pyscf.gto package¶

Subpackages¶

pyscf.gto.basis package

Submodules¶

pyscf.gto.cmd_args module¶

pyscf.gto.cmd_args.cmd_args()[source]¶: get input from cmdline

pyscf.gto.ecp module¶

Effective core potential (ECP)

This module exposes some ecp integration functions from the C implementation.

Reference for ecp integral computation * Analytical integration J. Chem. Phys. 65, 3826 J. Chem. Phys. 111, 8778 J. Comput. Phys. 44, 289

Numerical integration

J. Comput. Chem. 27, 1009 Chem. Phys. Lett. 296, 445

pyscf.gto.ecp.core_configuration(nelec_core, atom_symbol=None)[source]¶

pyscf.gto.ecp.so_by_shell(mol, shls)[source]¶: Spin-orbit coupling ECP in spinor basis i/2 <Pauli_matrix dot l U(r)>

pyscf.gto.ecp.type1_by_shell(mol, shls, cart=False)[source]¶

pyscf.gto.ecp.type2_by_shell(mol, shls, cart=False)[source]¶

pyscf.gto.eval_gto module¶

pyscf.gto.eval_gto.eval_gto(mol, eval_name, coords, comp=None, shls_slice=None, non0tab=None, ao_loc=None, cutoff=None, out=None)[source]¶

Evaluate AO function value on the given grids,

Args:

eval_name : str

Function

comp

Expression

“GTOval_sph”

1

|AO>

“GTOval_ip_sph”

3

nabla |AO>

“GTOval_ig_sph”

3

(#C(0 1) g) |AO>

“GTOval_ipig_sph”

9

(#C(0 1) nabla g) |AO>

“GTOval_cart”

1

|AO>

“GTOval_ip_cart”

3

nabla |AO>

“GTOval_ig_cart”

3

(#C(0 1) g)|AO>

“GTOval_sph_deriv1”

4

GTO value and 1st order GTO values

“GTOval_sph_deriv2”

10

All derivatives up to 2nd order

“GTOval_sph_deriv3”

20

All derivatives up to 3rd order

“GTOval_sph_deriv4”

35

All derivatives up to 4th order

“GTOval_sp_spinor”

1

sigma dot p |AO> (spinor basis)

“GTOval_ipsp_spinor”

3

nabla sigma dot p |AO> (spinor basis)

“GTOval_ipipsp_spinor”

9

nabla nabla sigma dot p |AO> (spinor basis)

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:

compint: Number of the components of the operator
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 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:

2D array of shape (N,nao) Or 3D array of shape (*,N,nao) to store AO values on grids.

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 = mol.eval_gto("GTOval_sph", coords)
>>> print(ao_value.shape)
(100, 24)
>>> ao_value = mol.eval_gto("GTOval_ig_sph", coords)
>>> print(ao_value.shape)
(3, 100, 24)

pyscf.gto.eval_gto.make_screen_index(mol, coords, shls_slice=None, cutoff=1e-15, blksize=56)[source]¶

Screen index indicates how important a shell is on grid. The shell is ignorable if its screen index is 0. Screen index ~= nbins + log(ao)

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.
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)
verboseint or object of Logger: No effects.

Returns:

2D array of shape (N,nbas), where N is the number of grids, nbas is the number of shells.

pyscf.gto.ft_ao module¶

Analytical Fourier transformation for AO and AO-pair value

pyscf.gto.ft_ao.ft_ao(mol, Gv, shls_slice=None, b=array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]), gxyz=None, Gvbase=None, verbose=None)[source]¶

Analytical FT transform AO int mu(r) exp(-ikr) dr^3

The output tensor has the shape [nGv, nao]

pyscf.gto.ft_ao.ft_aopair(mol, Gv, shls_slice=None, aosym='s1', b=array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]), gxyz=None, Gvbase=None, out=None, intor='GTO_ft_ovlp', comp=1, q=array([0., 0., 0.]), return_complex=True, ovlp_mask=None, verbose=None)[source]¶: FT transform AO pair int i(r) j(r) exp(-ikr) dr^3

pyscf.gto.mole module¶

Mole class and helper functions to handle parameters and attributes for GTO integrals. This module serves the interface to the integral library libcint.

pyscf.gto.mole.M(*args, **kwargs)[source]¶

This is a shortcut to build up Mole object.

Args: Same to Mole.build()

Examples:

>>> from pyscf import gto
>>> mol = gto.M(atom='H 0 0 0; F 0 0 1', basis='6-31g')

class pyscf.gto.mole.Mole(**kwargs)[source]¶

Bases: MoleBase

A Mole object to hold the basic information of a molecule.

property DFT¶

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’, ‘chkfile’. Default is ‘minao’

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_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
SCF converged or not

e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)

mo_energy :
Orbital energies

mo_occ
Orbital occupancy

mo_coeff
Orbital coefficients

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_adjust

None : to switch off atomic radii adjustment

grids.atomic_radii

radi.BRAGG_RADII (default)

radi.COVALENT_RADII

None : to switch off atomic radii adjustment

grids.radi_method scheme for radial grids

radi.treutler (default)

radi.delley

radi.mura_knowles

radi.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_prune

gen_grid.treutler_prune

None : 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

property DHF¶

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’, ‘chkfile’. Default is ‘minao’
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_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
SCF converged or not

e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)

mo_energy :
Orbital energies

mo_occ
Orbital occupancy

mo_coeff
Orbital coefficients

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 Dirac-Hartree-Fock

with_ssssbool or string, for Dirac-Hartree-Fock only: If False, ignore small component integrals (SS|SS). Default is True.
with_gauntbool, for Dirac-Hartree-Fock only: Default is False.
with_breitbool, for Dirac-Hartree-Fock only: Gaunt + gauge term. Default is False.

Examples:

>>> mol = gto.M(atom='H 0 0 0; H 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol)
>>> e0 = mf.scf()
>>> mf = scf.DHF(mol)
>>> e1 = mf.scf()
>>> print('Relativistic effects = %.12f' % (e1-e0))
Relativistic effects = -0.000008854205

property DKS¶

property GHF¶

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’, ‘chkfile’. Default is ‘minao’
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_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
SCF converged or not

e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)

mo_energy :
Orbital energies

mo_occ
Orbital occupancy

mo_coeff
Orbital coefficients

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 GHF method: GHF orbital coefficients are 2D array. Let nao be the number of spatial AOs, mo_coeff[:nao] are the coefficients of AO with alpha spin; mo_coeff[nao:nao*2] are the coefficients of AO with beta spin.

property GKS¶: Generalized Kohn-Sham

property HF¶

A wrap function to create SCF class (RHF or UHF).

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’, ‘chkfile’. Default is ‘minao’

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_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
SCF converged or not

e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)

mo_energy :
Orbital energies

mo_occ
Orbital occupancy

mo_coeff
Orbital coefficients

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

property KS¶

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’, ‘chkfile’. Default is ‘minao’

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_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
SCF converged or not

e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)

mo_energy :
Orbital energies

mo_occ
Orbital occupancy

mo_coeff
Orbital coefficients

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_adjust

None : to switch off atomic radii adjustment

grids.atomic_radii

radi.BRAGG_RADII (default)

radi.COVALENT_RADII

None : to switch off atomic radii adjustment

grids.radi_method scheme for radial grids

radi.treutler (default)

radi.delley

radi.mura_knowles

radi.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_prune

gen_grid.treutler_prune

None : 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

property RDKS¶: Kramers restricted Dirac-Kohn-Sham

property RHF¶

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’, ‘chkfile’. Default is ‘minao’
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_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
SCF converged or not

e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)

mo_energy :
Orbital energies

mo_occ
Orbital occupancy

mo_coeff
Orbital coefficients

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

property RKS¶

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’, ‘chkfile’. Default is ‘minao’

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_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
SCF converged or not

e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)

mo_energy :
Orbital energies

mo_occ
Orbital occupancy

mo_coeff
Orbital coefficients

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_adjust

None : to switch off atomic radii adjustment

grids.atomic_radii

radi.BRAGG_RADII (default)

radi.COVALENT_RADII

None : to switch off atomic radii adjustment

grids.radi_method scheme for radial grids

radi.treutler (default)

radi.delley

radi.mura_knowles

radi.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_prune

gen_grid.treutler_prune

None : 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

property ROHF¶

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’, ‘chkfile’. Default is ‘minao’
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_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
SCF converged or not

e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)

mo_energy :
Orbital energies

mo_occ
Orbital occupancy

mo_coeff
Orbital coefficients

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

property ROKS¶: Restricted open-shell Kohn-Sham See pyscf/dft/rks.py RKS class for the usage of the attributes

property UDKS¶: Kramers unrestricted Dirac-Kohn-Sham

property UHF¶

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’, ‘chkfile’. Default is ‘minao’
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_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
SCF converged or not

e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)

mo_energy :
Orbital energies

mo_occ
Orbital occupancy

mo_coeff
Orbital coefficients

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 UHF:

nelec(int, int): If given, freeze the number of (alpha,beta) electrons to the given value.
level_shiftnumber or two-element list: level shift (in Eh) for alpha and beta Fock if two-element list is given.
init_guess_breaksymlogical: If given, overwrite BREAKSYM.

Examples:

>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz', charge=1, spin=1, verbose=0)
>>> mf = scf.UHF(mol)
>>> mf.kernel()
-75.623975516256706
>>> print('S^2 = %.7f, 2S+1 = %.7f' % mf.spin_square())
S^2 = 0.7570150, 2S+1 = 2.0070027

property UKS¶: Unrestricted Kohn-Sham See pyscf/dft/rks.py RKS class for document of the attributes

property X2C¶: X2C Hartree-Fock

property X2C_HF¶: X2C Hartree-Fock

property X2C_KS¶: X2C Kohn-Sham

ao2mo(mo_coeffs, erifile=None, dataname='eri_mo', intor='int2e', **kwargs)[source]¶

Integral transformation for arbitrary orbitals and arbitrary integrals. See more detalied documentation in func:ao2mo.kernel.

Args:

mo_coeffs (an np array or a list of arrays)A matrix of orbital: coefficients if it is a numpy ndarray, or four sets of orbital coefficients, corresponding to the four indices of (ij|kl).

Kwargs:

erifile (str or h5py File or h5py Group object)The file/object: to store the transformed integrals. If not given, the return value is an array (in memory) of the transformed integrals.
datanamestr: Note this argument is effective if erifile is given. The dataset name in the erifile (ref the hierarchy of HDF5 format http://www.hdfgroup.org/HDF5/doc1.6/UG/09_Groups.html). By assigning different dataname, the existed integral file can be reused. If the erifile contains the specified dataname, the old integrals will be replaced by the new one under the key dataname.
intor (str)integral name Name of the 2-electron integral. Ref: to getints_by_shell() for the complete list of available 2-electron integral names

Returns:

An array of transformed integrals if erifile is not given. Otherwise, return the file/fileobject if erifile is assigned.

Examples:

>>> import pyscf
>>> mol = pyscf.M(atom='O 0 0 0; H 0 1 0; H 0 0 1', basis='sto3g')
>>> mo1 = numpy.random.random((mol.nao_nr(), 10))
>>> mo2 = numpy.random.random((mol.nao_nr(), 8))

>>> eri1 = mol.ao2mo(mo1)
>>> print(eri1.shape)
(55, 55)

>>> eri1 = mol.ao2mo(mo1, compact=False)
>>> print(eri1.shape)
(100, 100)

>>> eri1 = mol.ao2mo(eri, (mo1,mo2,mo2,mo2))
>>> print(eri1.shape)
(80, 36)

>>> eri1 = mol.ao2mo(eri, (mo1,mo2,mo2,mo2), erifile='water.h5')

fromfile(filename, format=None)[source]¶: Update the Mole object based on the input geometry file

fromstring(string, format='xyz')[source]¶: Update the Mole object based on the input geometry string

inertia_moment(mass=None, coords=None)¶

to_cell(a, dimension=3)[source]¶

Put a molecule in a cell with periodic boundary condictions

Args:

a(3,3) ndarray: Lattice primitive vectors. Each row is a lattice vector

tofile(filename, format=None)¶

Write molecular geometry to a file of the required format.

Supported output formats:: raw: Each line is <symbol> <x> <y> <z>

xyz: XYZ cartesian coordinates format

zmat: Z-matrix format

tostring(format='raw')¶

Convert molecular geometry to a string of the required format.

