pyscf.x2c package

Submodules

pyscf.x2c.dft module

X2C 2-component DFT methods

class pyscf.x2c.dft.RKS(mol, xc='LDA,VWN')

Bases: KohnShamDFT, RHF

dump_flags(verbose=None)

to_hf()

Convert the input mean-field object to an X2C-HF object.

Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.

class pyscf.x2c.dft.UKS(mol, xc='LDA,VWN')

Bases: KohnShamDFT, UHF

dump_flags(verbose=None)

to_hf()

Convert the input mean-field object to an X2C-HF object.

Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.

pyscf.x2c.dft.X2C_RKS

alias of RKS

pyscf.x2c.dft.X2C_UKS

alias of UKS

pyscf.x2c.newton_ah module

Second order X2C-SCF solver

class pyscf.x2c.newton_ah.SecondOrderX2CRHF(mf)

Bases: _CIAH_SOSCF

gen_g_hop(mo_coeff, mo_occ, fock_ao=None, h1e=None, with_symmetry=False)

rotate_mo(mo_coeff, u, log=None)

update_rotate_matrix(dx, mo_occ, u0=1, mo_coeff=None)

class pyscf.x2c.newton_ah.SecondOrderX2CUHF(mf)

Bases: _CIAH_SOSCF

gen_g_hop(mo_coeff, mo_occ, fock_ao=None, h1e=None, with_symmetry=False)

rotate_mo(mo_coeff, u, log=None)

update_rotate_matrix(dx, mo_occ, u0=1, mo_coeff=None)

pyscf.x2c.newton_ah.newton(mf)

Co-iterative augmented hessian (CIAH) second order SCF solver

Examples:

>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1', basis='cc-pvdz')
>>> mf = x2c.RHF(mol).newton()
>>> mf.kernel()
-1.0811707843774987

pyscf.x2c.sfx2c1e module

1-electron Spin-free X2C approximation

class pyscf.x2c.sfx2c1e.SFX2C1E_SCF(mf)

Bases: _X2C_SCF

Attributes for spin-free X2C:

with_x2c : X2C object

dip_moment(mol=None, dm=None, unit='Debye', verbose=3, picture_change=True, **kwargs)

Dipole moment calculation with picture change correction

Args:

mol: an instance of Mole dm : a 2D ndarrays density matrices

Kwarg:

picture_chang (bool) : Whether to compute the dipole moment with picture change correction.

Return:

A list: the dipole moment on x, y and z component

get_hcore(mol=None)

undo_x2c()

Remove the X2C Mixin

pyscf.x2c.sfx2c1e.SpinFreeX2C

alias of SpinFreeX2CHelper

class pyscf.x2c.sfx2c1e.SpinFreeX2CHelper(mol)

Bases: X2CHelperBase

1-component X2c (spin-free part only)

get_hcore(mol=None)

1-component X2c Foldy-Wouthuysen (FW Hamiltonian (spin-free part only)

get_xmat(mol=None)

hcore_deriv_generator(mol=None, deriv=1)

picture_change(even_operator=(None, None), odd_operator=None)

Picture change for even_operator + odd_operator

even_operator has two terms at diagonal blocks [ v 0 ] [ 0 w ]

odd_operator has the term at off-diagonal blocks [ 0 p ] [ p^T 0 ]

v, w, and p can be strings (integral name) or matrices.

pyscf.x2c.sfx2c1e.sfx2c(mf)

Spin-free X2C. For the given SCF object, it updates the hcore constructor. All integrals are computed in the real spherical GTO basis.

Args:

mf : an SCF object

Returns:

An SCF object

Examples:

>>> mol = gto.M(atom='H 0 0 0; F 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol).sfx2c1e()
>>> mf.scf()

>>> import pyscf.x2c.sfx2c1e
>>> mol.symmetry = 1
>>> mol.build(0, 0)
>>> mf = pyscf.x2c.sfx2c1e.sfx2c1e(scf.UHF(mol))
>>> mf.scf()

pyscf.x2c.sfx2c1e.sfx2c1e(mf)

Spin-free X2C. For the given SCF object, it updates the hcore constructor. All integrals are computed in the real spherical GTO basis.

