knowles | radi.gauss_chebyshev
- becke_schemefunction(v) => array_like_v
weight partition function, can be one of | gen_grid.original_becke (default) | gen_grid.stratmann
- prunefunction(nuc, rad_grids, n_ang) => list_n_ang_for_each_rad_grid
scheme to reduce number of grids, can be one of | gen_grid.nwchem_prune (default) | gen_grid.sg1_prune | gen_grid.treutler_prune | None : to switch off grid pruning
- symmetrybool
whether to symmetrize mesh grids (TODO)
- atom_griddict
Set (radial, angular) grids for particular atoms. Eg, grids.atom_grid = {‘H’: (20,110)} will generate 20 radial grids and 110 angular grids for H atom.
Examples:
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1') >>> grids = dft.gen_grid.Grids(mol) >>> grids.level = 4 >>> grids.build()
- alignment = 8#
- atomic_radii = array([3.77945036, 0.66140414, 2.64561657, 2.74010288, 1.98421243, 1.60626721, 1.32280829, 1.22832198, 1.13383567, 0.94486306, 2.83458919, 3.40150702, 2.83458919, 2.36215766, 2.07869874, 1.88972612, 1.88972612, 1.88972612, 3.40150702, 4.15739747, 3.40150702, 3.0235618 , 2.64561657, 2.55113027, 2.64561657, 2.64561657, 2.64561657, 2.55113027, 2.55113027, 2.55113027, 2.55113027, 2.45664396, 2.36215766, 2.17318504, 2.17318504, 2.17318504, 3.59047964, 4.44085639, 3.77945225, 3.40150702, 2.92907549, 2.74010288, 2.74010288, 2.55113027, 2.45664396, 2.55113027, 2.64561657, 3.0235618 , 2.92907549, 2.92907549, 2.74010288, 2.74010288, 2.64561657, 2.64561657, 3.96842486, 4.91328792, 4.06291117, 3.68496594, 3.49599333, 3.49599333, 3.49599333, 3.49599333, 3.49599333, 3.49599333, 3.40150702, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 2.92907549, 2.74010288, 2.55113027, 2.55113027, 2.45664396, 2.55113027, 2.55113027, 2.55113027, 2.83458919, 3.59047964, 3.40150702, 3.0235618 , 3.59047964, 2.74010288, 3.96842486, 3.40150702, 4.06291117, 3.68496594, 3.40150702, 3.40150702, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072])#
- static becke_scheme(g)#
Becke, JCP 88, 2547 (1988); DOI:10.1063/1.454033
- cutoff = 1e-15#
- gen_atomic_grids(mol=None, atom_grid=None, radi_method=None, level=None, prune=None, **kwargs)#
Generate number of radial grids and angular grids for the given molecule.
- Returns:
A dict, with the atom symbol for the dict key. For each atom type, the dict value has two items: one is the meshgrid coordinates wrt the atom center; the second is the volume of that grid.
- gen_partition(mol, atom_grids_tab=None, radii_adjust=None, atomic_radii=array([3.77945036, 0.66140414, 2.64561657, 2.74010288, 1.98421243, 1.60626721, 1.32280829, 1.22832198, 1.13383567, 0.94486306, 2.83458919, 3.40150702, 2.83458919, 2.36215766, 2.07869874, 1.88972612, 1.88972612, 1.88972612, 3.40150702, 4.15739747, 3.40150702, 3.0235618, 2.64561657, 2.55113027, 2.64561657, 2.64561657, 2.64561657, 2.55113027, 2.55113027, 2.55113027, 2.55113027, 2.45664396, 2.36215766, 2.17318504, 2.17318504, 2.17318504, 3.59047964, 4.44085639, 3.77945225, 3.40150702, 2.92907549, 2.74010288, 2.74010288, 2.55113027, 2.45664396, 2.55113027, 2.64561657, 3.0235618, 2.92907549, 2.92907549, 2.74010288, 2.74010288, 2.64561657, 2.64561657, 3.96842486, 4.91328792, 4.06291117, 3.68496594, 3.49599333, 3.49599333, 3.49599333, 3.49599333, 3.49599333, 3.49599333, 3.40150702, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 2.92907549, 2.74010288, 2.55113027, 2.55113027, 2.45664396, 2.55113027, 2.55113027, 2.55113027, 2.83458919, 3.59047964, 3.40150702, 3.0235618, 3.59047964, 2.74010288, 3.96842486, 3.40150702, 4.06291117, 3.68496594, 3.40150702, 3.40150702, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072]), becke_scheme=<function original_becke>, concat=True)#
Generate the mesh grid coordinates and weights for DFT numerical integration. We can change radii_adjust, becke_scheme functions to generate different meshgrid.
- Kwargs:
- concat: bool
Whether to concatenate grids and weights in return
- Returns:
grid_coord and grid_weight arrays. grid_coord array has shape (N,3); weight 1D array has N elements.
- get_partition(mol, atom_grids_tab=None, radii_adjust=None, atomic_radii=array([3.77945036, 0.66140414, 2.64561657, 2.74010288, 1.98421243, 1.60626721, 1.32280829, 1.22832198, 1.13383567, 0.94486306, 2.83458919, 3.40150702, 2.83458919, 2.36215766, 2.07869874, 1.88972612, 1.88972612, 1.88972612, 3.40150702, 4.15739747, 3.40150702, 3.0235618, 2.64561657, 2.55113027, 2.64561657, 2.64561657, 2.64561657, 2.55113027, 2.55113027, 2.55113027, 2.55113027, 2.45664396, 2.36215766, 2.17318504, 2.17318504, 2.17318504, 3.59047964, 4.44085639, 3.77945225, 3.40150702, 2.92907549, 2.74010288, 2.74010288, 2.55113027, 2.45664396, 2.55113027, 2.64561657, 3.0235618, 2.92907549, 2.92907549, 2.74010288, 2.74010288, 2.64561657, 2.64561657, 3.96842486, 4.91328792, 4.06291117, 3.68496594, 3.49599333, 3.49599333, 3.49599333, 3.49599333, 3.49599333, 3.49599333, 3.40150702, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 2.92907549, 2.74010288, 2.55113027, 2.55113027, 2.45664396, 2.55113027, 2.55113027, 2.55113027, 2.83458919, 3.59047964, 3.40150702, 3.0235618, 3.59047964, 2.74010288, 3.96842486, 3.40150702, 4.06291117, 3.68496594, 3.40150702, 3.40150702, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072]), becke_scheme=<function original_becke>, concat=True)[source]#
Generate the mesh grid coordinates and weights for DFT numerical integration. We can change radii_adjust, becke_scheme functions to generate different meshgrid.
- Kwargs:
- concat: bool
Whether to concatenate grids and weights in return
- Returns:
grid_coord and grid_weight arrays. grid_coord array has shape (N,3); weight 1D array has N elements.
- kernel(mol=None, with_non0tab=False)[source]#
Kernel function is the main driver of a method. Every method should define the kernel function as the entry of the calculation. Note the return value of kernel function is not strictly defined. It can be anything related to the method (such as the energy, the wave-function, the DFT mesh grids etc.).
- level = 3#
- make_mask(mol=None, coords=None, relativity=0, shls_slice=None, cutoff=None, verbose=None)#
Mask to indicate whether a shell is ignorable on grids. See also the function gto.eval_gto.make_screen_index
- Args:
mol : an instance of
Mole- coords2D array, shape (N,3)
The coordinates of grids.
- Kwargs:
- relativitybool
No effects.
- shls_slice2-element list
(shl_start, shl_end). If given, only part of AOs (shl_start <= shell_id < shl_end) are evaluated. By default, all shells defined in mol will be evaluated.
- verboseint or object of
Logger No effects.
- Returns:
2D mask array of shape (N,nbas), where N is the number of grids, nbas is the number of shells.
- static prune(nuc, rads, n_ang, radii=array([3.77945036, 0.66140414, 2.64561657, 2.74010288, 1.98421243, 1.60626721, 1.32280829, 1.22832198, 1.13383567, 0.94486306, 2.83458919, 3.40150702, 2.83458919, 2.36215766, 2.07869874, 1.88972612, 1.88972612, 1.88972612, 3.40150702, 4.15739747, 3.40150702, 3.0235618, 2.64561657, 2.55113027, 2.64561657, 2.64561657, 2.64561657, 2.55113027, 2.55113027, 2.55113027, 2.55113027, 2.45664396, 2.36215766, 2.17318504, 2.17318504, 2.17318504, 3.59047964, 4.44085639, 3.77945225, 3.40150702, 2.92907549, 2.74010288, 2.74010288, 2.55113027, 2.45664396, 2.55113027, 2.64561657, 3.0235618, 2.92907549, 2.92907549, 2.74010288, 2.74010288, 2.64561657, 2.64561657, 3.96842486, 4.91328792, 4.06291117, 3.68496594, 3.49599333, 3.49599333, 3.49599333, 3.49599333, 3.49599333, 3.49599333, 3.40150702, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 2.92907549, 2.74010288, 2.55113027, 2.55113027, 2.45664396, 2.55113027, 2.55113027, 2.55113027, 2.83458919, 3.59047964, 3.40150702, 3.0235618, 3.59047964, 2.74010288, 3.96842486, 3.40150702, 4.06291117, 3.68496594, 3.40150702, 3.40150702, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072]))#
NWChem
- Args:
- nucint
Nuclear charge.
- rads1D array
Grid coordinates on radical axis.
- n_angint
Max number of grids over angular part.
- Kwargs:
- radii1D array
radii (in Bohr) for atoms in periodic table
- Returns:
A list has the same length as rads. The list element is the number of grids over angular part for each radial grid.
- prune_by_density_(rho, threshold=0)[source]#
Prune grids if the electron density on the grid is small
- static radi_method(n, chg, *args, **kwargs)#
Treutler-Ahlrichs [JCP 102, 346 (1995); DOI:10.1063/1.469408] (M4) radial grids
- static radii_adjust(mol, atomic_radii)#
Treutler atomic radii adjust function: [JCP 102, 346 (1995); DOI:10.1063/1.469408]
- property size#
- to_gpu(out=None)#
Convert a method to its corresponding GPU variant, and recursively converts all attributes of a method to cupy objects or gpu4pyscf objects.
- pyscf.dft.gen_grid.arg_group_grids(mol, coords, box_size=1.2)[source]#
Partition the entire space into small boxes according to the input box_size. Group the grids against these boxes.
- pyscf.dft.gen_grid.gen_atomic_grids(mol, atom_grid={}, radi_method=<function gauss_chebyshev>, level=3, prune=<function nwchem_prune>, **kwargs)[source]#
Generate number of radial grids and angular grids for the given molecule.
- Returns:
A dict, with the atom symbol for the dict key. For each atom type, the dict value has two items: one is the meshgrid coordinates wrt the atom center; the second is the volume of that grid.
- pyscf.dft.gen_grid.gen_partition(mol, atom_grids_tab, radii_adjust=None, atomic_radii=array([3.77945036, 0.66140414, 2.64561657, 2.74010288, 1.98421243, 1.60626721, 1.32280829, 1.22832198, 1.13383567, 0.94486306, 2.83458919, 3.40150702, 2.83458919, 2.36215766, 2.07869874, 1.88972612, 1.88972612, 1.88972612, 3.40150702, 4.15739747, 3.40150702, 3.0235618, 2.64561657, 2.55113027, 2.64561657, 2.64561657, 2.64561657, 2.55113027, 2.55113027, 2.55113027, 2.55113027, 2.45664396, 2.36215766, 2.17318504, 2.17318504, 2.17318504, 3.59047964, 4.44085639, 3.77945225, 3.40150702, 2.92907549, 2.74010288, 2.74010288, 2.55113027, 2.45664396, 2.55113027, 2.64561657, 3.0235618, 2.92907549, 2.92907549, 2.74010288, 2.74010288, 2.64561657, 2.64561657, 3.96842486, 4.91328792, 4.06291117, 3.68496594, 3.49599333, 3.49599333, 3.49599333, 3.49599333, 3.49599333, 3.49599333, 3.40150702, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 2.92907549, 2.74010288, 2.55113027, 2.55113027, 2.45664396, 2.55113027, 2.55113027, 2.55113027, 2.83458919, 3.59047964, 3.40150702, 3.0235618, 3.59047964, 2.74010288, 3.96842486, 3.40150702, 4.06291117, 3.68496594, 3.40150702, 3.40150702, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072]), becke_scheme=<function original_becke>, concat=True)#
Generate the mesh grid coordinates and weights for DFT numerical integration. We can change radii_adjust, becke_scheme functions to generate different meshgrid.
- Kwargs:
- concat: bool
Whether to concatenate grids and weights in return
- Returns:
grid_coord and grid_weight arrays. grid_coord array has shape (N,3); weight 1D array has N elements.
- pyscf.dft.gen_grid.get_partition(mol, atom_grids_tab, radii_adjust=None, atomic_radii=array([3.77945036, 0.66140414, 2.64561657, 2.74010288, 1.98421243, 1.60626721, 1.32280829, 1.22832198, 1.13383567, 0.94486306, 2.83458919, 3.40150702, 2.83458919, 2.36215766, 2.07869874, 1.88972612, 1.88972612, 1.88972612, 3.40150702, 4.15739747, 3.40150702, 3.0235618, 2.64561657, 2.55113027, 2.64561657, 2.64561657, 2.64561657, 2.55113027, 2.55113027, 2.55113027, 2.55113027, 2.45664396, 2.36215766, 2.17318504, 2.17318504, 2.17318504, 3.59047964, 4.44085639, 3.77945225, 3.40150702, 2.92907549, 2.74010288, 2.74010288, 2.55113027, 2.45664396, 2.55113027, 2.64561657, 3.0235618, 2.92907549, 2.92907549, 2.74010288, 2.74010288, 2.64561657, 2.64561657, 3.96842486, 4.91328792, 4.06291117, 3.68496594, 3.49599333, 3.49599333, 3.49599333, 3.49599333, 3.49599333, 3.49599333, 3.40150702, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 2.92907549, 2.74010288, 2.55113027, 2.55113027, 2.45664396, 2.55113027, 2.55113027, 2.55113027, 2.83458919, 3.59047964, 3.40150702, 3.0235618, 3.59047964, 2.74010288, 3.96842486, 3.40150702, 4.06291117, 3.68496594, 3.40150702, 3.40150702, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072]), becke_scheme=<function original_becke>, concat=True)[source]#
Generate the mesh grid coordinates and weights for DFT numerical integration. We can change radii_adjust, becke_scheme functions to generate different meshgrid.
- Kwargs:
- concat: bool
Whether to concatenate grids and weights in return
- Returns:
grid_coord and grid_weight arrays. grid_coord array has shape (N,3); weight 1D array has N elements.
- pyscf.dft.gen_grid.make_mask(mol, coords, relativity=0, shls_slice=None, cutoff=1e-15, verbose=None)[source]#
Mask to indicate whether a shell is ignorable on grids. See also the function gto.eval_gto.make_screen_index
- Args:
mol : an instance of
Mole- coords2D array, shape (N,3)
The coordinates of grids.
- Kwargs:
- relativitybool
No effects.
- shls_slice2-element list
(shl_start, shl_end). If given, only part of AOs (shl_start <= shell_id < shl_end) are evaluated. By default, all shells defined in mol will be evaluated.
- verboseint or object of
Logger No effects.
- Returns:
2D mask array of shape (N,nbas), where N is the number of grids, nbas is the number of shells.
- pyscf.dft.gen_grid.nwchem_prune(nuc, rads, n_ang, radii=array([3.77945036, 0.66140414, 2.64561657, 2.74010288, 1.98421243, 1.60626721, 1.32280829, 1.22832198, 1.13383567, 0.94486306, 2.83458919, 3.40150702, 2.83458919, 2.36215766, 2.07869874, 1.88972612, 1.88972612, 1.88972612, 3.40150702, 4.15739747, 3.40150702, 3.0235618, 2.64561657, 2.55113027, 2.64561657, 2.64561657, 2.64561657, 2.55113027, 2.55113027, 2.55113027, 2.55113027, 2.45664396, 2.36215766, 2.17318504, 2.17318504, 2.17318504, 3.59047964, 4.44085639, 3.77945225, 3.40150702, 2.92907549, 2.74010288, 2.74010288, 2.55113027, 2.45664396, 2.55113027, 2.64561657, 3.0235618, 2.92907549, 2.92907549, 2.74010288, 2.74010288, 2.64561657, 2.64561657, 3.96842486, 4.91328792, 4.06291117, 3.68496594, 3.49599333, 3.49599333, 3.49599333, 3.49599333, 3.49599333, 3.49599333, 3.40150702, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 2.92907549, 2.74010288, 2.55113027, 2.55113027, 2.45664396, 2.55113027, 2.55113027, 2.55113027, 2.83458919, 3.59047964, 3.40150702, 3.0235618, 3.59047964, 2.74010288, 3.96842486, 3.40150702, 4.06291117, 3.68496594, 3.40150702, 3.40150702, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072, 3.30702072]))[source]#
NWChem
- Args:
- nucint
Nuclear charge.
- rads1D array
Grid coordinates on radical axis.
- n_angint
Max number of grids over angular part.
- Kwargs:
- radii1D array
radii (in Bohr) for atoms in periodic table
- Returns:
A list has the same length as rads. The list element is the number of grids over angular part for each radial grid.
- pyscf.dft.gen_grid.sg1_prune(nuc, rads, n_ang, radii=array([0., 1., 0.5882, 3.0769, 2.0513, 1.5385, 1.2308, 1.0256, 0.8791, 0.7692, 0.6838, 4.0909, 3.1579, 2.5714, 2.1687, 1.875, 1.6514, 1.4754, 1.3333]))[source]#
SG1, CPL, 209, 506
- Args:
- nucint
Nuclear charge.
- rads1D array
Grid coordinates on radical axis.
- n_angint
Max number of grids over angular part.
- Kwargs:
- radii1D array
radii (in Bohr) for atoms in periodic table
- Returns:
A list has the same length as rads. The list element is the number of grids over angular part for each radial grid.
- pyscf.dft.gen_grid.stratmann(g)[source]#
Stratmann, Scuseria, Frisch. CPL, 257, 213 (1996); DOI:10.1016/0009-2614(96)00600-8
- pyscf.dft.gen_grid.treutler_prune(nuc, rads, n_ang, radii=None)[source]#
Treutler-Ahlrichs
- Args:
- nucint
Nuclear charge.
- rads1D array
Grid coordinates on radical axis.
- n_angint
Max number of grids over angular part.
- Returns:
A list has the same length as rads. The list element is the number of grids over angular part for each radial grid.
pyscf.dft.gks module#
Generalized Kohn-Sham
- class pyscf.dft.gks.GKS(mol, xc='LDA,VWN')[source]#
Bases:
KohnShamDFT,GHFGeneralized Kohn-Sham
- CasidaTDDFT(*args, **kwargs)#
Solve the Casida TDDFT formula (A-B)(A+B)(X+Y) = (X+Y)w^2
- TDA(*args, **kwargs)#
Tamm-Dancoff approximation
- Attributes:
- conv_tolfloat
Diagonalization convergence tolerance. Default is 1e-9.
- nstatesint
Number of TD states to be computed. Default is 3.
Saved results:
- convergedbool
Diagonalization converged or not
- e1D array
excitation energy for each excited state.
- xyA list of two 2D arrays
The two 2D arrays are Excitation coefficients X (shape [nocc,nvir]) and de-excitation coefficients Y (shape [nocc,nvir]) for each excited state. (X,Y) are normalized to 1/2 in RHF/RKS methods and normalized to 1 for UHF/UKS methods. In the TDA calculation, Y = 0.
- TDDFT()#
Driver to create TDDFT or CasidaTDDFT object
- TDDFTNoHybrid(*args, **kwargs)#
Solve the Casida TDDFT formula (A-B)(A+B)(X+Y) = (X+Y)w^2
- TDHF = None#
- property collinear#
- energy_elec(dm=None, h1e=None, vhf=None)#
Electronic part of RKS energy.
Note this function has side effects which cause mf.scf_summary updated.
- Args:
ks : an instance of DFT class
- dm2D ndarray
one-particle density matrix
- h1e2D ndarray
Core hamiltonian
- Returns:
RKS electronic energy and the 2-electron contribution
- get_veff(mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1)#
Coulomb + XC functional
Note
This function will change the ks object.
- Args:
- ksan instance of
RKS XC functional are controlled by ks.xc attribute. Attribute ks.grids might be initialized.
- dmndarray or list of ndarrays
A density matrix or a list of density matrices
- ksan instance of
- Kwargs:
- dm_lastndarray or a list of ndarrays or 0
The density matrix baseline. If not 0, this function computes the increment of HF potential w.r.t. the reference HF potential matrix.
- vhf_lastndarray or a list of ndarrays or 0
The reference Vxc potential matrix.
- hermiint
Whether J, K matrix is hermitian
0 : no hermitian or symmetric1 : hermitian2 : anti-hermitian
- Returns:
matrix Veff = J + Vxc. Veff can be a list matrices, if the input dm is a list of density matrices.
- property spin_samples#
- to_gpu(out=None)#
Convert a method to its corresponding GPU variant, and recursively converts all attributes of a method to cupy objects or gpu4pyscf objects.
- pyscf.dft.gks.get_veff(ks, mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1)[source]#
Coulomb + XC functional
Note
This function will change the ks object.
- Args:
- ksan instance of
RKS XC functional are controlled by ks.xc attribute. Attribute ks.grids might be initialized.