Supported output formats:: raw: Each line is <symbol> <x> <y> <z>

xyz: XYZ cartesian coordinates format

zmat: Z-matrix format

class pyscf.gto.mole.MoleBase[source]¶

Bases: StreamObject

Basic class to hold molecular structure, integrals and global options

Attributes:

verboseint: Print level
outputstr or None: Output file, default is None which dumps msg to sys.stdout
max_memoryint, float: Allowed memory in MB
chargeint: Charge of molecule. It affects the electron numbers
spinint or None: 2S, num. alpha electrons - num. beta electrons to control multiplicity. If spin = None is set, multiplicity will be guessed based on the neutral molecule.
symmetrybool or str: Whether to use symmetry. When this variable is set to True, the molecule will be rotated and the highest rotation axis will be placed z-axis. If a string is given as the name of point group, the given point group symmetry will be used. Note that the input molecular coordinates will not be changed in this case.
symmetry_subgroupstr: subgroup
atomlist or str: To define molecluar structure. The internal format is

atom = [[atom1, (x, y, z)],

[atom2, (x, y, z)],

…

[atomN, (x, y, z)]]
unitstr: Angstrom or Bohr
basisdict or str: To define basis set.
nucmoddict or str or [function(nuc_charge, nucprop) => zeta]: Nuclear model. 0 or None means point nuclear model. Other values will enable Gaussian nuclear model. If a function is assigned to this attribute, the function will be called to generate the nuclear charge distribution value “zeta” and the relevant nuclear model will be set to Gaussian model. Default is point nuclear model.
nucpropdict: Nuclear properties (like g-factor ‘g’, quadrupole moments ‘Q’). It is needed by pyscf.prop module and submodules.
cartboolean: Using Cartesian GTO basis and integrals (6d,10f,15g)
magmomlist: Collinear spin of each atom. Default is [0,]*natm

** Following attributes are generated by Mole.build() **

stdoutfile object: Default is sys.stdout if Mole.output is not set
topgroupstr: Point group of the system.
groupnamestr: The supported subgroup of the point group. It can be one of SO3, Dooh, Coov, D2h, C2h, C2v, D2, Cs, Ci, C2, C1
nelectronint: sum of nuclear charges - Mole.charge
symm_orba list of numpy.ndarray: Symmetry adapted basis. Each element is a set of symm-adapted orbitals for one irreducible representation. The list index does not correspond to the id of irreducible representation.
irrep_ida list of int: Each element is one irreducible representation id associated with the basis stored in symm_orb. One irrep id stands for one irreducible representation symbol. The irrep symbol and the relevant id are defined in symm.param.IRREP_ID_TABLE
irrep_namea list of str: Each element is one irreducible representation symbol associated with the basis stored in symm_orb. The irrep symbols are defined in symm.param.IRREP_ID_TABLE
_builtbool: To label whether Mole.build() has been called. It is to ensure certain functions being initialized only once.
_basisdict: like Mole.basis, the internal format which is returned from the parser format_basis()

** Following attributes are arguments used by libcint library **

_atm :: [[charge, ptr-of-coord, nuc-model, ptr-zeta, 0, 0], [...]] each element represents one atom
natm :: number of atoms
_bas :: [[atom-id, angular-momentum, num-primitive-GTO, num-contracted-GTO, 0, ptr-of-exps, ptr-of-contract-coeff, 0], [...]] each element represents one shell
nbas :: number of shells
_env :: list of floats to store the coordinates, GTO exponents, contract-coefficients

Examples:

>>> mol = Mole(atom='H^2 0 0 0; H 0 0 1.1', basis='sto3g').build()
>>> print(mol.atom_symbol(0))
H^2
>>> print(mol.atom_pure_symbol(0))
H
>>> print(mol.nao_nr())
2
>>> print(mol.intor('int1e_ovlp_sph'))
[[ 0.99999999  0.43958641]
 [ 0.43958641  0.99999999]]
>>> mol.charge = 1
>>> mol.build()
<class 'pyscf.gto.mole.Mole'> has no attributes Charge

ao_labels(fmt=True, base=0)¶

Labels of AO basis functions

Kwargs:

fmtstr or bool: if fmt is boolean, it controls whether to format the labels and the default format is “%d%3s %s%-4s”. if fmt is string, the string will be used as the print format.

Returns:

List of [(atom-id, symbol-str, nl-str, str-of-AO-notation)] or formatted strings based on the argument “fmt”

property ao_loc¶

Offset of every shell in the spherical basis function spectrum

Returns:: list, each entry is the corresponding start basis function id

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.ao_loc_nr(mol)
[0, 1, 2, 3, 6, 9, 10, 11, 12, 15, 18]

ao_loc_2c()¶

Offset of every shell in the spinor basis function spectrum

Returns:: list, each entry is the corresponding start id of spinor function

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.ao_loc_2c(mol)
[0, 2, 4, 6, 12, 18, 20, 22, 24, 30, 36]

ao_loc_nr(cart=None)¶

Offset of every shell in the spherical basis function spectrum

Returns:: list, each entry is the corresponding start basis function id

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.ao_loc_nr(mol)
[0, 1, 2, 3, 6, 9, 10, 11, 12, 15, 18]

ao_rotation_matrix(orientation)¶

Matrix u to rotate AO basis to a new orientation.

atom_new_coords = mol.atom_coords().dot(orientation.T) new_AO = u * mol.AO new_orbitals_coef = u.dot(orbitals_coef)

aoslice_2c_by_atom()¶: 2-component AO offset for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

aoslice_by_atom(ao_loc=None)¶: AO offsets for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

aoslice_nr_by_atom(ao_loc=None)¶: AO offsets for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

apply(fn, *args, **kwargs)[source]¶: Apply the fn to rest arguments: return fn(*args, **kwargs). The return value of method set is the object itself. This allows a series of functions/methods to be executed in pipe.

atom_charge(atm_id)[source]¶

Nuclear effective charge of the given atom id Note “atom_charge /= charge(atom_symbol)” when ECP is enabled. Number of electrons screened by ECP can be obtained by charge(atom_symbol)-atom_charge

Args:

atm_idint: 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1')
>>> mol.atom_charge(1)
17

atom_charges()[source]¶: np.asarray([mol.atom_charge(i) for i in range(mol.natm)])

atom_coord(atm_id, unit='Bohr')[source]¶

Coordinates (ndarray) of the given atom id

Args:

atm_idint: 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1')
>>> mol.atom_coord(1)
[ 0.          0.          2.07869874]

atom_coords(unit='Bohr')[source]¶: np.asarray([mol.atom_coords(i) for i in range(mol.natm)])

atom_mass_list(isotope_avg=False)¶

A list of mass for all atoms in the molecule

Kwargs:

isotope_avgboolean: Whether to use the isotope average mass as the atomic mass

atom_nelec_core(atm_id)[source]¶: Number of core electrons for pseudo potential.

atom_nshells(atm_id)[source]¶

Number of basis/shells of the given atom

Args:

atm_idint: 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1')
>>> mol.atom_nshells(1)
5

atom_pure_symbol(atm_id)[source]¶

For the given atom id, return the standard symbol (striping special characters)

Args:

atm_idint: 0-based

Examples:

>>> mol.build(atom='H^2 0 0 0; H 0 0 1.1')
>>> mol.atom_symbol(0)
H

atom_shell_ids(atm_id)[source]¶

A list of the shell-ids of the given atom

Args:

atm_idint: 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.atom_shell_ids(1)
[3, 4, 5, 6, 7]

atom_symbol(atm_id)[source]¶

For the given atom id, return the input symbol (without striping special characters)

Args:

atm_idint: 0-based

Examples:

>>> mol.build(atom='H^2 0 0 0; H 0 0 1.1')
>>> mol.atom_symbol(0)
H^2

bas_angular(bas_id)[source]¶

The angular momentum associated with the given basis

Args:

bas_idint: 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_atom(7)
2

bas_atom(bas_id)[source]¶

The atom (0-based id) that the given basis sits on

Args:

bas_idint: 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_atom(7)
1

bas_coord(bas_id)[source]¶

Coordinates (ndarray) associated with the given basis id

Args:

bas_idint: 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1')
>>> mol.bas_coord(1)
[ 0.          0.          2.07869874]

bas_ctr_coeff(bas_id)[source]¶

Contract coefficients (ndarray) of the given shell

Args:

bas_idint: 0-based

Examples:

>>> mol.M(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_ctr_coeff(0)
[[ 10.03400444]
 [  4.1188704 ]
 [  1.53971186]]

bas_exp(bas_id)[source]¶

exponents (ndarray) of the given shell

Args:

bas_idint: 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_kappa(0)
[ 13.01     1.962    0.4446]

bas_exps()[source]¶: exponents of all basis return [mol.bas_exp(i) for i in range(self.nbas)]

bas_kappa(bas_id)[source]¶

Kappa (if l < j, -l-1, else l) of the given shell

Args:

bas_idint: 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_kappa(3)
0

bas_len_cart(bas_id)[source]¶: The number of Cartesian function associated with given basis

bas_len_spinor(bas_id)[source]¶: The number of spinor associated with given basis If kappa is 0, return 4l+2

bas_nctr(bas_id)[source]¶

The number of contracted GTOs for the given shell

Args:

bas_idint: 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_atom(3)
3

bas_nprim(bas_id)[source]¶

The number of primitive GTOs for the given shell

Args:

bas_idint: 0-based

Examples:

>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_atom(3)
11

build(dump_input=True, parse_arg=False, verbose=None, output=None, max_memory=None, atom=None, basis=None, unit=None, nucmod=None, ecp=None, pseudo=None, charge=None, spin=0, symmetry=None, symmetry_subgroup=None, cart=None, magmom=None)[source]¶

Setup moleclue and initialize some control parameters. Whenever you change the value of the attributes of Mole, you need call this function to refresh the internal data of Mole.

Kwargs:

dump_inputbool: whether to dump the contents of input file in the output file
parse_argbool: whether to read the sys.argv and overwrite the relevant parameters
verboseint: Print level. If given, overwrite Mole.verbose
outputstr or None: Output file. If given, overwrite Mole.output
max_memoryint, float: Allowd memory in MB. If given, overwrite Mole.max_memory
atomlist or str: To define molecluar structure.
basisdict or str: To define basis set.
nucmoddict or str: Nuclear model. If given, overwrite Mole.nucmod
chargeint: Charge of molecule. It affects the electron numbers If given, overwrite Mole.charge
spinint: 2S, num. alpha electrons - num. beta electrons to control multiplicity. If setting spin = None , multiplicity will be guessed based on the neutral molecule. If given, overwrite Mole.spin
symmetrybool or str: Whether to use symmetry. If given a string of point group name, the given point group symmetry will be used.
magmomlist: Collinear spin of each atom. Default is [0.0,]*natm

cart = False¶

cart2sph_coeff(normalized='sp')[source]¶

Transformation matrix that transforms Cartesian GTOs to spherical GTOs for all basis functions

Kwargs:

normalizedstring or boolean: How the Cartesian GTOs are normalized. Except s and p functions, Cartesian GTOs do not have the universal normalization coefficients for the different components of the same shell. The value of this argument can be one of ‘sp’, ‘all’, None. ‘sp’ means the Cartesian s and p basis are normalized. ‘all’ means all Cartesian functions are normalized. None means none of the Cartesian functions are normalized. The default value ‘sp’ is the convention used by libcint library.

Examples:

>>> mol = gto.M(atom='H 0 0 0; F 0 0 1', basis='ccpvtz')
>>> c = mol.cart2sph_coeff()
>>> s0 = mol.intor('int1e_ovlp_sph')
>>> s1 = c.T.dot(mol.intor('int1e_ovlp_cart')).dot(c)
>>> print(abs(s1-s0).sum())
>>> 4.58676826646e-15

cart_labels(fmt=True, base=0)¶

Labels of Cartesian GTO functions

Kwargs:: fmt : str or bool if fmt is boolean, it controls whether to format the labels and the default format is “%d%3s %s%-4s”. if fmt is string, the string will be used as the print format.
Returns:: List of [(atom-id, symbol-str, nl-str, str-of-xyz-notation)] or formatted strings based on the argument “fmt”

charge = 0¶

condense_to_shell(mat, compressor='max')¶

The given matrix is first partitioned to blocks, based on AO shell as delimiter. Then call compressor function to abstract each block.

Args:

compressor: string or function: if compressor is a string, its value can be sum, max, min, abssum, absmax, absmin, norm

copy(deep=True)¶

Deepcopy of the given Mole object

Some attributes are shared between the original and copied objects. Deepcopy is utilized here to ensure that operations on the copied object do not affect the original object.

decontract_basis(atoms=None, to_cart=False)¶

Decontract the basis of a Mole or a Cell. Returns a Mole (Cell) object with the uncontracted basis environment and a list of coefficients that transform the uncontracted basis to the original basis. Each element in the coefficients list corresponds to one shell of the original Mole (Cell).

Kwargs:

atoms: list or str: Atoms on which the basis to be decontracted. By default, all basis are decontracted
to_cart: bool: Decontract basis and transfer to Cartesian basis

Examples:

>>> mol = gto.M(atom='Ne', basis='ccpvdz')
>>> pmol, ctr_coeff = mol.decontract_basis()
>>> c = scipy.linalg.block_diag(*ctr_coeff)
>>> s = reduce(numpy.dot, (c.T, pmol.intor('int1e_ovlp'), c))
>>> abs(s-mol.intor('int1e_ovlp')).max()
0.0

dump_input()[source]¶

dumps()¶: Serialize Mole object to a JSON formatted str.

property elements¶: A list of elements in the molecule

energy_nuc(charges=None, coords=None)¶

Compute nuclear repulsion energy (AU) or static Coulomb energy

Returns: float

etbs(etbs)¶

Generate even tempered basis. See also expand_etb()

Args:: etbs = [(l, n, alpha, beta), (l, n, alpha, beta),…]
Returns:: Formatted basis

Examples:

>>> gto.expand_etbs([(0, 2, 1.5, 2.), (1, 2, 1, 2.)])
[[0, [6.0, 1]], [0, [3.0, 1]], [1, [1., 1]], [1, [2., 1]]]

eval_ao(eval_name, coords, comp=None, shls_slice=None, non0tab=None, ao_loc=None, cutoff=None, out=None)¶

Evaluate AO function value on the given grids,

Args:

eval_name : str

Function

comp

Expression

“GTOval_sph”

1

|AO>

“GTOval_ip_sph”

3

nabla |AO>

“GTOval_ig_sph”

3

(#C(0 1) g) |AO>

“GTOval_ipig_sph”

9

(#C(0 1) nabla g) |AO>

“GTOval_cart”

1

|AO>

“GTOval_ip_cart”

3

nabla |AO>

“GTOval_ig_cart”

3

(#C(0 1) g)|AO>

“GTOval_sph_deriv1”

4

GTO value and 1st order GTO values

“GTOval_sph_deriv2”

10

All derivatives up to 2nd order

“GTOval_sph_deriv3”

20

All derivatives up to 3rd order

“GTOval_sph_deriv4”

35

All derivatives up to 4th order

“GTOval_sp_spinor”

1

sigma dot p |AO> (spinor basis)

“GTOval_ipsp_spinor”

3

nabla sigma dot p |AO> (spinor basis)

“GTOval_ipipsp_spinor”

9

nabla nabla sigma dot p |AO> (spinor basis)

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:

compint: Number of the components of the operator
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 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:

2D array of shape (N,nao) Or 3D array of shape (*,N,nao) to store AO values on grids.

