pyscf.pbc.gto package¶
Subpackages¶
Submodules¶
pyscf.pbc.gto.cell module¶
- pyscf.pbc.gto.cell.C(*args, **kwargs)¶
This is a shortcut to build up Cell object.
Examples:
>>> from pyscf.pbc import gto >>> cell = gto.M(a=numpy.eye(3)*4, atom='He 1 1 1', basis='6-31g')
- class pyscf.pbc.gto.cell.Cell(**kwargs)[source]¶
Bases:
MoleBaseA Cell object holds the basic information of a crystal.
- Attributes:
- a(3,3) ndarray
Lattice primitive vectors. Each row represents a lattice vector Reciprocal lattice vectors are given by b1,b2,b3 = 2 pi inv(a).T
- mesh(3,) list of ints
The number G-vectors along each direction. The default value is estimated based on
precision- pseudodict or str
To define pseudopotential.
- precisionfloat
To control Ewald sums and lattice sums accuracy
- rcutfloat
Cutoff radius (unit Bohr) in lattice summation. The default value is estimated based on the required
precision.- ke_cutofffloat
If set, defines a spherical cutoff of planewaves, with .5 * G**2 < ke_cutoff The default value is estimated based on
precision- dimensionint
Periodic dimensions. Default is 3
- low_dim_ft_typestr
For semi-empirical periodic systems, whether to calculate integrals at the non-PBC dimension using the sampled mesh grids in infinity vacuum (inf_vacuum) or truncated Coulomb potential (analytic_2d_1). Unless explicitly specified, analytic_2d_1 is used for 2D system and inf_vacuum is assumed for 1D and 0D.
- space_group_symmetrybool
Whether to consider space group symmetry. Default is False.
- symmorphicbool
Whether the lattice is symmorphic. If set to True, even if the lattice is non-symmorphic, only symmorphic space group symmetry will be considered. Default is False, meaning the space group is determined by the lattice symmetry to be symmorphic or non-symmorphic.
- lattice_symmetryNone or
pbc.symm.Symmetryinstance The object containing the lattice symmetry information. Default is None.
(See other attributes in
Mole)Examples:
>>> mol = Mole(atom='H^2 0 0 0; H 0 0 1.1', basis='sto3g') >>> cl = Cell() >>> cl.build(a='3 0 0; 0 3 0; 0 0 3', atom='C 1 1 1', basis='sto3g') >>> print(cl.atom_symbol(0)) C
- property GHF¶
GHF class for PBCs.
- property GKS¶
GKS class adapted for PBCs at a single k-point.
This is a literal duplication of the molecular GKS class with some mol variables replaced by cell.
- property Gv¶
- property HF¶
- property KGHF¶
- property KGKS¶
GKS class adapted for PBCs with k-point sampling.
- property KHF¶
- property KKS¶
A wrap function to create DFT object with k-point sampling (KRKS or KUKS).
RKS class adapted for PBCs with k-point sampling.
- property KRHF¶
- property KRKS¶
- property KRKSpU¶
- property KROHF¶
UHF class with k-point sampling.
- property KROKS¶
RKS class adapted for PBCs with k-point sampling.
- property KS¶
A wrap function to create DFT object (RKS or UKS) for PBC systems.
RKS class adapted for PBCs.
This is a literal duplication of the molecular RKS class with some mol variables replaced by cell.
- property KUHF¶
- property KUKS¶
- property KUKSpU¶
- property RHF¶
- property RKS¶
RKS class adapted for PBCs.
This is a literal duplication of the molecular RKS class with some mol variables replaced by cell.
- property ROHF¶
ROHF class for PBCs.
- property ROKS¶
UKS class adapted for PBCs.
This is a literal duplication of the molecular UKS class with some mol variables replaced by cell.
- property UHF¶
UHF class for PBCs.
- property UKS¶
UKS class adapted for PBCs.
This is a literal duplication of the molecular UKS class with some mol variables replaced by cell.
- bas_rcut(bas_id, precision=None)¶
Estimate the largest distance between the function and its image to reach the precision in overlap
precision ~ int g(r-0) g(r-Rcut)
- build(dump_input=True, parse_arg=False, a=None, mesh=None, ke_cutoff=None, precision=None, nimgs=None, h=None, dimension=None, rcut=None, low_dim_ft_type=None, space_group_symmetry=None, symmorphic=None, *args, **kwargs)[source]¶
Setup Mole molecule and Cell and initialize some control parameters. Whenever you change the value of the attributes of
Cell, you need call this function to refresh the internal data of Cell.- Kwargs:
- a(3,3) ndarray
The real-space cell lattice vectors. Each row represents a lattice vector.
