#!/usr/bin/env python
# Copyright 2014-2021 The PySCF Developers. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
# Author: Qiming Sun <osirpt.sun@gmail.com>
#
'''
Mole class and helper functions to handle parameters and attributes for GTO
integrals. This module serves the interface to the integral library libcint.
'''
import os
import sys
import types
import re
import platform
import gc
import time
import json
import ctypes
import numpy
import numpy as np
import h5py
import scipy.special
import scipy.linalg
import contextlib
import threading
from pyscf import lib
from pyscf.lib import param
from pyscf.data import elements
from pyscf.lib import logger
from pyscf.gto import cmd_args
from pyscf.gto import basis
from pyscf.gto import moleintor
from pyscf.gto.eval_gto import eval_gto
from pyscf.gto.ecp import core_configuration
from pyscf import __config__
from pyscf.data.elements import ELEMENTS, ELEMENTS_PROTON, \
_rm_digit, charge, _symbol, _std_symbol, _atom_symbol, is_ghost_atom, \
_std_symbol_without_ghost
from pyscf.lib.exceptions import BasisNotFoundError, PointGroupSymmetryError
import warnings
# for _atm, _bas, _env
CHARGE_OF = 0
PTR_COORD = 1
NUC_MOD_OF = 2
PTR_ZETA = 3
PTR_FRAC_CHARGE = 4
ATM_SLOTS = 6
ATOM_OF = 0
ANG_OF = 1
NPRIM_OF = 2
NCTR_OF = 3
RADI_POWER = 3 # for ECP
KAPPA_OF = 4
SO_TYPE_OF = 4 # for ECP
PTR_EXP = 5
PTR_COEFF = 6
BAS_SLOTS = 8
# pointer to env
PTR_EXPCUTOFF = 0
PTR_COMMON_ORIG = 1
PTR_RINV_ORIG = 4
PTR_RINV_ZETA = 7
PTR_RANGE_OMEGA = 8
PTR_F12_ZETA = 9
PTR_GTG_ZETA = 10
NGRIDS = 11
PTR_GRIDS = 12
AS_RINV_ORIG_ATOM = 17
AS_ECPBAS_OFFSET = 18
AS_NECPBAS = 19
PTR_ENV_START = 20
# parameters from libcint
NUC_POINT = 1
NUC_GAUSS = 2
# nucleus with fractional charges. It can be used to mimic MM particles
NUC_FRAC_CHARGE = 3
NUC_ECP = 4 # atoms with pseudo potential
BASE = getattr(__config__, 'BASE', 0)
NORMALIZE_GTO = getattr(__config__, 'NORMALIZE_GTO', True)
DISABLE_EVAL = getattr(__config__, 'DISABLE_EVAL', False)
ARGPARSE = getattr(__config__, 'ARGPARSE', False)
[docs]
def M(*args, **kwargs):
r'''This is a shortcut to build up Mole object.
Args: Same to :func:`Mole.build`
Examples:
>>> from pyscf import gto
>>> mol = gto.M(atom='H 0 0 0; F 0 0 1', basis='6-31g')
'''
mol = Mole()
mol.build(*args, **kwargs)
return mol
[docs]
def gaussian_int(n, alpha):
r'''int_0^inf x^n exp(-alpha x^2) dx'''
n1 = (n + 1) * .5
return scipy.special.gamma(n1) / (2. * alpha**n1)
[docs]
def gto_norm(l, expnt):
r'''Normalized factor for GTO radial part :math:`g=r^l e^{-\alpha r^2}`
.. math::
\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 :math:`\alpha`
Returns:
normalization factor
Examples:
>>> print(gto_norm(0, 1))
2.5264751109842591
'''
if numpy.all(l >= 0):
#f = 2**(2*l+3) * math.factorial(l+1) * (2*expnt)**(l+1.5) \
# / (math.factorial(2*l+2) * math.sqrt(math.pi))
#return math.sqrt(f)
return 1/numpy.sqrt(gaussian_int(l*2+2, 2*expnt))
else:
raise ValueError('l should be >= 0')
[docs]
def cart2sph(l, c_tensor=None, normalized=None):
'''
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).