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 = mol.eval_gto("GTOval_sph", coords)
>>> print(ao_value.shape)
(100, 24)
>>> ao_value = mol.eval_gto("GTOval_ig_sph", coords)
>>> print(ao_value.shape)
(3, 100, 24)

eval_gto(eval_name, coords, comp=None, shls_slice=None, non0tab=None, ao_loc=None, cutoff=None, out=None)¶

Evaluate AO function value on the given grids,

Args:

eval_name : str

Function

comp

Expression

“GTOval_sph”

1

|AO>

“GTOval_ip_sph”

3

nabla |AO>

“GTOval_ig_sph”

3

(#C(0 1) g) |AO>

“GTOval_ipig_sph”

9

(#C(0 1) nabla g) |AO>

“GTOval_cart”

1

|AO>

“GTOval_ip_cart”

3

nabla |AO>

“GTOval_ig_cart”

3

(#C(0 1) g)|AO>

“GTOval_sph_deriv1”

4

GTO value and 1st order GTO values

“GTOval_sph_deriv2”

10

All derivatives up to 2nd order

“GTOval_sph_deriv3”

20

All derivatives up to 3rd order

“GTOval_sph_deriv4”

35

All derivatives up to 4th order

“GTOval_sp_spinor”

1

sigma dot p |AO> (spinor basis)

“GTOval_ipsp_spinor”

3

nabla sigma dot p |AO> (spinor basis)

“GTOval_ipipsp_spinor”

9

nabla nabla sigma dot p |AO> (spinor basis)

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:

compint: Number of the components of the operator
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 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:

2D array of shape (N,nao) Or 3D array of shape (*,N,nao) to store AO values on grids.

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 = mol.eval_gto("GTOval_sph", coords)
>>> print(ao_value.shape)
(100, 24)
>>> ao_value = mol.eval_gto("GTOval_ig_sph", coords)
>>> print(ao_value.shape)
(3, 100, 24)

expand_etb(l, n, alpha, beta)[source]¶

Generate the exponents of even tempered basis for Mole.basis. .. math:

e = e^{-\alpha * \beta^{i-1}} for i = 1 .. n

Args:

lint: Angular momentum
nint: Number of GTOs

Returns:

Formatted basis

Examples:

>>> gto.expand_etb(1, 3, 1.5, 2)
[[1, [6.0, 1]], [1, [3.0, 1]], [1, [1.5, 1]]]

expand_etbs(etbs)[source]¶

Generate even tempered basis. See also expand_etb()

Args:: etbs = [(l, n, alpha, beta), (l, n, alpha, beta),…]
Returns:: Formatted basis

Examples:

>>> gto.expand_etbs([(0, 2, 1.5, 2.), (1, 2, 1, 2.)])
[[0, [6.0, 1]], [0, [3.0, 1]], [1, [1., 1]], [1, [2., 1]]]

format_atom(atom, origin=0, axes=None, unit='Ang')[source]¶

Convert the input Mole.atom to the internal data format. Including, changing the nuclear charge to atom symbol, converting the coordinates to AU, rotate and shift the molecule. If the atom is a string, it takes “;” and “n” for the mark to separate atoms; “,” and arbitrary length of blank space to spearate the individual terms for an atom. Blank line will be ignored.

Args:

atomslist or str: the same to Mole.atom

Kwargs:

originndarray: new axis origin.
axesndarray: (new_x, new_y, new_z), new coordinates
unitstr or number: If unit is one of strings (B, b, Bohr, bohr, AU, au), the coordinates of the input atoms are the atomic unit; If unit is one of strings (A, a, Angstrom, angstrom, Ang, ang), the coordinates are in the unit of angstrom; If a number is given, the number are considered as the Bohr value (in angstrom), which should be around 0.53. Set unit=1 if wishing to preserve the unit of the coordinates.

Returns:

“atoms” in the internal format. The internal format is: atom = [[atom1, (x, y, z)],

[atom2, (x, y, z)],

…

[atomN, (x, y, z)]]

Examples:

>>> gto.format_atom('9,0,0,0; h@1 0 0 1', origin=(1,1,1))
[['F', [-1.0, -1.0, -1.0]], ['H@1', [-1.0, -1.0, 0.0]]]
>>> gto.format_atom(['9,0,0,0', (1, (0, 0, 1))], origin=(1,1,1))
[['F', [-1.0, -1.0, -1.0]], ['H', [-1, -1, 0]]]

format_basis(basis_tab)[source]¶

Convert the input Mole.basis to the internal data format.

``{ atom: [(l, ((-exp, c_1, c_2, ..),

(-exp, c_1, c_2, ..))),

(l, ((-exp, c_1, c_2, ..),: (-exp, c_1, c_2, ..)))], … }``

Args:

basis_tabdict: Similar to Mole.basis, it cannot be a str

Returns:

Formatted basis

Examples:

>>> gto.format_basis({'H':'sto-3g', 'H^2': '3-21g'})
{'H': [[0,
    [3.4252509099999999, 0.15432897000000001],
    [0.62391373000000006, 0.53532813999999995],
    [0.16885539999999999, 0.44463454000000002]]],
 'H^2': [[0,
    [5.4471780000000001, 0.15628500000000001],
    [0.82454700000000003, 0.90469100000000002]],
    [0, [0.18319199999999999, 1.0]]]}

>>> gto.format_basis({'H':'gth-szv'})
{'H': [[0,
    (8.3744350009, -0.0283380461),
    (1.8058681460, -0.1333810052),
    (0.4852528328, -0.3995676063),
    (0.1658236932, -0.5531027541)]]}

format_ecp(ecp_tab)[source]¶

Convert the input ecp (dict) to the internal data format:

{ atom: (nelec,  # core electrons

((l, # l=-1 for UL, l>=0 for Ul to indicate |l><l|

(((exp_1, c_1), # for r^0

(exp_2, c_2), …),

((exp_1, c_1), # for r^1
(exp_2, c_2), …),

((exp_1, c_1), # for r^2
…))))),

…}

format_pseudo(pseudo_tab)[source]¶

Convert the input pseudo (dict) to the internal data format:

{ atom: ( (nelec_s, nele_p, nelec_d, ...),
         rloc, nexp, (cexp_1, cexp_2, ..., cexp_nexp),
         nproj_types,
         (r1, nproj1, ( (hproj1[1,1], hproj1[1,2], ..., hproj1[1,nproj1]),
                        (hproj1[2,1], hproj1[2,2], ..., hproj1[2,nproj1]),
                        ...
                        (hproj1[nproj1,1], hproj1[nproj1,2], ...        ) )),
         (r2, nproj2, ( (hproj2[1,1], hproj2[1,2], ..., hproj2[1,nproj1]),
         ... ) )
         )
 ... }

Args:

pseudo_tabdict: Similar to pseudo (a dict), it cannot be a str

Returns:

Formatted pseudo

Examples:

>>> pbc.format_pseudo({'H':'gth-blyp', 'He': 'gth-pade'})
{'H': [[1],
    0.2, 2, [-4.19596147, 0.73049821], 0],
 'He': [[2],
    0.2, 2, [-9.1120234, 1.69836797], 0]}

get_ao_indices(bas_list, ao_loc=None)[source]¶: Generate (dis-continued) AO indices for basis specified in bas_list

get_enuc(charges=None, coords=None)¶

Compute nuclear repulsion energy (AU) or static Coulomb energy

Returns: float

get_overlap_cond(shls_slice=None)¶

Overlap magnitudes measured by -log(overlap) between two shells

Args:: mol : an instance of Mole
Returns:: 2D mask array of shape (nbas,nbas)

gto_norm(l, expnt)[source]¶

Normalized factor for GTO radial part \(g=r^l e^{-\alpha r^2}\)

\[\frac{1}{\sqrt{\int g^2 r^2 dr}} = \sqrt{\frac{2^{2l+3} (l+1)! (2a)^{l+1.5}}{(2l+2)!\sqrt{\pi}}}\]

Ref: H. B. Schlegel and M. J. Frisch, Int. J. Quant. Chem., 54(1995), 83-87.

Args:

l (int):: angular momentum
expnt :: exponent \(\alpha\)

Returns:

normalization factor

Examples:

>>> print(gto_norm(0, 1))
2.5264751109842591

has_ecp()[source]¶: Whether pseudo potential is used in the system.

has_ecp_soc()[source]¶: Whether spin-orbit coupling is enabled in ECP.

incore_anyway = False¶

intor(intor, comp=None, hermi=0, aosym='s1', out=None, shls_slice=None, grids=None)[source]¶

Integral generator.

Args:

intorstr: Name of the 1e or 2e AO integrals. Ref to getints() for the complete list of available 1-electron integral names

Kwargs:

compint: Components of the integrals, e.g. int1e_ipovlp_sph has 3 components.
hermiint: Symmetry of the integrals

0 : no symmetry assumed (default)

1 : hermitian

2 : anti-hermitian
gridsndarray: Coordinates of grids for the int1e_grids integrals

Returns:

ndarray of 1-electron integrals, can be either 2-dim or 3-dim, depending on comp

Examples:

>>> mol.build(atom='H 0 0 0; H 0 0 1.1', basis='sto-3g')
>>> mol.intor('int1e_ipnuc_sph', comp=3) # <nabla i | V_nuc | j>
[[[ 0.          0.        ]
  [ 0.          0.        ]]
 [[ 0.          0.        ]
  [ 0.          0.        ]]
 [[ 0.10289944  0.48176097]
  [-0.48176097 -0.10289944]]]
>>> mol.intor('int1e_nuc_spinor')
[[-1.69771092+0.j  0.00000000+0.j -0.67146312+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -1.69771092+0.j  0.00000000+0.j -0.67146312+0.j]
 [-0.67146312+0.j  0.00000000+0.j -1.69771092+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -0.67146312+0.j  0.00000000+0.j -1.69771092+0.j]]

intor_asymmetric(intor, comp=None, grids=None)[source]¶

One-electron integral generator. The integrals are assumed to be anti-hermitian

Args:

intorstr: Name of the 1-electron integral. Ref to getints() for the complete list of available 1-electron integral names

Kwargs:

compint: Components of the integrals, e.g. int1e_ipovlp has 3 components.
gridsndarray: Coordinates of grids for the int1e_grids integrals

Returns:

ndarray of 1-electron integrals, can be either 2-dim or 3-dim, depending on comp

Examples:

>>> mol.build(atom='H 0 0 0; H 0 0 1.1', basis='sto-3g')
>>> mol.intor_asymmetric('int1e_nuc_spinor')
[[-1.69771092+0.j  0.00000000+0.j  0.67146312+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -1.69771092+0.j  0.00000000+0.j  0.67146312+0.j]
 [-0.67146312+0.j  0.00000000+0.j -1.69771092+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -0.67146312+0.j  0.00000000+0.j -1.69771092+0.j]]

intor_by_shell(intor, shells, comp=None, grids=None)[source]¶

For given 2, 3 or 4 shells, interface for libcint to get 1e, 2e, 2-center-2e or 3-center-2e integrals

Args:

intor_namestr: See also getints() for the supported intor_name
shlslist of int: The AO shell-ids of the integrals
atmint32 ndarray: libcint integral function argument
basint32 ndarray: libcint integral function argument
envfloat64 ndarray: libcint integral function argument

Kwargs:

compint: Components of the integrals, e.g. int1e_ipovlp has 3 components.

Returns:

ndarray of 2-dim to 5-dim, depending on the integral type (1e, 2e, 3c-2e, 2c2e) and the value of comp

Examples:

The gradients of the spherical 2e integrals

>>> mol.build(atom='H 0 0 0; H 0 0 1.1', basis='sto-3g')
>>> gto.getints_by_shell('int2e_ip1_sph', (0,1,0,1), mol._atm, mol._bas, mol._env, comp=3)
[[[[[-0.        ]]]]
  [[[[-0.        ]]]]
  [[[[-0.08760462]]]]]

intor_symmetric(intor, comp=None, grids=None)[source]¶

One-electron integral generator. The integrals are assumed to be hermitian

Args:

intorstr: Name of the 1-electron integral. Ref to getints() for the complete list of available 1-electron integral names

Kwargs:

compint: Components of the integrals, e.g. int1e_ipovlp_sph has 3 components.
gridsndarray: Coordinates of grids for the int1e_grids integrals

Returns:

ndarray of 1-electron integrals, can be either 2-dim or 3-dim, depending on comp

Examples:

>>> mol.build(atom='H 0 0 0; H 0 0 1.1', basis='sto-3g')
>>> mol.intor_symmetric('int1e_nuc_spinor')
[[-1.69771092+0.j  0.00000000+0.j -0.67146312+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -1.69771092+0.j  0.00000000+0.j -0.67146312+0.j]
 [-0.67146312+0.j  0.00000000+0.j -1.69771092+0.j  0.00000000+0.j]
 [ 0.00000000+0.j -0.67146312+0.j  0.00000000+0.j -1.69771092+0.j]]

kernel(dump_input=True, parse_arg=False, verbose=None, output=None, max_memory=None, atom=None, basis=None, unit=None, nucmod=None, ecp=None, pseudo=None, charge=None, spin=0, symmetry=None, symmetry_subgroup=None, cart=None, magmom=None)¶

Setup moleclue and initialize some control parameters. Whenever you change the value of the attributes of Mole, you need call this function to refresh the internal data of Mole.

Kwargs:

dump_inputbool: whether to dump the contents of input file in the output file
parse_argbool: whether to read the sys.argv and overwrite the relevant parameters
verboseint: Print level. If given, overwrite Mole.verbose
outputstr or None: Output file. If given, overwrite Mole.output
max_memoryint, float: Allowd memory in MB. If given, overwrite Mole.max_memory
atomlist or str: To define molecluar structure.
basisdict or str: To define basis set.
nucmoddict or str: Nuclear model. If given, overwrite Mole.nucmod
chargeint: Charge of molecule. It affects the electron numbers If given, overwrite Mole.charge
spinint: 2S, num. alpha electrons - num. beta electrons to control multiplicity. If setting spin = None , multiplicity will be guessed based on the neutral molecule. If given, overwrite Mole.spin
symmetrybool or str: Whether to use symmetry. If given a string of point group name, the given point group symmetry will be used.
magmomlist: Collinear spin of each atom. Default is [0.0,]*natm

classmethod loads(molstr)[source]¶: Deserialize a str containing a JSON document to a Mole object.

loads_(molstr)[source]¶: Deserialize a str containing a JSON document to a Mole object.

make_atm_env(atom, ptr=0, nucmod=1, nucprop=None)[source]¶: Convert the internal format Mole._atom to the format required by libcint integrals

make_bas_env(basis_add, atom_id=0, ptr=0)[source]¶: Convert Mole.basis to the argument bas for libcint integrals

make_ecp_env(_atm, _ecp, pre_env=[])[source]¶: Generate the input arguments _ecpbas for ECP integrals

make_env(atoms, basis, pre_env=[], nucmod={}, nucprop=None)[source]¶: Generate the input arguments for libcint library based on internal format Mole._atom and Mole._basis

max_memory = 4000¶

property ms¶: Spin quantum number. multiplicity = ms*2+1

property multiplicity¶

property nao¶

nao_2c()¶: Total number of contracted spinor GTOs for the given Mole object

nao_2c_range(bas_id0, bas_id1)¶

Lower and upper boundary of contracted spinor basis functions associated with the given shell range

Args:

mol :: Mole object
bas_id0int: start shell id, 0-based
bas_id1int: stop shell id, 0-based

Returns:

tuple of start basis function id and the stop function id

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.nao_2c_range(mol, 2, 4)
(4, 12)

nao_cart()¶: Total number of contracted cartesian GTOs for the given Mole object

nao_nr(cart=None)¶: Total number of contracted GTOs for the given Mole object

nao_nr_range(bas_id0, bas_id1)¶

Lower and upper boundary of contracted spherical basis functions associated with the given shell range

Args:

mol :: Mole object
bas_id0int: start shell id
bas_id1int: stop shell id

Returns:

tuple of start basis function id and the stop function id

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.nao_nr_range(mol, 2, 4)
(2, 6)

property natm¶

property nbas¶

property nelec¶

property nelectron¶

npgto_nr(cart=None)¶: Total number of primitive spherical GTOs for the given Mole object

offset_2c_by_atom()¶: 2-component AO offset for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

offset_ao_by_atom(ao_loc=None)¶: AO offsets for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

offset_nr_by_atom(ao_loc=None)¶: AO offsets for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

property omega¶

output = None¶

pack()¶

Pack the input args of Mole to a dict.