- mesh(3,) ndarray of ints
The number of positive G-vectors along each direction.
- ke_cutofffloat
If set, defines a spherical cutoff of planewaves, with .5 * G**2 < ke_cutoff The default value is estimated based on
precision- precisionfloat
To control Ewald sums and lattice sums accuracy
- nimgs(3,) ndarray of ints
Number of repeated images in lattice summation to produce periodicity. This value can be estimated based on the required precision. It’s recommended NOT making changes to this value.
- rcutfloat
Cutoff radius (unit Bohr) in lattice summation to produce periodicity. The value can be estimated based on the required precision. It’s recommended NOT making changes to this value.
- h(3,3) ndarray
a.T. Deprecated
- dimensionint
Default is 3
- low_dim_ft_typestr
For semi-empirical periodic systems, whether to calculate integrals at the non-PBC dimension using the sampled mesh grids in infinity vacuum (inf_vacuum) or truncated Coulomb potential (analytic_2d_1). Unless explicitly specified, analytic_2d_1 is used for 2D system and inf_vacuum is assumed for 1D and 0D.
- space_group_symmetrybool
Whether to consider space group symmetry. Default is False.
- symmorphicbool
Whether the lattice is symmorphic. If set to True, even if the lattice is non-symmorphic, only symmorphic space group symmetry will be considered. Default is False, meaning the space group is determined by the lattice symmetry to be symmorphic or non-symmorphic.
- build_lattice_symmetry(check_mesh_symmetry=True)[source]¶
Build cell.lattice_symmetry object.
- Kwargs:
- check_mesh_symmetrybool
For nonsymmorphic symmetry groups, cell.mesh may have lower symmetry than the lattice. In this case, if check_mesh_symmetry is True, the lower symmetry group will be used. Otherwise, if check_mesh_symmetry is False, the mesh grid will be modified to satisfy the higher symmetry. Default value is True.
- Note:
This function modifies the attributes of cell.
- cutoff_to_mesh(ke_cutoff)[source]¶
Convert KE cutoff to FFT-mesh
- Args:
- ke_cutofffloat
KE energy cutoff in a.u.
- Returns:
mesh : (3,) array
- property drop_exponent¶
- dumps()¶
Serialize Cell object to a JSON formatted str.
- energy_nuc(ew_eta=None, ew_cut=None)¶
Perform real (R) and reciprocal (G) space Ewald sum for the energy.
Formulation of Martin, App. F2.
- Returns:
- float
The Ewald energy consisting of overlap, self, and G-space sum.
- See Also:
pyscf.pbc.gto.get_ewald_params
- eval_ao(eval_name, coords, comp=None, kpts=None, kpt=None, shls_slice=None, non0tab=None, ao_loc=None, cutoff=None, out=None)¶
Evaluate PBC-AO function value on the given grids,
- Args:
eval_name : str:
========================== ======================= Function Expression ========================== ======================= "GTOval_sph" \sum_T exp(ik*T) |AO> "GTOval_ip_sph" nabla \sum_T exp(ik*T) |AO> "GTOval_cart" \sum_T exp(ik*T) |AO> "GTOval_ip_cart" nabla \sum_T exp(ik*T) |AO> ========================== =======================
- atmint32 ndarray
libcint integral function argument
- basint32 ndarray
libcint integral function argument
- envfloat64 ndarray
libcint integral function argument
- coords2D array, shape (N,3)
The coordinates of the grids.
- Kwargs:
- 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 cell will be evaluated.
- non0tab2D bool array
mask array to indicate whether the AO values are zero. The mask array can be obtained by calling
dft.gen_grid.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.
- Returns:
A list of 2D (or 3D) arrays to hold the AO values on grids. Each element of the list corresponds to a k-point and it has the shape (N,nao) Or shape (*,N,nao).
Examples:
>>> cell = pbc.gto.M(a=numpy.eye(3)*4, atom='He 1 1 1', basis='6-31g') >>> coords = cell.get_uniform_grids([10,10,10]) >>> kpts = cell.make_kpts([3,3,3]) >>> ao_value = cell.pbc_eval_gto("GTOval_sph", coords, kpts) >>> len(ao_value) 27 >>> ao_value[0].shape (1000, 2) >>> ao_value = cell.pbc_eval_gto("GTOval_ig_sph", coords, kpts, comp=3) >>> print(ao_value.shape) >>> len(ao_value) 27 >>> ao_value[0].shape (3, 1000, 2)
- eval_gto(eval_name, coords, comp=None, kpts=None, kpt=None, shls_slice=None, non0tab=None, ao_loc=None, cutoff=None, out=None)[source]¶
Evaluate PBC-AO function value on the given grids,
- Args:
eval_name : str:
========================== ======================= Function Expression ========================== ======================= "GTOval_sph" \sum_T exp(ik*T) |AO> "GTOval_ip_sph" nabla \sum_T exp(ik*T) |AO> "GTOval_cart" \sum_T exp(ik*T) |AO> "GTOval_ip_cart" nabla \sum_T exp(ik*T) |AO> ========================== =======================
- atmint32 ndarray
libcint integral function argument
- basint32 ndarray
libcint integral function argument
- envfloat64 ndarray
libcint integral function argument
- coords2D array, shape (N,3)
The coordinates of the grids.