- dmndarray or list of ndarrays
A density matrix or a list of density matrices
- ksan instance of
- Kwargs:
- dm_lastndarray or a list of ndarrays or 0
The density matrix baseline. If not 0, this function computes the increment of HF potential w.r.t. the reference HF potential matrix.
- vhf_lastndarray or a list of ndarrays or 0
The reference Vxc potential matrix.
- hermiint
Whether J, K matrix is hermitian
0 : no hermitian or symmetric1 : hermitian2 : anti-hermitian
- Returns:
matrix Veff = J + Vxc. Veff can be a list matrices, if the input dm is a list of density matrices.
pyscf.dft.gks_symm module#
Generalized Kohn-Sham
- class pyscf.dft.gks_symm.GKS(mol, xc='LDA,VWN')[source]#
Bases:
KohnShamDFT,SymAdaptedGHFRestricted Kohn-Sham
- CasidaTDDFT(*args, **kwargs)#
Solve the Casida TDDFT formula (A-B)(A+B)(X+Y) = (X+Y)w^2
- TDA(*args, **kwargs)#
Tamm-Dancoff approximation
- Attributes:
- conv_tolfloat
Diagonalization convergence tolerance. Default is 1e-9.
- nstatesint
Number of TD states to be computed. Default is 3.
Saved results:
- convergedbool
Diagonalization converged or not
- e1D array
excitation energy for each excited state.
- xyA list of two 2D arrays
The two 2D arrays are Excitation coefficients X (shape [nocc,nvir]) and de-excitation coefficients Y (shape [nocc,nvir]) for each excited state. (X,Y) are normalized to 1/2 in RHF/RKS methods and normalized to 1 for UHF/UKS methods. In the TDA calculation, Y = 0.
- TDDFT()#
Driver to create TDDFT or CasidaTDDFT object
- TDDFTNoHybrid(*args, **kwargs)#
Solve the Casida TDDFT formula (A-B)(A+B)(X+Y) = (X+Y)w^2
- TDHF = None#
- property collinear#
- energy_elec(dm=None, h1e=None, vhf=None)#
Electronic part of RKS energy.
Note this function has side effects which cause mf.scf_summary updated.
- Args:
ks : an instance of DFT class
- dm2D ndarray
one-particle density matrix
- h1e2D ndarray
Core hamiltonian
- Returns:
RKS electronic energy and the 2-electron contribution
- get_veff(mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1)#
Coulomb + XC functional
Note
This function will change the ks object.
- Args:
- ksan instance of
RKS XC functional are controlled by ks.xc attribute. Attribute ks.grids might be initialized.
- dmndarray or list of ndarrays
A density matrix or a list of density matrices
- ksan instance of
- Kwargs:
- dm_lastndarray or a list of ndarrays or 0
The density matrix baseline. If not 0, this function computes the increment of HF potential w.r.t. the reference HF potential matrix.
- vhf_lastndarray or a list of ndarrays or 0
The reference Vxc potential matrix.
- hermiint
Whether J, K matrix is hermitian
0 : no hermitian or symmetric1 : hermitian2 : anti-hermitian
- Returns:
matrix Veff = J + Vxc. Veff can be a list matrices, if the input dm is a list of density matrices.
- to_gpu(out=None)#
Convert a method to its corresponding GPU variant, and recursively converts all attributes of a method to cupy objects or gpu4pyscf objects.
pyscf.dft.libxc module#
XC functional, the interface to libxc (http://www.tddft.org/programs/octopus/wiki/index.php/Libxc)
- pyscf.dft.libxc.define_xc(ni, description, xctype='LDA', hyb=0, rsh=(0, 0, 0))[source]#
Define XC functional. See also
eval_xc()for the rules of input description.- Args:
ni : an instance of
NumInt- descriptionstr
A string to describe the linear combination of different XC functionals. The X and C functional are separated by comma like ‘.8*LDA+.2*B86,VWN’. If “HF” was appeared in the string, it stands for the exact exchange.
- Kwargs:
- xctypestr
‘LDA’ or ‘GGA’ or ‘MGGA’
- hybfloat
hybrid functional coefficient
- rsha list of three floats
coefficients (omega, alpha, beta) for range-separated hybrid functional. omega is the exponent factor in attenuated Coulomb operator e^{-omega r_{12}}/r_{12} alpha is the coefficient for long-range part, hybrid coefficient can be obtained by alpha + beta
Examples:
>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz') >>> mf = dft.RKS(mol) >>> define_xc_(mf._numint, '.2*HF + .08*LDA + .72*B88, .81*LYP + .19*VWN') >>> mf.kernel() -76.3783361189611 >>> define_xc_(mf._numint, 'LDA*.08 + .72*B88 + .2*HF, .81*LYP + .19*VWN') >>> mf.kernel() -76.3783361189611 >>> def eval_xc(xc_code, rho, *args, **kwargs): ... exc = 0.01 * rho**2 ... vrho = 0.01 * 3 * rho**2 ... vxc = (vrho, None, None, None) ... fxc = None # 2nd order functional derivative ... kxc = None # 3rd order functional derivative ... return exc, vxc, fxc, kxc >>> define_xc_(mf._numint, eval_xc, xctype='LDA') >>> mf.kernel() 48.8525211046668
- pyscf.dft.libxc.define_xc_(ni, description, xctype='LDA', hyb=0, rsh=(0, 0, 0))[source]#
Define XC functional. See also
eval_xc()for the rules of input description.- Args:
ni : an instance of
NumInt- descriptionstr
A string to describe the linear combination of different XC functionals. The X and C functional are separated by comma like ‘.8*LDA+.2*B86,VWN’. If “HF” was appeared in the string, it stands for the exact exchange.
- Kwargs:
- xctypestr
‘LDA’ or ‘GGA’ or ‘MGGA’
- hybfloat
hybrid functional coefficient
- rsha list of three floats
coefficients (omega, alpha, beta) for range-separated hybrid functional. omega is the exponent factor in attenuated Coulomb operator e^{-omega r_{12}}/r_{12} alpha is the coefficient for long-range part, hybrid coefficient can be obtained by alpha + beta
Examples:
>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz') >>> mf = dft.RKS(mol) >>> define_xc_(mf._numint, '.2*HF + .08*LDA + .72*B88, .81*LYP + .19*VWN') >>> mf.kernel() -76.3783361189611 >>> define_xc_(mf._numint, 'LDA*.08 + .72*B88 + .2*HF, .81*LYP + .19*VWN') >>> mf.kernel() -76.3783361189611 >>> def eval_xc(xc_code, rho, *args, **kwargs): ... exc = 0.01 * rho**2 ... vrho = 0.01 * 3 * rho**2 ... vxc = (vrho, None, None, None) ... fxc = None # 2nd order functional derivative ... kxc = None # 3rd order functional derivative ... return exc, vxc, fxc, kxc >>> define_xc_(mf._numint, eval_xc, xctype='LDA') >>> mf.kernel() 48.8525211046668
- pyscf.dft.libxc.eval_xc(xc_code, rho, spin=0, relativity=0, deriv=1, omega=None, verbose=None)[source]#
Interface to call libxc library to evaluate XC functional, potential and functional derivatives.
The given functional xc_code must be a one-line string.
The functional xc_code is case-insensitive.
The functional xc_code string has two parts, separated by “,”. The first part describes the exchange functional, the second part sets the correlation functional.
If “,” not appeared in string, the entire string is treated as the name of a compound functional (containing both the exchange and the correlation functional) which was declared in the functional aliases list. The full list of functional aliases can be obtained by calling the function pyscf.dft.xcfun.XC_ALIAS.keys() .
If the string was not found in the aliased functional list, it is treated as X functional.
To input only X functional (without C functional), leave the second part blank. E.g. description=’slater,’ means a functional with LDA contribution only.
To neglect the contribution of X functional (just apply C functional), leave blank in the first part, e.g. description=’,vwn’ means a functional with VWN only.
If compound XC functional is specified, no matter whether it is in the X part (the string in front of comma) or the C part (the string behind comma), both X and C functionals of the compound XC functional will be used.
The functional name can be placed in arbitrary order. Two names need to be separated by operators “+” or “-”. Blank spaces are ignored. NOTE the parser only reads operators “+” “-” “*”. / is not supported.
A functional name can have at most one factor. If the factor is not given, it is set to 1. Compound functional can be scaled as a unit. For example ‘0.5*b3lyp’ is equivalent to ‘HF*0.1 + .04*LDA + .36*B88, .405*LYP + .095*VWN’
String “HF” stands for exact exchange (HF K matrix). “HF” can be put in the correlation functional part (after comma). Putting “HF” in the correlation part is the same to putting “HF” in the exchange part.
String “RSH” means range-separated operator. Its format is RSH(omega, alpha, beta). Another way to input RSH is to use keywords SR_HF and LR_HF: “SR_HF(0.1) * alpha_plus_beta” and “LR_HF(0.1) * alpha” where the number in parenthesis is the value of omega.
Be careful with the libxc convention of GGA functional, in which the LDA contribution is included.
- Args:
- xc_codestr
A string to describe the linear combination of different XC functionals. The X and C functional are separated by comma like ‘.8*LDA+.2*B86,VWN’. If “HF” (exact exchange) is appeared in the string, the HF part will be skipped. If an empty string “” is given, the returns exc, vxc,… will be vectors of zeros.
- rhondarray
Shape of ((,N)) for electron density (and derivatives) if spin = 0; Shape of ((,N),(,N)) for alpha/beta electron density (and derivatives) if spin > 0; where N is number of grids. rho (,N) are ordered as (den,grad_x,grad_y,grad_z,laplacian,tau) where grad_x = d/dx den, laplacian = nabla^2 den, tau = 1/2(nabla f)^2 In spin unrestricted case, rho is ((den_u,grad_xu,grad_yu,grad_zu,laplacian_u,tau_u)
(den_d,grad_xd,grad_yd,grad_zd,laplacian_d,tau_d))
- Kwargs:
- spinint
spin polarized if spin > 0
- relativityint
No effects.
- verboseint or object of
Logger No effects.
- Returns:
ex, vxc, fxc, kxc
where
vxc = (vrho, vsigma, vlapl, vtau) for restricted case
vxc for unrestricted case | vrho[:,2] = (u, d) | vsigma[:,3] = (uu, ud, dd) | vlapl[:,2] = (u, d) | vtau[:,2] = (u, d)
fxc for restricted case: (v2rho2, v2rhosigma, v2sigma2, v2lapl2, vtau2, v2rholapl, v2rhotau, v2lapltau, v2sigmalapl, v2sigmatau)
fxc for unrestricted case: | v2rho2[:,3] = (u_u, u_d, d_d) | v2rhosigma[:,6] = (u_uu, u_ud, u_dd, d_uu, d_ud, d_dd) | v2sigma2[:,6] = (uu_uu, uu_ud, uu_dd, ud_ud, ud_dd, dd_dd) | v2lapl2[:,3] | v2tau2[:,3] = (u_u, u_d, d_d) | v2rholapl[:,4] | v2rhotau[:,4] = (u_u, u_d, d_u, d_d) | v2lapltau[:,4] | v2sigmalapl[:,6] | v2sigmatau[:,6] = (uu_u, uu_d, ud_u, ud_d, dd_u, dd_d)
kxc for restricted case: (v3rho3, v3rho2sigma, v3rhosigma2, v3sigma3,
v3rho2lapl, v3rho2tau, v3rhosigmalapl, v3rhosigmatau, v3rholapl2, v3rholapltau, v3rhotau2, v3sigma2lapl, v3sigma2tau, v3sigmalapl2, v3sigmalapltau, v3sigmatau2, v3lapl3, v3lapl2tau, v3lapltau2, v3tau3)
kxc for unrestricted case: | v3rho3[:,4] = (u_u_u, u_u_d, u_d_d, d_d_d) | v3rho2sigma[:,9] = (u_u_uu, u_u_ud, u_u_dd, u_d_uu, u_d_ud, u_d_dd, d_d_uu, d_d_ud, d_d_dd) | v3rhosigma2[:,12] = (u_uu_uu, u_uu_ud, u_uu_dd, u_ud_ud, u_ud_dd, u_dd_dd, d_uu_uu, d_uu_ud, d_uu_dd, d_ud_ud, d_ud_dd, d_dd_dd) | v3sigma3[:,10] = (uu_uu_uu, uu_uu_ud, uu_uu_dd, uu_ud_ud, uu_ud_dd, uu_dd_dd, ud_ud_ud, ud_ud_dd, ud_dd_dd, dd_dd_dd) | v3rho2lapl[:,6] | v3rho2tau[:,6] = (u_u_u, u_u_d, u_d_u, u_d_d, d_d_u, d_d_d) | v3rhosigmalapl[:,12] | v3rhosigmatau[:,12] = (u_uu_u, u_uu_d, u_ud_u, u_ud_d, u_dd_u, u_dd_d,
d_uu_u, d_uu_d, d_ud_u, d_ud_d, d_dd_u, d_dd_d)
v3rholapl2[:,6]v3rholapltau[:,8]v3rhotau2[:,6] = (u_u_u, u_u_d, u_d_d, d_u_u, d_u_d, d_d_d)v3sigma2lapl[:,12]v3sigma2tau[:,12] = (uu_uu_u, uu_uu_d, uu_ud_u, uu_ud_d, uu_dd_u, uu_dd_d, ud_ud_u, ud_ud_d, ud_dd_u, ud_dd_d, dd_dd_u, dd_dd_d)v3sigmalapl2[:,9]v3sigmalapltau[:,12]v3sigmatau2[:,9] = (uu_u_u, uu_u_d, uu_d_d, ud_u_u, ud_u_d, ud_d_d, dd_u_u, dd_u_d, dd_d_d)v3lapl3[:,4]v3lapl2tau[:,6]v3lapltau2[:,6]v3tau3[:,4] = (u_u_u, u_u_d, u_d_d, d_d_d)
see also libxc_itrf.c
- pyscf.dft.libxc.eval_xc1(xc_code, rho, spin=0, deriv=1, omega=None)[source]#
Similar to eval_xc. Returns an array with the order of derivatives following xcfun convention.
- pyscf.dft.libxc.eval_xc_eff(xc_code, rho, deriv=1, omega=None)[source]#
Returns the derivative tensor against the density parameters
[density_a, (nabla_x)_a, (nabla_y)_a, (nabla_z)_a, tau_a]
or spin-polarized density parameters
- [[density_a, (nabla_x)_a, (nabla_y)_a, (nabla_z)_a, tau_a],
[density_b, (nabla_x)_b, (nabla_y)_b, (nabla_z)_b, tau_b]].
It differs from the eval_xc method in the derivatives of non-local part. The eval_xc method returns the XC functional derivatives to sigma (|nabla rho|^2)
- Args:
- rho: 2-dimensional or 3-dimensional array
Total density or (spin-up, spin-down) densities (and their derivatives if GGA or MGGA functionals) on grids
- Kwargs:
- deriv: int
derivative orders
- omega: float
define the exponent in the attenuated Coulomb for RSH functional
- pyscf.dft.libxc.hybrid_coeff(xc_code, spin=0)[source]#
Support recursively defining hybrid functional
- pyscf.dft.libxc.parse_xc(description)[source]#
Rules to input functional description:
The given functional description must be a one-line string.
The functional description is case-insensitive.
The functional description string has two parts, separated by “,”. The first part describes the exchange functional, the second is the correlation functional.
If “,” was not in string, the entire string is considered as a compound XC functional (including both X and C functionals, such as b3lyp).
To input only X functional (without C functional), leave the second part blank. E.g. description=’slater,’ means pure LDA functional.
To neglect X functional (just apply C functional), leave the first part blank. E.g. description=’,vwn’ means pure VWN functional.
If compound XC functional is specified, no matter whether it is in the X part (the string in front of comma) or the C part (the string behind comma), both X and C functionals of the compound XC functional will be used.
The functional name can be placed in arbitrary order. Two name needs to be separated by operators “+” or “-”. Blank spaces are ignored. NOTE the parser only reads operators “+” “-” “*”. / is not in support.
A functional name can have at most one factor. If the factor is not given, it is set to 1. Compound functional can be scaled as a unit. For example ‘0.5*b3lyp’ is equivalent to ‘HF*0.1 + .04*LDA + .36*B88, .405*LYP + .095*VWN’
String “HF” stands for exact exchange (HF K matrix). Putting “HF” in correlation functional part is the same to putting “HF” in exchange part.
String “RSH” means range-separated operator. Its format is RSH(omega, alpha, beta). Another way to input RSH is to use keywords SR_HF and LR_HF: “SR_HF(0.1) * alpha_plus_beta” and “LR_HF(0.1) * alpha” where the number in parenthesis is the value of omega.
Be careful with the libxc convention on GGA functional, in which the LDA contribution has been included.
- Args:
- descriptionstr
A string to describe the linear combination of different XC functionals. The X and C functional are separated by comma like ‘.8*LDA+.2*B86,VWN’. If “HF” was appeared in the string, it stands for the exact exchange.
- Returns:
decoded XC description, with the data structure (hybrid, alpha, omega), ((libxc-Id, fac), (libxc-Id, fac), …)
- pyscf.dft.libxc.parse_xc_name(xc_name='LDA,VWN')[source]#
Convert the XC functional name to libxc library internal ID.
- pyscf.dft.libxc.print_XC_CODES()[source]#
Dump the built-in libxc XC_CODES along with their references in a readable format.
- pyscf.dft.libxc.rsh_coeff(xc_code)[source]#
Range-separated parameter and HF exchange components: omega, alpha, beta
- Exc_RSH = c_LR * LR_HFX + c_SR * SR_HFX + (1-c_SR) * Ex_SR + (1-c_LR) * Ex_LR + Ec
= alpha * HFX + beta * SR_HFX + (1-c_SR) * Ex_SR + (1-c_LR) * Ex_LR + Ec = alpha * LR_HFX + hyb * SR_HFX + (1-c_SR) * Ex_SR + (1-c_LR) * Ex_LR + Ec
SR_HFX = < pi | (1-erf(-omega r_{12}))/r_{12} | iq > LR_HFX = < pi | erf(-omega r_{12})/r_{12} | iq > alpha = c_LR beta = c_SR - c_LR = hyb - alpha
pyscf.dft.numint module#
Numerical integration functions for RKS and UKS with real AO basis
- class pyscf.dft.numint.LibXCMixin[source]#
Bases:
object- eval_xc(xc_code, rho, spin=0, relativity=0, deriv=1, omega=None, verbose=None)[source]#
Interface to call libxc library to evaluate XC functional, potential and functional derivatives.
The given functional xc_code must be a one-line string.
The functional xc_code is case-insensitive.
The functional xc_code string has two parts, separated by “,”. The first part describes the exchange functional, the second part sets the correlation functional.
If “,” not appeared in string, the entire string is treated as the name of a compound functional (containing both the exchange and the correlation functional) which was declared in the functional aliases list. The full list of functional aliases can be obtained by calling the function pyscf.dft.xcfun.XC_ALIAS.keys() .
If the string was not found in the aliased functional list, it is treated as X functional.
To input only X functional (without C functional), leave the second part blank. E.g. description=’slater,’ means a functional with LDA contribution only.
To neglect the contribution of X functional (just apply C functional), leave blank in the first part, e.g. description=’,vwn’ means a functional with VWN only.
If compound XC functional is specified, no matter whether it is in the X part (the string in front of comma) or the C part (the string behind comma), both X and C functionals of the compound XC functional will be used.
The functional name can be placed in arbitrary order. Two names need to be separated by operators “+” or “-”. Blank spaces are ignored. NOTE the parser only reads operators “+” “-” “*”. / is not supported.
A functional name can have at most one factor. If the factor is not given, it is set to 1. Compound functional can be scaled as a unit. For example ‘0.5*b3lyp’ is equivalent to ‘HF*0.1 + .04*LDA + .36*B88, .405*LYP + .095*VWN’
String “HF” stands for exact exchange (HF K matrix). “HF” can be put in the correlation functional part (after comma). Putting “HF” in the correlation part is the same to putting “HF” in the exchange part.
String “RSH” means range-separated operator. Its format is RSH(omega, alpha, beta). Another way to input RSH is to use keywords SR_HF and LR_HF: “SR_HF(0.1) * alpha_plus_beta” and “LR_HF(0.1) * alpha” where the number in parenthesis is the value of omega.
Be careful with the libxc convention of GGA functional, in which the LDA contribution is included.
- Args:
- xc_codestr
A string to describe the linear combination of different XC functionals. The X and C functional are separated by comma like ‘.8*LDA+.2*B86,VWN’. If “HF” (exact exchange) is appeared in the string, the HF part will be skipped. If an empty string “” is given, the returns exc, vxc,… will be vectors of zeros.
- rhondarray
Shape of ((,N)) for electron density (and derivatives) if spin = 0; Shape of ((,N),(,N)) for alpha/beta electron density (and derivatives) if spin > 0; where N is number of grids. rho (,N) are ordered as (den,grad_x,grad_y,grad_z,laplacian,tau) where grad_x = d/dx den, laplacian = nabla^2 den, tau = 1/2(nabla f)^2 In spin unrestricted case, rho is ((den_u,grad_xu,grad_yu,grad_zu,laplacian_u,tau_u)
(den_d,grad_xd,grad_yd,grad_zd,laplacian_d,tau_d))
- Kwargs:
- spinint
spin polarized if spin > 0
- relativityint
No effects.
- verboseint or object of
Logger No effects.