Args:

mf : an SCF object

Returns:

An SCF object

Examples:

>>> mol = gto.M(atom='H 0 0 0; F 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol).sfx2c1e()
>>> mf.scf()

>>> import pyscf.x2c.sfx2c1e
>>> mol.symmetry = 1
>>> mol.build(0, 0)
>>> mf = pyscf.x2c.sfx2c1e.sfx2c1e(scf.UHF(mol))
>>> mf.scf()

pyscf.x2c.sfx2c1e_grad module

Analytical nuclear gradients for 1-electron spin-free x2c method

Ref. JCP 135, 084114 (2011); DOI:10.1063/1.3624397

pyscf.x2c.sfx2c1e_grad.gen_sf_hfw(mol, approx='1E')

pyscf.x2c.sfx2c1e_grad.hcore_grad_generator(x2cobj, mol=None)

nuclear gradients of 1-component X2c hcore Hamiltonian (spin-free part only)

pyscf.x2c.sfx2c1e_hess module

Analytical nuclear hessian for 1-electron spin-free x2c method

Ref. JCP 135, 244104 (2011); DOI:10.1063/1.3667202 JCTC 8, 2617 (2012); DOI:10.1021/ct300127e

pyscf.x2c.sfx2c1e_hess.gen_sf_hfw(mol, approx='1E')

pyscf.x2c.sfx2c1e_hess.hcore_hess_generator(x2cobj, mol=None)

nuclear gradients of 1-component X2c hcore Hamiltonian (spin-free part only)

pyscf.x2c.stability module

Generate X2C-SCF response functions

pyscf.x2c.stability.x2chf_stability(mf, verbose=None, return_status=False)

Stability analysis for X2C-HF/X2C-KS method.

Args:

mf : DHF or DKS object

Kwargs:

return_status: bool

Whether to return stable_i and stable_e

Returns:

If return_status is False (default), the return value includes a new set of orbitals, which are more close to the stable condition.

Else, another one boolean variable (indicating current status: stable or unstable) is returned.

pyscf.x2c.tdscf module

class pyscf.x2c.tdscf.TDA(mf)

Bases: TDBase, TDA

gen_vind(mf=None)

Generate function to compute Ax

init_guess(mf, nstates=None, wfnsym=None)

kernel(x0=None, nstates=None)

TDA diagonalization solver

class pyscf.x2c.tdscf.TDBase(mf)

Bases: TDBase

analyze(verbose=None)

get_ab(mf=None)

A and B matrices for TDDFT response function.

A[i,a,j,b] = delta_{ab}delta_{ij}(E_a - E_i) + (ia||bj) B[i,a,j,b] = (ia||jb)

get_nto(state=1, threshold=0.3, verbose=None)

Natural transition orbital analysis.

The natural transition density matrix between ground state and excited state \(Tia = \langle \Psi_{ex} | i a^\dagger | \Psi_0 \rangle\) can be transformed to diagonal form through SVD \(T = O \sqrt{\lambda} V^\dagger\). O and V are occupied and virtual natural transition orbitals. The diagonal elements \(\lambda\) are the weights of the occupied-virtual orbital pair in the excitation.

Ref: Martin, R. L., JCP, 118, 4775-4777

Note in the TDHF/TDDFT calculations, the excitation part (X) is interpreted as the CIS coefficients and normalized to 1. The de-excitation part (Y) is ignored.

Args:

tdobj : TDA, or TDHF, or TDDFT object

stateint

Excited state ID. state = 1 means the first excited state. If state < 0, state ID is counted from the last excited state.

Kwargs:

thresholdfloat

Above which the NTO coefficients will be printed in the output.

Returns:

A list (weights, NTOs). NTOs are natural orbitals represented in AO basis. The first N_occ NTOs are occupied NTOs and the rest are virtual NTOs.

nuc_grad_method()

pyscf.x2c.tdscf.TDDFT

alias of TDHF

class pyscf.x2c.tdscf.TDHF(mf)

Bases: TDBase, TDHF

gen_vind(mf=None)

Generate function to compute

[ A B][X] [-B -A][Y]

init_guess(mf, nstates=None, wfnsym=None)

kernel(x0=None, nstates=None)

TDHF diagonalization with non-Hermitian eigenvalue solver

pyscf.x2c.tdscf.analyze(tdobj, verbose=None)

pyscf.x2c.tdscf.gen_tda_hop(mf, fock_ao=None)

A x

pyscf.x2c.tdscf.gen_tda_operation(mf, fock_ao=None)

A x

pyscf.x2c.tdscf.gen_tdhf_operation(mf, fock_ao=None)

Generate function to compute

[ A B][X] [-B -A][Y]

pyscf.x2c.tdscf.get_ab(mf, mo_energy=None, mo_coeff=None, mo_occ=None)

A and B matrices for TDDFT response function.