- Kwargs:
- 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 cell will be evaluated.
- non0tab2D bool array
mask array to indicate whether the AO values are zero. The mask array can be obtained by calling
dft.gen_grid.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.
- Returns:
A list of 2D (or 3D) arrays to hold the AO values on grids. Each element of the list corresponds to a k-point and it has the shape (N,nao) Or shape (*,N,nao).
Examples:
>>> cell = pbc.gto.M(a=numpy.eye(3)*4, atom='He 1 1 1', basis='6-31g') >>> coords = cell.get_uniform_grids([10,10,10]) >>> kpts = cell.make_kpts([3,3,3]) >>> ao_value = cell.pbc_eval_gto("GTOval_sph", coords, kpts) >>> len(ao_value) 27 >>> ao_value[0].shape (1000, 2) >>> ao_value = cell.pbc_eval_gto("GTOval_ig_sph", coords, kpts, comp=3) >>> print(ao_value.shape) >>> len(ao_value) 27 >>> ao_value[0].shape (3, 1000, 2)
- property ew_cut¶
- property ew_eta¶
- ewald(ew_eta=None, ew_cut=None)¶
Perform real (R) and reciprocal (G) space Ewald sum for the energy.
Formulation of Martin, App. F2.
- Returns:
- float
The Ewald energy consisting of overlap, self, and G-space sum.
- See Also:
pyscf.pbc.gto.get_ewald_params
- exp_to_discard = None¶
- from_ase(ase_atom)[source]¶
Update cell based on given ase atom object
Examples:
>>> from ase.lattice import bulk >>> cell.from_ase(bulk('C', 'diamond', a=LATTICE_CONST))
- gen_uniform_grids(mesh=None, wrap_around=True)¶
Generate a uniform real-space grid consistent w/ samp thm; see MH (3.19).
- Args:
cell : instance of
Cell- Returns:
- coords(ngx*ngy*ngz, 3) ndarray
The real-space grid point coordinates.
- get_Gv(mesh=None, **kwargs)¶
Calculate three-dimensional G-vectors for the cell; see MH (3.8).
Indices along each direction go as [0…N-1, -N…-1] to follow FFT convention.
- Args:
cell : instance of
Cell- Returns:
- Gv(ngrids, 3) ndarray of floats
The array of G-vectors.
- get_Gv_weights(mesh=None, **kwargs)¶
Calculate G-vectors and weights.
- Returns:
- Gv(ngris, 3) ndarray of floats
The array of G-vectors.
- get_SI(Gv=None, mesh=None)¶
Calculate the structure factor (0D, 1D, 2D, 3D) for all atoms; see MH (3.34).
- Args:
cell : instance of
Cell- Gv(N,3) array
G vectors
- Returns:
- SI(natm, ngrids) ndarray, dtype=np.complex128
The structure factor for each atom at each G-vector.
- get_abs_kpts(scaled_kpts)[source]¶
Get absolute k-points (in 1/Bohr), given “scaled” k-points in fractions of lattice vectors.
- Args:
scaled_kpts : (nkpts, 3) ndarray of floats
- Returns:
abs_kpts : (nkpts, 3) ndarray of floats
- get_bounding_sphere(rcut)¶
Finds all the lattice points within a sphere of radius rcut.
Defines a parallelipiped given by -N_x <= n_x <= N_x, with x in [1,3] See Martin p. 85
- Args:
- rcutnumber
real space cut-off for interaction
- Returns:
cut : ndarray of 3 ints defining N_x
- get_enuc(ew_eta=None, ew_cut=None)¶
Perform real (R) and reciprocal (G) space Ewald sum for the energy.
Formulation of Martin, App. F2.
- Returns:
- float
The Ewald energy consisting of overlap, self, and G-space sum.