'''
nf = (l+1)*(l+2)//2
if c_tensor is None:
c_tensor = numpy.eye(nf)
else:
c_tensor = numpy.asarray(c_tensor, order='F').reshape(-1,nf)
if l == 0 or l == 1:
if normalized == 'sp':
return c_tensor
elif l == 0:
return c_tensor * 0.282094791773878143
else:
return c_tensor * 0.488602511902919921
else:
assert l <= 15
nd = l * 2 + 1
ngrid = c_tensor.shape[0]
c2sph = numpy.zeros((ngrid,nd), order='F')
fn = moleintor.libcgto.CINTc2s_ket_sph
fn(c2sph.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(ngrid),
c_tensor.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(l))
return c2sph
[docs]
def cart2spinor_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).
'''
if kappa < 0:
l = -kappa - 1
nd = l * 2 + 2
elif kappa > 0:
l = kappa
nd = l * 2
else:
assert (l is not None)
assert (l <= 12)
nd = l * 4 + 2
nf = (l+1)*(l+2)//2
c2smat = numpy.zeros((nf*2,nd), order='F', dtype=numpy.complex128)
cmat = numpy.eye(nf)
fn = moleintor.libcgto.CINTc2s_ket_spinor_sf1
fn(c2smat.ctypes.data_as(ctypes.c_void_p),
c2smat[nf:].ctypes.data_as(ctypes.c_void_p),
cmat.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(nf*2), ctypes.c_int(nf),
ctypes.c_int(1), ctypes.c_int(kappa), ctypes.c_int(l))
if normalized != 'sp':
if l == 0:
c2smat *= 0.282094791773878143
elif l == 1:
c2smat *= 0.488602511902919921
# c2smat[0] is the transformation for spin up
# c2smat[1] is the transformation for spin down
c2smat = c2smat.reshape(2,nf,nd)
return c2smat
cart2j_kappa = cart2spinor_kappa
[docs]
def cart2spinor_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).
'''
return cart2spinor_kappa(0, l, normalized)
cart2j_l = cart2spinor_l
[docs]
def sph2spinor_kappa(kappa, l=None):
'''Real spherical to spinor transformation matrix for kappa'''
from pyscf.symm.sph import sph2spinor
ua, ub = sph2spinor(l)
if kappa < 0:
l = -kappa - 1
ua = ua[:,l*2:]
ub = ub[:,l*2:]
elif kappa > 0:
l = kappa
ua = ua[:,:l*2]
ub = ub[:,:l*2]
else:
assert (l is not None)
assert (l <= 12)
return ua, ub
[docs]
def sph2spinor_l(l):
'''Real spherical to spinor transformation matrix for angular moment l'''
return sph2spinor_kappa(0, l)
[docs]
def ao_rotation_matrix(mol, 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)
'''
from pyscf.symm.basis import _momentum_rotation_matrices
Ds = _momentum_rotation_matrices(mol, orientation)
u = []
for i in range(mol.nbas):
l = mol.bas_angular(i)
nc = mol.bas_nctr(i)
u.extend([Ds[l]] * nc)
return scipy.linalg.block_diag(*u)
[docs]
def atom_types(atoms, basis=None, magmom=None):
'''symmetry inequivalent atoms'''
atmgroup = {}
for ia, a in enumerate(atoms):
if 'GHOST' in a[0].upper():
a = ['X'+a[0][5:]] + list(a[1:])
if a[0] in atmgroup:
atmgroup[a[0]].append(ia)
elif basis is None:
atmgroup[a[0]] = [ia]
else:
stdsymb = _std_symbol(a[0])
if a[0] in basis:
if stdsymb in basis and basis[a[0]] == basis[stdsymb]:
if stdsymb in atmgroup:
atmgroup[stdsymb].append(ia)
else:
atmgroup[stdsymb] = [ia]
else:
atmgroup[a[0]] = [ia]
elif stdsymb in atmgroup:
atmgroup[stdsymb].append(ia)
else:
atmgroup[stdsymb] = [ia]
if magmom is not None:
atmgroup_new = {}
suffix = {1:'u', -1:'d', 0:'o'}
magmom = np.asarray(magmom)
for elem, idx in atmgroup.items():
uniq_mag = np.unique(magmom[idx])