- Returns:
ex, vxc, fxc, kxc
where
vxc = (vrho, vsigma, vlapl, vtau) for restricted case
vxc for unrestricted case | vrho[:,2] = (u, d) | vsigma[:,3] = (uu, ud, dd) | vlapl[:,2] = (u, d) | vtau[:,2] = (u, d)
fxc for restricted case: (v2rho2, v2rhosigma, v2sigma2, v2lapl2, vtau2, v2rholapl, v2rhotau, v2lapltau, v2sigmalapl, v2sigmatau)
fxc for unrestricted case: | v2rho2[:,3] = (u_u, u_d, d_d) | v2rhosigma[:,6] = (u_uu, u_ud, u_dd, d_uu, d_ud, d_dd) | v2sigma2[:,6] = (uu_uu, uu_ud, uu_dd, ud_ud, ud_dd, dd_dd) | v2lapl2[:,3] | v2tau2[:,3] = (u_u, u_d, d_d) | v2rholapl[:,4] | v2rhotau[:,4] = (u_u, u_d, d_u, d_d) | v2lapltau[:,4] | v2sigmalapl[:,6] | v2sigmatau[:,6] = (uu_u, uu_d, ud_u, ud_d, dd_u, dd_d)
kxc for restricted case: (v3rho3, v3rho2sigma, v3rhosigma2, v3sigma3,
v3rho2lapl, v3rho2tau, v3rhosigmalapl, v3rhosigmatau, v3rholapl2, v3rholapltau, v3rhotau2, v3sigma2lapl, v3sigma2tau, v3sigmalapl2, v3sigmalapltau, v3sigmatau2, v3lapl3, v3lapl2tau, v3lapltau2, v3tau3)
kxc for unrestricted case: | v3rho3[:,4] = (u_u_u, u_u_d, u_d_d, d_d_d) | v3rho2sigma[:,9] = (u_u_uu, u_u_ud, u_u_dd, u_d_uu, u_d_ud, u_d_dd, d_d_uu, d_d_ud, d_d_dd) | v3rhosigma2[:,12] = (u_uu_uu, u_uu_ud, u_uu_dd, u_ud_ud, u_ud_dd, u_dd_dd, d_uu_uu, d_uu_ud, d_uu_dd, d_ud_ud, d_ud_dd, d_dd_dd) | v3sigma3[:,10] = (uu_uu_uu, uu_uu_ud, uu_uu_dd, uu_ud_ud, uu_ud_dd, uu_dd_dd, ud_ud_ud, ud_ud_dd, ud_dd_dd, dd_dd_dd) | v3rho2lapl[:,6] | v3rho2tau[:,6] = (u_u_u, u_u_d, u_d_u, u_d_d, d_d_u, d_d_d) | v3rhosigmalapl[:,12] | v3rhosigmatau[:,12] = (u_uu_u, u_uu_d, u_ud_u, u_ud_d, u_dd_u, u_dd_d,
d_uu_u, d_uu_d, d_ud_u, d_ud_d, d_dd_u, d_dd_d)
v3rholapl2[:,6]v3rholapltau[:,8]v3rhotau2[:,6] = (u_u_u, u_u_d, u_d_d, d_u_u, d_u_d, d_d_d)v3sigma2lapl[:,12]v3sigma2tau[:,12] = (uu_uu_u, uu_uu_d, uu_ud_u, uu_ud_d, uu_dd_u, uu_dd_d, ud_ud_u, ud_ud_d, ud_dd_u, ud_dd_d, dd_dd_u, dd_dd_d)v3sigmalapl2[:,9]v3sigmalapltau[:,12]v3sigmatau2[:,9] = (uu_u_u, uu_u_d, uu_d_d, ud_u_u, ud_u_d, ud_d_d, dd_u_u, dd_u_d, dd_d_d)v3lapl3[:,4]v3lapl2tau[:,6]v3lapltau2[:,6]v3tau3[:,4] = (u_u_u, u_u_d, u_d_d, d_d_d)
see also libxc_itrf.c
- eval_xc_eff(xc_code, rho, deriv=1, omega=None, xctype=None, verbose=None)[source]#
Returns the derivative tensor against the density parameters
[density_a, (nabla_x)_a, (nabla_y)_a, (nabla_z)_a, tau_a]
or spin-polarized density parameters
- [[density_a, (nabla_x)_a, (nabla_y)_a, (nabla_z)_a, tau_a],
[density_b, (nabla_x)_b, (nabla_y)_b, (nabla_z)_b, tau_b]].
It differs from the eval_xc method in the derivatives of non-local part. The eval_xc method returns the XC functional derivatives to sigma (|nabla rho|^2)
- Args:
- rho: 2-dimensional or 3-dimensional array
Total density or (spin-up, spin-down) densities (and their derivatives if GGA or MGGA functionals) on grids
- Kwargs:
- deriv: int
derivative orders
- omega: float
define the exponent in the attenuated Coulomb for RSH functional
- libxc = <module 'pyscf.dft.libxc' from '/home/runner/.local/lib/python3.10/site-packages/pyscf/dft/libxc.py'>#
- omega = None#
- rsh_and_hybrid_coeff(xc_code, spin=0)[source]#
Range-separated parameter and HF exchange components: omega, alpha, beta
- Exc_RSH = c_SR * SR_HFX + c_LR * LR_HFX + (1-c_SR) * Ex_SR + (1-c_LR) * Ex_LR + Ec
= alpha * HFX + beta * SR_HFX + (1-c_SR) * Ex_SR + (1-c_LR) * Ex_LR + Ec = alpha * LR_HFX + hyb * SR_HFX + (1-c_SR) * Ex_SR + (1-c_LR) * Ex_LR + Ec
SR_HFX = < pi | (1-erf(-omega r_{12}))/r_{12} | iq > LR_HFX = < pi | erf(-omega r_{12})/r_{12} | iq > alpha = c_LR beta = c_SR - c_LR
- class pyscf.dft.numint.NumInt[source]#
Bases:
StreamObject,LibXCMixinNumerical integration methods for non-relativistic RKS and UKS
- block_loop(mol, grids, nao=None, deriv=0, max_memory=2000, non0tab=None, blksize=None, buf=None)[source]#
Define this macro to loop over grids by blocks.
- cache_xc_kernel(mol, grids, xc_code, mo_coeff, mo_occ, spin=0, max_memory=2000)#
Compute the 0th order density, Vxc and fxc. They can be used in TDDFT, DFT hessian module etc.
- cache_xc_kernel1(mol, grids, xc_code, dm, spin=0, max_memory=2000)#
Compute the 0th order density, Vxc and fxc. They can be used in TDDFT, DFT hessian module etc. Note dm the zeroth order density matrix must be a hermitian matrix.
- cutoff = 1e-13#
- static eval_ao(mol, coords, deriv=0, shls_slice=None, non0tab=None, cutoff=None, out=None, verbose=None)#
Evaluate AO function value on the given grids.
- Args:
mol : an instance of
Mole- coords2D array, shape (N,3)
The coordinates of the grids.
- Kwargs:
- derivint
AO derivative order. It affects the shape of the return array. If deriv=0, the returned AO values are stored in a (N,nao) array. Otherwise the AO values are stored in an array of shape (M,N,nao). Here N is the number of grids, nao is the number of AO functions, M is the size associated to the derivative deriv.
- relativitybool
No effects.
- shls_slice2-element list
(shl_start, shl_end). If given, only part of AOs (shl_start <= shell_id < shl_end) are evaluated. By default, all shells defined in mol will be evaluated.
- non0tab2D bool array
mask array to indicate whether the AO values are zero. The mask array can be obtained by calling
make_mask()- cutofffloat
AO values smaller than cutoff will be set to zero. The default cutoff threshold is ~1e-22 (defined in gto/grid_ao_drv.h)
- outndarray
If provided, results are written into this array.
- verboseint or object of
Logger No effects.
- Returns:
2D array of shape (N,nao) for AO values if deriv = 0. Or 3D array of shape (:,N,nao) for AO values and AO derivatives if deriv > 0. In the 3D array, the first (N,nao) elements are the AO values, followed by (3,N,nao) for x,y,z components; Then 2nd derivatives (6,N,nao) for xx, xy, xz, yy, yz, zz; Then 3rd derivatives (10,N,nao) for xxx, xxy, xxz, xyy, xyz, xzz, yyy, yyz, yzz, zzz; …
Examples:
>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz') >>> coords = numpy.random.random((100,3)) # 100 random points >>> ao_value = eval_ao(mol, coords) >>> print(ao_value.shape) (100, 24) >>> ao_value = eval_ao(mol, coords, deriv=1, shls_slice=(1,4)) >>> print(ao_value.shape) (4, 100, 7) >>> ao_value = eval_ao(mol, coords, deriv=2, shls_slice=(1,4)) >>> print(ao_value.shape) (10, 100, 7)
- static eval_rho(mol, ao, dm, non0tab=None, xctype='LDA', hermi=0, with_lapl=True, verbose=None)#
Calculate the electron density for LDA functional, and the density derivatives for GGA and MGGA functionals.
- Args:
mol : an instance of
Mole- ao2D array of shape (N,nao) for LDA, 3D array of shape (4,N,nao) for GGA
or meta-GGA. N is the number of grids, nao is the number of AO functions. If xctype is GGA (MGGA), ao[0] is AO value and ao[1:3] are the AO gradients. ao[4:10] are second derivatives of ao values if applicable.
- dm2D array
Density matrix
- Kwargs:
- non0tab2D bool array
mask array to indicate whether the AO values are zero. The mask array can be obtained by calling
make_mask()- xctypestr
LDA/GGA/mGGA. It affects the shape of the return density.
- hermibool
dm is hermitian or not
- verboseint or object of
Logger No effects.
- Returns:
1D array of size N to store electron density if xctype = LDA; 2D array of (4,N) to store density and “density derivatives” for x,y,z components if xctype = GGA; For meta-GGA, returns can be a (6,N) (with_lapl=True) array where last two rows are nabla^2 rho and tau = 1/2(nabla f)^2 or (5,N) (with_lapl=False) where the last row is tau = 1/2(nabla f)^2
Examples:
>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz') >>> coords = numpy.random.random((100,3)) # 100 random points >>> ao_value = eval_ao(mol, coords, deriv=0) >>> dm = numpy.random.random((mol.nao_nr(),mol.nao_nr())) >>> dm = dm + dm.T >>> rho, dx_rho, dy_rho, dz_rho = eval_rho(mol, ao, dm, xctype='LDA')
- eval_rho1(mol=None, ao=None, dm=None, screen_index=None, xctype='LDA', hermi=0, with_lapl=True, cutoff=None, ao_cutoff=1e-15, pair_mask=None, verbose=None)#
Calculate the electron density for LDA and the density derivatives for GGA and MGGA with sparsity information.
- Args:
mol : an instance of
Mole- ao2D array of shape (N,nao) for LDA, 3D array of shape (4,N,nao) for GGA
or meta-GGA. N is the number of grids, nao is the number of AO functions. If xctype is GGA (MGGA), ao[0] is AO value and ao[1:3] are the AO gradients. ao[4:10] are second derivatives of ao values if applicable.
- dm2D array
Density matrix
- Kwargs:
- screen_index2D uint8 array
How likely the AO values on grids are negligible. This array can be obtained by calling
gen_grid.make_screen_index()- xctypestr
LDA/GGA/mGGA. It affects the shape of the return density.
- hermibool
dm is hermitian or not
- cutofffloat
cutoff for density value
- ao_cutofffloat
cutoff for AO value. Needs to be the same to the cutoff when generating screen_index
- verboseint or object of
Logger No effects.
- Returns:
1D array of size N to store electron density if xctype = LDA; 2D array of (4,N) to store density and “density derivatives” for x,y,z components if xctype = GGA; For meta-GGA, returns can be a (6,N) (with_lapl=True) array where last two rows are nabla^2 rho and tau = 1/2(nabla f)^2 or (5,N) (with_lapl=False) where the last row is tau = 1/2(nabla f)^2
- static eval_rho2(mol, ao, mo_coeff, mo_occ, non0tab=None, xctype='LDA', with_lapl=True, verbose=None)#
Calculate the electron density for LDA functional, and the density derivatives for GGA functional. This function has the same functionality as
eval_rho()except that the density are evaluated based on orbital coefficients and orbital occupancy. It is more efficient thaneval_rho()in most scenario.- Args:
mol : an instance of
Mole- ao2D array of shape (N,nao) for LDA, 3D array of shape (4,N,nao) for GGA
or meta-GGA. N is the number of grids, nao is the number of AO functions. If xctype is GGA (MGGA), ao[0] is AO value and ao[1:3] are the AO gradients. ao[4:10] are second derivatives of ao values if applicable.
- dm2D array
Density matrix
- Kwargs:
- non0tab2D bool array
mask array to indicate whether the AO values are zero. The mask array can be obtained by calling
make_mask()- xctypestr
LDA/GGA/mGGA. It affects the shape of the return density.
- with_lapl: bool
Whether to compute laplacian. It affects the shape of returns.
- verboseint or object of
Logger No effects.
- Returns:
1D array of size N to store electron density if xctype = LDA; 2D array of (4,N) to store density and “density derivatives” for x,y,z components if xctype = GGA; For meta-GGA, returns can be a (6,N) (with_lapl=True) array where last two rows are nabla^2 rho and tau = 1/2(nabla f)^2 or (5,N) (with_lapl=False) where the last row is tau = 1/2(nabla f)^2
- get_fxc(mol, grids, xc_code, dm0, dms, spin=0, relativity=0, hermi=0, rho0=None, vxc=None, fxc=None, max_memory=2000, verbose=None)#
Contract XC kernel matrix with given density matrices
… math:
a_{pq} = f_{pq,rs} * x_{rs}
- get_rho(mol, dm, grids, max_memory=2000)#
Density in real space
- get_vxc(mol, grids, xc_code, dms, spin=0, relativity=0, hermi=0, max_memory=2000, verbose=None)#
Evaluate RKS/UKS XC functional and potential matrix on given meshgrids for a set of density matrices. See
nr_rks()andnr_uks()for more details.- Args:
mol : an instance of
Mole- gridsan instance of
Grids grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
- xc_codestr
XC functional description. See
parse_xc()of pyscf/dft/libxc.py for more details.- dms2D array or a list of 2D arrays
Density matrix or multiple density matrices
- gridsan instance of
- Kwargs:
- hermiint
Input density matrices symmetric or not
- max_memoryint or float
The maximum size of cache to use (in MB).
- Returns:
nelec, excsum, vmat. nelec is the number of electrons generated by numerical integration. excsum is the XC functional value. vmat is the XC potential matrix in 2D array of shape (nao,nao) where nao is the number of AO functions.
Examples:
>>> from pyscf import gto, dft >>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1') >>> grids = dft.gen_grid.Grids(mol) >>> grids.coords = numpy.random.random((100,3)) # 100 random points >>> grids.weights = numpy.random.random(100) >>> nao = mol.nao_nr() >>> dm = numpy.random.random((2,nao,nao)) >>> nelec, exc, vxc = dft.numint.nr_vxc(mol, grids, 'lda,vwn', dm, spin=1)
- static make_mask(mol, coords, relativity=0, shls_slice=None, cutoff=1e-15, verbose=None)#
Mask to indicate whether a shell is ignorable on grids. See also the function gto.eval_gto.make_screen_index
- Args:
mol : an instance of
Mole- coords2D array, shape (N,3)
The coordinates of grids.
- Kwargs:
- relativitybool
No effects.
- shls_slice2-element list
(shl_start, shl_end). If given, only part of AOs (shl_start <= shell_id < shl_end) are evaluated. By default, all shells defined in mol will be evaluated.
- verboseint or object of
Logger No effects.
- Returns:
2D mask array of shape (N,nbas), where N is the number of grids, nbas is the number of shells.
- nr_fxc(mol, grids, xc_code, dm0, dms, spin=0, relativity=0, hermi=0, rho0=None, vxc=None, fxc=None, max_memory=2000, verbose=None)[source]#
Contract XC kernel matrix with given density matrices
… math:
a_{pq} = f_{pq,rs} * x_{rs}
- nr_nlc_vxc(mol, grids, xc_code, dm, relativity=0, hermi=1, max_memory=2000, verbose=None)#
Calculate NLC functional and potential matrix on given grids
- Args:
ni : an instance of
NumIntmol : an instance of
Mole- gridsan instance of
Grids grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
- xc_codestr
XC functional description. See
parse_xc()of pyscf/dft/libxc.py for more details.- dm2D array
Density matrix or multiple density matrices
- gridsan instance of
- Kwargs:
- hermiint
Input density matrices symmetric or not. It also indicates whether the potential matrices in return are symmetric or not.
- max_memoryint or float
The maximum size of cache to use (in MB).
- Returns:
nelec, excsum, vmat. nelec is the number of electrons generated by numerical integration. excsum is the XC functional value. vmat is the XC potential matrix in 2D array of shape (nao,nao) where nao is the number of AO functions.
- nr_rks(mol, grids, xc_code, dms, relativity=0, hermi=1, max_memory=2000, verbose=None)#
Calculate RKS XC functional and potential matrix on given meshgrids for a set of density matrices
- Args:
ni : an instance of
NumIntmol : an instance of
Mole- gridsan instance of
Grids grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
- xc_codestr
XC functional description. See
parse_xc()of pyscf/dft/libxc.py for more details.- dms2D array or a list of 2D arrays
Density matrix or multiple density matrices
- gridsan instance of
- Kwargs:
- hermiint
Input density matrices symmetric or not. It also indicates whether the potential matrices in return are symmetric or not.
- max_memoryint or float
The maximum size of cache to use (in MB).
- Returns:
nelec, excsum, vmat. nelec is the number of electrons generated by numerical integration. excsum is the XC functional value. vmat is the XC potential matrix in 2D array of shape (nao,nao) where nao is the number of AO functions.
Examples:
>>> from pyscf import gto, dft >>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1') >>> grids = dft.gen_grid.Grids(mol) >>> grids.coords = numpy.random.random((100,3)) # 100 random points >>> grids.weights = numpy.random.random(100) >>> nao = mol.nao_nr() >>> dm = numpy.random.random((nao,nao)) >>> ni = dft.numint.NumInt() >>> nelec, exc, vxc = ni.nr_rks(mol, grids, 'lda,vwn', dm)
- nr_rks_fxc(mol, grids, xc_code, dm0, dms, relativity=0, hermi=0, rho0=None, vxc=None, fxc=None, max_memory=2000, verbose=None)#
Contract RKS XC (singlet hessian) kernel matrix with given density matrices
- Args:
ni : an instance of
NumIntmol : an instance of
Mole- gridsan instance of
Grids grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
- xc_codestr
XC functional description. See
parse_xc()of pyscf/dft/libxc.py for more details.- dm02D array
Zeroth order density matrix
- dms2D array a list of 2D arrays
First order density matrix or density matrices
- gridsan instance of
- Kwargs:
- hermiint
First order density matrix symmetric or not. It also indicates whether the matrices in return are symmetric or not.
- max_memoryint or float
The maximum size of cache to use (in MB).
- rho0float array
Zero-order density (and density derivative for GGA). Giving kwargs rho0, vxc and fxc to improve better performance.
- vxcfloat array
First order XC derivatives
- fxcfloat array
Second order XC derivatives
- Returns:
nelec, excsum, vmat. nelec is the number of electrons generated by numerical integration. excsum is the XC functional value. vmat is the XC potential matrix in 2D array of shape (nao,nao) where nao is the number of AO functions.
Examples:
- nr_rks_fxc_st(mol, grids, xc_code, dm0, dms_alpha, relativity=0, singlet=True, rho0=None, vxc=None, fxc=None, max_memory=2000, verbose=None)#
Associated to singlet or triplet Hessian Note the difference to nr_rks_fxc, dms_alpha is the response density matrices of alpha spin, alpha+/-beta DM is applied due to singlet/triplet coupling
Ref. CPL, 256, 454
- nr_sap(mol, grids, max_memory=2000, verbose=None)#
Calculate superposition of atomic potentials matrix on given meshgrids.
- Args:
ni : an instance of
NumIntmol : an instance of
Mole- gridsan instance of
Grids grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
- gridsan instance of
- Kwargs:
- max_memoryint or float
The maximum size of cache to use (in MB).
- Returns:
vmat is the XC potential matrix in 2D array of shape (nao,nao) where nao is the number of AO functions.
Examples: >>> import numpy >>> from pyscf import gto, dft >>> mol = gto.M(atom=’H 0 0 0; H 0 0 1.1’) >>> grids = dft.gen_grid.Grids(mol) >>> ni = dft.numint.NumInt() >>> vsap = ni.nr_sap(mol, grids)
- nr_sap_vxc(mol, grids, max_memory=2000, verbose=None)#
Calculate superposition of atomic potentials matrix on given meshgrids.
- Args:
ni : an instance of
NumIntmol : an instance of
Mole- gridsan instance of
Grids grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
- gridsan instance of
- Kwargs:
- max_memoryint or float
The maximum size of cache to use (in MB).
- Returns:
vmat is the XC potential matrix in 2D array of shape (nao,nao) where nao is the number of AO functions.