Note this function only pack the input arguments (not the entire Mole class). Modifications to mol._atm, mol._bas, mol._env are not tracked. Use dumps() to serialize the entire Mole object.

search_ao_label(label)¶

Find the index of the AO basis function based on the given ao_label

Args:

ao_labelstring or a list of strings: The regular expression pattern to match the orbital labels returned by mol.ao_labels()

Returns:

A list of index for the AOs that matches the given ao_label RE pattern

Examples:

>>> mol = gto.M(atom='H 0 0 0; Cl 0 0 1', basis='ccpvtz')
>>> mol.search_ao_label('Cl.*p')
[19 20 21 22 23 24 25 26 27 28 29 30]
>>> mol.search_ao_label('Cl 2p')
[19 20 21]
>>> mol.search_ao_label(['Cl.*d', 'Cl 4p'])
[25 26 27 31 32 33 34 35 36 37 38 39 40]

search_ao_nr(atm_id, l, m, atmshell)¶

Search the first basis function id (not the shell id) which matches the given atom-id, angular momentum magnetic angular momentum, principal shell.

Args:

atm_idint: atom id, 0-based
lint: angular momentum
mint: magnetic angular momentum
atmshellint: principal quantum number

Returns:

basis function id, 0-based. If not found, return None

Examples:

>>> mol = gto.M(atom='H 0 0 0; Cl 0 0 1', basis='sto-3g')
>>> mol.search_ao_nr(1, 1, -1, 3) # Cl 3px
7

search_ao_r(atm_id, l, j, m, atmshell)¶

search_shell_id(atm_id, l)[source]¶

set_common_orig(coord)¶

Update common origin for integrals of dipole, rxp etc. Note the unit of the coordinates needs to be Bohr

Examples:

>>> mol.set_common_origin(0)
>>> mol.set_common_origin((1,0,0))

set_common_orig_(coord)¶

Update common origin for integrals of dipole, rxp etc. Note the unit of the coordinates needs to be Bohr

Examples:

>>> mol.set_common_origin(0)
>>> mol.set_common_origin((1,0,0))

set_common_origin(coord)[source]¶

Update common origin for integrals of dipole, rxp etc. Note the unit of the coordinates needs to be Bohr

Examples:

>>> mol.set_common_origin(0)
>>> mol.set_common_origin((1,0,0))

set_common_origin_(coord)¶

Update common origin for integrals of dipole, rxp etc. Note the unit of the coordinates needs to be Bohr

Examples:

>>> mol.set_common_origin(0)
>>> mol.set_common_origin((1,0,0))

set_f12_zeta(zeta)[source]¶: Set zeta for YP exp(-zeta r12)/r12 or STG exp(-zeta r12) type integrals

set_geom_(atoms_or_coords, unit=None, symmetry=None, inplace=True)[source]¶: Update geometry

set_nuc_mod(atm_id, zeta)[source]¶

Change the nuclear charge distribution of the given atom ID. The charge distribution is defined as: rho(r) = nuc_charge * Norm * exp(-zeta * r^2). This function can only be called after .build() method is executed.

Examples:

>>> for ia in range(mol.natm):
...     zeta = gto.filatov_nuc_mod(mol.atom_charge(ia))
...     mol.set_nuc_mod(ia, zeta)

set_nuc_mod_(atm_id, zeta)¶

Change the nuclear charge distribution of the given atom ID. The charge distribution is defined as: rho(r) = nuc_charge * Norm * exp(-zeta * r^2). This function can only be called after .build() method is executed.

Examples:

>>> for ia in range(mol.natm):
...     zeta = gto.filatov_nuc_mod(mol.atom_charge(ia))
...     mol.set_nuc_mod(ia, zeta)

set_range_coulomb(omega)[source]¶

Switch on range-separated Coulomb operator for all 2e integrals

Args:: omega : double

= 0 : Regular electron repulsion integral

> 0 : Long-range operator erf(omega r12) / r12

< 0 : Short-range operator erfc(omega r12) /r12

set_range_coulomb_(omega)¶

Switch on range-separated Coulomb operator for all 2e integrals

Args:: omega : double

= 0 : Regular electron repulsion integral

> 0 : Long-range operator erf(omega r12) / r12

< 0 : Short-range operator erfc(omega r12) /r12

set_rinv_orig(coord)¶

Update origin for operator \(\frac{1}{|r-R_O|}\). Note the unit is Bohr

Examples:

>>> mol.set_rinv_origin(0)
>>> mol.set_rinv_origin((0,1,0))

set_rinv_orig_(coord)¶

Update origin for operator \(\frac{1}{|r-R_O|}\). Note the unit is Bohr

Examples:

>>> mol.set_rinv_origin(0)
>>> mol.set_rinv_origin((0,1,0))

set_rinv_origin(coord)[source]¶

Update origin for operator \(\frac{1}{|r-R_O|}\). Note the unit is Bohr

Examples:

>>> mol.set_rinv_origin(0)
>>> mol.set_rinv_origin((0,1,0))

set_rinv_origin_(coord)¶

Update origin for operator \(\frac{1}{|r-R_O|}\). Note the unit is Bohr

Examples:

>>> mol.set_rinv_origin(0)
>>> mol.set_rinv_origin((0,1,0))

set_rinv_zeta(zeta)[source]¶: Assume the charge distribution on the “rinv_origin”. zeta is the parameter to control the charge distribution: rho(r) = Norm * exp(-zeta * r^2). Be careful when call this function. It affects the behavior of int1e_rinv_* functions. Make sure to set it back to 0 after using it!

set_rinv_zeta_(zeta)¶: Assume the charge distribution on the “rinv_origin”. zeta is the parameter to control the charge distribution: rho(r) = Norm * exp(-zeta * r^2). Be careful when call this function. It affects the behavior of int1e_rinv_* functions. Make sure to set it back to 0 after using it!

sph2spinor_coeff()[source]¶

Transformation matrix that transforms real-spherical GTOs to spinor GTOs for all basis functions

Examples:

>>> mol = gto.M(atom='H 0 0 0; F 0 0 1', basis='ccpvtz')
>>> ca, cb = mol.sph2spinor_coeff()
>>> s0 = mol.intor('int1e_ovlp_spinor')
>>> s1 = ca.conj().T.dot(mol.intor('int1e_ovlp_sph')).dot(ca)
>>> s1+= cb.conj().T.dot(mol.intor('int1e_ovlp_sph')).dot(cb)
>>> print(abs(s1-s0).max())
>>> 6.66133814775e-16

sph_labels(fmt=True, base=0)¶

Labels for spherical GTO functions

Kwargs:: fmt : str or bool if fmt is boolean, it controls whether to format the labels and the default format is “%d%3s %s%-4s”. if fmt is string, the string will be used as the print format.
Returns:: List of [(atom-id, symbol-str, nl-str, str-of-real-spherical-notation] or formatted strings based on the argument “fmt”

Examples:

>>> mol = gto.M(atom='H 0 0 0; Cl 0 0 1', basis='sto-3g')
>>> gto.sph_labels(mol)
[(0, 'H', '1s', ''), (1, 'Cl', '1s', ''), (1, 'Cl', '2s', ''), (1, 'Cl', '3s', ''),
 (1, 'Cl', '2p', 'x'), (1, 'Cl', '2p', 'y'), (1, 'Cl', '2p', 'z'), (1, 'Cl', '3p', 'x'),
 (1, 'Cl', '3p', 'y'), (1, 'Cl', '3p', 'z')]

spheric_labels(fmt=True, base=0)¶

Labels for spherical GTO functions

Kwargs:: fmt : str or bool if fmt is boolean, it controls whether to format the labels and the default format is “%d%3s %s%-4s”. if fmt is string, the string will be used as the print format.
Returns:: List of [(atom-id, symbol-str, nl-str, str-of-real-spherical-notation] or formatted strings based on the argument “fmt”

Examples:

>>> mol = gto.M(atom='H 0 0 0; Cl 0 0 1', basis='sto-3g')
>>> gto.sph_labels(mol)
[(0, 'H', '1s', ''), (1, 'Cl', '1s', ''), (1, 'Cl', '2s', ''), (1, 'Cl', '3s', ''),
 (1, 'Cl', '2p', 'x'), (1, 'Cl', '2p', 'y'), (1, 'Cl', '2p', 'z'), (1, 'Cl', '3p', 'x'),
 (1, 'Cl', '3p', 'y'), (1, 'Cl', '3p', 'z')]

spin = 0¶

spinor_labels(fmt=True, base=0)¶: Labels of spinor GTO functions

symmetry = False¶

symmetry_subgroup = None¶

time_reversal_map()¶: The index to map the spinor functions and its time reversal counterpart. The returned indices have positive or negative values. For the i-th basis function, if the returned j = idx[i] < 0, it means \(T|i\rangle = -|j\rangle\), otherwise \(T|i\rangle = |j\rangle\)

tmap()¶: The index to map the spinor functions and its time reversal counterpart. The returned indices have positive or negative values. For the i-th basis function, if the returned j = idx[i] < 0, it means \(T|i\rangle = -|j\rangle\), otherwise \(T|i\rangle = |j\rangle\)

to_uncontracted_cartesian_basis()¶

Decontract the basis of a Mole or a Cell. Returns a Mole (Cell) object with uncontracted Cartesian basis and a list of coefficients that transform the uncontracted basis to the original basis. Each element in the coefficients list corresponds to one shell of the original Mole (Cell).

Examples:

>>> mol = gto.M(atom='Ne', basis='ccpvdz')
>>> pmol, ctr_coeff = mol.to_uncontracted_cartesian_basis()
>>> c = scipy.linalg.block_diag(*ctr_coeff)
>>> s = reduce(numpy.dot, (c.T, pmol.intor('int1e_ovlp'), c))
>>> abs(s-mol.intor('int1e_ovlp')).max()
0.0

tot_electrons()¶

Total number of electrons for the given molecule

Returns:: electron number in integer

Examples:

>>> mol = gto.M(atom='H 0 1 0; C 0 0 1', charge=1)
>>> mol.tot_electrons()
6

unit = 'angstrom'¶

classmethod unpack(moldic)[source]¶: Unpack a dict which is packed by pack(), to generate the input arguments for Mole object.

unpack_(moldic)[source]¶: Unpack a dict which is packed by pack(), to generate the input arguments for Mole object.

update(chkfile)[source]¶

update_from_chk(chkfile)[source]¶

verbose = 3¶

with_common_orig(coord)¶

Return a temporary mol context which has the rquired common origin. The required common origin has no effects out of the temporary context. See also mol.set_common_origin()

Examples:

>>> with mol.with_common_origin((1,0,0)):
...     mol.intor('int1e_r', comp=3)

with_common_origin(coord)[source]¶

Return a temporary mol context which has the rquired common origin. The required common origin has no effects out of the temporary context. See also mol.set_common_origin()

Examples:

>>> with mol.with_common_origin((1,0,0)):
...     mol.intor('int1e_r', comp=3)

with_integral_screen(threshold)[source]¶: Return a temporary mol context which has the required integral screen threshold

with_long_range_coulomb(omega)[source]¶: Return a temporary mol context for long-range part of range-separated Coulomb operator.

with_range_coulomb(omega)[source]¶

Return a temporary mol context which sets the required parameter omega for range-separated Coulomb operator. If omega = None, return the context for regular Coulomb integrals. See also mol.set_range_coulomb()

Examples:

>>> with mol.with_range_coulomb(omega=1.5):
...     mol.intor('int2e')

with_rinv_as_nucleus(atm_id)¶

Return a temporary mol context in which the rinv operator (1/r) is treated like the Coulomb potential of a Gaussian charge distribution rho(r) = Norm * exp(-zeta * r^2) at the place of the input atm_id.

Examples:

>>> with mol.with_rinv_at_nucleus(3):
...     mol.intor('int1e_rinv')

with_rinv_at_nucleus(atm_id)[source]¶

Return a temporary mol context in which the rinv operator (1/r) is treated like the Coulomb potential of a Gaussian charge distribution rho(r) = Norm * exp(-zeta * r^2) at the place of the input atm_id.

Examples:

>>> with mol.with_rinv_at_nucleus(3):
...     mol.intor('int1e_rinv')

with_rinv_orig(coord)¶

Return a temporary mol context which has the rquired origin of 1/r operator. The required origin has no effects out of the temporary context. See also mol.set_rinv_origin()

Examples:

>>> with mol.with_rinv_origin((1,0,0)):
...     mol.intor('int1e_rinv')

with_rinv_origin(coord)[source]¶

Return a temporary mol context which has the rquired origin of 1/r operator. The required origin has no effects out of the temporary context. See also mol.set_rinv_origin()

Examples:

>>> with mol.with_rinv_origin((1,0,0)):
...     mol.intor('int1e_rinv')

with_rinv_zeta(zeta)[source]¶

Return a temporary mol context which has the rquired Gaussian charge distribution placed at “rinv_origin”: rho(r) = Norm * exp(-zeta * r^2). See also mol.set_rinv_zeta()

Examples:

>>> with mol.with_rinv_zeta(zeta=1.5), mol.with_rinv_origin((1.,0,0)):
...     mol.intor('int1e_rinv')

with_short_range_coulomb(omega)[source]¶: Return a temporary mol context for short-range part of range-separated Coulomb operator.

pyscf.gto.mole.ao_labels(mol, fmt=True, base=0)[source]¶

Labels of AO basis functions

Kwargs:

fmtstr or bool: if fmt is boolean, it controls whether to format the labels and the default format is “%d%3s %s%-4s”. if fmt is string, the string will be used as the print format.