if len(uniq_mag) > 1:
for i, mag in enumerate(uniq_mag):
subgrp = np.asarray(idx)[np.where(magmom[idx] == mag)[0]]
if mag not in suffix:
raise RuntimeError("Magmom should be chosen from [-1, 0, 1], but %s is given" % mag)
atmgroup_new[elem+'_'+suffix[mag]] = subgrp.tolist()
else:
atmgroup_new[elem] = idx
atmgroup = atmgroup_new
return atmgroup
#TODO: sort exponents
def _generate_basis_converter():
def nparray_to_list(item):
val = []
for x in item:
if isinstance(x, (tuple, list)):
val.append(nparray_to_list(x))
elif isinstance(x, numpy.ndarray):
val.append(x.tolist())
else:
val.append(x)
return val
def load(basis_name, symb):
unc = basis_name.lower().startswith('unc')
if unc:
basis_name = basis_name[3:]
if 'gth' in basis_name:
from pyscf.pbc.gto.basis import load as pbc_basis_load
_basis = pbc_basis_load(basis_name, symb)
else:
_basis = basis.load(basis_name, symb)
if unc:
_basis = uncontracted_basis(_basis)
return _basis
def converter(symb, raw_basis):
if isinstance(raw_basis, str):
_basis = load(raw_basis, _std_symbol_without_ghost(symb))
elif (any(isinstance(x, str) for x in raw_basis)
# The first element is the basis of internal format
or not isinstance(raw_basis[0][0], int)):
stdsymb = _std_symbol_without_ghost(symb)
_basis = []
for rawb in raw_basis:
if isinstance(rawb, str):
_basis.extend(load(rawb, stdsymb))
else:
_basis.extend(nparray_to_list(rawb))
else:
_basis = nparray_to_list(raw_basis)
# Sort basis accroding to angular momentum. This is important for method
# decontract_basis, which assumes that basis functions with the same
# angular momentum are grouped together. Related to issue #1620 #1770
_basis = sorted([b for b in _basis if b], key=lambda b: b[0])
return _basis
return converter
[docs]
def uncontracted_basis(_basis):
'''Uncontract internal format _basis
Examples:
>>> gto.uncontract(gto.load('sto3g', 'He'))
[[0, [6.36242139, 1]], [0, [1.158923, 1]], [0, [0.31364979, 1]]]
'''
MAXL = 10
ubasis_raw = [[] for l in range(MAXL)]
ubasis_exp = [[] for l in range(MAXL)]
for b in _basis:
angl = b[0]
kappa = b[1]
if isinstance(kappa, int):
coeffs = b[2:]
else:
coeffs = b[1:]
if isinstance(kappa, int) and kappa != 0:
warnings.warn('For basis with kappa != 0, the uncontract basis might be wrong. '
'Please double check the resultant attribute mol._basis')
for p in coeffs:
ubasis_raw[angl].append([angl, kappa, [p[0], 1]])
ubasis_exp[angl].append(p[0])
else:
for p in coeffs:
ubasis_raw[angl].append([angl, [p[0], 1]])
ubasis_exp[angl].append(p[0])
# Check linear dependency
ubasis = []
for l in range(MAXL):
basis_l = ubasis_raw[l]
if basis_l:
es = numpy.array(ubasis_exp[l])
# Remove duplicated primitive basis functions
es, e_idx = numpy.unique(es.round(9), True)
# from large exponent to small exponent
for i in reversed(e_idx):
ubasis.append(basis_l[i])
return ubasis
uncontract = uncontracted_basis
contract = contracted_basis = basis.to_general_contraction
[docs]
def to_uncontracted_cartesian_basis(mol):
'''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
'''
return decontract_basis(mol, to_cart=True)
[docs]
def decontract_basis(mol, 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
'''
pmol = mol.copy(deep=False)