Examples: >>> import numpy >>> from pyscf import gto, dft >>> mol = gto.M(atom=’H 0 0 0; H 0 0 1.1’) >>> grids = dft.gen_grid.Grids(mol) >>> ni = dft.numint.NumInt() >>> vsap = ni.nr_sap(mol, grids)
- nr_uks(mol, grids, xc_code, dms, relativity=0, hermi=1, max_memory=2000, verbose=None)#
Calculate UKS XC functional and potential matrix on given meshgrids for a set of density matrices
- Args:
mol : an instance of
Mole- gridsan instance of
Grids grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
- xc_codestr
XC functional description. See
parse_xc()of pyscf/dft/libxc.py for more details.- dmsa list of 2D arrays
A list of density matrices, stored as (alpha,alpha,…,beta,beta,…)
- gridsan instance of
- Kwargs:
- hermiint
Input density matrices symmetric or not. It also indicates whether the potential matrices in return are symmetric or not.
- max_memoryint or float
The maximum size of cache to use (in MB).
- Returns:
nelec, excsum, vmat. nelec is the number of (alpha,beta) electrons generated by numerical integration. excsum is the XC functional value. vmat is the XC potential matrix for (alpha,beta) spin.
Examples:
>>> from pyscf import gto, dft >>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1') >>> grids = dft.gen_grid.Grids(mol) >>> grids.coords = numpy.random.random((100,3)) # 100 random points >>> grids.weights = numpy.random.random(100) >>> nao = mol.nao_nr() >>> dm = numpy.random.random((2,nao,nao)) >>> ni = dft.numint.NumInt() >>> nelec, exc, vxc = ni.nr_uks(mol, grids, 'lda,vwn', dm)
- nr_uks_fxc(mol, grids, xc_code, dm0, dms, relativity=0, hermi=0, rho0=None, vxc=None, fxc=None, max_memory=2000, verbose=None)#
Contract UKS XC kernel matrix with given density matrices
- Args:
ni : an instance of
NumIntmol : an instance of
Mole- gridsan instance of
Grids grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
- xc_codestr
XC functional description. See
parse_xc()of pyscf/dft/libxc.py for more details.- dm0(2, N, N) array
Zeroth order density matrices
- dms2D array a list of 2D arrays
First order density matrices
- gridsan instance of
- Kwargs:
- hermiint
First order density matrix symmetric or not. It also indicates whether the matrices in return are symmetric or not.
- max_memoryint or float
The maximum size of cache to use (in MB).
- rho0float array
Zero-order density (and density derivative for GGA). Giving kwargs rho0, vxc and fxc to improve better performance.
- vxcfloat array
First order XC derivatives
- fxcfloat array
Second order XC derivatives
- Returns:
nelec, excsum, vmat. nelec is the number of electrons generated by numerical integration. excsum is the XC functional value. vmat is the XC potential matrix in 2D array of shape (nao,nao) where nao is the number of AO functions.
Examples:
- nr_vxc(mol, grids, xc_code, dms, spin=0, relativity=0, hermi=0, max_memory=2000, verbose=None)[source]#
Evaluate RKS/UKS XC functional and potential matrix on given meshgrids for a set of density matrices. See
nr_rks()andnr_uks()for more details.- Args:
mol : an instance of
Mole- gridsan instance of
Grids grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
- xc_codestr
XC functional description. See
parse_xc()of pyscf/dft/libxc.py for more details.- dms2D array or a list of 2D arrays
Density matrix or multiple density matrices
- gridsan instance of
- Kwargs:
- hermiint
Input density matrices symmetric or not
- max_memoryint or float
The maximum size of cache to use (in MB).
- Returns:
nelec, excsum, vmat. nelec is the number of electrons generated by numerical integration. excsum is the XC functional value. vmat is the XC potential matrix in 2D array of shape (nao,nao) where nao is the number of AO functions.
Examples:
>>> from pyscf import gto, dft >>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1') >>> grids = dft.gen_grid.Grids(mol) >>> grids.coords = numpy.random.random((100,3)) # 100 random points >>> grids.weights = numpy.random.random(100) >>> nao = mol.nao_nr() >>> dm = numpy.random.random((2,nao,nao)) >>> nelec, exc, vxc = dft.numint.nr_vxc(mol, grids, 'lda,vwn', dm, spin=1)
- pyscf.dft.numint.cache_xc_kernel(ni, mol, grids, xc_code, mo_coeff, mo_occ, spin=0, max_memory=2000)[source]#
Compute the 0th order density, Vxc and fxc. They can be used in TDDFT, DFT hessian module etc.
- pyscf.dft.numint.cache_xc_kernel1(ni, mol, grids, xc_code, dm, spin=0, max_memory=2000)[source]#
Compute the 0th order density, Vxc and fxc. They can be used in TDDFT, DFT hessian module etc. Note dm the zeroth order density matrix must be a hermitian matrix.
- pyscf.dft.numint.eval_ao(mol, coords, deriv=0, shls_slice=None, non0tab=None, cutoff=None, out=None, verbose=None)[source]#
Evaluate AO function value on the given grids.
- Args:
mol : an instance of
Mole- coords2D array, shape (N,3)
The coordinates of the grids.
- Kwargs:
- derivint
AO derivative order. It affects the shape of the return array. If deriv=0, the returned AO values are stored in a (N,nao) array. Otherwise the AO values are stored in an array of shape (M,N,nao). Here N is the number of grids, nao is the number of AO functions, M is the size associated to the derivative deriv.
- relativitybool
No effects.
- shls_slice2-element list
(shl_start, shl_end). If given, only part of AOs (shl_start <= shell_id < shl_end) are evaluated. By default, all shells defined in mol will be evaluated.
- non0tab2D bool array
mask array to indicate whether the AO values are zero. The mask array can be obtained by calling
make_mask()- cutofffloat
AO values smaller than cutoff will be set to zero. The default cutoff threshold is ~1e-22 (defined in gto/grid_ao_drv.h)
- outndarray
If provided, results are written into this array.
- verboseint or object of
Logger No effects.
- Returns:
2D array of shape (N,nao) for AO values if deriv = 0. Or 3D array of shape (:,N,nao) for AO values and AO derivatives if deriv > 0. In the 3D array, the first (N,nao) elements are the AO values, followed by (3,N,nao) for x,y,z components; Then 2nd derivatives (6,N,nao) for xx, xy, xz, yy, yz, zz; Then 3rd derivatives (10,N,nao) for xxx, xxy, xxz, xyy, xyz, xzz, yyy, yyz, yzz, zzz; …
Examples:
>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz') >>> coords = numpy.random.random((100,3)) # 100 random points >>> ao_value = eval_ao(mol, coords) >>> print(ao_value.shape) (100, 24) >>> ao_value = eval_ao(mol, coords, deriv=1, shls_slice=(1,4)) >>> print(ao_value.shape) (4, 100, 7) >>> ao_value = eval_ao(mol, coords, deriv=2, shls_slice=(1,4)) >>> print(ao_value.shape) (10, 100, 7)
- pyscf.dft.numint.eval_mat(mol, ao, weight, rho, vxc, non0tab=None, xctype='LDA', spin=0, verbose=None)[source]#
Calculate XC potential matrix.
- Args:
mol : an instance of
Mole- ao([4/10,] ngrids, nao) ndarray
2D array of shape (N,nao) for LDA, 3D array of shape (4,N,nao) for GGA or (10,N,nao) for meta-GGA. N is the number of grids, nao is the number of AO functions. If xctype is GGA (MGGA), ao[0] is AO value and ao[1:3] are the real space gradients. ao[4:10] are second derivatives of ao values if applicable.
- weight1D array
Integral weights on grids.
- rho([4/6,] ngrids) ndarray
Shape of ((,N)) for electron density (and derivatives) if spin = 0; Shape of ((,N),(,N)) for alpha/beta electron density (and derivatives) if spin > 0; where N is number of grids. rho (,N) are ordered as (den,grad_x,grad_y,grad_z,laplacian,tau) where grad_x = d/dx den, laplacian = nabla^2 den, tau = 1/2(nabla f)^2 In spin unrestricted case, rho is ((den_u,grad_xu,grad_yu,grad_zu,laplacian_u,tau_u)
(den_d,grad_xd,grad_yd,grad_zd,laplacian_d,tau_d))
- vxc([4,] ngrids) ndarray
XC potential value on each grid = (vrho, vsigma, vlapl, vtau) vsigma is GGA potential value on each grid. If the kwarg spin != 0, a list [vsigma_uu,vsigma_ud] is required.
- Kwargs:
- xctypestr
LDA/GGA/mGGA. It affects the shape of ao and rho
- non0tab2D bool array
mask array to indicate whether the AO values are zero. The mask array can be obtained by calling
make_mask()- spinint
If not 0, the returned matrix is the Vxc matrix of alpha-spin. It is computed with the spin non-degenerated UKS formula.
- Returns:
XC potential matrix in 2D array of shape (nao,nao) where nao is the number of AO functions.
- pyscf.dft.numint.eval_rho(mol, ao, dm, non0tab=None, xctype='LDA', hermi=0, with_lapl=True, verbose=None)[source]#
Calculate the electron density for LDA functional, and the density derivatives for GGA and MGGA functionals.
- Args:
mol : an instance of
Mole- ao2D array of shape (N,nao) for LDA, 3D array of shape (4,N,nao) for GGA
or meta-GGA. N is the number of grids, nao is the number of AO functions. If xctype is GGA (MGGA), ao[0] is AO value and ao[1:3] are the AO gradients. ao[4:10] are second derivatives of ao values if applicable.
- dm2D array
Density matrix
- Kwargs:
- non0tab2D bool array
mask array to indicate whether the AO values are zero. The mask array can be obtained by calling
make_mask()- xctypestr
LDA/GGA/mGGA. It affects the shape of the return density.
- hermibool
dm is hermitian or not
- verboseint or object of
Logger No effects.
- Returns:
1D array of size N to store electron density if xctype = LDA; 2D array of (4,N) to store density and “density derivatives” for x,y,z components if xctype = GGA; For meta-GGA, returns can be a (6,N) (with_lapl=True) array where last two rows are nabla^2 rho and tau = 1/2(nabla f)^2 or (5,N) (with_lapl=False) where the last row is tau = 1/2(nabla f)^2
Examples:
>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz') >>> coords = numpy.random.random((100,3)) # 100 random points >>> ao_value = eval_ao(mol, coords, deriv=0) >>> dm = numpy.random.random((mol.nao_nr(),mol.nao_nr())) >>> dm = dm + dm.T >>> rho, dx_rho, dy_rho, dz_rho = eval_rho(mol, ao, dm, xctype='LDA')
- pyscf.dft.numint.eval_rho1(mol, ao, dm, screen_index=None, xctype='LDA', hermi=0, with_lapl=True, cutoff=None, ao_cutoff=1e-15, pair_mask=None, verbose=None)[source]#
Calculate the electron density for LDA and the density derivatives for GGA and MGGA with sparsity information.
- Args:
mol : an instance of
Mole- ao2D array of shape (N,nao) for LDA, 3D array of shape (4,N,nao) for GGA
or meta-GGA. N is the number of grids, nao is the number of AO functions. If xctype is GGA (MGGA), ao[0] is AO value and ao[1:3] are the AO gradients. ao[4:10] are second derivatives of ao values if applicable.
- dm2D array
Density matrix
- Kwargs:
- screen_index2D uint8 array
How likely the AO values on grids are negligible. This array can be obtained by calling
gen_grid.make_screen_index()- xctypestr
LDA/GGA/mGGA. It affects the shape of the return density.
- hermibool
dm is hermitian or not
- cutofffloat
cutoff for density value
- ao_cutofffloat
cutoff for AO value. Needs to be the same to the cutoff when generating screen_index
- verboseint or object of
Logger No effects.
- Returns:
1D array of size N to store electron density if xctype = LDA; 2D array of (4,N) to store density and “density derivatives” for x,y,z components if xctype = GGA; For meta-GGA, returns can be a (6,N) (with_lapl=True) array where last two rows are nabla^2 rho and tau = 1/2(nabla f)^2 or (5,N) (with_lapl=False) where the last row is tau = 1/2(nabla f)^2
- pyscf.dft.numint.eval_rho2(mol, ao, mo_coeff, mo_occ, non0tab=None, xctype='LDA', with_lapl=True, verbose=None)[source]#
Calculate the electron density for LDA functional, and the density derivatives for GGA functional. This function has the same functionality as
eval_rho()except that the density are evaluated based on orbital coefficients and orbital occupancy. It is more efficient thaneval_rho()in most scenario.- Args:
mol : an instance of
Mole- ao2D array of shape (N,nao) for LDA, 3D array of shape (4,N,nao) for GGA
or meta-GGA. N is the number of grids, nao is the number of AO functions. If xctype is GGA (MGGA), ao[0] is AO value and ao[1:3] are the AO gradients. ao[4:10] are second derivatives of ao values if applicable.
- dm2D array
Density matrix
- Kwargs:
- non0tab2D bool array
mask array to indicate whether the AO values are zero. The mask array can be obtained by calling
make_mask()- xctypestr
LDA/GGA/mGGA. It affects the shape of the return density.
- with_lapl: bool
Whether to compute laplacian. It affects the shape of returns.
- verboseint or object of
Logger No effects.
- Returns:
1D array of size N to store electron density if xctype = LDA; 2D array of (4,N) to store density and “density derivatives” for x,y,z components if xctype = GGA; For meta-GGA, returns can be a (6,N) (with_lapl=True) array where last two rows are nabla^2 rho and tau = 1/2(nabla f)^2 or (5,N) (with_lapl=False) where the last row is tau = 1/2(nabla f)^2
- pyscf.dft.numint.nr_fxc(mol, grids, xc_code, dm0, dms, spin=0, relativity=0, hermi=0, rho0=None, vxc=None, fxc=None, max_memory=2000, verbose=None)[source]#
Contract XC kernel matrix with given density matrices
… math:
a_{pq} = f_{pq,rs} * x_{rs}
- pyscf.dft.numint.nr_nlc_vxc(ni, mol, grids, xc_code, dm, relativity=0, hermi=1, max_memory=2000, verbose=None)[source]#
Calculate NLC functional and potential matrix on given grids
- Args:
ni : an instance of
NumIntmol : an instance of
Mole- gridsan instance of
Grids grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
- xc_codestr
XC functional description. See
parse_xc()of pyscf/dft/libxc.py for more details.- dm2D array
Density matrix or multiple density matrices
- gridsan instance of
- Kwargs:
- hermiint
Input density matrices symmetric or not. It also indicates whether the potential matrices in return are symmetric or not.
- max_memoryint or float
The maximum size of cache to use (in MB).
- Returns:
nelec, excsum, vmat. nelec is the number of electrons generated by numerical integration. excsum is the XC functional value. vmat is the XC potential matrix in 2D array of shape (nao,nao) where nao is the number of AO functions.
- pyscf.dft.numint.nr_rks(ni, mol, grids, xc_code, dms, relativity=0, hermi=1, max_memory=2000, verbose=None)[source]#
Calculate RKS XC functional and potential matrix on given meshgrids for a set of density matrices
- Args:
ni : an instance of
NumIntmol : an instance of
Mole- gridsan instance of
Grids grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
- xc_codestr
XC functional description. See
parse_xc()of pyscf/dft/libxc.py for more details.- dms2D array or a list of 2D arrays
Density matrix or multiple density matrices
- gridsan instance of
- Kwargs:
- hermiint
Input density matrices symmetric or not. It also indicates whether the potential matrices in return are symmetric or not.
- max_memoryint or float
The maximum size of cache to use (in MB).
- Returns:
nelec, excsum, vmat. nelec is the number of electrons generated by numerical integration. excsum is the XC functional value. vmat is the XC potential matrix in 2D array of shape (nao,nao) where nao is the number of AO functions.
Examples:
>>> from pyscf import gto, dft >>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1') >>> grids = dft.gen_grid.Grids(mol) >>> grids.coords = numpy.random.random((100,3)) # 100 random points >>> grids.weights = numpy.random.random(100) >>> nao = mol.nao_nr() >>> dm = numpy.random.random((nao,nao)) >>> ni = dft.numint.NumInt() >>> nelec, exc, vxc = ni.nr_rks(mol, grids, 'lda,vwn', dm)
- pyscf.dft.numint.nr_rks_fxc(ni, mol, grids, xc_code, dm0, dms, relativity=0, hermi=0, rho0=None, vxc=None, fxc=None, max_memory=2000, verbose=None)[source]#
Contract RKS XC (singlet hessian) kernel matrix with given density matrices
- Args:
ni : an instance of
NumIntmol : an instance of
Mole- gridsan instance of
Grids grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
- xc_codestr
XC functional description. See
parse_xc()of pyscf/dft/libxc.py for more details.- dm02D array
Zeroth order density matrix
- dms2D array a list of 2D arrays
First order density matrix or density matrices
- gridsan instance of
- Kwargs:
- hermiint
First order density matrix symmetric or not. It also indicates whether the matrices in return are symmetric or not.
- max_memoryint or float
The maximum size of cache to use (in MB).
- rho0float array
Zero-order density (and density derivative for GGA). Giving kwargs rho0, vxc and fxc to improve better performance.
- vxcfloat array
First order XC derivatives
- fxcfloat array
Second order XC derivatives
- Returns:
nelec, excsum, vmat. nelec is the number of electrons generated by numerical integration. excsum is the XC functional value. vmat is the XC potential matrix in 2D array of shape (nao,nao) where nao is the number of AO functions.
Examples:
- pyscf.dft.numint.nr_rks_fxc_st(ni, mol, grids, xc_code, dm0, dms_alpha, relativity=0, singlet=True, rho0=None, vxc=None, fxc=None, max_memory=2000, verbose=None)[source]#
Associated to singlet or triplet Hessian Note the difference to nr_rks_fxc, dms_alpha is the response density matrices of alpha spin, alpha+/-beta DM is applied due to singlet/triplet coupling
Ref. CPL, 256, 454
- pyscf.dft.numint.nr_rks_vxc(ni, mol, grids, xc_code, dms, relativity=0, hermi=1, max_memory=2000, verbose=None)#
Calculate RKS XC functional and potential matrix on given meshgrids for a set of density matrices
- Args:
ni : an instance of
NumIntmol : an instance of
Mole- gridsan instance of
Grids grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
- xc_codestr
XC functional description. See
parse_xc()of pyscf/dft/libxc.py for more details.- dms2D array or a list of 2D arrays
Density matrix or multiple density matrices
- gridsan instance of
- Kwargs:
- hermiint
Input density matrices symmetric or not. It also indicates whether the potential matrices in return are symmetric or not.
- max_memoryint or float
The maximum size of cache to use (in MB).
- Returns:
nelec, excsum, vmat. nelec is the number of electrons generated by numerical integration. excsum is the XC functional value. vmat is the XC potential matrix in 2D array of shape (nao,nao) where nao is the number of AO functions.
Examples:
>>> from pyscf import gto, dft >>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1') >>> grids = dft.gen_grid.Grids(mol) >>> grids.coords = numpy.random.random((100,3)) # 100 random points >>> grids.weights = numpy.random.random(100) >>> nao = mol.nao_nr() >>> dm = numpy.random.random((nao,nao)) >>> ni = dft.numint.NumInt() >>> nelec, exc, vxc = ni.nr_rks(mol, grids, 'lda,vwn', dm)
- pyscf.dft.numint.nr_sap_vxc(ni, mol, grids, max_memory=2000, verbose=None)[source]#
Calculate superposition of atomic potentials matrix on given meshgrids.
- Args:
ni : an instance of
NumIntmol : an instance of
Mole- gridsan instance of
Grids grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
- gridsan instance of
- Kwargs:
- max_memoryint or float
The maximum size of cache to use (in MB).
- Returns:
vmat is the XC potential matrix in 2D array of shape (nao,nao) where nao is the number of AO functions.
Examples: >>> import numpy >>> from pyscf import gto, dft >>> mol = gto.M(atom=’H 0 0 0; H 0 0 1.1’) >>> grids = dft.gen_grid.Grids(mol) >>> ni = dft.numint.NumInt() >>> vsap = ni.nr_sap(mol, grids)
- pyscf.dft.numint.nr_uks(ni, mol, grids, xc_code, dms, relativity=0, hermi=1, max_memory=2000, verbose=None)[source]#
Calculate UKS XC functional and potential matrix on given meshgrids for a set of density matrices
- Args:
mol : an instance of
Mole- gridsan instance of
Grids grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
- xc_codestr
XC functional description. See
parse_xc()of pyscf/dft/libxc.py for more details.- dmsa list of 2D arrays
A list of density matrices, stored as (alpha,alpha,…,beta,beta,…)
- gridsan instance of
- Kwargs:
- hermiint
Input density matrices symmetric or not. It also indicates whether the potential matrices in return are symmetric or not.
- max_memoryint or float
The maximum size of cache to use (in MB).
- Returns:
nelec, excsum, vmat. nelec is the number of (alpha,beta) electrons generated by numerical integration. excsum is the XC functional value. vmat is the XC potential matrix for (alpha,beta) spin.
Examples:
>>> from pyscf import gto, dft >>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1') >>> grids = dft.gen_grid.Grids(mol) >>> grids.coords = numpy.random.random((100,3)) # 100 random points >>> grids.weights = numpy.random.random(100) >>> nao = mol.nao_nr() >>> dm = numpy.random.random((2,nao,nao)) >>> ni = dft.numint.NumInt() >>> nelec, exc, vxc = ni.nr_uks(mol, grids, 'lda,vwn', dm)
- pyscf.dft.numint.nr_uks_fxc(ni, mol, grids, xc_code, dm0, dms, relativity=0, hermi=0, rho0=None, vxc=None, fxc=None, max_memory=2000, verbose=None)[source]#
Contract UKS XC kernel matrix with given density matrices
- Args:
ni : an instance of
NumIntmol : an instance of
Mole- gridsan instance of
Grids grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
- xc_codestr
XC functional description. See
parse_xc()of pyscf/dft/libxc.py for more details.- dm0(2, N, N) array
Zeroth order density matrices
- dms2D array a list of 2D arrays
First order density matrices
- gridsan instance of
- Kwargs:
- hermiint
First order density matrix symmetric or not. It also indicates whether the matrices in return are symmetric or not.