Returns:

List of [(atom-id, symbol-str, nl-str, str-of-AO-notation)] or formatted strings based on the argument “fmt”

pyscf.gto.mole.ao_loc_2c(mol)[source]¶

Offset of every shell in the spinor basis function spectrum

Returns:: list, each entry is the corresponding start id of spinor function

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.ao_loc_2c(mol)
[0, 2, 4, 6, 12, 18, 20, 22, 24, 30, 36]

pyscf.gto.mole.ao_loc_nr(mol, cart=None)[source]¶

Offset of every shell in the spherical basis function spectrum

Returns:: list, each entry is the corresponding start basis function id

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.ao_loc_nr(mol)
[0, 1, 2, 3, 6, 9, 10, 11, 12, 15, 18]

pyscf.gto.mole.ao_rotation_matrix(mol, orientation)[source]¶

Matrix u to rotate AO basis to a new orientation.

atom_new_coords = mol.atom_coords().dot(orientation.T) new_AO = u * mol.AO new_orbitals_coef = u.dot(orbitals_coef)

pyscf.gto.mole.aoslice_by_atom(mol, ao_loc=None)[source]¶: AO offsets for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

pyscf.gto.mole.atom_mass_list(mol, isotope_avg=False)[source]¶

A list of mass for all atoms in the molecule

Kwargs:

isotope_avgboolean: Whether to use the isotope average mass as the atomic mass

pyscf.gto.mole.atom_types(atoms, basis=None, magmom=None)[source]¶: symmetry inequivalent atoms

pyscf.gto.mole.cart2j_kappa(kappa, l=None, normalized=None)¶

Cartesian to spinor transformation matrix for kappa

Kwargs:

normalized :: How the Cartesian GTOs are normalized. ‘sp’ means the s and p functions are normalized (this is the convention used by libcint library).

pyscf.gto.mole.cart2j_l(l, normalized=None)¶

Cartesian to spinor transformation matrix for angular moment l

Kwargs:

normalized :: How the Cartesian GTOs are normalized. ‘sp’ means the s and p functions are normalized (this is the convention used by libcint library).

pyscf.gto.mole.cart2sph(l, c_tensor=None, normalized=None)[source]¶

Cartesian to real spherical transformation matrix

Kwargs:

normalized :: How the Cartesian GTOs are normalized. ‘sp’ means the s and p functions are normalized (this is the convention used by libcint library).

pyscf.gto.mole.cart2spinor_kappa(kappa, l=None, normalized=None)[source]¶

Cartesian to spinor transformation matrix for kappa

Kwargs:

normalized :: How the Cartesian GTOs are normalized. ‘sp’ means the s and p functions are normalized (this is the convention used by libcint library).

pyscf.gto.mole.cart2spinor_l(l, normalized=None)[source]¶

Cartesian to spinor transformation matrix for angular moment l

Kwargs:

normalized :: How the Cartesian GTOs are normalized. ‘sp’ means the s and p functions are normalized (this is the convention used by libcint library).

pyscf.gto.mole.cart2zmat(coord)[source]¶

>>> c = numpy.array((
(0.000000000000,  1.889726124565,  0.000000000000),
(0.000000000000,  0.000000000000, -1.889726124565),
(1.889726124565, -1.889726124565,  0.000000000000),
(1.889726124565,  0.000000000000,  1.133835674739)))
>>> print(cart2zmat(c))
1
1 2.67247631453057
1 4.22555607338457 2 50.7684795164077
1 2.90305235726773 2 79.3904651036893 3 6.20854462618583

pyscf.gto.mole.cart_labels(mol, fmt=True, base=0)[source]¶

Labels of Cartesian GTO functions

Kwargs:: fmt : str or bool if fmt is boolean, it controls whether to format the labels and the default format is “%d%3s %s%-4s”. if fmt is string, the string will be used as the print format.
Returns:: List of [(atom-id, symbol-str, nl-str, str-of-xyz-notation)] or formatted strings based on the argument “fmt”

pyscf.gto.mole.chiral_mol(mol1, mol2=None)[source]¶: Detect whether the given molelcule is chiral molecule or two molecules are chiral isomers.

pyscf.gto.mole.classical_coulomb_energy(mol, charges=None, coords=None)[source]¶

Compute nuclear repulsion energy (AU) or static Coulomb energy

Returns: float

pyscf.gto.mole.classify_ecp_pseudo(mol, ecp, pp)[source]¶: Check whether ecp keywords are presented in pp and whether pp keywords are presented in ecp. The return (ecp, pp) should have only the ecp keywords and pp keywords in each dict. The “misplaced” ecp/pp keywords have the lowest priority. E.g., if an atom is defined in ecp, the same ecp atom found in pp does NOT replace the definition in ecp, and vise versa.

pyscf.gto.mole.conc_env(atm1, bas1, env1, atm2, bas2, env2)[source]¶

Concatenate two Mole’s integral parameters. This function can be used to construct the environment for cross integrals like

\[\langle \mu | \nu \rangle, \mu \in mol1, \nu \in mol2\]

Returns:: Concatenated atm, bas, env
Examples:: Compute the overlap between H2 molecule and O atom

>>> mol1 = gto.M(atom='H 0 1 0; H 0 0 1', basis='sto3g')
>>> mol2 = gto.M(atom='O 0 0 0', basis='sto3g')
>>> atm3, bas3, env3 = gto.conc_env(mol1._atm, mol1._bas, mol1._env,
...                                 mol2._atm, mol2._bas, mol2._env)
>>> gto.moleintor.getints('int1e_ovlp_sph', atm3, bas3, env3, range(2), range(2,5))
[[ 0.04875181  0.44714688  0.          0.37820346  0.        ]
 [ 0.04875181  0.44714688  0.          0.          0.37820346]]

pyscf.gto.mole.conc_mol(mol1, mol2)[source]¶: Concatenate two Mole objects.

pyscf.gto.mole.condense_to_shell(mol, mat, compressor='max')[source]¶

The given matrix is first partitioned to blocks, based on AO shell as delimiter. Then call compressor function to abstract each block.

Args:

compressor: string or function: if compressor is a string, its value can be sum, max, min, abssum, absmax, absmin, norm

pyscf.gto.mole.copy(mol, deep=True)[source]¶

Deepcopy of the given Mole object

Some attributes are shared between the original and copied objects. Deepcopy is utilized here to ensure that operations on the copied object do not affect the original object.

pyscf.gto.mole.decontract_basis(mol, atoms=None, to_cart=False)[source]¶

Decontract the basis of a Mole or a Cell. Returns a Mole (Cell) object with the uncontracted basis environment and a list of coefficients that transform the uncontracted basis to the original basis. Each element in the coefficients list corresponds to one shell of the original Mole (Cell).

Kwargs:

atoms: list or str: Atoms on which the basis to be decontracted. By default, all basis are decontracted
to_cart: bool: Decontract basis and transfer to Cartesian basis

Examples:

>>> mol = gto.M(atom='Ne', basis='ccpvdz')
>>> pmol, ctr_coeff = mol.decontract_basis()
>>> c = scipy.linalg.block_diag(*ctr_coeff)
>>> s = reduce(numpy.dot, (c.T, pmol.intor('int1e_ovlp'), c))
>>> abs(s-mol.intor('int1e_ovlp')).max()
0.0

pyscf.gto.mole.dumps(mol)[source]¶: Serialize Mole object to a JSON formatted str.

pyscf.gto.mole.dyall_nuc_mod(nuc_charge, nucprop={})[source]¶

Generate the nuclear charge distribution parameter zeta rho(r) = nuc_charge * Norm * exp(-zeta * r^2)

Ref. L. Visscher and K. Dyall, At. Data Nucl. Data Tables, 67, 207 (1997)

pyscf.gto.mole.energy_nuc(mol, charges=None, coords=None)¶

Compute nuclear repulsion energy (AU) or static Coulomb energy

Returns: float

pyscf.gto.mole.etbs(etbs)¶

Generate even tempered basis. See also expand_etb()

Args:: etbs = [(l, n, alpha, beta), (l, n, alpha, beta),…]
Returns:: Formatted basis

Examples:

>>> gto.expand_etbs([(0, 2, 1.5, 2.), (1, 2, 1, 2.)])
[[0, [6.0, 1]], [0, [3.0, 1]], [1, [1., 1]], [1, [2., 1]]]

pyscf.gto.mole.expand_etb(l, n, alpha, beta)[source]¶

Generate the exponents of even tempered basis for Mole.basis. .. math:

e = e^{-\alpha * \beta^{i-1}} for i = 1 .. n

Args:

lint: Angular momentum
nint: Number of GTOs

Returns:

Formatted basis

Examples:

>>> gto.expand_etb(1, 3, 1.5, 2)
[[1, [6.0, 1]], [1, [3.0, 1]], [1, [1.5, 1]]]

pyscf.gto.mole.expand_etbs(etbs)[source]¶

Generate even tempered basis. See also expand_etb()

Args:: etbs = [(l, n, alpha, beta), (l, n, alpha, beta),…]
Returns:: Formatted basis

Examples:

>>> gto.expand_etbs([(0, 2, 1.5, 2.), (1, 2, 1, 2.)])
[[0, [6.0, 1]], [0, [3.0, 1]], [1, [1., 1]], [1, [2., 1]]]

pyscf.gto.mole.fakemol_for_charges(coords, expnt=1e+16)[source]¶: Construct a fake Mole object that holds the charges on the given coordinates (coords). The shape of the charge can be a normal distribution with the Gaussian exponent (expnt).

pyscf.gto.mole.filatov_nuc_mod(nuc_charge, nucprop={})[source]¶

Generate the nuclear charge distribution parameter zeta rho(r) = nuc_charge * Norm * exp(-zeta * r^2)

Ref. M. Filatov and D. Cremer, Theor. Chem. Acc. 108, 168 (2002)

Filatov and D. Cremer, Chem. Phys. Lett. 351, 259 (2002)

pyscf.gto.mole.format_atom(atoms, origin=0, axes=None, unit='angstrom')[source]¶

Convert the input Mole.atom to the internal data format. Including, changing the nuclear charge to atom symbol, converting the coordinates to AU, rotate and shift the molecule. If the atom is a string, it takes “;” and “n” for the mark to separate atoms; “,” and arbitrary length of blank space to spearate the individual terms for an atom. Blank line will be ignored.

Args:

atomslist or str: the same to Mole.atom

Kwargs:

originndarray: new axis origin.
axesndarray: (new_x, new_y, new_z), new coordinates
unitstr or number: If unit is one of strings (B, b, Bohr, bohr, AU, au), the coordinates of the input atoms are the atomic unit; If unit is one of strings (A, a, Angstrom, angstrom, Ang, ang), the coordinates are in the unit of angstrom; If a number is given, the number are considered as the Bohr value (in angstrom), which should be around 0.53. Set unit=1 if wishing to preserve the unit of the coordinates.

Returns:

“atoms” in the internal format. The internal format is: atom = [[atom1, (x, y, z)],

[atom2, (x, y, z)],

…

[atomN, (x, y, z)]]

Examples:

>>> gto.format_atom('9,0,0,0; h@1 0 0 1', origin=(1,1,1))
[['F', [-1.0, -1.0, -1.0]], ['H@1', [-1.0, -1.0, 0.0]]]
>>> gto.format_atom(['9,0,0,0', (1, (0, 0, 1))], origin=(1,1,1))
[['F', [-1.0, -1.0, -1.0]], ['H', [-1, -1, 0]]]

pyscf.gto.mole.format_basis(basis_tab)[source]¶

Convert the input Mole.basis to the internal data format.