# Some input basis may be segmented basis from a general contracted set.
# This may lead to duplicated pGTOs. First contract all basis to remove
# duplicated primitive functions.
bas_exps = mol.bas_exps()
def _to_full_contraction(mol, bas_idx):
es = numpy.hstack([bas_exps[i] for i in bas_idx])
cs = scipy.linalg.block_diag(*[mol._libcint_ctr_coeff(ib) for ib in bas_idx])
es, e_idx, rev_idx = numpy.unique(es.round(9), True, True)
cs_new = numpy.zeros((es.size, cs.shape[1]))
for i, j in enumerate(rev_idx):
cs_new[j] += cs[i]
return es[::-1], cs_new[::-1]
_bas = []
_env = mol._env.copy()
contr_coeff = []
lmax = mol._bas[:,ANG_OF].max()
if mol.cart:
c2s = [numpy.eye((l+1)*(l+2)//2) for l in range(lmax+1)]
elif to_cart:
c2s = [cart2sph(l, normalized='sp') for l in range(lmax+1)]
pmol.cart = True
else:
c2s = [numpy.eye(l*2+1) for l in range(lmax+1)]
aoslices = mol.aoslice_by_atom()
for ia, (ib0, ib1) in enumerate(aoslices[:,:2]):
if atoms is not None:
if isinstance(atoms, str):
to_apply = ((atoms == mol.atom_pure_symbol(ia)) or
(atoms == mol.atom_symbol(ia)))
elif isinstance(atoms, (tuple, list)):
to_apply = ((mol.atom_pure_symbol(ia) in atoms) or
(mol.atom_symbol(ia) in atoms) or
(ia in atoms))
else:
to_apply = True
if not to_apply:
for ib in range(ib0, ib1):
l = mol.bas_angular(ib)
nc = mol.bas_nctr(ib)
c = numpy.einsum('pi,xm->pxim', numpy.eye(nc), c2s[l])
contr_coeff.append(c.reshape(nc * c2s[l].shape[0], -1))
_bas.append(mol._bas[ib0:ib1])
continue
lmax = mol._bas[ib0:ib1,ANG_OF].max()
pexp = mol._bas[ib0,PTR_EXP]
for l in range(lmax+1):
bas_idx = ib0 + numpy.where(mol._bas[ib0:ib1,ANG_OF] == l)[0]
if len(bas_idx) == 0:
continue
mol_exps, b_coeff = _to_full_contraction(mol, bas_idx)
nprim, nc = b_coeff.shape
bs = numpy.zeros((nprim, BAS_SLOTS), dtype=numpy.int32)
bs[:,ATOM_OF] = ia
bs[:,ANG_OF ] = l
bs[:,NCTR_OF] = bs[:,NPRIM_OF] = 1
norm = gto_norm(l, mol_exps)
if atoms is None:
bs[:,PTR_EXP] = pexp + numpy.arange(nprim)
bs[:,PTR_COEFF] = pexp + numpy.arange(nprim, nprim*2)
_env[pexp:pexp+nprim] = mol_exps
_env[pexp+nprim:pexp+nprim*2] = norm
pexp += nprim * 2
else:
bs[:,PTR_EXP] = _env.size + numpy.arange(nprim)
bs[:,PTR_COEFF] = _env.size + numpy.arange(nprim, nprim*2)
_env = np.hstack([_env, mol_exps, norm])
_bas.append(bs)
c = numpy.einsum('pi,p,xm->pxim', b_coeff, 1./norm, c2s[l])
contr_coeff.append(c.reshape(nprim * c2s[l].shape[0], -1))
pmol._bas = numpy.asarray(numpy.vstack(_bas), dtype=numpy.int32)
pmol._env = _env
return pmol, contr_coeff
# transform etb to basis format
[docs]
def expand_etb(l, n, alpha, beta):
r'''Generate the exponents of even tempered basis for :attr:`Mole.basis`.