- max_memoryint or float
The maximum size of cache to use (in MB).
- rho0float array
Zero-order density (and density derivative for GGA). Giving kwargs rho0, vxc and fxc to improve better performance.
- vxcfloat array
First order XC derivatives
- fxcfloat array
Second order XC derivatives
- Returns:
nelec, excsum, vmat. nelec is the number of electrons generated by numerical integration. excsum is the XC functional value. vmat is the XC potential matrix in 2D array of shape (nao,nao) where nao is the number of AO functions.
Examples:
- pyscf.dft.numint.nr_uks_vxc(ni, mol, grids, xc_code, dms, relativity=0, hermi=1, max_memory=2000, verbose=None)#
Calculate UKS XC functional and potential matrix on given meshgrids for a set of density matrices
- Args:
mol : an instance of
Mole- gridsan instance of
Grids grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
- xc_codestr
XC functional description. See
parse_xc()of pyscf/dft/libxc.py for more details.- dmsa list of 2D arrays
A list of density matrices, stored as (alpha,alpha,…,beta,beta,…)
- gridsan instance of
- Kwargs:
- hermiint
Input density matrices symmetric or not. It also indicates whether the potential matrices in return are symmetric or not.
- max_memoryint or float
The maximum size of cache to use (in MB).
- Returns:
nelec, excsum, vmat. nelec is the number of (alpha,beta) electrons generated by numerical integration. excsum is the XC functional value. vmat is the XC potential matrix for (alpha,beta) spin.
Examples:
>>> from pyscf import gto, dft >>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1') >>> grids = dft.gen_grid.Grids(mol) >>> grids.coords = numpy.random.random((100,3)) # 100 random points >>> grids.weights = numpy.random.random(100) >>> nao = mol.nao_nr() >>> dm = numpy.random.random((2,nao,nao)) >>> ni = dft.numint.NumInt() >>> nelec, exc, vxc = ni.nr_uks(mol, grids, 'lda,vwn', dm)
- pyscf.dft.numint.nr_vxc(mol, grids, xc_code, dms, spin=0, relativity=0, hermi=0, max_memory=2000, verbose=None)[source]#
Evaluate RKS/UKS XC functional and potential matrix on given meshgrids for a set of density matrices. See
nr_rks()andnr_uks()for more details.- Args:
mol : an instance of
Mole- gridsan instance of
Grids grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
- xc_codestr
XC functional description. See
parse_xc()of pyscf/dft/libxc.py for more details.- dms2D array or a list of 2D arrays
Density matrix or multiple density matrices
- gridsan instance of
- Kwargs:
- hermiint
Input density matrices symmetric or not
- max_memoryint or float
The maximum size of cache to use (in MB).
- Returns:
nelec, excsum, vmat. nelec is the number of electrons generated by numerical integration. excsum is the XC functional value. vmat is the XC potential matrix in 2D array of shape (nao,nao) where nao is the number of AO functions.
Examples:
>>> from pyscf import gto, dft >>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1') >>> grids = dft.gen_grid.Grids(mol) >>> grids.coords = numpy.random.random((100,3)) # 100 random points >>> grids.weights = numpy.random.random(100) >>> nao = mol.nao_nr() >>> dm = numpy.random.random((2,nao,nao)) >>> nelec, exc, vxc = dft.numint.nr_vxc(mol, grids, 'lda,vwn', dm, spin=1)
pyscf.dft.numint2c module#
Numerical integration functions for (2-component) GKS with real AO basis
- class pyscf.dft.numint2c.NumInt2C[source]#
Bases:
StreamObject,LibXCMixinNumerical integration methods for 2-component basis (used by GKS)
- block_loop(mol, grids, nao=None, deriv=0, max_memory=2000, non0tab=None, blksize=None, buf=None)#
Define this macro to loop over grids by blocks.
- cache_xc_kernel(mol, grids, xc_code, mo_coeff, mo_occ, spin=0, max_memory=2000)[source]#
Compute the 0th order density, Vxc and fxc. They can be used in TDDFT, DFT hessian module etc.
- cache_xc_kernel1(mol, grids, xc_code, dm, spin=0, max_memory=2000)[source]#
Compute the 0th order density, Vxc and fxc. They can be used in TDDFT, DFT hessian module etc.
- collinear = 'col'#
- collinear_samples = 200#
- collinear_thrd = 0.99#
- static eval_ao(mol, coords, deriv=0, shls_slice=None, non0tab=None, cutoff=None, out=None, verbose=None)#
Evaluate AO function value on the given grids.
- Args:
mol : an instance of
Mole- coords2D array, shape (N,3)
The coordinates of the grids.
- Kwargs:
- derivint
AO derivative order. It affects the shape of the return array. If deriv=0, the returned AO values are stored in a (N,nao) array. Otherwise the AO values are stored in an array of shape (M,N,nao). Here N is the number of grids, nao is the number of AO functions, M is the size associated to the derivative deriv.
- relativitybool
No effects.
- shls_slice2-element list
(shl_start, shl_end). If given, only part of AOs (shl_start <= shell_id < shl_end) are evaluated. By default, all shells defined in mol will be evaluated.
- non0tab2D bool array
mask array to indicate whether the AO values are zero. The mask array can be obtained by calling
make_mask()- cutofffloat
AO values smaller than cutoff will be set to zero. The default cutoff threshold is ~1e-22 (defined in gto/grid_ao_drv.h)
- outndarray
If provided, results are written into this array.
- verboseint or object of
Logger No effects.
- Returns:
2D array of shape (N,nao) for AO values if deriv = 0. Or 3D array of shape (:,N,nao) for AO values and AO derivatives if deriv > 0. In the 3D array, the first (N,nao) elements are the AO values, followed by (3,N,nao) for x,y,z components; Then 2nd derivatives (6,N,nao) for xx, xy, xz, yy, yz, zz; Then 3rd derivatives (10,N,nao) for xxx, xxy, xxz, xyy, xyz, xzz, yyy, yyz, yzz, zzz; …
Examples:
>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz') >>> coords = numpy.random.random((100,3)) # 100 random points >>> ao_value = eval_ao(mol, coords) >>> print(ao_value.shape) (100, 24) >>> ao_value = eval_ao(mol, coords, deriv=1, shls_slice=(1,4)) >>> print(ao_value.shape) (4, 100, 7) >>> ao_value = eval_ao(mol, coords, deriv=2, shls_slice=(1,4)) >>> print(ao_value.shape) (10, 100, 7)
- static eval_rho(mol, ao, dm, non0tab=None, xctype='LDA', hermi=0, with_lapl=True, verbose=None)#
Calculate the electron density and magnetization spin density in the framework of 2-component real basis. Calculate the electron density for LDA functional, and the density derivatives for GGA and MGGA functionals.
- Args:
mol : an instance of
Mole- ao2D array of shape (N,nao) for LDA, 3D array of shape (4,N,nao) for GGA
or meta-GGA. N is the number of grids, nao is the number of AO functions. If xctype is GGA (MGGA), ao[0] is AO value and ao[1:3] are the AO gradients. ao[4:10] are second derivatives of ao values if applicable.
- dm2D array
Density matrix
- Kwargs:
- non0tab2D bool array
mask array to indicate whether the AO values are zero. The mask array can be obtained by calling
make_mask()- xctypestr
LDA/GGA/mGGA. It affects the shape of the return density.
- hermibool
dm is hermitian or not
- verboseint or object of
Logger No effects.
- Returns:
1D array of size N to store electron density if xctype = LDA; 2D array of (4,N) to store density and “density derivatives” for x,y,z components if xctype = GGA; For meta-GGA, returns can be a (6,N) (with_lapl=True) array where last two rows are nabla^2 rho and tau = 1/2(nabla f)^2 or (5,N) (with_lapl=False) where the last row is tau = 1/2(nabla f)^2
Examples:
>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz') >>> coords = numpy.random.random((100,3)) # 100 random points >>> ao_value = eval_ao(mol, coords, deriv=0) >>> dm = numpy.random.random((mol.nao_nr(),mol.nao_nr())) >>> dm = dm + dm.T >>> rho, dx_rho, dy_rho, dz_rho = eval_rho(mol, ao, dm, xctype='LDA')
- eval_rho1(mol, ao, dm, screen_index=None, xctype='LDA', hermi=0, with_lapl=True, cutoff=None, ao_cutoff=None, pair_mask=None, verbose=None)[source]#
- eval_rho2(mol, ao, mo_coeff, mo_occ, non0tab=None, xctype='LDA', with_lapl=True, verbose=None)[source]#
Calculate the electron density for LDA functional and the density derivatives for GGA functional in the framework of 2-component basis.
- eval_xc_eff(xc_code, rho, deriv=1, omega=None, xctype=None, verbose=None)#
Returns the derivative tensor against the density parameters
- [[density_a, (nabla_x)_a, (nabla_y)_a, (nabla_z)_a, tau_a],
[density_b, (nabla_x)_b, (nabla_y)_b, (nabla_z)_b, tau_b]].
It differs from the eval_xc method in the derivatives of non-local part. The eval_xc method returns the XC functional derivatives to sigma (|nabla rho|^2)
- Args:
- rho: 2-dimensional or 3-dimensional array
Total density and spin density (and their derivatives if GGA or MGGA functionals) on grids
- Kwargs:
- deriv: int
derivative orders
- omega: float
define the exponent in the attenuated Coulomb for RSH functional
- get_fxc(mol, grids, xc_code, dm0, dms, spin=0, relativity=0, hermi=0, rho0=None, vxc=None, fxc=None, max_memory=2000, verbose=None)#
Contract RKS XC (singlet hessian) kernel matrix with given density matrices
- Args:
ni : an instance of
NumIntmol : an instance of
Mole- gridsan instance of
Grids grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
- xc_codestr
XC functional description. See
parse_xc()of pyscf/dft/libxc.py for more details.- dm02D array
Zeroth order density matrix
- dms2D array a list of 2D arrays
First order density matrix or density matrices
- gridsan instance of
- Kwargs:
- hermiint
First order density matrix symmetric or not. It also indicates whether the matrices in return are symmetric or not.
- max_memoryint or float
The maximum size of cache to use (in MB).
- rho0float array
Zero-order density (and density derivative for GGA). Giving kwargs rho0, vxc and fxc to improve better performance.
- vxcfloat array
First order XC derivatives
- fxcfloat array
Second order XC derivatives
- Returns:
nelec, excsum, vmat. nelec is the number of electrons generated by numerical integration. excsum is the XC functional value. vmat is the XC potential matrix in 2D array of shape (nao,nao) where nao is the number of AO functions.
Examples:
- get_vxc(mol, grids, xc_code, dms, spin=0, relativity=0, hermi=1, max_memory=2000, verbose=None)#
Calculate RKS XC functional and potential matrix on given meshgrids for a set of density matrices
- Args:
ni : an instance of
NumIntmol : an instance of
Mole- gridsan instance of
Grids grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
- xc_codestr
XC functional description. See
parse_xc()of pyscf/dft/libxc.py for more details.- dms2D array or a list of 2D arrays
Density matrix or multiple density matrices
- gridsan instance of
- Kwargs:
- hermiint
Input density matrices symmetric or not. It also indicates whether the potential matrices in return are symmetric or not.
- max_memoryint or float
The maximum size of cache to use (in MB).
- Returns:
nelec, excsum, vmat. nelec is the number of electrons generated by numerical integration. excsum is the XC functional value. vmat is the XC potential matrix in 2D array of shape (nao,nao) where nao is the number of AO functions.
Examples:
>>> from pyscf import gto, dft >>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1') >>> grids = dft.gen_grid.Grids(mol) >>> grids.coords = numpy.random.random((100,3)) # 100 random points >>> grids.weights = numpy.random.random(100) >>> nao = mol.nao_nr() >>> dm = numpy.random.random((nao,nao)) >>> ni = dft.numint.NumInt() >>> nelec, exc, vxc = ni.nr_rks(mol, grids, 'lda,vwn', dm)
- static make_mask(mol, coords, relativity=0, shls_slice=None, cutoff=1e-15, verbose=None)#
Mask to indicate whether a shell is ignorable on grids. See also the function gto.eval_gto.make_screen_index
- Args:
mol : an instance of
Mole- coords2D array, shape (N,3)
The coordinates of grids.
- Kwargs:
- relativitybool
No effects.
- shls_slice2-element list
(shl_start, shl_end). If given, only part of AOs (shl_start <= shell_id < shl_end) are evaluated. By default, all shells defined in mol will be evaluated.
- verboseint or object of
Logger No effects.
- Returns:
2D mask array of shape (N,nbas), where N is the number of grids, nbas is the number of shells.
- mcfun_eval_xc_adapter(xc_code)#
Wrapper to generate the eval_xc function required by mcfun
- nr_fxc(mol, grids, xc_code, dm0, dms, spin=0, relativity=0, hermi=0, rho0=None, vxc=None, fxc=None, max_memory=2000, verbose=None)[source]#
Contract RKS XC (singlet hessian) kernel matrix with given density matrices
- Args:
ni : an instance of
NumIntmol : an instance of
Mole- gridsan instance of
Grids grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
- xc_codestr
XC functional description. See
parse_xc()of pyscf/dft/libxc.py for more details.- dm02D array
Zeroth order density matrix
- dms2D array a list of 2D arrays
First order density matrix or density matrices
- gridsan instance of
- Kwargs:
- hermiint
First order density matrix symmetric or not. It also indicates whether the matrices in return are symmetric or not.
- max_memoryint or float
The maximum size of cache to use (in MB).
- rho0float array
Zero-order density (and density derivative for GGA). Giving kwargs rho0, vxc and fxc to improve better performance.
- vxcfloat array
First order XC derivatives
- fxcfloat array
Second order XC derivatives
- Returns:
nelec, excsum, vmat. nelec is the number of electrons generated by numerical integration. excsum is the XC functional value. vmat is the XC potential matrix in 2D array of shape (nao,nao) where nao is the number of AO functions.
Examples:
- nr_gks_fxc(mol, grids, xc_code, dm0, dms, spin=0, relativity=0, hermi=0, rho0=None, vxc=None, fxc=None, max_memory=2000, verbose=None)#
Contract RKS XC (singlet hessian) kernel matrix with given density matrices
- Args:
ni : an instance of
NumIntmol : an instance of
Mole- gridsan instance of
Grids grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
- xc_codestr
XC functional description. See
parse_xc()of pyscf/dft/libxc.py for more details.- dm02D array
Zeroth order density matrix
- dms2D array a list of 2D arrays
First order density matrix or density matrices
- gridsan instance of
- Kwargs:
- hermiint
First order density matrix symmetric or not. It also indicates whether the matrices in return are symmetric or not.
- max_memoryint or float
The maximum size of cache to use (in MB).
- rho0float array
Zero-order density (and density derivative for GGA). Giving kwargs rho0, vxc and fxc to improve better performance.
- vxcfloat array
First order XC derivatives
- fxcfloat array
Second order XC derivatives
- Returns:
nelec, excsum, vmat. nelec is the number of electrons generated by numerical integration. excsum is the XC functional value. vmat is the XC potential matrix in 2D array of shape (nao,nao) where nao is the number of AO functions.
Examples:
- nr_gks_vxc(mol, grids, xc_code, dms, spin=0, relativity=0, hermi=1, max_memory=2000, verbose=None)#
Calculate RKS XC functional and potential matrix on given meshgrids for a set of density matrices
- Args:
ni : an instance of
NumIntmol : an instance of
Mole- gridsan instance of
Grids grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
- xc_codestr
XC functional description. See
parse_xc()of pyscf/dft/libxc.py for more details.- dms2D array or a list of 2D arrays
Density matrix or multiple density matrices
- gridsan instance of
- Kwargs:
- hermiint
Input density matrices symmetric or not. It also indicates whether the potential matrices in return are symmetric or not.
- max_memoryint or float
The maximum size of cache to use (in MB).
- Returns:
nelec, excsum, vmat. nelec is the number of electrons generated by numerical integration. excsum is the XC functional value. vmat is the XC potential matrix in 2D array of shape (nao,nao) where nao is the number of AO functions.
Examples:
>>> from pyscf import gto, dft >>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1') >>> grids = dft.gen_grid.Grids(mol) >>> grids.coords = numpy.random.random((100,3)) # 100 random points >>> grids.weights = numpy.random.random(100) >>> nao = mol.nao_nr() >>> dm = numpy.random.random((nao,nao)) >>> ni = dft.numint.NumInt() >>> nelec, exc, vxc = ni.nr_rks(mol, grids, 'lda,vwn', dm)
- nr_nlc_vxc(mol, grids, xc_code, dm, spin=0, relativity=0, hermi=1, max_memory=2000, verbose=None)[source]#
Calculate NLC functional and potential matrix on given grids
- Args:
ni : an instance of
NumIntmol : an instance of
Mole- gridsan instance of
Grids grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
- xc_codestr
XC functional description. See
parse_xc()of pyscf/dft/libxc.py for more details.- dm2D array
Density matrix or multiple density matrices
- gridsan instance of
- Kwargs:
- hermiint
Input density matrices symmetric or not. It also indicates whether the potential matrices in return are symmetric or not.
- max_memoryint or float
The maximum size of cache to use (in MB).
- Returns:
nelec, excsum, vmat. nelec is the number of electrons generated by numerical integration. excsum is the XC functional value. vmat is the XC potential matrix in 2D array of shape (nao,nao) where nao is the number of AO functions.
- nr_vxc(mol, grids, xc_code, dms, spin=0, relativity=0, hermi=1, max_memory=2000, verbose=None)[source]#
Calculate RKS XC functional and potential matrix on given meshgrids for a set of density matrices
- Args:
ni : an instance of
NumIntmol : an instance of
Mole- gridsan instance of
Grids grids.coords and grids.weights are needed for coordinates and weights of meshgrids.
- xc_codestr
XC functional description. See
parse_xc()of pyscf/dft/libxc.py for more details.- dms2D array or a list of 2D arrays
Density matrix or multiple density matrices
- gridsan instance of
- Kwargs:
- hermiint
Input density matrices symmetric or not. It also indicates whether the potential matrices in return are symmetric or not.
- max_memoryint or float
The maximum size of cache to use (in MB).
- Returns:
nelec, excsum, vmat. nelec is the number of electrons generated by numerical integration. excsum is the XC functional value. vmat is the XC potential matrix in 2D array of shape (nao,nao) where nao is the number of AO functions.
Examples:
>>> from pyscf import gto, dft >>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1') >>> grids = dft.gen_grid.Grids(mol) >>> grids.coords = numpy.random.random((100,3)) # 100 random points >>> grids.weights = numpy.random.random(100) >>> nao = mol.nao_nr() >>> dm = numpy.random.random((nao,nao)) >>> ni = dft.numint.NumInt() >>> nelec, exc, vxc = ni.nr_rks(mol, grids, 'lda,vwn', dm)
- spin_samples = 770#
- pyscf.dft.numint2c.eval_rho(mol, ao, dm, non0tab=None, xctype='LDA', hermi=0, with_lapl=True, verbose=None)[source]#
Calculate the electron density and magnetization spin density in the framework of 2-component real basis. Calculate the electron density for LDA functional, and the density derivatives for GGA and MGGA functionals.
- Args:
mol : an instance of
Mole- ao2D array of shape (N,nao) for LDA, 3D array of shape (4,N,nao) for GGA
or meta-GGA. N is the number of grids, nao is the number of AO functions. If xctype is GGA (MGGA), ao[0] is AO value and ao[1:3] are the AO gradients. ao[4:10] are second derivatives of ao values if applicable.
- dm2D array
Density matrix
- Kwargs:
- non0tab2D bool array
mask array to indicate whether the AO values are zero. The mask array can be obtained by calling
make_mask()- xctypestr
LDA/GGA/mGGA. It affects the shape of the return density.
- hermibool
dm is hermitian or not
- verboseint or object of
Logger No effects.
- Returns:
1D array of size N to store electron density if xctype = LDA; 2D array of (4,N) to store density and “density derivatives” for x,y,z components if xctype = GGA; For meta-GGA, returns can be a (6,N) (with_lapl=True) array where last two rows are nabla^2 rho and tau = 1/2(nabla f)^2 or (5,N) (with_lapl=False) where the last row is tau = 1/2(nabla f)^2
Examples:
>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz') >>> coords = numpy.random.random((100,3)) # 100 random points >>> ao_value = eval_ao(mol, coords, deriv=0) >>> dm = numpy.random.random((mol.nao_nr(),mol.nao_nr())) >>> dm = dm + dm.T >>> rho, dx_rho, dy_rho, dz_rho = eval_rho(mol, ao, dm, xctype='LDA')
pyscf.dft.r_numint module#
Numerical integration functions for 4-component or 2-component relativistic methods with j-adapted AO basis
- class pyscf.dft.r_numint.RNumInt[source]#
Bases:
StreamObject,LibXCMixinNumInt for j-adapted (spinor) basis
- block_loop(mol, grids, nao, deriv=0, max_memory=2000, non0tab=None, blksize=None, buf=None, with_s=False)[source]#
Define this macro to loop over grids by blocks.