``{ atom: [(l, ((-exp, c_1, c_2, ..),

(-exp, c_1, c_2, ..))),

(l, ((-exp, c_1, c_2, ..),: (-exp, c_1, c_2, ..)))], … }``

Args:

basis_tabdict: Similar to Mole.basis, it cannot be a str

Returns:

Formatted basis

Examples:

>>> gto.format_basis({'H':'sto-3g', 'H^2': '3-21g'})
{'H': [[0,
    [3.4252509099999999, 0.15432897000000001],
    [0.62391373000000006, 0.53532813999999995],
    [0.16885539999999999, 0.44463454000000002]]],
 'H^2': [[0,
    [5.4471780000000001, 0.15628500000000001],
    [0.82454700000000003, 0.90469100000000002]],
    [0, [0.18319199999999999, 1.0]]]}

>>> gto.format_basis({'H':'gth-szv'})
{'H': [[0,
    (8.3744350009, -0.0283380461),
    (1.8058681460, -0.1333810052),
    (0.4852528328, -0.3995676063),
    (0.1658236932, -0.5531027541)]]}

pyscf.gto.mole.format_ecp(ecp_tab)[source]¶

Convert the input ecp (dict) to the internal data format:

{ atom: (nelec,  # core electrons

((l, # l=-1 for UL, l>=0 for Ul to indicate |l><l|

(((exp_1, c_1), # for r^0

(exp_2, c_2), …),

((exp_1, c_1), # for r^1
(exp_2, c_2), …),

((exp_1, c_1), # for r^2
…))))),

…}

pyscf.gto.mole.format_pseudo(pseudo_tab)[source]¶

Convert the input pseudo (dict) to the internal data format:

{ atom: ( (nelec_s, nele_p, nelec_d, ...),
         rloc, nexp, (cexp_1, cexp_2, ..., cexp_nexp),
         nproj_types,
         (r1, nproj1, ( (hproj1[1,1], hproj1[1,2], ..., hproj1[1,nproj1]),
                        (hproj1[2,1], hproj1[2,2], ..., hproj1[2,nproj1]),
                        ...
                        (hproj1[nproj1,1], hproj1[nproj1,2], ...        ) )),
         (r2, nproj2, ( (hproj2[1,1], hproj2[1,2], ..., hproj2[1,nproj1]),
         ... ) )
         )
 ... }

Args:

pseudo_tabdict: Similar to pseudo (a dict), it cannot be a str

Returns:

Formatted pseudo

Examples:

>>> pbc.format_pseudo({'H':'gth-blyp', 'He': 'gth-pade'})
{'H': [[1],
    0.2, 2, [-4.19596147, 0.73049821], 0],
 'He': [[2],
    0.2, 2, [-9.1120234, 1.69836797], 0]}

pyscf.gto.mole.from_zmatrix(atomstr)[source]¶

>>> a = """H
H 1 2.67247631453057
H 1 4.22555607338457 2 50.7684795164077
H 1 2.90305235726773 2 79.3904651036893 3 6.20854462618583"""
>>> for x in zmat2cart(a): print(x)
['H', array([ 0.,  0.,  0.])]
['H', array([ 2.67247631,  0.        ,  0.        ])]
['H', array([ 2.67247631,  0.        ,  3.27310166])]
['H', array([ 0.53449526,  0.30859098,  2.83668811])]

pyscf.gto.mole.fromfile(filename, format=None)[source]¶

Read molecular geometry from a file (in testing)

Supported formats:: raw: Each line is <symbol> <x> <y> <z>

xyz: XYZ cartesian coordinates format

zmat: Z-matrix format

pyscf.gto.mole.fromstring(string, format='xyz')[source]¶

Convert the string of the specified format to internal format (in testing)

Supported formats:: raw: Each line is <symbol> <x> <y> <z>

xyz: XYZ cartesian coordinates format

zmat: Z-matrix format

pyscf.gto.mole.gaussian_int(n, alpha)[source]¶: int_0^inf x^n exp(-alpha x^2) dx

pyscf.gto.mole.get_overlap_cond(mol, shls_slice=None)[source]¶

Overlap magnitudes measured by -log(overlap) between two shells

Args:: mol : an instance of Mole
Returns:: 2D mask array of shape (nbas,nbas)

pyscf.gto.mole.gto_norm(l, expnt)[source]¶

Normalized factor for GTO radial part \(g=r^l e^{-\alpha r^2}\)

\[\frac{1}{\sqrt{\int g^2 r^2 dr}} = \sqrt{\frac{2^{2l+3} (l+1)! (2a)^{l+1.5}}{(2l+2)!\sqrt{\pi}}}\]

Ref: H. B. Schlegel and M. J. Frisch, Int. J. Quant. Chem., 54(1995), 83-87.

Args:

l (int):: angular momentum
expnt :: exponent \(\alpha\)

Returns:

normalization factor

Examples:

>>> print(gto_norm(0, 1))
2.5264751109842591

pyscf.gto.mole.inertia_moment(mol, mass=None, coords=None)[source]¶

pyscf.gto.mole.inter_distance(mol, coords=None)[source]¶: Inter-particle distance array

pyscf.gto.mole.intor_cross(intor, mol1, mol2, comp=None, grids=None)[source]¶

1-electron integrals from two molecules like

\[\langle \mu | intor | \nu \rangle, \mu \in mol1, \nu \in mol2\]

Args:

intorstr: Name of the 1-electron integral, such as int1e_ovlp_sph (spherical overlap), int1e_nuc_cart (cartesian nuclear attraction), int1e_ipovlp_spinor (spinor overlap gradients), etc. Ref to getints() for the full list of available 1-electron integral names
mol1, mol2:: Mole objects

Kwargs:

compint: Components of the integrals, e.g. int1e_ipovlp_sph has 3 components
gridsndarray: Coordinates of grids for the int1e_grids integrals

Returns:

ndarray of 1-electron integrals, can be either 2-dim or 3-dim, depending on comp

Examples:

Compute the overlap between H2 molecule and O atom

>>> mol1 = gto.M(atom='H 0 1 0; H 0 0 1', basis='sto3g')
>>> mol2 = gto.M(atom='O 0 0 0', basis='sto3g')
>>> gto.intor_cross('int1e_ovlp_sph', mol1, mol2)
[[ 0.04875181  0.44714688  0.          0.37820346  0.        ]
 [ 0.04875181  0.44714688  0.          0.          0.37820346]]

pyscf.gto.mole.is_au(unit)[source]¶: Return whether the unit is recognized as A.U. or not

pyscf.gto.mole.is_same_mol(mol1, mol2, tol=1e-05, cmp_basis=True, ignore_chiral=False)¶

Compare the two molecules whether they have the same structure.

Kwargs:

tolfloat: In Bohr
cmp_basisbool: Whether to compare basis functions for the two molecules

pyscf.gto.mole.len_cart(l)[source]¶: The number of Cartesian function associated with given angular momentum.

pyscf.gto.mole.len_spinor(l, kappa)[source]¶: The number of spinor associated with given angular momentum and kappa. If kappa is 0, return 4l+2

pyscf.gto.mole.loads(molstr)[source]¶: Deserialize a str containing a JSON document to a Mole object.

pyscf.gto.mole.make_atm_env(atom, ptr=0, nuclear_model=1, nucprop={})[source]¶: Convert the internal format Mole._atom to the format required by libcint integrals

pyscf.gto.mole.make_bas_env(basis_add, atom_id=0, ptr=0)[source]¶: Convert Mole.basis to the argument bas for libcint integrals

pyscf.gto.mole.make_ecp_env(mol, _atm, ecp, pre_env=[])[source]¶: Generate the input arguments _ecpbas for ECP integrals

pyscf.gto.mole.make_env(atoms, basis, pre_env=[], nucmod={}, nucprop={})[source]¶: Generate the input arguments for libcint library based on internal format Mole._atom and Mole._basis

pyscf.gto.mole.nao_2c(mol)[source]¶: Total number of contracted spinor GTOs for the given Mole object

pyscf.gto.mole.nao_2c_range(mol, bas_id0, bas_id1)[source]¶

Lower and upper boundary of contracted spinor basis functions associated with the given shell range

Args:

mol :: Mole object
bas_id0int: start shell id, 0-based
bas_id1int: stop shell id, 0-based

Returns:

tuple of start basis function id and the stop function id

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.nao_2c_range(mol, 2, 4)
(4, 12)

pyscf.gto.mole.nao_cart(mol)[source]¶: Total number of contracted cartesian GTOs for the given Mole object

pyscf.gto.mole.nao_nr(mol, cart=None)[source]¶: Total number of contracted GTOs for the given Mole object

pyscf.gto.mole.nao_nr_range(mol, bas_id0, bas_id1)[source]¶

Lower and upper boundary of contracted spherical basis functions associated with the given shell range

Args:

mol :: Mole object
bas_id0int: start shell id
bas_id1int: stop shell id

Returns:

tuple of start basis function id and the stop function id

Examples:

>>> mol = gto.M(atom='O 0 0 0; C 0 0 1', basis='6-31g')
>>> gto.nao_nr_range(mol, 2, 4)
(2, 6)

pyscf.gto.mole.npgto_nr(mol, cart=None)[source]¶: Total number of primitive spherical GTOs for the given Mole object

pyscf.gto.mole.offset_2c_by_atom(mol)[source]¶: 2-component AO offset for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

pyscf.gto.mole.offset_nr_by_atom(mol, ao_loc=None)¶: AO offsets for each atom. Return a list, each item of the list gives (start-shell-id, stop-shell-id, start-AO-id, stop-AO-id)

pyscf.gto.mole.pack(mol)[source]¶

Pack the input args of Mole to a dict.

Note this function only pack the input arguments (not the entire Mole class). Modifications to mol._atm, mol._bas, mol._env are not tracked. Use dumps() to serialize the entire Mole object.

pyscf.gto.mole.same_basis_set(mol1, mol2)[source]¶: Check whether two molecules use the same basis sets. The two molecules can have different geometry.

pyscf.gto.mole.same_mol(mol1, mol2, tol=1e-05, cmp_basis=True, ignore_chiral=False)[source]¶

Compare the two molecules whether they have the same structure.

Kwargs:

tolfloat: In Bohr
cmp_basisbool: Whether to compare basis functions for the two molecules

pyscf.gto.mole.search_ao_label(mol, label)[source]¶

Find the index of the AO basis function based on the given ao_label

Args:

ao_labelstring or a list of strings: The regular expression pattern to match the orbital labels returned by mol.ao_labels()

Returns:

A list of index for the AOs that matches the given ao_label RE pattern

Examples:

>>> mol = gto.M(atom='H 0 0 0; Cl 0 0 1', basis='ccpvtz')
>>> mol.search_ao_label('Cl.*p')
[19 20 21 22 23 24 25 26 27 28 29 30]
>>> mol.search_ao_label('Cl 2p')
[19 20 21]
>>> mol.search_ao_label(['Cl.*d', 'Cl 4p'])
[25 26 27 31 32 33 34 35 36 37 38 39 40]

pyscf.gto.mole.search_ao_nr(mol, atm_id, l, m, atmshell)[source]¶

Search the first basis function id (not the shell id) which matches the given atom-id, angular momentum magnetic angular momentum, principal shell.

Args:

atm_idint: atom id, 0-based
lint: angular momentum
mint: magnetic angular momentum
atmshellint: principal quantum number

Returns:

basis function id, 0-based. If not found, return None

Examples:

>>> mol = gto.M(atom='H 0 0 0; Cl 0 0 1', basis='sto-3g')
>>> mol.search_ao_nr(1, 1, -1, 3) # Cl 3px
7

pyscf.gto.mole.search_ao_r(mol, atm_id, l, j, m, atmshell)[source]¶

pyscf.gto.mole.search_shell_id(mol, atm_id, l)[source]¶

Search the first basis/shell id (not the basis function id) which matches the given atom-id and angular momentum

Args:

atm_idint: atom id, 0-based
lint: angular momentum

Returns:

basis id, 0-based. If not found, return None

Examples:

>>> mol = gto.M(atom='H 0 0 0; Cl 0 0 1', basis='sto-3g')
>>> mol.search_shell_id(1, 1) # Cl p shell
4
>>> mol.search_shell_id(1, 2) # Cl d shell
None

pyscf.gto.mole.sph2spinor_kappa(kappa, l=None)[source]¶: Real spherical to spinor transformation matrix for kappa

pyscf.gto.mole.sph2spinor_l(l)[source]¶: Real spherical to spinor transformation matrix for angular moment l

pyscf.gto.mole.sph_labels(mol, fmt=True, base=0)[source]¶

Labels for spherical GTO functions

Kwargs:: fmt : str or bool if fmt is boolean, it controls whether to format the labels and the default format is “%d%3s %s%-4s”. if fmt is string, the string will be used as the print format.
Returns:: List of [(atom-id, symbol-str, nl-str, str-of-real-spherical-notation] or formatted strings based on the argument “fmt”

Examples:

>>> mol = gto.M(atom='H 0 0 0; Cl 0 0 1', basis='sto-3g')
>>> gto.sph_labels(mol)
[(0, 'H', '1s', ''), (1, 'Cl', '1s', ''), (1, 'Cl', '2s', ''), (1, 'Cl', '3s', ''),
 (1, 'Cl', '2p', 'x'), (1, 'Cl', '2p', 'y'), (1, 'Cl', '2p', 'z'), (1, 'Cl', '3p', 'x'),
 (1, 'Cl', '3p', 'y'), (1, 'Cl', '3p', 'z')]

pyscf.gto.mole.spheric_labels(mol, fmt=True, base=0)¶

Labels for spherical GTO functions

Kwargs:: fmt : str or bool if fmt is boolean, it controls whether to format the labels and the default format is “%d%3s %s%-4s”. if fmt is string, the string will be used as the print format.
Returns:: List of [(atom-id, symbol-str, nl-str, str-of-real-spherical-notation] or formatted strings based on the argument “fmt”

Examples:

>>> mol = gto.M(atom='H 0 0 0; Cl 0 0 1', basis='sto-3g')
>>> gto.sph_labels(mol)
[(0, 'H', '1s', ''), (1, 'Cl', '1s', ''), (1, 'Cl', '2s', ''), (1, 'Cl', '3s', ''),
 (1, 'Cl', '2p', 'x'), (1, 'Cl', '2p', 'y'), (1, 'Cl', '2p', 'z'), (1, 'Cl', '3p', 'x'),
 (1, 'Cl', '3p', 'y'), (1, 'Cl', '3p', 'z')]

pyscf.gto.mole.spherical_labels(mol, fmt=True, base=0)¶

Labels for spherical GTO functions

Kwargs:: fmt : str or bool if fmt is boolean, it controls whether to format the labels and the default format is “%d%3s %s%-4s”. if fmt is string, the string will be used as the print format.
Returns:: List of [(atom-id, symbol-str, nl-str, str-of-real-spherical-notation] or formatted strings based on the argument “fmt”

Examples:

>>> mol = gto.M(atom='H 0 0 0; Cl 0 0 1', basis='sto-3g')
>>> gto.sph_labels(mol)
[(0, 'H', '1s', ''), (1, 'Cl', '1s', ''), (1, 'Cl', '2s', ''), (1, 'Cl', '3s', ''),
 (1, 'Cl', '2p', 'x'), (1, 'Cl', '2p', 'y'), (1, 'Cl', '2p', 'z'), (1, 'Cl', '3p', 'x'),
 (1, 'Cl', '3p', 'y'), (1, 'Cl', '3p', 'z')]

pyscf.gto.mole.spinor_labels(mol, fmt=True, base=0)[source]¶: Labels of spinor GTO functions

pyscf.gto.mole.time_reversal_map(mol)[source]¶: The index to map the spinor functions and its time reversal counterpart. The returned indices have positive or negative values. For the i-th basis function, if the returned j = idx[i] < 0, it means \(T|i\rangle = -|j\rangle\), otherwise \(T|i\rangle = |j\rangle\)

pyscf.gto.mole.to_uncontracted_cartesian_basis(mol)[source]¶

Decontract the basis of a Mole or a Cell. Returns a Mole (Cell) object with uncontracted Cartesian basis and a list of coefficients that transform the uncontracted basis to the original basis. Each element in the coefficients list corresponds to one shell of the original Mole (Cell).