A[i,a,j,b] = delta_{ab}delta_{ij}(E_a - E_i) + (ia||bj) B[i,a,j,b] = (ia||jb)

pyscf.x2c.tdscf.get_nto(tdobj, state=1, threshold=0.3, verbose=None)

pyscf.x2c.x2c module

X2C 2-component HF methods

class pyscf.x2c.x2c.RHF(mol)

Bases: SCF

TDA(*args, **kwargs)

TDHF(*args, **kwargs)

gen_response(mo_coeff=None, mo_occ=None, with_j=True, hermi=0, max_memory=None)

Generate a function to compute the product of X2C-HF response function and density matrices.

to_ks(xc='HF')

Convert the input mean-field object to an X2C-KS object.

Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.

class pyscf.x2c.x2c.SCF(mol)

Bases: SCF

The full X2C problem (scaler + soc terms) in j-adapted spinor basis

analyze(verbose=None)

Analyze the given SCF object: print orbital energies, occupancies; print orbital coefficients; Mulliken population analysis; Diople moment.

build(mol=None)

dip_moment(mol=None, dm=None, unit='Debye', verbose=3, picture_change=True, **kwargs)

Dipole moment calculation with picture change correction

Args:

mol: an instance of Mole dm : a 2D ndarrays density matrices

Kwarg:

picture_change (bool) : Whether to compute the dipole moment with picture change correction.

Return:

A list: the dipole moment on x, y and z component

dump_flags(verbose=None)

get_hcore(mol=None)

get_jk(mol=None, dm=None, hermi=1, with_j=True, with_k=True, omega=None)

Compute J, K matrices for all input density matrices

Args:

mol : an instance of Mole

dmndarray or list of ndarrays

A density matrix or a list of density matrices

Kwargs:

hermiint

Whether J, K matrix is hermitian

0 : not hermitian and not symmetric

1 : hermitian or symmetric

2 : anti-hermitian

vhfopt :

A class which holds precomputed quantities to optimize the computation of J, K matrices

with_jboolean

Whether to compute J matrices

with_kboolean

Whether to compute K matrices

omegafloat

Parameter of range-seperated Coulomb operator: erf( omega * r12 ) / r12. If specified, integration are evaluated based on the long-range part of the range-seperated Coulomb operator.

Returns:

Depending on the given dm, the function returns one J and one K matrix, or a list of J matrices and a list of K matrices, corresponding to the input density matrices.

Examples:

>>> from pyscf import gto, scf
>>> from pyscf.scf import _vhf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> dms = numpy.random.random((3,mol.nao_nr(),mol.nao_nr()))
>>> j, k = scf.hf.get_jk(mol, dms, hermi=0)
>>> print(j.shape)
(3, 2, 2)

get_occ(mo_energy=None, mo_coeff=None)

Label the occupancies for each orbital

Kwargs:

mo_energy1D ndarray

Obital energies

mo_coeff2D ndarray

Obital coefficients

Examples:

>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; F 0 0 1.1')
>>> mf = scf.hf.SCF(mol)
>>> energy = numpy.array([-10., -1., 1, -2., 0, -3])
>>> mf.get_occ(energy)
array([2, 2, 0, 2, 2, 2])

get_ovlp(mol=None)

get_veff(mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1)

Dirac-Coulomb

init_direct_scf(mol=None)

init_guess_by_atom(mol=None)

Generate initial guess density matrix from superposition of atomic HF density matrix. The atomic HF is occupancy averaged RHF

Returns:

Density matrix, 2D ndarray

init_guess_by_chkfile(chkfile=None, project=None)

Read the HF results from checkpoint file, then project it to the basis defined by mol

Returns:

Density matrix, 2D ndarray

init_guess_by_minao(mol=None)

Initial guess in terms of the overlap to minimal basis.

make_rdm1(mo_coeff=None, mo_occ=None, **kwargs)

One-particle density matrix in AO representation

Args:

mo_coeff2D ndarray

Orbital coefficients. Each column is one orbital.

mo_occ1D ndarray

Occupancy

Returns:

One-particle density matrix, 2D ndarray

newton()

Create an SOSCF object based on the mean-field object

nuc_grad_method()

Hook to create object for analytical nuclear gradients.

sfx2c1e()

stability(internal=None, external=None, verbose=None, return_status=False)

X2C-HF/X2C-KS stability analysis.

See also pyscf.scf.stability.rhf_stability function.

Kwargs:

return_status: bool

Whether to return stable_i and stable_e

Returns:

If return_status is False (default), the return value includes two set of orbitals, which are more close to the stable condition. The first corresponds to the internal stability and the second corresponds to the external stability.