- cache_xc_kernel(mol, grids, xc_code, mo_coeff, mo_occ, spin=1, max_memory=2000)#
Compute the 0th order density, Vxc and fxc. They can be used in TDDFT, DFT hessian module etc.
- cache_xc_kernel1(mol, grids, xc_code, dm, spin=1, max_memory=2000)#
- collinear = 'col'#
- collinear_samples = 200#
- collinear_thrd = 0.99#
- static eval_ao(mol, coords, deriv=0, with_s=True, shls_slice=None, non0tab=None, cutoff=None, out=None, verbose=None)#
Evaluates the value of 2-component or 4-component j-adapted basis on grids.
- static eval_rho(mol, ao, dm, non0tab=None, xctype='LDA', hermi=0, with_lapl=False, verbose=None)#
- eval_rho1(mol, ao, dm, screen_index=None, xctype='LDA', hermi=0, with_lapl=True, cutoff=None, ao_cutoff=None, pair_mask=None, verbose=None)[source]#
- eval_rho2(mol, ao, mo_coeff, mo_occ, non0tab=None, xctype='LDA', with_lapl=True, verbose=None)[source]#
- eval_xc_eff(xc_code, rho, deriv=1, omega=None, xctype=None, verbose=None)#
Returns the derivative tensor against the density parameters
- [[density_a, (nabla_x)_a, (nabla_y)_a, (nabla_z)_a, tau_a],
[density_b, (nabla_x)_b, (nabla_y)_b, (nabla_z)_b, tau_b]].
It differs from the eval_xc method in the derivatives of non-local part. The eval_xc method returns the XC functional derivatives to sigma (|nabla rho|^2)
- Args:
- rho: 2-dimensional or 3-dimensional array
Total density and spin density (and their derivatives if GGA or MGGA functionals) on grids
- Kwargs:
- deriv: int
derivative orders
- omega: float
define the exponent in the attenuated Coulomb for RSH functional
- get_fxc(mol, grids, xc_code, dm0, dms, spin=0, relativity=1, hermi=0, rho0=None, vxc=None, fxc=None, max_memory=2000, verbose=None)#
- get_rho(mol, dm, grids, max_memory=2000)#
- get_vxc(mol, grids, xc_code, dms, spin=0, relativity=1, hermi=1, max_memory=2000, verbose=None)#
- mcfun_eval_xc_adapter(xc_code)#
Wrapper to generate the eval_xc function required by mcfun
- r_fxc(mol, grids, xc_code, dm0, dms, spin=0, relativity=1, hermi=0, rho0=None, vxc=None, fxc=None, max_memory=2000, verbose=None)#
- r_vxc(mol, grids, xc_code, dms, spin=0, relativity=1, hermi=1, max_memory=2000, verbose=None)#
- spin_samples = 770#
- pyscf.dft.r_numint.cache_xc_kernel(ni, mol, grids, xc_code, mo_coeff, mo_occ, spin=1, max_memory=2000)[source]#
Compute the 0th order density, Vxc and fxc. They can be used in TDDFT, DFT hessian module etc.
- pyscf.dft.r_numint.eval_ao(mol, coords, deriv=0, with_s=True, shls_slice=None, non0tab=None, cutoff=None, out=None, verbose=None)[source]#
Evaluates the value of 2-component or 4-component j-adapted basis on grids.
- pyscf.dft.r_numint.eval_rho(mol, ao, dm, non0tab=None, xctype='LDA', hermi=0, with_lapl=False, verbose=None)[source]#
pyscf.dft.radi module#
radii grids
- pyscf.dft.radi.becke(n, charge, *args, **kwargs)[source]#
Becke, JCP 88, 2547 (1988); DOI:10.1063/1.454033
- pyscf.dft.radi.becke_atomic_radii_adjust(mol, atomic_radii)[source]#
Becke atomic radii adjust function
- pyscf.dft.radi.delley(n, *args, **kwargs)[source]#
Delley radial grids. Ref. JCP 104, 9848 (1996); DOI:10.1063/1.471749. log2 algorithm
- pyscf.dft.radi.gauss_chebyshev(n, *args, **kwargs)[source]#
Gauss-Chebyshev [JCP 108, 3226 (1998); DOI:10.1063/1.475719) radial grids
- pyscf.dft.radi.gauss_legendre(n, *args, **kwargs)#
Delley radial grids. Ref. JCP 104, 9848 (1996); DOI:10.1063/1.471749. log2 algorithm
- pyscf.dft.radi.mura_knowles(n, charge=None, *args, **kwargs)[source]#
Mura-Knowles [JCP 104, 9848 (1996); DOI:10.1063/1.471749] log3 quadrature radial grids
- pyscf.dft.radi.treutler(n, chg, *args, **kwargs)#
Treutler-Ahlrichs [JCP 102, 346 (1995); DOI:10.1063/1.469408] (M4) radial grids
pyscf.dft.rks module#
Non-relativistic restricted Kohn-Sham
- class pyscf.dft.rks.KohnShamDFT(xc='LDA,VWN')[source]#
Bases:
object- Attributes for Kohn-Sham DFT:
- xcstr
‘X_name,C_name’ for the XC functional. Default is ‘lda,vwn’
- nlcstr
‘NLC_name’ for the NLC functional. Default is ‘’ (i.e., None)
- omegafloat
Omega of the range-separated Coulomb operator e^{-omega r_{12}^2} / r_{12}
- gridsGrids object
grids.level (0 - 9) big number for large mesh grids. Default is 3
- radii_adjust
- radi.treutler_atomic_radii_adjust (default)radi.becke_atomic_radii_adjustNone : to switch off atomic radii adjustment
- grids.atomic_radii
- radi.BRAGG_RADII (default)radi.COVALENT_RADIINone : to switch off atomic radii adjustment
- grids.radi_method scheme for radial grids
- radi.treutler (default)radi.delleyradi.mura_knowlesradi.gauss_chebyshev
- grids.becke_scheme weight partition function
- gen_grid.original_becke (default)gen_grid.stratmann
- grids.prune scheme to reduce number of grids
- gen_grid.nwchem_prune (default)gen_grid.sg1_prunegen_grid.treutler_pruneNone : to switch off grids pruning
grids.symmetry True/False to symmetrize mesh grids (TODO)
grids.atom_grid Set (radial, angular) grids for particular atoms. Eg, grids.atom_grid = {‘H’: (20,110)} will generate 20 radial grids and 110 angular grids for H atom.
- small_rho_cutofffloat
Drop grids if their contribution to total electrons smaller than this cutoff value. Default is 1e-7.
Examples:
>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz', verbose=0) >>> mf = dft.RKS(mol) >>> mf.xc = 'b3lyp' >>> mf.kernel() -76.415443079840458
- define_xc_(description, xctype='LDA', hyb=0, rsh=(0, 0, 0))#
- do_nlc()[source]#
Check if the object needs to do nlc calculations
if self.nlc == False (or 0), nlc is disabled regardless the value of self.xc if self.nlc == ‘vv10’, do nlc (vv10) regardless the value of self.xc if self.nlc == ‘’, determined by self.xc, certain xc allows the nlc part
- property omega#
- to_ghf()[source]#
Convert the input mean-field object to a GHF object.
Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.
- to_gks(xc=None)[source]#
Convert the input mean-field object to a GKS object.
Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.
- to_hf()[source]#
Convert the input KS object to the associated HF object.
Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.
- to_rhf()[source]#
Convert the input mean-field object to a RHF/ROHF object.
Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.
- to_rks(xc=None)[source]#
Convert the input mean-field object to a RKS/ROKS object.
Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.
- class pyscf.dft.rks.RKS(mol, xc='LDA,VWN')[source]#
Bases:
KohnShamDFT,RHFRestricted Kohn-Sham SCF base class. non-relativistic RHF.
- Attributes:
- verboseint
Print level. Default value equals to
Mole.verbose- max_memoryfloat or int
Allowed memory in MB. Default equals to
Mole.max_memory- chkfilestr
checkpoint file to save MOs, orbital energies etc. Writing to chkfile can be disabled if this attribute is set to None or False.
- conv_tolfloat
converge threshold. Default is 1e-9
- conv_tol_gradfloat
gradients converge threshold. Default is sqrt(conv_tol)
- max_cycleint
max number of iterations. If max_cycle <= 0, SCF iteration will be skipped and the kernel function will compute only the total energy based on the initial guess. Default value is 50.
- init_guessstr
initial guess method. It can be one of ‘minao’, ‘atom’, ‘huckel’, ‘hcore’, ‘1e’, ‘sap’, ‘chkfile’. Default is ‘minao’
- sap_basisstr or dict
basis for SAP initial guess, either filename or path as str or internal format dictionary.
- DIISDIIS class
The class to generate diis object. It can be one of diis.SCF_DIIS, diis.ADIIS, diis.EDIIS.
- diisboolean or object of DIIS class defined in
scf.diis. Default is the object associated to the attribute
self.DIIS. Set it to None/False to turn off DIIS. Note if this attribute is initialized as a DIIS object, the SCF driver will use this object in the iteration. The DIIS information (vector basis and error vector) will be held inside this object. When kernel function is called again, the old states (vector basis and error vector) will be reused.- diis_spaceint
DIIS space size. By default, 8 Fock matrices and errors vector are stored.
- diis_dampfloat
DIIS damping factor. Default is 0.
- diis_start_cycleint
The step to start DIIS. Default is 1.
- diis_file: ‘str’
File to store DIIS vectors and error vectors.
- level_shiftfloat or int
Level shift (in AU) for virtual space. Default is 0.
- direct_scfbool
Direct SCF is used by default.
- direct_scf_tolfloat
Direct SCF cutoff threshold. Default is 1e-13.
- callbackfunction(envs_dict) => None
callback function takes one dict as the argument which is generated by the builtin function
locals(), so that the callback function can access all local variables in the current environment.- conv_checkbool
An extra cycle to check convergence after SCF iterations.
- check_convergencefunction(envs) => bool
A hook for overloading convergence criteria in SCF iterations.
Saved results:
- convergedbool
Whether the SCF iteration converged
- e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)
- mo_energy :
Orbital energies
- mo_occ
Orbital occupancy
- mo_coeff
Orbital coefficients
- cyclesint
The number of iteration cycles performed
Examples:
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1', basis='cc-pvdz') >>> mf = scf.hf.SCF(mol) >>> mf.verbose = 0 >>> mf.level_shift = .4 >>> mf.scf() -1.0811707843775884
- Attributes for Kohn-Sham DFT:
- xcstr
‘X_name,C_name’ for the XC functional. Default is ‘lda,vwn’
- nlcstr
‘NLC_name’ for the NLC functional. Default is ‘’ (i.e., None)
- omegafloat
Omega of the range-separated Coulomb operator e^{-omega r_{12}^2} / r_{12}
- gridsGrids object
grids.level (0 - 9) big number for large mesh grids. Default is 3
- radii_adjust
- radi.treutler_atomic_radii_adjust (default)radi.becke_atomic_radii_adjustNone : to switch off atomic radii adjustment
- grids.atomic_radii
- radi.BRAGG_RADII (default)radi.COVALENT_RADIINone : to switch off atomic radii adjustment
- grids.radi_method scheme for radial grids
- radi.treutler (default)radi.delleyradi.mura_knowlesradi.gauss_chebyshev
- grids.becke_scheme weight partition function
- gen_grid.original_becke (default)gen_grid.stratmann
- grids.prune scheme to reduce number of grids
- gen_grid.nwchem_prune (default)gen_grid.sg1_prunegen_grid.treutler_pruneNone : to switch off grids pruning
grids.symmetry True/False to symmetrize mesh grids (TODO)
grids.atom_grid Set (radial, angular) grids for particular atoms. Eg, grids.atom_grid = {‘H’: (20,110)} will generate 20 radial grids and 110 angular grids for H atom.
- small_rho_cutofffloat
Drop grids if their contribution to total electrons smaller than this cutoff value. Default is 1e-7.
Examples:
>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz', verbose=0) >>> mf = dft.RKS(mol) >>> mf.xc = 'b3lyp' >>> mf.kernel() -76.415443079840458
- CasidaTDDFT(*args, **kwargs)#
Solve the Casida TDDFT formula (A-B)(A+B)(X+Y) = (X+Y)w^2
- Gradients(*args, **kwargs)#
Non-relativistic restricted Hartree-Fock gradients
- Hessian(*args, **kwargs)#
Non-relativistic RKS hessian
- TDA(*args, **kwargs)#
Tamm-Dancoff approximation
- Attributes:
- conv_tolfloat
Diagonalization convergence tolerance. Default is 1e-9.
- nstatesint
Number of TD states to be computed. Default is 3.
Saved results:
- convergedbool
Diagonalization converged or not
- e1D array
excitation energy for each excited state.
- xyA list of two 2D arrays
The two 2D arrays are Excitation coefficients X (shape [nocc,nvir]) and de-excitation coefficients Y (shape [nocc,nvir]) for each excited state. (X,Y) are normalized to 1/2 in RHF/RKS methods and normalized to 1 for UHF/UKS methods. In the TDA calculation, Y = 0.
- TDDFT()#
Driver to create TDDFT or CasidaTDDFT object
- TDDFTNoHybrid(*args, **kwargs)#
Solve the Casida TDDFT formula (A-B)(A+B)(X+Y) = (X+Y)w^2
- TDHF = None#
- dRPA(*args, **kwargs)#
- dTDA(*args, **kwargs)#
- energy_elec(dm=None, h1e=None, vhf=None)#
Electronic part of RKS energy.
Note this function has side effects which cause mf.scf_summary updated.
- Args:
ks : an instance of DFT class
- dm2D ndarray
one-particle density matrix
- h1e2D ndarray
Core hamiltonian
- Returns:
RKS electronic energy and the 2-electron contribution
- get_veff(mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1)#
Coulomb + XC functional
Note
This function will modify the input ks object.
- Args:
- ksan instance of
RKS XC functional are controlled by ks.xc attribute. Attribute ks.grids might be initialized.
- dmndarray or list of ndarrays
A density matrix or a list of density matrices
- ksan instance of
- Kwargs:
- dm_lastndarray or a list of ndarrays or 0
The density matrix baseline. If not 0, this function computes the increment of HF potential w.r.t. the reference HF potential matrix.
- vhf_lastndarray or a list of ndarrays or 0
The reference Vxc potential matrix.
- hermiint
Whether J, K matrix is hermitian
0 : no hermitian or symmetric1 : hermitian2 : anti-hermitian
- Returns:
matrix Veff = J + Vxc. Veff can be a list matrices, if the input dm is a list of density matrices.
- get_vsap(mol=None)#
Superposition of atomic potentials
S. Lehtola, Assessment of initial guesses for self-consistent field calculations. Superposition of Atomic Potentials: simple yet efficient, J. Chem. Theory Comput. 15, 1593 (2019). DOI: 10.1021/acs.jctc.8b01089. arXiv:1810.11659.
This function evaluates the effective charge of a neutral atom, given by exchange-only LDA on top of spherically symmetric unrestricted Hartree-Fock calculations as described in
S. Lehtola, L. Visscher, E. Engel, Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets, J. Chem. Phys., in press (2020).
The potentials have been calculated for the ground-states of spherically symmetric atoms at the non-relativistic level of theory as described in
S. Lehtola, “Fully numerical calculations on atoms with fractional occupations and range-separated exchange functionals”, Phys. Rev. A 101, 012516 (2020). DOI: 10.1103/PhysRevA.101.012516
using accurate finite-element calculations as described in
S. Lehtola, “Fully numerical Hartree-Fock and density functional calculations. I. Atoms”, Int. J. Quantum Chem. e25945 (2019). DOI: 10.1002/qua.25945
Note
This function will modify the input ks object.
- Args:
- ksan instance of
RKS XC functional are controlled by ks.xc attribute. Attribute ks.grids might be initialized.
- ksan instance of
- Returns:
matrix Vsap = Vnuc + J + Vxc.
- init_guess_by_vsap(mol=None)#
Form SAP guess
- to_gpu(out=None)#
Convert a method to its corresponding GPU variant, and recursively converts all attributes of a method to cupy objects or gpu4pyscf objects.
- pyscf.dft.rks.energy_elec(ks, dm=None, h1e=None, vhf=None)[source]#
Electronic part of RKS energy.
Note this function has side effects which cause mf.scf_summary updated.
- Args:
ks : an instance of DFT class
- dm2D ndarray
one-particle density matrix
- h1e2D ndarray
Core hamiltonian
- Returns:
RKS electronic energy and the 2-electron contribution
- pyscf.dft.rks.get_veff(ks, mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1)[source]#
Coulomb + XC functional
Note
This function will modify the input ks object.
- Args:
- ksan instance of
RKS XC functional are controlled by ks.xc attribute. Attribute ks.grids might be initialized.
- dmndarray or list of ndarrays
A density matrix or a list of density matrices
- ksan instance of
- Kwargs:
- dm_lastndarray or a list of ndarrays or 0
The density matrix baseline. If not 0, this function computes the increment of HF potential w.r.t. the reference HF potential matrix.
- vhf_lastndarray or a list of ndarrays or 0
The reference Vxc potential matrix.
- hermiint
Whether J, K matrix is hermitian
0 : no hermitian or symmetric1 : hermitian2 : anti-hermitian
- Returns:
matrix Veff = J + Vxc. Veff can be a list matrices, if the input dm is a list of density matrices.
- pyscf.dft.rks.get_vsap(ks, mol=None)[source]#
Superposition of atomic potentials
S. Lehtola, Assessment of initial guesses for self-consistent field calculations. Superposition of Atomic Potentials: simple yet efficient, J. Chem. Theory Comput. 15, 1593 (2019). DOI: 10.1021/acs.jctc.8b01089. arXiv:1810.11659.
This function evaluates the effective charge of a neutral atom, given by exchange-only LDA on top of spherically symmetric unrestricted Hartree-Fock calculations as described in
S. Lehtola, L. Visscher, E. Engel, Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets, J. Chem. Phys., in press (2020).
The potentials have been calculated for the ground-states of spherically symmetric atoms at the non-relativistic level of theory as described in
S. Lehtola, “Fully numerical calculations on atoms with fractional occupations and range-separated exchange functionals”, Phys. Rev. A 101, 012516 (2020). DOI: 10.1103/PhysRevA.101.012516
using accurate finite-element calculations as described in
S. Lehtola, “Fully numerical Hartree-Fock and density functional calculations. I. Atoms”, Int. J. Quantum Chem. e25945 (2019). DOI: 10.1002/qua.25945
Note
This function will modify the input ks object.
- Args:
- ksan instance of
RKS XC functional are controlled by ks.xc attribute. Attribute ks.grids might be initialized.
- ksan instance of
- Returns:
matrix Vsap = Vnuc + J + Vxc.
pyscf.dft.rks_symm module#
Non-relativistic Restricted Kohn-Sham
- pyscf.dft.rks_symm.RKS#
alias of
SymAdaptedRKS
- pyscf.dft.rks_symm.ROKS#
alias of
SymAdaptedROKS
- class pyscf.dft.rks_symm.SymAdaptedRKS(mol, xc='LDA,VWN')[source]#
Bases:
KohnShamDFT,SymAdaptedRHFRestricted Kohn-Sham
- CasidaTDDFT(*args, **kwargs)#
Solve the Casida TDDFT formula (A-B)(A+B)(X+Y) = (X+Y)w^2
- Gradients(*args, **kwargs)#
Non-relativistic restricted Hartree-Fock gradients
- Hessian(*args, **kwargs)#
Non-relativistic RKS hessian
- TDA(*args, **kwargs)#
Tamm-Dancoff approximation
- Attributes:
- conv_tolfloat
Diagonalization convergence tolerance. Default is 1e-9.
- nstatesint
Number of TD states to be computed. Default is 3.
Saved results:
- convergedbool
Diagonalization converged or not
- e1D array
excitation energy for each excited state.
- xyA list of two 2D arrays
The two 2D arrays are Excitation coefficients X (shape [nocc,nvir]) and de-excitation coefficients Y (shape [nocc,nvir]) for each excited state. (X,Y) are normalized to 1/2 in RHF/RKS methods and normalized to 1 for UHF/UKS methods. In the TDA calculation, Y = 0.
- TDDFT()#
Driver to create TDDFT or CasidaTDDFT object
- TDDFTNoHybrid(*args, **kwargs)#
Solve the Casida TDDFT formula (A-B)(A+B)(X+Y) = (X+Y)w^2
- TDHF = None#
- dRPA(*args, **kwargs)#
- dTDA(*args, **kwargs)#
- energy_elec(dm=None, h1e=None, vhf=None)#
Electronic part of RKS energy.
Note this function has side effects which cause mf.scf_summary updated.
- Args:
ks : an instance of DFT class
- dm2D ndarray
one-particle density matrix
- h1e2D ndarray
Core hamiltonian
- Returns:
RKS electronic energy and the 2-electron contribution
- get_veff(mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1)#
Coulomb + XC functional
Note
This function will modify the input ks object.
- Args:
- ksan instance of
RKS XC functional are controlled by ks.xc attribute. Attribute ks.grids might be initialized.
- dmndarray or list of ndarrays
A density matrix or a list of density matrices
- ksan instance of
- Kwargs:
- dm_lastndarray or a list of ndarrays or 0
The density matrix baseline. If not 0, this function computes the increment of HF potential w.r.t. the reference HF potential matrix.