- See Also:
pyscf.pbc.gto.get_ewald_params
- get_ewald_params(precision=None, mesh=None)¶
Choose a reasonable value of Ewald ‘eta’ and ‘cut’ parameters. eta^2 is the exponent coefficient of the model Gaussian charge for nucleus at R: frac{eta^3}{pi^1.5} e^{-eta^2 (r-R)^2}
Choice is based on largest G vector and desired relative precision.
The relative error in the G-space sum is given by
precision ~ 4pi Gmax^2 e^{(-Gmax^2)/(4 eta^2)}
which determines eta. Then, real-space cutoff is determined by (exp. factors only)
precision ~ erfc(eta*rcut) / rcut ~ e^{(-eta**2 rcut*2)}
- Returns:
- ew_eta, ew_cutfloat
The Ewald ‘eta’ and ‘cut’ parameters.
- get_kpts(nks, wrap_around=False, with_gamma_point=True, scaled_center=None, space_group_symmetry=False, time_reversal_symmetry=False, **kwargs)¶
Given number of kpoints along x,y,z , generate kpoints
- Args:
nks : (3,) ndarray
- Kwargs:
- wrap_aroundbool
To ensure all kpts are in first Brillouin zone.
- with_gamma_pointbool
Whether to shift Monkhorst-pack grid to include gamma-point.
- scaled_center(3,) array
Shift all points in the Monkhorst-pack grid to be centered on scaled_center, given as the zeroth index of the returned kpts. Scaled meaning that the k-points are scaled to a grid from [-1,1] x [-1,1] x [-1,1]
- space_group_symmetrybool
Whether to consider space group symmetry
- time_reversal_symmetrybool
Whether to consider time reversal symmetry
- Returns:
kpts in absolute value (unit 1/Bohr). Gamma point is placed at the first place in the k-points list; instance of
KPointsif k-point symmetry is considered
Examples:
>>> cell.make_kpts((4,4,4))
- get_lattice_Ls(nimgs=None, rcut=None, dimension=None, discard=True)¶
Get the (Cartesian, unitful) lattice translation vectors for nearby images. The translation vectors can be used for the lattice summation.
- Kwargs:
- discard:
Drop less important Ls based on AO values on grid
- get_nimgs(precision=None)¶
Choose number of basis function images in lattice sums to include for given precision in overlap, using
precision ~ int r^l e^{-alpha r^2} (r-rcut)^l e^{-alpha (r-rcut)^2} ~ (rcut^2/(2alpha))^l e^{alpha/2 rcut^2}
where alpha is the smallest exponent in the basis. Note that assumes an isolated exponent in the middle of the box, so it adds one additional lattice vector to be safe.
- get_scaled_kpts(abs_kpts, kpts_in_ibz=True)[source]¶
Get scaled k-points, given absolute k-points in 1/Bohr.
- Args:
abs_kpts : (nkpts, 3) ndarray of floats or
KPointsobject- kpts_in_ibzbool
If True, return k-points in IBZ; otherwise, return k-points in BZ. Default value is True. This has effects only if abs_kpts is a
KPointsobject
- Returns:
scaled_kpts : (nkpts, 3) ndarray of floats
- get_uniform_grids(mesh=None, wrap_around=True)¶
Generate a uniform real-space grid consistent w/ samp thm; see MH (3.19).
- Args:
cell : instance of
Cell- Returns:
- coords(ngx*ngy*ngz, 3) ndarray
The real-space grid point coordinates.
- property gs¶
- property h¶
- kernel(dump_input=True, parse_arg=False, a=None, mesh=None, ke_cutoff=None, precision=None, nimgs=None, h=None, dimension=None, rcut=None, low_dim_ft_type=None, space_group_symmetry=None, symmorphic=None, *args, **kwargs)¶
Setup Mole molecule and Cell and initialize some control parameters. Whenever you change the value of the attributes of
Cell, you need call this function to refresh the internal data of Cell.- Kwargs:
- a(3,3) ndarray
The real-space cell lattice vectors. Each row represents a lattice vector.
- mesh(3,) ndarray of ints
The number of positive G-vectors along each direction.
- ke_cutofffloat
If set, defines a spherical cutoff of planewaves, with .5 * G**2 < ke_cutoff The default value is estimated based on
precision- precisionfloat
To control Ewald sums and lattice sums accuracy
- nimgs(3,) ndarray of ints
Number of repeated images in lattice summation to produce periodicity. This value can be estimated based on the required precision. It’s recommended NOT making changes to this value.
- rcutfloat
Cutoff radius (unit Bohr) in lattice summation to produce periodicity. The value can be estimated based on the required precision. It’s recommended NOT making changes to this value.