.. math::
e = e^{-\alpha * \beta^{i-1}} for i = 1 .. n
Args:
l : int
Angular momentum
n : int
Number of GTOs
Returns:
Formatted :attr:`~Mole.basis`
Examples:
>>> gto.expand_etb(1, 3, 1.5, 2)
[[1, [6.0, 1]], [1, [3.0, 1]], [1, [1.5, 1]]]
'''
return [[l, [alpha*beta**i, 1]] for i in reversed(range(n))]
[docs]
def expand_etbs(etbs):
r'''Generate even tempered basis. See also :func:`expand_etb`
Args:
etbs = [(l, n, alpha, beta), (l, n, alpha, beta),...]
Returns:
Formatted :attr:`~Mole.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]]]
'''
return lib.flatten([expand_etb(*etb) for etb in etbs])
etbs = expand_etbs
# concatenate two mol
[docs]
def conc_env(atm1, bas1, env1, atm2, bas2, env2):
r'''Concatenate two Mole's integral parameters. This function can be used
to construct the environment for cross integrals like
.. math::
\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]]
'''
off = len(env1)
natm_off = len(atm1)
atm2 = numpy.copy(atm2)
bas2 = numpy.copy(bas2)
atm2[:,PTR_COORD] += off
atm2[:,PTR_ZETA ] += off
bas2[:,ATOM_OF ] += natm_off
bas2[:,PTR_EXP ] += off
bas2[:,PTR_COEFF] += off
return (numpy.asarray(numpy.vstack((atm1,atm2)), dtype=numpy.int32),
numpy.asarray(numpy.vstack((bas1,bas2)), dtype=numpy.int32),
numpy.hstack((env1,env2)))
[docs]
def conc_mol(mol1, mol2):
'''Concatenate two Mole objects.
'''
if not mol1._built:
logger.warn(mol1, 'Warning: object %s not initialized. Initializing %s',
mol1, mol1)
mol1.build()
if not mol2._built:
logger.warn(mol2, 'Warning: object %s not initialized. Initializing %s',
mol2, mol2)
mol2.build()
mol3 = Mole()
mol3._built = True
mol3._atm, mol3._bas, mol3._env = \
conc_env(mol1._atm, mol1._bas, mol1._env,
mol2._atm, mol2._bas, mol2._env)
off = len(mol1._env)
natm_off = len(mol1._atm)
if len(mol2._ecpbas) == 0:
mol3._ecpbas = mol1._ecpbas
else:
ecpbas2 = numpy.copy(mol2._ecpbas)
ecpbas2[:,ATOM_OF ] += natm_off
ecpbas2[:,PTR_EXP ] += off
ecpbas2[:,PTR_COEFF] += off
if len(mol1._ecpbas) == 0:
mol3._ecpbas = ecpbas2
else:
mol3._ecpbas = numpy.vstack((mol1._ecpbas, ecpbas2))
mol3.verbose = mol1.verbose
mol3.output = mol1.output
mol3.max_memory = mol1.max_memory
mol3.charge = mol1.charge + mol2.charge
mol3.spin = abs(mol1.spin - mol2.spin)
mol3.symmetry = False
mol3.symmetry_subgroup = None
mol3.cart = mol1.cart and mol2.cart
mol3._atom = mol1._atom + mol2._atom
mol3.atom = mol3._atom
mol3.unit = 'Bohr'
mol3._basis.update(mol2._basis)
mol3._basis.update(mol1._basis)
mol3._pseudo.update(mol2._pseudo)
mol3._pseudo.update(mol1._pseudo)
mol3._ecp.update(mol2._ecp)
mol3._ecp.update(mol1._ecp)
mol3._pseudo.update(mol2._pseudo)
mol3._pseudo.update(mol1._pseudo)
mol3.basis = mol3._basis
mol3.ecp = mol3._ecp
mol3.pseudo = mol3._pseudo
mol3.nucprop.update(mol1.nucprop)
mol3.nucprop.update(mol2.nucprop)
return mol3
# <bas-of-mol1|intor|bas-of-mol2>
[docs]
def intor_cross(intor, mol1, mol2, comp=None, grids=None):
r'''1-electron integrals from two molecules like