Examples:

>>> mol = gto.M(atom='Ne', basis='ccpvdz')
>>> pmol, ctr_coeff = mol.to_uncontracted_cartesian_basis()
>>> c = scipy.linalg.block_diag(*ctr_coeff)
>>> s = reduce(numpy.dot, (c.T, pmol.intor('int1e_ovlp'), c))
>>> abs(s-mol.intor('int1e_ovlp')).max()
0.0

pyscf.gto.mole.tofile(mol, filename, format=None)[source]¶

Write molecular geometry to a file of the required format.

Supported output formats:: raw: Each line is <symbol> <x> <y> <z>

xyz: XYZ cartesian coordinates format

zmat: Z-matrix format

pyscf.gto.mole.tostring(mol, format='raw')[source]¶

Convert molecular geometry to a string of the required format.

Supported output formats:: raw: Each line is <symbol> <x> <y> <z>

xyz: XYZ cartesian coordinates format

zmat: Z-matrix format

pyscf.gto.mole.tot_electrons(mol)[source]¶

Total number of electrons for the given molecule

Returns:: electron number in integer

Examples:

>>> mol = gto.M(atom='H 0 1 0; C 0 0 1', charge=1)
>>> mol.tot_electrons()
6

pyscf.gto.mole.uncontract(_basis)¶

Uncontract internal format _basis

Examples:

>>> gto.uncontract(gto.load('sto3g', 'He'))
[[0, [6.36242139, 1]], [0, [1.158923, 1]], [0, [0.31364979, 1]]]

pyscf.gto.mole.uncontracted_basis(_basis)[source]¶

Uncontract internal format _basis

Examples:

>>> gto.uncontract(gto.load('sto3g', 'He'))
[[0, [6.36242139, 1]], [0, [1.158923, 1]], [0, [0.31364979, 1]]]

pyscf.gto.mole.unpack(moldic)[source]¶: Unpack a dict which is packed by pack(), to generate the input arguments for Mole object.

pyscf.gto.mole.zmat(atomstr)¶

>>> a = """H
H 1 2.67247631453057
H 1 4.22555607338457 2 50.7684795164077
H 1 2.90305235726773 2 79.3904651036893 3 6.20854462618583"""
>>> for x in zmat2cart(a): print(x)
['H', array([ 0.,  0.,  0.])]
['H', array([ 2.67247631,  0.        ,  0.        ])]
['H', array([ 2.67247631,  0.        ,  3.27310166])]
['H', array([ 0.53449526,  0.30859098,  2.83668811])]

pyscf.gto.mole.zmat2cart(atomstr)¶

>>> a = """H
H 1 2.67247631453057
H 1 4.22555607338457 2 50.7684795164077
H 1 2.90305235726773 2 79.3904651036893 3 6.20854462618583"""
>>> for x in zmat2cart(a): print(x)
['H', array([ 0.,  0.,  0.])]
['H', array([ 2.67247631,  0.        ,  0.        ])]
['H', array([ 2.67247631,  0.        ,  3.27310166])]
['H', array([ 0.53449526,  0.30859098,  2.83668811])]

pyscf.gto.moleintor module¶

A low level interface to libcint library. It’s recommended to use the Mole.intor method to drive the integral evaluation functions.

pyscf.gto.moleintor.ascint3(intor_name)[source]¶: convert cint2 function name to cint3 function name

pyscf.gto.moleintor.getints(intor_name, atm, bas, env, shls_slice=None, comp=None, hermi=0, aosym='s1', ao_loc=None, cintopt=None, out=None)[source]¶

1e and 2e integral generator.

Args:

intor_name : str

Function

Expression

“int1e_ovlp”

( | )

“int1e_nuc”

( | nuc | )

“int1e_kin”

(.5 | p dot p)

“int1e_ia01p”

(#C(0 1) | nabla-rinv | cross p)

“int1e_giao_irjxp”

(#C(0 1) | r cross p)

“int1e_cg_irxp”

(#C(0 1) | rc cross p)

“int1e_giao_a11part”

(-.5 | nabla-rinv | r)

“int1e_cg_a11part”

(-.5 | nabla-rinv | rc)

“int1e_a01gp”

(g | nabla-rinv cross p |)

“int1e_igkin”

(#C(0 .5) g | p dot p)

“int1e_igovlp”

(#C(0 1) g |)

“int1e_ignuc”

(#C(0 1) g | nuc |)

“int1e_z”

( | zc | )

“int1e_zz”

( | zc zc | )

“int1e_r”

( | rc | )

“int1e_r2”

( | rc dot rc | )

“int1e_rr”

( | rc rc | )

“int1e_rrr”

( | rc rc rc | )

“int1e_rrrr”

( | rc rc rc rc | )

“int1e_pnucp”

(p* | nuc dot p | )

“int1e_prinvxp”

(p* | rinv cross p | )

“int1e_ipovlp”

(nabla |)

“int1e_ipkin”

(.5 nabla | p dot p)

“int1e_ipnuc”

(nabla | nuc |)

“int1e_iprinv”

(nabla | rinv |)

“int1e_rinv”

(| rinv |)

“int1e_pnucxp”

(p* | nuc cross p | )

“int1e_irp”

( | rc nabla | )

“int1e_irrp”

( | rc rc nabla | )

“int1e_irpr”

( | rc nabla rc | )

“int1e_ggovlp”

( | g g | )

“int1e_ggkin”

(.5 | g g p dot p | )

“int1e_ggnuc”

( | g g nuc | )

“int1e_grjxp”

( | g r cross p | )

“ECPscalar”

AREP ECP integrals, similar to int1e_nuc

“ECPscalar_ipnuc”

(nabla i | ECP | ), similar to int1e_ipnuc

“ECPscalar_iprinv”

similar to int1e_iprinv for a specific atom

“ECPscalar_ignuc”

similar to int1e_ignuc

“ECPscalar_iprinvip”

similar to int1e_iprinvip

“ECPso”

< | Spin-orbit ECP | >

“int1e_ovlp_spinor”

( | )

“int1e_nuc_spinor”

( | nuc |)

“int1e_srsr_spinor”

(sigma dot r | sigma dot r)

“int1e_sr_spinor”

(sigma dot r |)

“int1e_srsp_spinor”

(sigma dot r | sigma dot p)

“int1e_spsp_spinor”

(sigma dot p | sigma dot p)

“int1e_sp_spinor”

(sigma dot p |)

“int1e_spnucsp_spinor”

(sigma dot p | nuc | sigma dot p)

“int1e_srnucsr_spinor”

(sigma dot r | nuc | sigma dot r)

“int1e_govlp_spinor”

(g |)

“int1e_gnuc_spinor”

(g | nuc |)

“int1e_cg_sa10sa01_spinor”

(.5 sigma cross rc | sigma cross nabla-rinv |)

“int1e_cg_sa10sp_spinor”

(.5 rc cross sigma | sigma dot p)

“int1e_cg_sa10nucsp_spinor”

(.5 rc cross sigma | nuc | sigma dot p)

“int1e_giao_sa10sa01_spinor”

(.5 sigma cross r | sigma cross nabla-rinv |)

“int1e_giao_sa10sp_spinor”

(.5 r cross sigma | sigma dot p)

“int1e_giao_sa10nucsp_spinor”

(.5 r cross sigma | nuc | sigma dot p)

“int1e_sa01sp_spinor”

(| nabla-rinv cross sigma | sigma dot p)

“int1e_spgsp_spinor”

(g sigma dot p | sigma dot p)

“int1e_spgnucsp_spinor”

(g sigma dot p | nuc | sigma dot p)

“int1e_spgsa01_spinor”

(g sigma dot p | nabla-rinv cross sigma |)

“int1e_spspsp_spinor”

(sigma dot p | sigma dot p sigma dot p)

“int1e_spnuc_spinor”

(sigma dot p | nuc |)

“int1e_ipovlp_spinor”

(nabla |)

“int1e_ipkin_spinor”

(.5 nabla | p dot p)

“int1e_ipnuc_spinor”

(nabla | nuc |)

“int1e_iprinv_spinor”

(nabla | rinv |)

“int1e_ipspnucsp_spinor”

(nabla sigma dot p | nuc | sigma dot p)

“int1e_ipsprinvsp_spinor”

(nabla sigma dot p | rinv | sigma dot p)

“int1e_grids”

( | 1/r_grids | )

“int1e_grids_spinor”

( | 1/r_grids | )

“int1e_grids_ip”

(nabla | 1/r_grids | )

“int1e_grids_ip_spinor”

(nabla | 1/r_grids | )

“int1e_grids_spvsp_spinor”

(sigma dot p | 1/r_grids | sigma dot p)

“int2e”

( , | , )

“int2e_ig1”

(#C(0 1) g , | , )

“int2e_gg1”

(g g , | , )

“int2e_g1g2”

(g , | g , )

“int2e_p1vxp1”

( p* , cross p | , ) ; SSO

“int2e_spinor”

(, | , )

“int2e_spsp1_spinor”

(sigma dot p , sigma dot p | , )

“int2e_spsp1spsp2_spinor”

(sigma dot p , sigma dot p | sigma dot p , sigma dot p )

“int2e_srsr1_spinor”

(sigma dot r , sigma dot r | ,)

“int2e_srsr1srsr2_spinor”

(sigma dot r , sigma dot r | sigma dot r , sigma dot r)

“int2e_cg_sa10sp1_spinor”

(.5 rc cross sigma , sigma dot p | ,)

“int2e_cg_sa10sp1spsp2_spinor”

(.5 rc cross sigma , sigma dot p | sigma dot p , sigma dot p )

“int2e_giao_sa10sp1_spinor”

(.5 r cross sigma , sigma dot p | ,)

“int2e_giao_sa10sp1spsp2_spinor”

(.5 r cross sigma , sigma dot p | sigma dot p , sigma dot p )

“int2e_g1_spinor”

(g , | ,)

“int2e_spgsp1_spinor”

(g sigma dot p , sigma dot p | ,)

“int2e_g1spsp2_spinor”

(g , | sigma dot p , sigma dot p)

“int2e_spgsp1spsp2_spinor”

(g sigma dot p , sigma dot p | sigma dot p , sigma dot p)

“int2e_spv1_spinor”

(sigma dot p , | ,)

“int2e_vsp1_spinor”

(, sigma dot p | ,)

“int2e_spsp2_spinor”

(, | sigma dot p , sigma dot p)

“int2e_spv1spv2_spinor”

(sigma dot p , | sigma dot p ,)

“int2e_vsp1spv2_spinor”

(, sigma dot p | sigma dot p ,)

“int2e_spv1vsp2_spinor”

(sigma dot p , | , sigma dot p)

“int2e_vsp1vsp2_spinor”

(, sigma dot p | , sigma dot p)

“int2e_spv1spsp2_spinor”

(sigma dot p , | sigma dot p , sigma dot p)

“int2e_vsp1spsp2_spinor”

(, sigma dot p | sigma dot p , sigma dot p)

“int2e_ig1”

(#C(0 1) g , | , )

“int2e_ip1”

(nabla , | ,)

“int2e_ip1_spinor”

(nabla , | ,)

“int2e_ipspsp1_spinor”

(nabla sigma dot p , sigma dot p | ,)

“int2e_ip1spsp2_spinor”

(nabla , | sigma dot p , sigma dot p)

“int2e_ipspsp1spsp2_spinor”

(nabla sigma dot p , sigma dot p | sigma dot p , sigma dot p)

“int2e_ipsrsr1_spinor”

(nabla sigma dot r , sigma dot r | ,)

“int2e_ip1srsr2_spinor”

(nabla , | sigma dot r , sigma dot r)

“int2e_ipsrsr1srsr2_spinor”

(nabla sigma dot r , sigma dot r | sigma dot r , sigma dot r)

“int2e_ip1”

(nabla , | ,)

“int2e_ssp1ssp2_spinor”

( , sigma dot p | gaunt | , sigma dot p)

“int2e_cg_ssa10ssp2_spinor”

(rc cross sigma , | gaunt | , sigma dot p)

“int2e_giao_ssa10ssp2_spinor”

(r cross sigma , | gaunt | , sigma dot p)

“int2e_gssp1ssp2_spinor”

(g , sigma dot p | gaunt | , sigma dot p)

“int2e_ipip1”

( nabla nabla , | , )

“int2e_ipvip1”

( nabla , nabla | , )

“int2e_ip1ip2”

( nabla , | nabla , )

“int3c2e_ip1”

(nabla , | )

“int3c2e_ip2”

( , | nabla)

“int2c2e_ip1”

(nabla | r12 | )

“int3c2e_spinor”

(nabla , | )

“int3c2e_spsp1_spinor”

(nabla , | )

“int3c2e_ip1_spinor”

(nabla , | )

“int3c2e_ip2_spinor”

( , | nabla)

“int3c2e_ipspsp1_spinor”

(nabla sigma dot p , sigma dot p | )

“int3c2e_spsp1ip2_spinor”

(sigma dot p , sigma dot p | nabla )

“ECPscalar_spinor”

AREP ECP integrals, similar to int1e_nuc

“ECPscalar_ipnuc_spinor”

(nabla i | ECP | ), similar to int1e_ipnuc

“ECPscalar_iprinv_spinor”

similar to int1e_iprinv for a specific atom

“ECPscalar_ignuc_spinor”

similar to int1e_ignuc

“ECPscalar_iprinvip_spinor”

similar to int1e_iprinvip

“ECPso_spinor”

< | sigam dot Spin-orbit ECP | >

atmint32 ndarray: libcint integral function argument
basint32 ndarray: libcint integral function argument
envfloat64 ndarray: libcint integral function argument

Kwargs:

shls_slice8-element list: (ish_start, ish_end, jsh_start, jsh_end, ksh_start, ksh_end, lsh_start, lsh_end)
compint: Components of the integrals, e.g. int1e_ipovlp has 3 components.
hermiint (1e integral only): Symmetry of the 1e integrals

0 : no symmetry assumed (default)

1 : hermitian

2 : anti-hermitian
aosymstr (2e integral only): Symmetry of the 2e integrals

4 or ‘4’ or ‘s4’: 4-fold symmetry (default)

‘2ij’ or ‘s2ij’ : symmetry between i, j in (ij|kl)

‘2kl’ or ‘s2kl’ : symmetry between k, l in (ij|kl)

1 or ‘1’ or ‘s1’: no symmetry
outndarray (2e integral only): array to store the 2e AO integrals

Returns:

ndarray of 1-electron integrals, can be either 2-dim or 3-dim, depending on comp

Examples:

>>> mol.build(atom='H 0 0 0; H 0 0 1.1', basis='sto-3g')
>>> gto.getints('int1e_ipnuc_sph', mol._atm, mol._bas, mol._env, comp=3) # <nabla i | V_nuc | j>
[[[ 0.          0.        ]
  [ 0.          0.        ]]
 [[ 0.          0.        ]
  [ 0.          0.        ]]
 [[ 0.10289944  0.48176097]
  [-0.48176097 -0.10289944]]]

pyscf.gto.moleintor.getints2c(intor_name, atm, bas, env, shls_slice=None, comp=1, hermi=0, ao_loc=None, cintopt=None, out=None)[source]¶

pyscf.gto.moleintor.getints3c(intor_name, atm, bas, env, shls_slice=None, comp=1, aosym='s1', ao_loc=None, cintopt=None, out=None)[source]¶

pyscf.gto.moleintor.getints4c(intor_name, atm, bas, env, shls_slice=None, comp=1, aosym='s1', ao_loc=None, cintopt=None, out=None)[source]¶

pyscf.gto.moleintor.getints_by_shell(intor_name, shls, atm, bas, env, comp=1)[source]¶

For given 2, 3 or 4 shells, interface for libcint to get 1e, 2e, 2-center-2e or 3-center-2e integrals

Args:

intor_namestr: See also getints() for the supported intor_name
shlslist of int: The AO shell-ids of the integrals
atmint32 ndarray: libcint integral function argument
basint32 ndarray: libcint integral function argument
envfloat64 ndarray: libcint integral function argument

Kwargs:

compint: Components of the integrals, e.g. int1e_ipovlp has 3 components.