- h(3,3) ndarray
a.T. Deprecated
- dimensionint
Default is 3
- low_dim_ft_typestr
For semi-empirical periodic systems, whether to calculate integrals at the non-PBC dimension using the sampled mesh grids in infinity vacuum (inf_vacuum) or truncated Coulomb potential (analytic_2d_1). Unless explicitly specified, analytic_2d_1 is used for 2D system and inf_vacuum is assumed for 1D and 0D.
- space_group_symmetrybool
Whether to consider space group symmetry. Default is False.
- symmorphicbool
Whether the lattice is symmorphic. If set to True, even if the lattice is non-symmorphic, only symmorphic space group symmetry will be considered. Default is False, meaning the space group is determined by the lattice symmetry to be symmorphic or non-symmorphic.
- lattice_vectors()[source]¶
Convert the primitive lattice vectors.
Return 3x3 array in which each row represents one direction of the lattice vectors (unit in Bohr)
- loads_(molstr)[source]¶
Convert the packed dict to a
Cellobject, to generate the input arguments forCellobject.
- make_kpts(nks, wrap_around=False, with_gamma_point=True, scaled_center=None, space_group_symmetry=False, time_reversal_symmetry=False, **kwargs)¶
Given number of kpoints along x,y,z , generate kpoints
- Args:
nks : (3,) ndarray
- Kwargs:
- wrap_aroundbool
To ensure all kpts are in first Brillouin zone.
- with_gamma_pointbool
Whether to shift Monkhorst-pack grid to include gamma-point.
- scaled_center(3,) array
Shift all points in the Monkhorst-pack grid to be centered on scaled_center, given as the zeroth index of the returned kpts. Scaled meaning that the k-points are scaled to a grid from [-1,1] x [-1,1] x [-1,1]
- space_group_symmetrybool
Whether to consider space group symmetry
- time_reversal_symmetrybool
Whether to consider time reversal symmetry
- Returns:
kpts in absolute value (unit 1/Bohr). Gamma point is placed at the first place in the k-points list; instance of
KPointsif k-point symmetry is considered
Examples:
>>> cell.make_kpts((4,4,4))
- property mesh¶
- property nelec¶
- property nimgs¶
- pbc_eval_ao(eval_name, coords, comp=None, kpts=None, kpt=None, shls_slice=None, non0tab=None, ao_loc=None, cutoff=None, out=None, Ls=None, rcut=None)¶
Evaluate PBC-AO function value on the given grids,
- Args:
eval_name : str:
========================== ======================= Function Expression ========================== ======================= "GTOval_sph" \sum_T exp(ik*T) |AO> "GTOval_ip_sph" nabla \sum_T exp(ik*T) |AO> "GTOval_cart" \sum_T exp(ik*T) |AO> "GTOval_ip_cart" nabla \sum_T exp(ik*T) |AO> ========================== =======================
- atmint32 ndarray
libcint integral function argument
- basint32 ndarray
libcint integral function argument
- envfloat64 ndarray
libcint integral function argument
- coords2D array, shape (N,3)
The coordinates of the grids.
- Kwargs:
- 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 cell will be evaluated.
- non0tab2D bool array
mask array to indicate whether the AO values are zero. The mask array can be obtained by calling
dft.gen_grid.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.
- Returns:
A list of 2D (or 3D) arrays to hold the AO values on grids. Each element of the list corresponds to a k-point and it has the shape (N,nao) Or shape (*,N,nao).
Examples:
>>> cell = pbc.gto.M(a=numpy.eye(3)*4, atom='He 1 1 1', basis='6-31g') >>> coords = cell.get_uniform_grids([10,10,10]) >>> kpts = cell.make_kpts([3,3,3]) >>> ao_value = cell.pbc_eval_gto("GTOval_sph", coords, kpts) >>> len(ao_value) 27 >>> ao_value[0].shape (1000, 2) >>> ao_value = cell.pbc_eval_gto("GTOval_ig_sph", coords, kpts, comp=3) >>> print(ao_value.shape) >>> len(ao_value) 27 >>> ao_value[0].shape (3, 1000, 2)
- pbc_eval_gto(eval_name, coords, comp=None, kpts=None, kpt=None, shls_slice=None, non0tab=None, ao_loc=None, cutoff=None, out=None, Ls=None, rcut=None)¶
Evaluate PBC-AO function value on the given grids,
- Args:
eval_name : str:
========================== ======================= Function Expression ========================== ======================= "GTOval_sph" \sum_T exp(ik*T) |AO> "GTOval_ip_sph" nabla \sum_T exp(ik*T) |AO> "GTOval_cart" \sum_T exp(ik*T) |AO> "GTOval_ip_cart" nabla \sum_T exp(ik*T) |AO> ========================== =======================
- atmint32 ndarray
libcint integral function argument
- basint32 ndarray
libcint integral function argument
- envfloat64 ndarray
libcint integral function argument
- coords2D array, shape (N,3)
The coordinates of the grids.