.. math::
\langle \mu | intor | \nu \rangle, \mu \in mol1, \nu \in mol2
Args:
intor : str
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 :func:`getints` for the
full list of available 1-electron integral names
mol1, mol2:
:class:`Mole` objects
Kwargs:
comp : int
Components of the integrals, e.g. int1e_ipovlp_sph has 3 components
grids : ndarray
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]]
'''
nbas1 = len(mol1._bas)
nbas2 = len(mol2._bas)
atmc, basc, envc = conc_env(mol1._atm, mol1._bas, mol1._env,
mol2._atm, mol2._bas, mol2._env)
if '_grids' in intor:
assert grids is not None
envc = numpy.append(envc, grids.ravel())
envc[NGRIDS] = grids.shape[0]
envc[PTR_GRIDS] = envc.size - grids.size
shls_slice = (0, nbas1, nbas1, nbas1+nbas2)
if (intor.endswith('_sph') or intor.startswith('cint') or
intor.endswith('_spinor') or intor.endswith('_cart')):
return moleintor.getints(intor, atmc, basc, envc, shls_slice, comp, 0)
elif mol1.cart == mol2.cart:
intor = mol1._add_suffix(intor)
return moleintor.getints(intor, atmc, basc, envc, shls_slice, comp, 0)
elif mol1.cart:
mat = moleintor.getints(intor+'_cart', atmc, basc, envc, shls_slice, comp, 0)
return numpy.dot(mat, mol2.cart2sph_coeff())
else:
mat = moleintor.getints(intor+'_cart', atmc, basc, envc, shls_slice, comp, 0)
return numpy.dot(mol1.cart2sph_coeff().T, mat)
# append (charge, pointer to coordinates, nuc_mod) to _atm
[docs]
def make_atm_env(atom, ptr=0, nuclear_model=NUC_POINT, nucprop={}):
'''Convert the internal format :attr:`Mole._atom` to the format required
by ``libcint`` integrals
'''
nuc_charge = charge(atom[0])
if nuclear_model == NUC_POINT:
zeta = 0
elif nuclear_model == NUC_GAUSS:
zeta = dyall_nuc_mod(nuc_charge, nucprop)
else: # callable(nuclear_model)
zeta = nuclear_model(nuc_charge, nucprop)
nuclear_model = NUC_GAUSS
_env = numpy.hstack((atom[1], zeta))
_atm = numpy.zeros(6, dtype=numpy.int32)
_atm[CHARGE_OF] = nuc_charge
_atm[PTR_COORD] = ptr
_atm[NUC_MOD_OF] = nuclear_model
_atm[PTR_ZETA ] = ptr + 3
return _atm, _env
# append (atom, l, nprim, nctr, kappa, ptr_exp, ptr_coeff, 0) to bas
# absorb normalization into GTO contraction coefficients
[docs]
def make_bas_env(basis_add, atom_id=0, ptr=0):
'''Convert :attr:`Mole.basis` to the argument ``bas`` for ``libcint`` integrals
'''
_bas = []
_env = []
for b in basis_add:
angl = b[0]
if angl > 14:
sys.stderr.write('Warning: integral library does not support basis '
'with angular momentum > 14\n')
if isinstance(b[1], int):
kappa = b[1]
b_coeff = numpy.array(sorted(list(b[2:]), reverse=True))
else:
kappa = 0
b_coeff = numpy.array(sorted(list(b[1:]), reverse=True))
es = b_coeff[:,0]
cs = b_coeff[:,1:]
nprim, nctr = cs.shape
cs = numpy.einsum('pi,p->pi', cs, gto_norm(angl, es))
if NORMALIZE_GTO:
cs = _nomalize_contracted_ao(angl, es, cs)
_env.append(es)
_env.append(cs.T.reshape(-1))
ptr_exp = ptr
ptr_coeff = ptr_exp + nprim
ptr = ptr_coeff + nprim * nctr