Returns:

ndarray of 2-dim to 5-dim, depending on the integral type (1e, 2e, 3c-2e, 2c2e) and the value of comp

Examples:

The gradients of the spherical 2e integrals

>>> mol.build(atom='H 0 0 0; H 0 0 1.1', basis='sto-3g')
>>> gto.getints_by_shell('int2e_ip1_sph', (0,1,0,1), mol._atm, mol._bas, mol._env, comp=3)
[[[[[-0.        ]]]]
  [[[[-0.        ]]]]
  [[[[-0.08760462]]]]]

pyscf.gto.moleintor.make_cintopt(atm, bas, env, intor)[source]¶

pyscf.gto.moleintor.make_loc(bas, key)[source]¶

pyscf.gto.pp_int module¶

Analytic GTH-PP integrals for open boundary conditions.

Function	comp	Expression
“GTOval_sph”	1	\|AO>
“GTOval_ip_sph”	3	nabla \|AO>
“GTOval_ig_sph”	3	(#C(0 1) g) \|AO>
“GTOval_ipig_sph”	9	(#C(0 1) nabla g) \|AO>
“GTOval_cart”	1	\|AO>
“GTOval_ip_cart”	3	nabla \|AO>
“GTOval_ig_cart”	3	(#C(0 1) g)\|AO>
“GTOval_sph_deriv1”	4	GTO value and 1st order GTO values
“GTOval_sph_deriv2”	10	All derivatives up to 2nd order
“GTOval_sph_deriv3”	20	All derivatives up to 3rd order
“GTOval_sph_deriv4”	35	All derivatives up to 4th order
“GTOval_sp_spinor”	1	sigma dot p \|AO> (spinor basis)
“GTOval_ipsp_spinor”	3	nabla sigma dot p \|AO> (spinor basis)
“GTOval_ipipsp_spinor”	9	nabla nabla sigma dot p \|AO> (spinor basis)

Function	Expression
“int1e_ovlp”	( \| )
“int1e_nuc”	( \| nuc \| )
“int1e_kin”	(.5 \| p dot p)
“int1e_ia01p”	(#C(0 1) \| nabla-rinv \| cross p)
“int1e_giao_irjxp”	(#C(0 1) \| r cross p)
“int1e_cg_irxp”	(#C(0 1) \| rc cross p)
“int1e_giao_a11part”	(-.5 \| nabla-rinv \| r)
“int1e_cg_a11part”	(-.5 \| nabla-rinv \| rc)
“int1e_a01gp”	(g \| nabla-rinv cross p \|)
“int1e_igkin”	(#C(0 .5) g \| p dot p)
“int1e_igovlp”	(#C(0 1) g \|)
“int1e_ignuc”	(#C(0 1) g \| nuc \|)
“int1e_z”	( \| zc \| )
“int1e_zz”	( \| zc zc \| )
“int1e_r”	( \| rc \| )
“int1e_r2”	( \| rc dot rc \| )
“int1e_rr”	( \| rc rc \| )
“int1e_rrr”	( \| rc rc rc \| )
“int1e_rrrr”	( \| rc rc rc rc \| )
“int1e_pnucp”	(p* \| nuc dot p \| )
“int1e_prinvxp”	(p* \| rinv cross p \| )
“int1e_ipovlp”	(nabla \|)
“int1e_ipkin”	(.5 nabla \| p dot p)
“int1e_ipnuc”	(nabla \| nuc \|)
“int1e_iprinv”	(nabla \| rinv \|)
“int1e_rinv”	(\| rinv \|)
“int1e_pnucxp”	(p* \| nuc cross p \| )
“int1e_irp”	( \| rc nabla \| )
“int1e_irrp”	( \| rc rc nabla \| )
“int1e_irpr”	( \| rc nabla rc \| )
“int1e_ggovlp”	( \| g g \| )
“int1e_ggkin”	(.5 \| g g p dot p \| )
“int1e_ggnuc”	( \| g g nuc \| )
“int1e_grjxp”	( \| g r cross p \| )
“ECPscalar”	AREP ECP integrals, similar to int1e_nuc
“ECPscalar_ipnuc”	(nabla i \| ECP \| ), similar to int1e_ipnuc
“ECPscalar_iprinv”	similar to int1e_iprinv for a specific atom
“ECPscalar_ignuc”	similar to int1e_ignuc
“ECPscalar_iprinvip”	similar to int1e_iprinvip
“ECPso”	< \| Spin-orbit ECP \| >
“int1e_ovlp_spinor”	( \| )
“int1e_nuc_spinor”	( \| nuc \|)
“int1e_srsr_spinor”	(sigma dot r \| sigma dot r)
“int1e_sr_spinor”	(sigma dot r \|)
“int1e_srsp_spinor”	(sigma dot r \| sigma dot p)
“int1e_spsp_spinor”	(sigma dot p \| sigma dot p)
“int1e_sp_spinor”	(sigma dot p \|)
“int1e_spnucsp_spinor”	(sigma dot p \| nuc \| sigma dot p)
“int1e_srnucsr_spinor”	(sigma dot r \| nuc \| sigma dot r)
“int1e_govlp_spinor”	(g \|)
“int1e_gnuc_spinor”	(g \| nuc \|)
“int1e_cg_sa10sa01_spinor”	(.5 sigma cross rc \| sigma cross nabla-rinv \|)
“int1e_cg_sa10sp_spinor”	(.5 rc cross sigma \| sigma dot p)
“int1e_cg_sa10nucsp_spinor”	(.5 rc cross sigma \| nuc \| sigma dot p)
“int1e_giao_sa10sa01_spinor”	(.5 sigma cross r \| sigma cross nabla-rinv \|)
“int1e_giao_sa10sp_spinor”	(.5 r cross sigma \| sigma dot p)
“int1e_giao_sa10nucsp_spinor”	(.5 r cross sigma \| nuc \| sigma dot p)
“int1e_sa01sp_spinor”	(\| nabla-rinv cross sigma \| sigma dot p)
“int1e_spgsp_spinor”	(g sigma dot p \| sigma dot p)
“int1e_spgnucsp_spinor”	(g sigma dot p \| nuc \| sigma dot p)
“int1e_spgsa01_spinor”	(g sigma dot p \| nabla-rinv cross sigma \|)
“int1e_spspsp_spinor”	(sigma dot p \| sigma dot p sigma dot p)
“int1e_spnuc_spinor”	(sigma dot p \| nuc \|)
“int1e_ipovlp_spinor”	(nabla \|)
“int1e_ipkin_spinor”	(.5 nabla \| p dot p)
“int1e_ipnuc_spinor”	(nabla \| nuc \|)
“int1e_iprinv_spinor”	(nabla \| rinv \|)
“int1e_ipspnucsp_spinor”	(nabla sigma dot p \| nuc \| sigma dot p)
“int1e_ipsprinvsp_spinor”	(nabla sigma dot p \| rinv \| sigma dot p)
“int1e_grids”	( \| 1/r_grids \| )
“int1e_grids_spinor”	( \| 1/r_grids \| )
“int1e_grids_ip”	(nabla \| 1/r_grids \| )
“int1e_grids_ip_spinor”	(nabla \| 1/r_grids \| )
“int1e_grids_spvsp_spinor”	(sigma dot p \| 1/r_grids \| sigma dot p)
“int2e”	( , \| , )
“int2e_ig1”	(#C(0 1) g , \| , )
“int2e_gg1”	(g g , \| , )
“int2e_g1g2”	(g , \| g , )
“int2e_p1vxp1”	( p* , cross p \| , ) ; SSO
“int2e_spinor”	(, \| , )
“int2e_spsp1_spinor”	(sigma dot p , sigma dot p \| , )
“int2e_spsp1spsp2_spinor”	(sigma dot p , sigma dot p \| sigma dot p , sigma dot p )
“int2e_srsr1_spinor”	(sigma dot r , sigma dot r \| ,)
“int2e_srsr1srsr2_spinor”	(sigma dot r , sigma dot r \| sigma dot r , sigma dot r)
“int2e_cg_sa10sp1_spinor”	(.5 rc cross sigma , sigma dot p \| ,)
“int2e_cg_sa10sp1spsp2_spinor”	(.5 rc cross sigma , sigma dot p \| sigma dot p , sigma dot p )
“int2e_giao_sa10sp1_spinor”	(.5 r cross sigma , sigma dot p \| ,)
“int2e_giao_sa10sp1spsp2_spinor”	(.5 r cross sigma , sigma dot p \| sigma dot p , sigma dot p )
“int2e_g1_spinor”	(g , \| ,)
“int2e_spgsp1_spinor”	(g sigma dot p , sigma dot p \| ,)
“int2e_g1spsp2_spinor”	(g , \| sigma dot p , sigma dot p)
“int2e_spgsp1spsp2_spinor”	(g sigma dot p , sigma dot p \| sigma dot p , sigma dot p)
“int2e_spv1_spinor”	(sigma dot p , \| ,)
“int2e_vsp1_spinor”	(, sigma dot p \| ,)
“int2e_spsp2_spinor”	(, \| sigma dot p , sigma dot p)
“int2e_spv1spv2_spinor”	(sigma dot p , \| sigma dot p ,)
“int2e_vsp1spv2_spinor”	(, sigma dot p \| sigma dot p ,)
“int2e_spv1vsp2_spinor”	(sigma dot p , \| , sigma dot p)
“int2e_vsp1vsp2_spinor”	(, sigma dot p \| , sigma dot p)
“int2e_spv1spsp2_spinor”	(sigma dot p , \| sigma dot p , sigma dot p)
“int2e_vsp1spsp2_spinor”	(, sigma dot p \| sigma dot p , sigma dot p)
“int2e_ig1”	(#C(0 1) g , \| , )
“int2e_ip1”	(nabla , \| ,)
“int2e_ip1_spinor”	(nabla , \| ,)
“int2e_ipspsp1_spinor”	(nabla sigma dot p , sigma dot p \| ,)
“int2e_ip1spsp2_spinor”	(nabla , \| sigma dot p , sigma dot p)
“int2e_ipspsp1spsp2_spinor”	(nabla sigma dot p , sigma dot p \| sigma dot p , sigma dot p)
“int2e_ipsrsr1_spinor”	(nabla sigma dot r , sigma dot r \| ,)
“int2e_ip1srsr2_spinor”	(nabla , \| sigma dot r , sigma dot r)
“int2e_ipsrsr1srsr2_spinor”	(nabla sigma dot r , sigma dot r \| sigma dot r , sigma dot r)
“int2e_ip1”	(nabla , \| ,)
“int2e_ssp1ssp2_spinor”	( , sigma dot p \| gaunt \| , sigma dot p)
“int2e_cg_ssa10ssp2_spinor”	(rc cross sigma , \| gaunt \| , sigma dot p)
“int2e_giao_ssa10ssp2_spinor”	(r cross sigma , \| gaunt \| , sigma dot p)
“int2e_gssp1ssp2_spinor”	(g , sigma dot p \| gaunt \| , sigma dot p)
“int2e_ipip1”	( nabla nabla , \| , )
“int2e_ipvip1”	( nabla , nabla \| , )
“int2e_ip1ip2”	( nabla , \| nabla , )
“int3c2e_ip1”	(nabla , \| )
“int3c2e_ip2”	( , \| nabla)
“int2c2e_ip1”	(nabla \| r12 \| )
“int3c2e_spinor”	(nabla , \| )
“int3c2e_spsp1_spinor”	(nabla , \| )
“int3c2e_ip1_spinor”	(nabla , \| )
“int3c2e_ip2_spinor”	( , \| nabla)
“int3c2e_ipspsp1_spinor”	(nabla sigma dot p , sigma dot p \| )
“int3c2e_spsp1ip2_spinor”	(sigma dot p , sigma dot p \| nabla )
“ECPscalar_spinor”	AREP ECP integrals, similar to int1e_nuc
“ECPscalar_ipnuc_spinor”	(nabla i \| ECP \| ), similar to int1e_ipnuc
“ECPscalar_iprinv_spinor”	similar to int1e_iprinv for a specific atom
“ECPscalar_ignuc_spinor”	similar to int1e_ignuc
“ECPscalar_iprinvip_spinor”	similar to int1e_iprinvip
“ECPso_spinor”	< \| sigam dot Spin-orbit ECP \| >

pyscf.gto package¶

Subpackages¶

Submodules¶

pyscf.gto.cmd_args module¶

pyscf.gto.ecp module¶

pyscf.gto.eval_gto module¶

pyscf.gto.ft_ao module¶

pyscf.gto.mole module¶

pyscf.gto.moleintor module¶

pyscf.gto.pp_int module¶

Module contents¶