- Kwargs:
- 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 cell will be evaluated.
- non0tab2D bool array
mask array to indicate whether the AO values are zero. The mask array can be obtained by calling
dft.gen_grid.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.
- Returns:
A list of 2D (or 3D) arrays to hold the AO values on grids. Each element of the list corresponds to a k-point and it has the shape (N,nao) Or shape (*,N,nao).
Examples:
>>> cell = pbc.gto.M(a=numpy.eye(3)*4, atom='He 1 1 1', basis='6-31g') >>> coords = cell.get_uniform_grids([10,10,10]) >>> kpts = cell.make_kpts([3,3,3]) >>> ao_value = cell.pbc_eval_gto("GTOval_sph", coords, kpts) >>> len(ao_value) 27 >>> ao_value[0].shape (1000, 2) >>> ao_value = cell.pbc_eval_gto("GTOval_ig_sph", coords, kpts, comp=3) >>> print(ao_value.shape) >>> len(ao_value) 27 >>> ao_value[0].shape (3, 1000, 2)
- pbc_intor(intor, comp=None, hermi=0, kpts=None, kpt=None, shls_slice=None, **kwargs)[source]¶
One-electron integrals with PBC.
\[\sum_T \int \mu(r) * [intor] * \nu (r-T) dr\]See also Mole.intor
- precision = 1e-08¶
- property rcut¶
- reciprocal_vectors(norm_to=6.283185307179586)[source]¶
- \[\begin{split}\begin{align} \mathbf{b_1} &= 2\pi \frac{\mathbf{a_2} \times \mathbf{a_3}}{\mathbf{a_1} \cdot (\mathbf{a_2} \times \mathbf{a_3})} \\ \mathbf{b_2} &= 2\pi \frac{\mathbf{a_3} \times \mathbf{a_1}}{\mathbf{a_2} \cdot (\mathbf{a_3} \times \mathbf{a_1})} \\ \mathbf{b_3} &= 2\pi \frac{\mathbf{a_1} \times \mathbf{a_2}}{\mathbf{a_3} \cdot (\mathbf{a_1} \times \mathbf{a_2})} \end{align}\end{split}\]
- tot_electrons(nkpts=1)¶
Total number of electrons
- classmethod unpack(moldic)[source]¶
Convert the packed dict to a
Cellobject, to generate the input arguments forCellobject.
- unpack_(moldic)[source]¶
Convert the packed dict to a
Cellobject, to generate the input arguments forCellobject.
- property vol¶
- pyscf.pbc.gto.cell.M(*args, **kwargs)[source]¶
This is a shortcut to build up Cell object.
Examples:
>>> from pyscf.pbc import gto >>> cell = gto.M(a=numpy.eye(3)*4, atom='He 1 1 1', basis='6-31g')
- pyscf.pbc.gto.cell.bas_rcut(cell, bas_id, precision=None)[source]¶
Estimate the largest distance between the function and its image to reach the precision in overlap
precision ~ int g(r-0) g(r-Rcut)
- pyscf.pbc.gto.cell.energy_nuc(cell, ew_eta=None, ew_cut=None)¶
Perform real (R) and reciprocal (G) space Ewald sum for the energy.
Formulation of Martin, App. F2.
- Returns:
- float
The Ewald energy consisting of overlap, self, and G-space sum.
- See Also:
pyscf.pbc.gto.get_ewald_params
- pyscf.pbc.gto.cell.error_for_ke_cutoff(cell, ke_cutoff, omega=None)[source]¶
Error estimation based on nuclear attraction integrals
- pyscf.pbc.gto.cell.estimate_ke_cutoff(cell, precision=None)[source]¶
Energy cutoff estimation for nuclear attraction integrals
- pyscf.pbc.gto.cell.estimate_rcut(cell, precision=None)[source]¶
Lattice-sum cutoff for the entire system
- pyscf.pbc.gto.cell.ewald(cell, ew_eta=None, ew_cut=None)[source]¶
Perform real (R) and reciprocal (G) space Ewald sum for the energy.
Formulation of Martin, App. F2.
- Returns:
- float
The Ewald energy consisting of overlap, self, and G-space sum.
- See Also:
pyscf.pbc.gto.get_ewald_params
- pyscf.pbc.gto.cell.gen_uniform_grids(cell, mesh=None, wrap_around=True)¶
Generate a uniform real-space grid consistent w/ samp thm; see MH (3.19).