Else, another two boolean variables (indicating current status: stable or unstable) are returned. The first corresponds to the internal stability and the second corresponds to the external stability.

x2c()

x2c1e()

class pyscf.x2c.x2c.SpinOrbitalX2CHelper(mol)

Bases: X2CHelperBase

2-component X2c (including spin-free and spin-dependent terms) in the Gaussian type spin-orbital basis (as the spin-orbital basis in GHF)

get_hcore(mol=None)

2-component X2c Foldy-Wouthuysen (FW) Hamiltonian (including spin-free and spin-dependent terms) in the j-adapted spinor basis.

get_xmat(mol=None)

picture_change(even_operator=(None, None), odd_operator=None)

Picture change for even_operator + odd_operator

even_operator has two terms at diagonal blocks [ v 0 ] [ 0 w ]

odd_operator has the term at off-diagonal blocks [ 0 p ] [ p^T 0 ]

v, w, and p can be strings (integral name) or matrices.

class pyscf.x2c.x2c.SpinorX2CHelper(mol)

Bases: X2CHelperBase

2-component X2c (including spin-free and spin-dependent terms) in the j-adapted spinor basis.

class pyscf.x2c.x2c.UHF(mol)

Bases: SCF

TDA(*args, **kwargs)

TDHF(*args, **kwargs)

gen_response(mo_coeff=None, mo_occ=None, with_j=True, hermi=0, max_memory=None)

Generate a function to compute the product of X2C-HF response function and density matrices.

to_ks(xc='HF')

Convert the input mean-field object to an X2C-KS object.

Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.

pyscf.x2c.x2c.X2C

alias of SpinorX2CHelper

class pyscf.x2c.x2c.X2C1E_GSCF(mf)

Bases: _X2C_SCF

Attributes for spin-orbital X2C:

with_x2c : X2C object

dip_moment(mol=None, dm=None, unit='Debye', verbose=3, picture_change=True, **kwargs)

Dipole moment calculation with picture change correction

Args:

mol: an instance of Mole dm : a 2D ndarrays density matrices

Kwarg:

picture_change (bool) : Whether to compute the dipole moment with picture change correction.

Return:

A list: the dipole moment on x, y and z component

get_hcore(mol=None)

to_ks(xc='HF')

undo_x2c()

Remove the X2C Mixin

class pyscf.x2c.x2c.X2CHelperBase(mol)

Bases: StreamObject

2-component X2c (including spin-free and spin-dependent terms) in the j-adapted spinor basis.

approx = '1e'

basis = None

dump_flags(verbose=None)

get_hcore(mol=None)

2-component X2c Foldy-Wouthuysen (FW) Hamiltonian (including spin-free and spin-dependent terms) in the j-adapted spinor basis.

get_xmat(mol=None)

get_xmol(mol=None)

picture_change(even_operator=(None, None), odd_operator=None)

Picture change for even_operator + odd_operator

even_operator has two terms at diagonal blocks [ v 0 ] [ 0 w ]

odd_operator has the term at off-diagonal blocks [ 0 p ] [ p^T 0 ]

v, w, and p can be strings (integral name) or matrices.

reset(mol)

Reset mol and clean up relevant attributes for scanner mode

xuncontract = True

pyscf.x2c.x2c.X2C_RHF

alias of RHF

pyscf.x2c.x2c.X2C_SCF

alias of SCF

pyscf.x2c.x2c.X2C_UHF

alias of UHF

pyscf.x2c.x2c.get_hcore(mol)

2-component X2c hcore Hamiltonian (including spin-free and spin-dependent terms) in the j-adapted spinor basis.

pyscf.x2c.x2c.get_init_guess(mol, key='minao')

pyscf.x2c.x2c.get_jk(mol, dm, hermi=1, mf_opt=None, with_j=True, with_k=True, omega=None)

non-relativistic J/K matrices (without SSO,SOO etc) in the j-adapted spinor basis.

pyscf.x2c.x2c.init_guess_by_1e(mol)

Initial guess from one electron system.

pyscf.x2c.x2c.init_guess_by_atom(mol)

Initial guess from atom calculation.

pyscf.x2c.x2c.init_guess_by_chkfile(mol, chkfile_name, project=None)

pyscf.x2c.x2c.init_guess_by_minao(mol)

Initial guess in terms of the overlap to minimal basis.

pyscf.x2c.x2c.x2c1e_ghf(mf)

For the given GHF object, generate X2C-GSCF object in GHF spin-orbital basis. Note the orbital basis of X2C_GSCF is different to the X2C_RHF and X2C_UHF objects. X2C_RHF and X2C_UHF use spinor basis.

Args:

mf : an GHF/GKS object

Returns:

An GHF/GKS object

Examples:

>>> mol = pyscf.M(atom='H 0 0 0; F 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.GHF(mol).x2c1e().run()

Module contents