- vhf_lastndarray or a list of ndarrays or 0
The reference Vxc potential matrix.
- hermiint
Whether J, K matrix is hermitian
0 : no hermitian or symmetric1 : hermitian2 : anti-hermitian
- Returns:
matrix Veff = J + Vxc. Veff can be a list matrices, if the input dm is a list of density matrices.
- get_vsap(mol=None)#
Superposition of atomic potentials
S. Lehtola, Assessment of initial guesses for self-consistent field calculations. Superposition of Atomic Potentials: simple yet efficient, J. Chem. Theory Comput. 15, 1593 (2019). DOI: 10.1021/acs.jctc.8b01089. arXiv:1810.11659.
This function evaluates the effective charge of a neutral atom, given by exchange-only LDA on top of spherically symmetric unrestricted Hartree-Fock calculations as described in
S. Lehtola, L. Visscher, E. Engel, Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets, J. Chem. Phys., in press (2020).
The potentials have been calculated for the ground-states of spherically symmetric atoms at the non-relativistic level of theory as described in
S. Lehtola, “Fully numerical calculations on atoms with fractional occupations and range-separated exchange functionals”, Phys. Rev. A 101, 012516 (2020). DOI: 10.1103/PhysRevA.101.012516
using accurate finite-element calculations as described in
S. Lehtola, “Fully numerical Hartree-Fock and density functional calculations. I. Atoms”, Int. J. Quantum Chem. e25945 (2019). DOI: 10.1002/qua.25945
Note
This function will modify the input ks object.
- Args:
- ksan instance of
RKS XC functional are controlled by ks.xc attribute. Attribute ks.grids might be initialized.
- ksan instance of
- Returns:
matrix Vsap = Vnuc + J + Vxc.
- init_guess_by_vsap(mol=None)#
Form SAP guess
- to_gpu(out=None)#
Convert a method to its corresponding GPU variant, and recursively converts all attributes of a method to cupy objects or gpu4pyscf objects.
- class pyscf.dft.rks_symm.SymAdaptedROKS(mol=None, xc='LDA,VWN')[source]#
Bases:
KohnShamDFT,SymAdaptedROHFRestricted Kohn-Sham
- Gradients(*args, **kwargs)#
Non-relativistic ROHF gradients
- Hessian(*args, **kwargs)#
- TDA = None#
- TDDFT = None#
- TDDFTNoHybrid = None#
- TDHF = None#
- dRPA = None#
- dTDA = None#
- energy_elec(dm=None, h1e=None, vhf=None)#
Electronic part of Hartree-Fock energy, for given core hamiltonian and HF potential
… math:
E = \sum_{ij}h_{ij} \gamma_{ji} + \frac{1}{2}\sum_{ijkl} \gamma_{ji}\gamma_{lk} \langle ik||jl\rangle
Note this function has side effects which cause mf.scf_summary updated.
- Args:
mf : an instance of SCF class
- Kwargs:
- dm2D ndarray
one-particle density matrix
- h1e2D ndarray
Core hamiltonian
- vhf2D ndarray
HF potential
- Returns:
Hartree-Fock electronic energy and the Coulomb energy
Examples:
>>> from pyscf import gto, scf >>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1') >>> mf = scf.RHF(mol) >>> mf.scf() >>> dm = mf.make_rdm1() >>> scf.hf.energy_elec(mf, dm) (-1.5176090667746334, 0.60917167853723675) >>> mf.energy_elec(dm) (-1.5176090667746334, 0.60917167853723675)
- get_veff(mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1)#
Coulomb + XC functional for UKS. See pyscf/dft/rks.py
get_veff()fore more details.
- get_vsap(mol=None)#
Superposition of atomic potentials
S. Lehtola, Assessment of initial guesses for self-consistent field calculations. Superposition of Atomic Potentials: simple yet efficient, J. Chem. Theory Comput. 15, 1593 (2019). DOI: 10.1021/acs.jctc.8b01089. arXiv:1810.11659.
This function evaluates the effective charge of a neutral atom, given by exchange-only LDA on top of spherically symmetric unrestricted Hartree-Fock calculations as described in
S. Lehtola, L. Visscher, E. Engel, Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets, J. Chem. Phys., in press (2020).
The potentials have been calculated for the ground-states of spherically symmetric atoms at the non-relativistic level of theory as described in
S. Lehtola, “Fully numerical calculations on atoms with fractional occupations and range-separated exchange functionals”, Phys. Rev. A 101, 012516 (2020). DOI: 10.1103/PhysRevA.101.012516
using accurate finite-element calculations as described in
S. Lehtola, “Fully numerical Hartree-Fock and density functional calculations. I. Atoms”, Int. J. Quantum Chem. e25945 (2019). DOI: 10.1002/qua.25945
Note
This function will modify the input ks object.
- Args:
- ksan instance of
RKS XC functional are controlled by ks.xc attribute. Attribute ks.grids might be initialized.
- ksan instance of
- Returns:
matrix Vsap = Vnuc + J + Vxc.
- init_guess_by_vsap(mol=None)#
Form SAP guess
- to_gpu(out=None)#
Convert a method to its corresponding GPU variant, and recursively converts all attributes of a method to cupy objects or gpu4pyscf objects.
pyscf.dft.roks module#
Non-relativistic restricted open-shell Kohn-Sham
- class pyscf.dft.roks.ROKS(mol, xc='LDA,VWN')[source]#
Bases:
KohnShamDFT,ROHFRestricted open-shell Kohn-Sham See pyscf/dft/rks.py RKS class for the usage of the attributes
- Gradients(*args, **kwargs)#
Non-relativistic ROHF gradients
- Hessian(*args, **kwargs)#
- TDA = None#
- TDDFT = None#
- TDDFTNoHybrid = None#
- TDHF = None#
- dRPA = None#
- dTDA = None#
- energy_elec(dm=None, h1e=None, vhf=None)#
Electronic part of Hartree-Fock energy, for given core hamiltonian and HF potential
… math:
E = \sum_{ij}h_{ij} \gamma_{ji} + \frac{1}{2}\sum_{ijkl} \gamma_{ji}\gamma_{lk} \langle ik||jl\rangle
Note this function has side effects which cause mf.scf_summary updated.
- Args:
mf : an instance of SCF class
- Kwargs:
- dm2D ndarray
one-particle density matrix
- h1e2D ndarray
Core hamiltonian
- vhf2D ndarray
HF potential
- Returns:
Hartree-Fock electronic energy and the Coulomb energy
Examples:
>>> from pyscf import gto, scf >>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1') >>> mf = scf.RHF(mol) >>> mf.scf() >>> dm = mf.make_rdm1() >>> scf.hf.energy_elec(mf, dm) (-1.5176090667746334, 0.60917167853723675) >>> mf.energy_elec(dm) (-1.5176090667746334, 0.60917167853723675)
- get_veff(mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1)#
Coulomb + XC functional for UKS. See pyscf/dft/rks.py
get_veff()fore more details.
- get_vsap(mol=None)#
Superposition of atomic potentials
S. Lehtola, Assessment of initial guesses for self-consistent field calculations. Superposition of Atomic Potentials: simple yet efficient, J. Chem. Theory Comput. 15, 1593 (2019). DOI: 10.1021/acs.jctc.8b01089. arXiv:1810.11659.
This function evaluates the effective charge of a neutral atom, given by exchange-only LDA on top of spherically symmetric unrestricted Hartree-Fock calculations as described in
S. Lehtola, L. Visscher, E. Engel, Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets, J. Chem. Phys., in press (2020).
The potentials have been calculated for the ground-states of spherically symmetric atoms at the non-relativistic level of theory as described in
S. Lehtola, “Fully numerical calculations on atoms with fractional occupations and range-separated exchange functionals”, Phys. Rev. A 101, 012516 (2020). DOI: 10.1103/PhysRevA.101.012516
using accurate finite-element calculations as described in
S. Lehtola, “Fully numerical Hartree-Fock and density functional calculations. I. Atoms”, Int. J. Quantum Chem. e25945 (2019). DOI: 10.1002/qua.25945
Note
This function will modify the input ks object.
- Args:
- ksan instance of
RKS XC functional are controlled by ks.xc attribute. Attribute ks.grids might be initialized.
- ksan instance of
- Returns:
matrix Vsap = Vnuc + J + Vxc.
- init_guess_by_vsap(mol=None)#
Form SAP guess
- to_gpu(out=None)#
Convert a method to its corresponding GPU variant, and recursively converts all attributes of a method to cupy objects or gpu4pyscf objects.
- pyscf.dft.roks.get_veff(ks, mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1)[source]#
Coulomb + XC functional for UKS. See pyscf/dft/rks.py
get_veff()fore more details.
pyscf.dft.sap module#
- pyscf.dft.sap.sap_effective_charge(Z, r)[source]#
Calculates the effective charge for the superposition of atomic potentials.
S. Lehtola, “Assessment of Initial Guesses for Self-Consistent Field Calculations. Superposition of Atomic Potentials: Simple yet Efficient”, J. Chem. Theory Comput. 15, 1593 (2019). DOI: 10.1021/acs.jctc.8b01089
This function evaluates the effective charge of a neutral atom, given by exchange-only LDA on top of spherically symmetric unrestricted Hartree-Fock calculations as described in
S. Lehtola, L. Visscher, E. Engel, Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets, J. Chem. Phys., in press (2020).
The potentials have been calculated for the ground-states of spherically symmetric atoms at the non-relativistic level of theory as described in
S. Lehtola, “Fully numerical calculations on atoms with fractional occupations and range-separated exchange functionals”, Phys. Rev. A 101, 012516 (2020). DOI: 10.1103/PhysRevA.101.012516
using accurate finite-element calculations as described in
S. Lehtola, “Fully numerical Hartree-Fock and density functional calculations. I. Atoms”, Int. J. Quantum Chem. e25945 (2019). DOI: 10.1002/qua.25945
- Input:
Z: atomic charge r: distance from nucleus
- Output:
Z(r): screened charge
pyscf.dft.sap_data module#
pyscf.dft.uks module#
Non-relativistic Unrestricted Kohn-Sham
- class pyscf.dft.uks.UKS(mol, xc='LDA,VWN')[source]#
Bases:
KohnShamDFT,UHFUnrestricted Kohn-Sham See pyscf/dft/rks.py RKS class for document of the attributes
- CasidaTDDFT(*args, **kwargs)#
Solve the Casida TDDFT formula (A-B)(A+B)(X+Y) = (X+Y)w^2
- Gradients(*args, **kwargs)#
Non-relativistic unrestricted Hartree-Fock gradients
- Hessian(*args, **kwargs)#
Non-relativistic UKS hessian
- TDA(*args, **kwargs)#
Tamm-Dancoff approximation
- Attributes:
- conv_tolfloat
Diagonalization convergence tolerance. Default is 1e-9.
- nstatesint
Number of TD states to be computed. Default is 3.
Saved results:
- convergedbool
Diagonalization converged or not
- e1D array
excitation energy for each excited state.
- xyA list of two 2D arrays
The two 2D arrays are Excitation coefficients X (shape [nocc,nvir]) and de-excitation coefficients Y (shape [nocc,nvir]) for each excited state. (X,Y) are normalized to 1/2 in RHF/RKS methods and normalized to 1 for UHF/UKS methods. In the TDA calculation, Y = 0.
- TDDFT()#
Driver to create TDDFT or CasidaTDDFT object
- TDDFTNoHybrid(*args, **kwargs)#
Solve the Casida TDDFT formula (A-B)(A+B)(X+Y) = (X+Y)w^2
- TDHF = None#
- dRPA(*args, **kwargs)#
- dTDA(*args, **kwargs)#
- energy_elec(dm=None, h1e=None, vhf=None)#
Electronic energy of Unrestricted Hartree-Fock
Note this function has side effects which cause mf.scf_summary updated.
- Returns:
Hartree-Fock electronic energy and the 2-electron part contribution
- get_veff(mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1)#
Coulomb + XC functional for UKS. See pyscf/dft/rks.py
get_veff()fore more details.
- get_vsap(mol=None)#
Superposition of atomic potentials
S. Lehtola, Assessment of initial guesses for self-consistent field calculations. Superposition of Atomic Potentials: simple yet efficient, J. Chem. Theory Comput. 15, 1593 (2019). DOI: 10.1021/acs.jctc.8b01089. arXiv:1810.11659.
This function evaluates the effective charge of a neutral atom, given by exchange-only LDA on top of spherically symmetric unrestricted Hartree-Fock calculations as described in
S. Lehtola, L. Visscher, E. Engel, Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets, J. Chem. Phys., in press (2020).
The potentials have been calculated for the ground-states of spherically symmetric atoms at the non-relativistic level of theory as described in
S. Lehtola, “Fully numerical calculations on atoms with fractional occupations and range-separated exchange functionals”, Phys. Rev. A 101, 012516 (2020). DOI: 10.1103/PhysRevA.101.012516
using accurate finite-element calculations as described in
S. Lehtola, “Fully numerical Hartree-Fock and density functional calculations. I. Atoms”, Int. J. Quantum Chem. e25945 (2019). DOI: 10.1002/qua.25945
Note
This function will modify the input ks object.
- Args:
- ksan instance of
RKS XC functional are controlled by ks.xc attribute. Attribute ks.grids might be initialized.
- ksan instance of
- Returns:
matrix Vsap = Vnuc + J + Vxc.
- init_guess_by_vsap(mol=None)#
Form SAP guess
- to_gpu(out=None)#
Convert a method to its corresponding GPU variant, and recursively converts all attributes of a method to cupy objects or gpu4pyscf objects.
- pyscf.dft.uks.get_veff(ks, mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1)[source]#
Coulomb + XC functional for UKS. See pyscf/dft/rks.py
get_veff()fore more details.
- pyscf.dft.uks.get_vsap(ks, mol=None)[source]#
Superposition of atomic potentials
S. Lehtola, Assessment of initial guesses for self-consistent field calculations. Superposition of Atomic Potentials: simple yet efficient, J. Chem. Theory Comput. 15, 1593 (2019). DOI: 10.1021/acs.jctc.8b01089. arXiv:1810.11659.
This function evaluates the effective charge of a neutral atom, given by exchange-only LDA on top of spherically symmetric unrestricted Hartree-Fock calculations as described in
S. Lehtola, L. Visscher, E. Engel, Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets, J. Chem. Phys., in press (2020).
The potentials have been calculated for the ground-states of spherically symmetric atoms at the non-relativistic level of theory as described in
S. Lehtola, “Fully numerical calculations on atoms with fractional occupations and range-separated exchange functionals”, Phys. Rev. A 101, 012516 (2020). DOI: 10.1103/PhysRevA.101.012516
using accurate finite-element calculations as described in
S. Lehtola, “Fully numerical Hartree-Fock and density functional calculations. I. Atoms”, Int. J. Quantum Chem. e25945 (2019). DOI: 10.1002/qua.25945
Note
This function will modify the input ks object.
- Args:
- ksan instance of
RKS XC functional are controlled by ks.xc attribute. Attribute ks.grids might be initialized.
- ksan instance of
- Returns:
matrix Vsap = Vnuc + J + Vxc.
pyscf.dft.uks_symm module#
Non-relativistic Unrestricted Kohn-Sham
- class pyscf.dft.uks_symm.SymAdaptedUKS(mol, xc='LDA,VWN')[source]#
Bases:
KohnShamDFT,SymAdaptedUHFRestricted Kohn-Sham
- CasidaTDDFT(*args, **kwargs)#
Solve the Casida TDDFT formula (A-B)(A+B)(X+Y) = (X+Y)w^2
- Gradients(*args, **kwargs)#
Non-relativistic unrestricted Hartree-Fock gradients
- Hessian(*args, **kwargs)#
Non-relativistic UKS hessian
- TDA(*args, **kwargs)#
Tamm-Dancoff approximation
- Attributes:
- conv_tolfloat
Diagonalization convergence tolerance. Default is 1e-9.
- nstatesint
Number of TD states to be computed. Default is 3.
Saved results:
- convergedbool
Diagonalization converged or not
- e1D array
excitation energy for each excited state.
- xyA list of two 2D arrays
The two 2D arrays are Excitation coefficients X (shape [nocc,nvir]) and de-excitation coefficients Y (shape [nocc,nvir]) for each excited state. (X,Y) are normalized to 1/2 in RHF/RKS methods and normalized to 1 for UHF/UKS methods. In the TDA calculation, Y = 0.
- TDDFT()#
Driver to create TDDFT or CasidaTDDFT object
- TDDFTNoHybrid(*args, **kwargs)#
Solve the Casida TDDFT formula (A-B)(A+B)(X+Y) = (X+Y)w^2
- TDHF = None#
- dRPA(*args, **kwargs)#
- dTDA(*args, **kwargs)#
- energy_elec(dm=None, h1e=None, vhf=None)#
Electronic energy of Unrestricted Hartree-Fock
Note this function has side effects which cause mf.scf_summary updated.
- Returns:
Hartree-Fock electronic energy and the 2-electron part contribution
- get_veff(mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1)#
Coulomb + XC functional for UKS. See pyscf/dft/rks.py
get_veff()fore more details.
- get_vsap(mol=None)#
Superposition of atomic potentials
S. Lehtola, Assessment of initial guesses for self-consistent field calculations. Superposition of Atomic Potentials: simple yet efficient, J. Chem. Theory Comput. 15, 1593 (2019). DOI: 10.1021/acs.jctc.8b01089. arXiv:1810.11659.
This function evaluates the effective charge of a neutral atom, given by exchange-only LDA on top of spherically symmetric unrestricted Hartree-Fock calculations as described in
S. Lehtola, L. Visscher, E. Engel, Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets, J. Chem. Phys., in press (2020).
The potentials have been calculated for the ground-states of spherically symmetric atoms at the non-relativistic level of theory as described in
S. Lehtola, “Fully numerical calculations on atoms with fractional occupations and range-separated exchange functionals”, Phys. Rev. A 101, 012516 (2020). DOI: 10.1103/PhysRevA.101.012516
using accurate finite-element calculations as described in
S. Lehtola, “Fully numerical Hartree-Fock and density functional calculations. I. Atoms”, Int. J. Quantum Chem. e25945 (2019). DOI: 10.1002/qua.25945
Note
This function will modify the input ks object.
- Args:
- ksan instance of
RKS XC functional are controlled by ks.xc attribute. Attribute ks.grids might be initialized.
- ksan instance of
- Returns:
matrix Vsap = Vnuc + J + Vxc.
- init_guess_by_vsap(mol=None)#
Form SAP guess
- to_gpu(out=None)#
Convert a method to its corresponding GPU variant, and recursively converts all attributes of a method to cupy objects or gpu4pyscf objects.
- pyscf.dft.uks_symm.UKS#
alias of
SymAdaptedUKS
pyscf.dft.xc_deriv module#
Transform XC functional derivatives between different representations
- pyscf.dft.xc_deriv.count_combinations(nvar, order)[source]#
sum(len(combinations_with_replacement(range(nvar), o) for o in range(order))
- pyscf.dft.xc_deriv.transform_fxc(rho, vxc, fxc, xctype, spin=0)[source]#
Transform libxc functional derivatives to the derivative tensor of parameters in rho:
- [[density_a, (nabla_x)_a, (nabla_y)_a, (nabla_z)_a, tau_a],
[density_b, (nabla_x)_b, (nabla_y)_b, (nabla_z)_b, tau_b]].
- The output tensor has the shape:
- spin polarized
LDA : [2,1,2,1,N] GGA : [2,4,2,4,N] MGGA: [2,5,2,5,N]
- spin unpolarized
LDA : [1,1,N] GGA : [4,4,N] MGGA: [5,5,N]
- pyscf.dft.xc_deriv.transform_kxc(rho, fxc, kxc, xctype, spin=0)[source]#
Transform libxc functional derivatives to the derivative tensor of parameters in rho:
- [[density_a, (nabla_x)_a, (nabla_y)_a, (nabla_z)_a, tau_a],
[density_b, (nabla_x)_b, (nabla_y)_b, (nabla_z)_b, tau_b]].
- The output tensor has the shape:
- spin polarized
LDA : [2,1,2,1,2,1,N] GGA : [2,4,2,4,2,4,N] MGGA: [2,5,2,5,2,5,N]
- spin unpolarized
LDA : [1,1,1,N] GGA : [4,4,4,N] MGGA: [5,5,5,N]
- pyscf.dft.xc_deriv.transform_lxc(rho, fxc, kxc, lxc, xctype, spin=0)[source]#
Transform libxc vxc functional output to the derivative tensor of parameters in rho: [density, nabla_x, nabla_y, nabla_z, tau]. The output tensor has the shape:
- spin polarized
LDA : [2,1,2,1,2,1,2,1,N] GGA : [2,4,2,4,2,4,2,4,N] MGGA: [2,5,2,5,2,5,2,5,N]
- spin unpolarized
LDA : [1,1,1,1,N] GGA : [4,4,4,4,N] MGGA: [5,5,5,5,N]
- pyscf.dft.xc_deriv.transform_vxc(rho, vxc, xctype, spin=0)[source]#
Transform libxc functional derivatives to the derivative tensor of parameters in rho:
- [[density_a, (nabla_x)_a, (nabla_y)_a, (nabla_z)_a, tau_a],
[density_b, (nabla_x)_b, (nabla_y)_b, (nabla_z)_b, tau_b]].