- Args:
cell : instance of
Cell- Returns:
- coords(ngx*ngy*ngz, 3) ndarray
The real-space grid point coordinates.
- pyscf.pbc.gto.cell.get_Gv(cell, mesh=None, **kwargs)[source]¶
Calculate three-dimensional G-vectors for the cell; see MH (3.8).
Indices along each direction go as [0…N-1, -N…-1] to follow FFT convention.
- Args:
cell : instance of
Cell- Returns:
- Gv(ngrids, 3) ndarray of floats
The array of G-vectors.
- pyscf.pbc.gto.cell.get_Gv_weights(cell, mesh=None, **kwargs)[source]¶
Calculate G-vectors and weights.
- Returns:
- Gv(ngris, 3) ndarray of floats
The array of G-vectors.
- pyscf.pbc.gto.cell.get_SI(cell, Gv=None, mesh=None)[source]¶
Calculate the structure factor (0D, 1D, 2D, 3D) for all atoms; see MH (3.34).
- Args:
cell : instance of
Cell- Gv(N,3) array
G vectors
- Returns:
- SI(natm, ngrids) ndarray, dtype=np.complex128
The structure factor for each atom at each G-vector.
- pyscf.pbc.gto.cell.get_bounding_sphere(cell, rcut)[source]¶
Finds all the lattice points within a sphere of radius rcut.
Defines a parallelipiped given by -N_x <= n_x <= N_x, with x in [1,3] See Martin p. 85
- Args:
- rcutnumber
real space cut-off for interaction
- Returns:
cut : ndarray of 3 ints defining N_x
- pyscf.pbc.gto.cell.get_ewald_params(cell, precision=None, mesh=None)[source]¶
Choose a reasonable value of Ewald ‘eta’ and ‘cut’ parameters. eta^2 is the exponent coefficient of the model Gaussian charge for nucleus at R: frac{eta^3}{pi^1.5} e^{-eta^2 (r-R)^2}
Choice is based on largest G vector and desired relative precision.
The relative error in the G-space sum is given by
precision ~ 4pi Gmax^2 e^{(-Gmax^2)/(4 eta^2)}
which determines eta. Then, real-space cutoff is determined by (exp. factors only)
precision ~ erfc(eta*rcut) / rcut ~ e^{(-eta**2 rcut*2)}
- Returns:
- ew_eta, ew_cutfloat
The Ewald ‘eta’ and ‘cut’ parameters.
- pyscf.pbc.gto.cell.get_nimgs(cell, precision=None)[source]¶
Choose number of basis function images in lattice sums to include for given precision in overlap, using
precision ~ int r^l e^{-alpha r^2} (r-rcut)^l e^{-alpha (r-rcut)^2} ~ (rcut^2/(2alpha))^l e^{alpha/2 rcut^2}
where alpha is the smallest exponent in the basis. Note that assumes an isolated exponent in the middle of the box, so it adds one additional lattice vector to be safe.
- pyscf.pbc.gto.cell.get_uniform_grids(cell, mesh=None, wrap_around=True)[source]¶
Generate a uniform real-space grid consistent w/ samp thm; see MH (3.19).
- Args:
cell : instance of
Cell- Returns:
- coords(ngx*ngy*ngz, 3) ndarray
The real-space grid point coordinates.
- pyscf.pbc.gto.cell.intor_cross(intor, cell1, cell2, comp=None, hermi=0, kpts=None, kpt=None, shls_slice=None, **kwargs)[source]¶
1-electron integrals from two cells like
\[\langle \mu | intor | \nu \rangle, \mu \in cell1, \nu \in cell2\]
- pyscf.pbc.gto.cell.loads(cellstr)[source]¶
Deserialize a str containing a JSON document to a Cell object.
- pyscf.pbc.gto.cell.make_kpts(cell, nks, wrap_around=False, with_gamma_point=True, scaled_center=None, space_group_symmetry=False, time_reversal_symmetry=False, **kwargs)[source]¶
Given number of kpoints along x,y,z , generate kpoints
- Args:
nks : (3,) ndarray
- Kwargs:
- wrap_aroundbool
To ensure all kpts are in first Brillouin zone.
- with_gamma_pointbool
Whether to shift Monkhorst-pack grid to include gamma-point.
- scaled_center(3,) array
Shift all points in the Monkhorst-pack grid to be centered on scaled_center, given as the zeroth index of the returned kpts. Scaled meaning that the k-points are scaled to a grid from [-1,1] x [-1,1] x [-1,1]
- space_group_symmetrybool
Whether to consider space group symmetry
- time_reversal_symmetrybool
Whether to consider time reversal symmetry
- Returns:
kpts in absolute value (unit 1/Bohr). Gamma point is placed at the first place in the k-points list; instance of
KPointsif k-point symmetry is considered
Examples:
>>> cell.make_kpts((4,4,4))
pyscf.pbc.gto.ecp module¶
Short range part of ECP under PBC
pyscf.pbc.gto.eval_gto module¶
- pyscf.pbc.gto.eval_gto.eval_gto(cell, eval_name, coords, comp=None, kpts=None, kpt=None, shls_slice=None, non0tab=None, ao_loc=None, cutoff=None, out=None, Ls=None, rcut=None)[source]¶
Evaluate PBC-AO function value on the given grids,
- Args:
eval_name : str:
========================== ======================= Function Expression ========================== ======================= "GTOval_sph" \sum_T exp(ik*T) |AO> "GTOval_ip_sph" nabla \sum_T exp(ik*T) |AO> "GTOval_cart" \sum_T exp(ik*T) |AO> "GTOval_ip_cart" nabla \sum_T exp(ik*T) |AO> ========================== =======================
- atmint32 ndarray
libcint integral function argument
- basint32 ndarray
libcint integral function argument
- envfloat64 ndarray
libcint integral function argument
- coords2D array, shape (N,3)
The coordinates of the grids.
- Kwargs:
- 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 cell will be evaluated.
- non0tab2D bool array
mask array to indicate whether the AO values are zero. The mask array can be obtained by calling
dft.gen_grid.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.
- Returns:
A list of 2D (or 3D) arrays to hold the AO values on grids. Each element of the list corresponds to a k-point and it has the shape (N,nao) Or shape (*,N,nao).
Examples:
>>> cell = pbc.gto.M(a=numpy.eye(3)*4, atom='He 1 1 1', basis='6-31g') >>> coords = cell.get_uniform_grids([10,10,10]) >>> kpts = cell.make_kpts([3,3,3]) >>> ao_value = cell.pbc_eval_gto("GTOval_sph", coords, kpts) >>> len(ao_value) 27 >>> ao_value[0].shape (1000, 2) >>> ao_value = cell.pbc_eval_gto("GTOval_ig_sph", coords, kpts, comp=3) >>> print(ao_value.shape) >>> len(ao_value) 27 >>> ao_value[0].shape (3, 1000, 2)
- pyscf.pbc.gto.eval_gto.get_lattice_Ls(cell, nimgs=None, rcut=None, dimension=None, discard=True)[source]¶
Get lattice-sum vectors for eval_gto
- pyscf.pbc.gto.eval_gto.pbc_eval_gto(cell, eval_name, coords, comp=None, kpts=None, kpt=None, shls_slice=None, non0tab=None, ao_loc=None, cutoff=None, out=None, Ls=None, rcut=None)¶
Evaluate PBC-AO function value on the given grids,
- Args:
eval_name : str:
========================== ======================= Function Expression ========================== ======================= "GTOval_sph" \sum_T exp(ik*T) |AO> "GTOval_ip_sph" nabla \sum_T exp(ik*T) |AO> "GTOval_cart" \sum_T exp(ik*T) |AO> "GTOval_ip_cart" nabla \sum_T exp(ik*T) |AO> ========================== =======================
- atmint32 ndarray
libcint integral function argument
- basint32 ndarray
libcint integral function argument
- envfloat64 ndarray
libcint integral function argument
- coords2D array, shape (N,3)
The coordinates of the grids.
- Kwargs:
- 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 cell will be evaluated.
- non0tab2D bool array
mask array to indicate whether the AO values are zero. The mask array can be obtained by calling
dft.gen_grid.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.
- Returns:
A list of 2D (or 3D) arrays to hold the AO values on grids. Each element of the list corresponds to a k-point and it has the shape (N,nao) Or shape (*,N,nao).
Examples:
>>> cell = pbc.gto.M(a=numpy.eye(3)*4, atom='He 1 1 1', basis='6-31g') >>> coords = cell.get_uniform_grids([10,10,10]) >>> kpts = cell.make_kpts([3,3,3]) >>> ao_value = cell.pbc_eval_gto("GTOval_sph", coords, kpts) >>> len(ao_value) 27 >>> ao_value[0].shape (1000, 2) >>> ao_value = cell.pbc_eval_gto("GTOval_ig_sph", coords, kpts, comp=3) >>> print(ao_value.shape) >>> len(ao_value) 27 >>> ao_value[0].shape (3, 1000, 2)