- The output tensor has the shape:
- spin polarized
LDA : [2,1,N] GGA : [2,4,N] MGGA: [2,5,N]
- spin unpolarized
LDA : [1,N] GGA : [4,N] MGGA: [5,N]
- pyscf.dft.xc_deriv.transform_xc(rho, xc_val, xctype, spin, order)[source]#
General transformation to construct XC derivative tensor
pyscf.dft.xcfun module#
XC functional, the interface to xcfun (dftlibs/xcfun) U. Ekstrom et al, J. Chem. Theory Comput., 6, 1971
- pyscf.dft.xcfun.define_xc(ni, description, xctype='LDA', hyb=0, rsh=(0, 0, 0))[source]#
Define XC functional. See also
eval_xc()for the rules of input description.- Args:
ni : an instance of
NumInt- descriptionstr
A string to describe the linear combination of different XC functionals. The X and C functional are separated by comma like ‘.8*LDA+.2*B86,VWN’. If “HF” was appeared in the string, it stands for the exact exchange.
- Kwargs:
- xctypestr
‘LDA’ or ‘GGA’ or ‘MGGA’
- hybfloat
hybrid functional coefficient
- rsha list of three floats
coefficients (omega, alpha, beta) for range-separated hybrid functional. omega is the exponent factor in attenuated Coulomb operator e^{-omega r_{12}}/r_{12} alpha is the coefficient for long-range part, hybrid coefficient can be obtained by alpha + beta
Examples:
>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz') >>> mf = dft.RKS(mol) >>> define_xc_(mf._numint, '.2*HF + .08*LDA + .72*B88, .81*LYP + .19*VWN') >>> mf.kernel() -76.3783361189611 >>> define_xc_(mf._numint, 'LDA*.08 + .72*B88 + .2*HF, .81*LYP + .19*VWN') >>> mf.kernel() -76.3783361189611 >>> def eval_xc(xc_code, rho, *args, **kwargs): ... exc = 0.01 * rho**2 ... vrho = 0.01 * 2 * rho ... vxc = (vrho, None, None, None) ... fxc = None # 2nd order functional derivative ... kxc = None # 3rd order functional derivative ... return exc, vxc, fxc, kxc >>> define_xc_(mf._numint, eval_xc, xctype='LDA') >>> mf.kernel() 48.8525211046668
- pyscf.dft.xcfun.define_xc_(ni, description, xctype='LDA', hyb=0, rsh=(0, 0, 0))[source]#
Define XC functional. See also
eval_xc()for the rules of input description.- Args:
ni : an instance of
NumInt- descriptionstr
A string to describe the linear combination of different XC functionals. The X and C functional are separated by comma like ‘.8*LDA+.2*B86,VWN’. If “HF” was appeared in the string, it stands for the exact exchange.
- Kwargs:
- xctypestr
‘LDA’ or ‘GGA’ or ‘MGGA’
- hybfloat
hybrid functional coefficient
- rsha list of three floats
coefficients (omega, alpha, beta) for range-separated hybrid functional. omega is the exponent factor in attenuated Coulomb operator e^{-omega r_{12}}/r_{12} alpha is the coefficient for long-range part, hybrid coefficient can be obtained by alpha + beta
Examples:
>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz') >>> mf = dft.RKS(mol) >>> define_xc_(mf._numint, '.2*HF + .08*LDA + .72*B88, .81*LYP + .19*VWN') >>> mf.kernel() -76.3783361189611 >>> define_xc_(mf._numint, 'LDA*.08 + .72*B88 + .2*HF, .81*LYP + .19*VWN') >>> mf.kernel() -76.3783361189611 >>> def eval_xc(xc_code, rho, *args, **kwargs): ... exc = 0.01 * rho**2 ... vrho = 0.01 * 2 * rho ... vxc = (vrho, None, None, None) ... fxc = None # 2nd order functional derivative ... kxc = None # 3rd order functional derivative ... return exc, vxc, fxc, kxc >>> define_xc_(mf._numint, eval_xc, xctype='LDA') >>> mf.kernel() 48.8525211046668
- pyscf.dft.xcfun.eval_xc(xc_code, rho, spin=0, relativity=0, deriv=1, omega=None, verbose=None)[source]#
Interface to call xcfun library to evaluate XC functional, potential and functional derivatives. Return derivatives following libxc convention.
See also
pyscf.dft.libxc.eval_xc()
- pyscf.dft.xcfun.eval_xc1(xc_code, rho, spin=0, deriv=1, omega=None)[source]#
Similar to eval_xc. Returns an array with the order of derivatives following xcfun convention.
- pyscf.dft.xcfun.eval_xc_eff(xc_code, rho, deriv=1, omega=None)[source]#
Returns the derivative tensor against the density parameters
[density_a, (nabla_x)_a, (nabla_y)_a, (nabla_z)_a, tau_a]
or spin-polarized density parameters
- [[density_a, (nabla_x)_a, (nabla_y)_a, (nabla_z)_a, tau_a],
[density_b, (nabla_x)_b, (nabla_y)_b, (nabla_z)_b, tau_b]].
It differs from the eval_xc method in the derivatives of non-local part. The eval_xc method returns the XC functional derivatives to sigma (|nabla rho|^2)
- Args:
- rho: 2-dimensional or 3-dimensional array
Total density or (spin-up, spin-down) densities (and their derivatives if GGA or MGGA functionals) on grids
- Kwargs:
- deriv: int
derivative orders
- omega: float
define the exponent in the attenuated Coulomb for RSH functional
- pyscf.dft.xcfun.parse_xc(description)[source]#
Rules to input functional description:
The given functional description must be a one-line string.
The functional description is case-insensitive.
The functional description string has two parts, separated by “,”. The first part describes the exchange functional, the second is the correlation functional.
If “,” not appeared in string, the entire string is treated as the name of a compound functional (containing both the exchange and the correlation functional) which was declared in the functional aliases list. The full list of functional aliases can be obtained by calling the function pyscf.dft.xcfun.XC_ALIAS.keys() .
To input only X functional (without C functional), leave the second part blank. E.g. description=’slater,’ means a functional with LDA contribution only.
To neglect the contribution of X functional (just apply C functional), leave blank in the first part, e.g. description=’,vwn’ means a functional with VWN only.
If compound XC functional is specified, no matter whether it is in the X part (the string in front of comma) or the C part (the string behind comma), both X and C functionals of the compound XC functional will be used.
The functional name can be placed in arbitrary order. Two names need to be separated by operators “+” or “-”. Blank spaces are ignored. NOTE the parser only reads operators “+” “-” “*”. / is not supported.
A functional name can have at most one factor. If the factor is not given, it is set to 1. Compound functional can be scaled as a unit. For example ‘0.5*b3lyp’ is equivalent to ‘HF*0.1 + .04*LDA + .36*B88, .405*LYP + .095*VWN’
String “HF” stands for exact exchange (HF K matrix). “HF” can be put in the correlation functional part (after comma). Putting “HF” in the correlation part is the same to putting “HF” in the exchange part.
String “RSH” means range-separated operator. Its format is RSH(omega, alpha, beta). Another way to input RSH is to use keywords SR_HF and LR_HF: “SR_HF(0.1) * alpha_plus_beta” and “LR_HF(0.1) * alpha” where the number in parenthesis is the value of omega.
Be careful with the convention of GGA functional, in which the LDA contribution has been included.
Module contents#
Density functional theory#
Simple usage:
>>> from pyscf import gto, dft
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='def2-tzvp')
>>> mf = dft.RKS(mol)
>>> mf.xc = 'pbe,pbe'
>>> mf.run()
- pyscf.dft.DFT(mol, xc='LDA,VWN')#
A wrap function to create DFT object (RKS or UKS).
Restricted Kohn-Sham SCF base class. non-relativistic RHF.
- Attributes:
- verboseint
Print level. Default value equals to
Mole.verbose- max_memoryfloat or int
Allowed memory in MB. Default equals to
Mole.max_memory- chkfilestr
checkpoint file to save MOs, orbital energies etc. Writing to chkfile can be disabled if this attribute is set to None or False.
- conv_tolfloat
converge threshold. Default is 1e-9
- conv_tol_gradfloat
gradients converge threshold. Default is sqrt(conv_tol)
- max_cycleint
max number of iterations. If max_cycle <= 0, SCF iteration will be skipped and the kernel function will compute only the total energy based on the initial guess. Default value is 50.
- init_guessstr
initial guess method. It can be one of ‘minao’, ‘atom’, ‘huckel’, ‘hcore’, ‘1e’, ‘sap’, ‘chkfile’. Default is ‘minao’
- sap_basisstr or dict
basis for SAP initial guess, either filename or path as str or internal format dictionary.
- DIISDIIS class
The class to generate diis object. It can be one of diis.SCF_DIIS, diis.ADIIS, diis.EDIIS.
- diisboolean or object of DIIS class defined in
scf.diis. Default is the object associated to the attribute
self.DIIS. Set it to None/False to turn off DIIS. Note if this attribute is initialized as a DIIS object, the SCF driver will use this object in the iteration. The DIIS information (vector basis and error vector) will be held inside this object. When kernel function is called again, the old states (vector basis and error vector) will be reused.- diis_spaceint
DIIS space size. By default, 8 Fock matrices and errors vector are stored.
- diis_dampfloat
DIIS damping factor. Default is 0.
- diis_start_cycleint
The step to start DIIS. Default is 1.
- diis_file: ‘str’
File to store DIIS vectors and error vectors.
- level_shiftfloat or int
Level shift (in AU) for virtual space. Default is 0.
- direct_scfbool
Direct SCF is used by default.
- direct_scf_tolfloat
Direct SCF cutoff threshold. Default is 1e-13.
- callbackfunction(envs_dict) => None
callback function takes one dict as the argument which is generated by the builtin function
locals(), so that the callback function can access all local variables in the current environment.- conv_checkbool
An extra cycle to check convergence after SCF iterations.
- check_convergencefunction(envs) => bool
A hook for overloading convergence criteria in SCF iterations.
Saved results:
- convergedbool
Whether the SCF iteration converged
- e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)
- mo_energy :
Orbital energies
- mo_occ
Orbital occupancy
- mo_coeff
Orbital coefficients
- cyclesint
The number of iteration cycles performed
Examples:
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1', basis='cc-pvdz') >>> mf = scf.hf.SCF(mol) >>> mf.verbose = 0 >>> mf.level_shift = .4 >>> mf.scf() -1.0811707843775884
- Attributes for Kohn-Sham DFT:
- xcstr
‘X_name,C_name’ for the XC functional. Default is ‘lda,vwn’
- nlcstr
‘NLC_name’ for the NLC functional. Default is ‘’ (i.e., None)
- omegafloat
Omega of the range-separated Coulomb operator e^{-omega r_{12}^2} / r_{12}
- gridsGrids object
grids.level (0 - 9) big number for large mesh grids. Default is 3
- radii_adjust
- radi.treutler_atomic_radii_adjust (default)radi.becke_atomic_radii_adjustNone : to switch off atomic radii adjustment
- grids.atomic_radii
- radi.BRAGG_RADII (default)radi.COVALENT_RADIINone : to switch off atomic radii adjustment
- grids.radi_method scheme for radial grids
- radi.treutler (default)radi.delleyradi.mura_knowlesradi.gauss_chebyshev
- grids.becke_scheme weight partition function
- gen_grid.original_becke (default)gen_grid.stratmann
- grids.prune scheme to reduce number of grids
- gen_grid.nwchem_prune (default)gen_grid.sg1_prunegen_grid.treutler_pruneNone : to switch off grids pruning
grids.symmetry True/False to symmetrize mesh grids (TODO)
grids.atom_grid Set (radial, angular) grids for particular atoms. Eg, grids.atom_grid = {‘H’: (20,110)} will generate 20 radial grids and 110 angular grids for H atom.
- small_rho_cutofffloat
Drop grids if their contribution to total electrons smaller than this cutoff value. Default is 1e-7.
Examples:
>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz', verbose=0) >>> mf = dft.RKS(mol) >>> mf.xc = 'b3lyp' >>> mf.kernel() -76.415443079840458
- pyscf.dft.KS(mol, xc='LDA,VWN')[source]#
A wrap function to create DFT object (RKS or UKS).
Restricted Kohn-Sham SCF base class. non-relativistic RHF.
- Attributes:
- verboseint
Print level. Default value equals to
Mole.verbose- max_memoryfloat or int
Allowed memory in MB. Default equals to
Mole.max_memory- chkfilestr
checkpoint file to save MOs, orbital energies etc. Writing to chkfile can be disabled if this attribute is set to None or False.
- conv_tolfloat
converge threshold. Default is 1e-9
- conv_tol_gradfloat
gradients converge threshold. Default is sqrt(conv_tol)
- max_cycleint
max number of iterations. If max_cycle <= 0, SCF iteration will be skipped and the kernel function will compute only the total energy based on the initial guess. Default value is 50.
- init_guessstr
initial guess method. It can be one of ‘minao’, ‘atom’, ‘huckel’, ‘hcore’, ‘1e’, ‘sap’, ‘chkfile’. Default is ‘minao’
- sap_basisstr or dict
basis for SAP initial guess, either filename or path as str or internal format dictionary.
- DIISDIIS class
The class to generate diis object. It can be one of diis.SCF_DIIS, diis.ADIIS, diis.EDIIS.
- diisboolean or object of DIIS class defined in
scf.diis. Default is the object associated to the attribute
self.DIIS. Set it to None/False to turn off DIIS. Note if this attribute is initialized as a DIIS object, the SCF driver will use this object in the iteration. The DIIS information (vector basis and error vector) will be held inside this object. When kernel function is called again, the old states (vector basis and error vector) will be reused.- diis_spaceint
DIIS space size. By default, 8 Fock matrices and errors vector are stored.
- diis_dampfloat
DIIS damping factor. Default is 0.
- diis_start_cycleint
The step to start DIIS. Default is 1.
- diis_file: ‘str’
File to store DIIS vectors and error vectors.
- level_shiftfloat or int
Level shift (in AU) for virtual space. Default is 0.
- direct_scfbool
Direct SCF is used by default.
- direct_scf_tolfloat
Direct SCF cutoff threshold. Default is 1e-13.
- callbackfunction(envs_dict) => None
callback function takes one dict as the argument which is generated by the builtin function
locals(), so that the callback function can access all local variables in the current environment.- conv_checkbool
An extra cycle to check convergence after SCF iterations.
- check_convergencefunction(envs) => bool
A hook for overloading convergence criteria in SCF iterations.
Saved results:
- convergedbool
Whether the SCF iteration converged
- e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)
- mo_energy :
Orbital energies
- mo_occ
Orbital occupancy
- mo_coeff
Orbital coefficients
- cyclesint
The number of iteration cycles performed
Examples:
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1', basis='cc-pvdz') >>> mf = scf.hf.SCF(mol) >>> mf.verbose = 0 >>> mf.level_shift = .4 >>> mf.scf() -1.0811707843775884
- Attributes for Kohn-Sham DFT:
- xcstr
‘X_name,C_name’ for the XC functional. Default is ‘lda,vwn’
- nlcstr
‘NLC_name’ for the NLC functional. Default is ‘’ (i.e., None)
- omegafloat
Omega of the range-separated Coulomb operator e^{-omega r_{12}^2} / r_{12}
- gridsGrids object
grids.level (0 - 9) big number for large mesh grids. Default is 3
- radii_adjust
- radi.treutler_atomic_radii_adjust (default)radi.becke_atomic_radii_adjustNone : to switch off atomic radii adjustment
- grids.atomic_radii
- radi.BRAGG_RADII (default)radi.COVALENT_RADIINone : to switch off atomic radii adjustment
- grids.radi_method scheme for radial grids
- radi.treutler (default)radi.delleyradi.mura_knowlesradi.gauss_chebyshev
- grids.becke_scheme weight partition function
- gen_grid.original_becke (default)gen_grid.stratmann
- grids.prune scheme to reduce number of grids
- gen_grid.nwchem_prune (default)gen_grid.sg1_prunegen_grid.treutler_pruneNone : to switch off grids pruning
grids.symmetry True/False to symmetrize mesh grids (TODO)
grids.atom_grid Set (radial, angular) grids for particular atoms. Eg, grids.atom_grid = {‘H’: (20,110)} will generate 20 radial grids and 110 angular grids for H atom.
- small_rho_cutofffloat
Drop grids if their contribution to total electrons smaller than this cutoff value. Default is 1e-7.
Examples:
>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz', verbose=0) >>> mf = dft.RKS(mol) >>> mf.xc = 'b3lyp' >>> mf.kernel() -76.415443079840458
- pyscf.dft.RKS(mol, xc='LDA,VWN')[source]#
Restricted Kohn-Sham SCF base class. non-relativistic RHF.
- Attributes:
- verboseint
Print level. Default value equals to
Mole.verbose- max_memoryfloat or int
Allowed memory in MB. Default equals to
Mole.max_memory- chkfilestr
checkpoint file to save MOs, orbital energies etc. Writing to chkfile can be disabled if this attribute is set to None or False.
- conv_tolfloat
converge threshold. Default is 1e-9
- conv_tol_gradfloat
gradients converge threshold. Default is sqrt(conv_tol)
- max_cycleint
max number of iterations. If max_cycle <= 0, SCF iteration will be skipped and the kernel function will compute only the total energy based on the initial guess. Default value is 50.
- init_guessstr
initial guess method. It can be one of ‘minao’, ‘atom’, ‘huckel’, ‘hcore’, ‘1e’, ‘sap’, ‘chkfile’. Default is ‘minao’
- sap_basisstr or dict
basis for SAP initial guess, either filename or path as str or internal format dictionary.
- DIISDIIS class
The class to generate diis object. It can be one of diis.SCF_DIIS, diis.ADIIS, diis.EDIIS.
- diisboolean or object of DIIS class defined in
scf.diis. Default is the object associated to the attribute
self.DIIS. Set it to None/False to turn off DIIS. Note if this attribute is initialized as a DIIS object, the SCF driver will use this object in the iteration. The DIIS information (vector basis and error vector) will be held inside this object. When kernel function is called again, the old states (vector basis and error vector) will be reused.- diis_spaceint
DIIS space size. By default, 8 Fock matrices and errors vector are stored.
- diis_dampfloat
DIIS damping factor. Default is 0.
- diis_start_cycleint
The step to start DIIS. Default is 1.
- diis_file: ‘str’
File to store DIIS vectors and error vectors.
- level_shiftfloat or int
Level shift (in AU) for virtual space. Default is 0.
- direct_scfbool
Direct SCF is used by default.
- direct_scf_tolfloat
Direct SCF cutoff threshold. Default is 1e-13.
- callbackfunction(envs_dict) => None
callback function takes one dict as the argument which is generated by the builtin function
locals(), so that the callback function can access all local variables in the current environment.- conv_checkbool
An extra cycle to check convergence after SCF iterations.
- check_convergencefunction(envs) => bool
A hook for overloading convergence criteria in SCF iterations.
Saved results:
- convergedbool
Whether the SCF iteration converged
- e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)
- mo_energy :
Orbital energies
- mo_occ
Orbital occupancy
- mo_coeff
Orbital coefficients
- cyclesint
The number of iteration cycles performed
Examples:
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1', basis='cc-pvdz') >>> mf = scf.hf.SCF(mol) >>> mf.verbose = 0 >>> mf.level_shift = .4 >>> mf.scf() -1.0811707843775884
- Attributes for Kohn-Sham DFT:
- xcstr
‘X_name,C_name’ for the XC functional. Default is ‘lda,vwn’
- nlcstr
‘NLC_name’ for the NLC functional. Default is ‘’ (i.e., None)
- omegafloat
Omega of the range-separated Coulomb operator e^{-omega r_{12}^2} / r_{12}
- gridsGrids object
grids.level (0 - 9) big number for large mesh grids. Default is 3
- radii_adjust
- radi.treutler_atomic_radii_adjust (default)radi.becke_atomic_radii_adjustNone : to switch off atomic radii adjustment
- grids.atomic_radii
- radi.BRAGG_RADII (default)radi.COVALENT_RADIINone : to switch off atomic radii adjustment
- grids.radi_method scheme for radial grids
- radi.treutler (default)radi.delleyradi.mura_knowlesradi.gauss_chebyshev
- grids.becke_scheme weight partition function
- gen_grid.original_becke (default)gen_grid.stratmann
- grids.prune scheme to reduce number of grids
- gen_grid.nwchem_prune (default)gen_grid.sg1_prunegen_grid.treutler_pruneNone : to switch off grids pruning
grids.symmetry True/False to symmetrize mesh grids (TODO)
grids.atom_grid Set (radial, angular) grids for particular atoms. Eg, grids.atom_grid = {‘H’: (20,110)} will generate 20 radial grids and 110 angular grids for H atom.
- small_rho_cutofffloat
Drop grids if their contribution to total electrons smaller than this cutoff value. Default is 1e-7.
Examples:
>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz', verbose=0) >>> mf = dft.RKS(mol) >>> mf.xc = 'b3lyp' >>> mf.kernel() -76.415443079840458
- pyscf.dft.ROKS(mol, xc='LDA,VWN')[source]#
Restricted open-shell Kohn-Sham See pyscf/dft/rks.py RKS class for the usage of the attributes
- pyscf.dft.UKS(mol, xc='LDA,VWN')[source]#
Unrestricted Kohn-Sham See pyscf/dft/rks.py RKS class for document of the attributes
- pyscf.dft.X2C_KS(mol, *args)#
X2C Kohn-Sham