_bas.append([atom_id, angl, nprim, nctr, kappa, ptr_exp, ptr_coeff, 0])
_env = lib.flatten(_env) # flatten nested lists
return (numpy.array(_bas, numpy.int32).reshape(-1,BAS_SLOTS),
numpy.array(_env, numpy.double))
def _nomalize_contracted_ao(l, es, cs):
#ee = numpy.empty((nprim,nprim))
#for i in range(nprim):
# for j in range(i+1):
# ee[i,j] = ee[j,i] = gaussian_int(angl*2+2, es[i]+es[j])
#s1 = 1/numpy.sqrt(numpy.einsum('pi,pq,qi->i', cs, ee, cs))
ee = es.reshape(-1,1) + es.reshape(1,-1)
ee = gaussian_int(l*2+2, ee)
s1 = 1. / numpy.sqrt(numpy.einsum('pi,pq,qi->i', cs, ee, cs))
return numpy.einsum('pi,i->pi', cs, s1)
[docs]
def make_env(atoms, basis, pre_env=[], nucmod={}, nucprop={}):
'''Generate the input arguments for ``libcint`` library based on internal
format :attr:`Mole._atom` and :attr:`Mole._basis`
'''
_atm = []
_bas = []
_env = []
ptr_env = len(pre_env)
for ia, atom in enumerate(atoms):
symb = atom[0]
stdsymb = _rm_digit(symb)
if ia+1 in nucprop:
prop = nucprop[ia+1]
elif symb in nucprop:
prop = nucprop[symb]
else:
prop = nucprop.get(stdsymb, {})
nuclear_model = NUC_POINT
if nucmod:
if nucmod is None:
nuclear_model = NUC_POINT
elif isinstance(nucmod, (int, str, types.FunctionType)):
nuclear_model = _parse_nuc_mod(nucmod)
elif ia+1 in nucmod:
nuclear_model = _parse_nuc_mod(nucmod[ia+1])
elif symb in nucmod:
nuclear_model = _parse_nuc_mod(nucmod[symb])
elif stdsymb in nucmod:
nuclear_model = _parse_nuc_mod(nucmod[stdsymb])
atm0, env0 = make_atm_env(atom, ptr_env, nuclear_model, prop)
ptr_env = ptr_env + len(env0)
_atm.append(atm0)
_env.append(env0)
_basdic = {}
for symb, basis_add in basis.items():
bas0, env0 = make_bas_env(basis_add, 0, ptr_env)
ptr_env = ptr_env + len(env0)
_basdic[symb] = bas0
_env.append(env0)
for ia, atom in enumerate(atoms):
symb = atom[0]
puresymb = _rm_digit(symb)
if symb in _basdic:
b = _basdic[symb].copy()
elif puresymb in _basdic:
b = _basdic[puresymb].copy()
else:
if symb[:2].upper() == 'X-':
symb = symb[2:]
elif symb[:6].upper() == 'GHOST-':
symb = symb[6:]
puresymb = _rm_digit(symb)
if symb in _basdic:
b = _basdic[symb].copy()
elif puresymb in _basdic:
b = _basdic[puresymb].copy()
else:
sys.stderr.write('Warning: Basis not found for atom %d %s\n' % (ia, symb))
continue
b[:,ATOM_OF] = ia
_bas.append(b)
if _atm:
_atm = numpy.asarray(numpy.vstack(_atm), numpy.int32).reshape(-1, ATM_SLOTS)
else:
_atm = numpy.zeros((0,ATM_SLOTS), numpy.int32)
if _bas:
_bas = numpy.asarray(numpy.vstack(_bas), numpy.int32).reshape(-1, BAS_SLOTS)
else:
_bas = numpy.zeros((0,BAS_SLOTS), numpy.int32)
if _env:
_env = numpy.hstack((pre_env,numpy.hstack(_env)))
else:
_env = numpy.array(pre_env, copy=False)
return _atm, _bas, _env
[docs]
def make_ecp_env(mol, _atm, ecp, pre_env=[]):
'''Generate the input arguments _ecpbas for ECP integrals
'''
_env = []
ptr_env = len(pre_env)
_ecpdic = {}
for symb, ecp_add in ecp.items():
ecp0 = []
nelec = ecp_add[0]
for lb in ecp_add[1]:
for rorder, bi in enumerate(lb[1]):
if len(bi) > 0:
ec = numpy.array(sorted(bi, reverse=True))
nexp, ncol = ec.shape
_env.append(ec[:,0])
_env.append(ec[:,1])
ptr_exp, ptr_coeff = ptr_env, ptr_env + nexp
ecp0.append([0, lb[0], nexp, rorder, 0,
ptr_exp, ptr_coeff, 0])
ptr_env += nexp * 2
if ncol == 3: # Has SO-ECP
_env.append(ec[:,2])
ptr_coeff, ptr_env = ptr_env, ptr_env + nexp
ecp0.append([0, lb[0], nexp, rorder, 1,
ptr_exp, ptr_coeff, 0])
_ecpdic[symb] = (nelec, numpy.asarray(ecp0, dtype=numpy.int32))
_ecpbas = []
if _ecpdic:
_atm = _atm.copy()
for ia, atom in enumerate(mol._atom):
symb = atom[0]
if symb in _ecpdic:
ecp0 = _ecpdic[symb]
elif _rm_digit(symb) in _ecpdic:
ecp0 = _ecpdic[_rm_digit(symb)]
else:
ecp0 = None
if ecp0 is not None:
_atm[ia,CHARGE_OF ] = charge(symb) - ecp0[0]
_atm[ia,NUC_MOD_OF] = NUC_ECP
b = ecp0[1].copy().reshape(-1,BAS_SLOTS)
b[:,ATOM_OF] = ia
_ecpbas.append(b)
if _ecpbas:
_ecpbas = numpy.asarray(numpy.vstack(_ecpbas), numpy.int32)
_env = numpy.hstack([pre_env] + _env)
else:
_ecpbas = numpy.zeros((0,BAS_SLOTS), numpy.int32)
_env = pre_env
return _atm, _ecpbas, _env
[docs]
def tot_electrons(mol):
'''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
'''
if mol._atm.size != 0:
nelectron = mol.atom_charges().sum()
elif mol._atom:
nelectron = sum(charge(a[0]) for a in mol._atom)
else:
nelectron = sum(charge(a[0]) for a in format_atom(mol.atom))
nelectron -= mol.charge
nelectron_int = int(round(nelectron))
if abs(nelectron - nelectron_int) > 1e-4:
logger.warn(mol, 'Found fractional number of electrons %f. Round it to %d',
nelectron, nelectron_int)
return nelectron_int
[docs]
def copy(mol, deep=True):
'''Deepcopy of the given :class:`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.
'''
# Avoid copy.copy(mol) for shallow copy because copy.copy automatically
# calls __copy__, __reduce__, __getstate__, __setstate__ methods
newmol = mol.view(mol.__class__)
if not deep:
return newmol
import copy
newmol._atm = numpy.copy(mol._atm)
newmol._bas = numpy.copy(mol._bas)
newmol._env = numpy.copy(mol._env)
newmol._ecpbas = numpy.copy(mol._ecpbas)
newmol.atom = copy.deepcopy(mol.atom)
newmol._atom = copy.deepcopy(mol._atom)
newmol.basis = copy.deepcopy(mol.basis)
newmol._basis = copy.deepcopy(mol._basis)
newmol.ecp = copy.deepcopy(mol.ecp)
newmol._ecp = copy.deepcopy(mol._ecp)
newmol.pseudo = copy.deepcopy(mol.pseudo)
newmol._pseudo = copy.deepcopy(mol._pseudo)
return newmol
[docs]
def pack(mol):
'''Pack the input args of :class:`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 :func:`dumps` to serialize the entire Mole object.
'''
mdic = {'atom' : mol.atom,
'unit' : mol.unit,
'basis' : mol.basis,
'charge' : mol.charge,
'spin' : mol.spin,
'symmetry': mol.symmetry,
'nucmod' : mol.nucmod,
'nucprop' : mol.nucprop,
'ecp' : mol.ecp,
'pseudo' : mol.pseudo,
'_nelectron': mol._nelectron,
'verbose' : mol.verbose}
return mdic
[docs]
def unpack(moldic):
'''Unpack a dict which is packed by :func:`pack`, to generate the input
arguments for :class:`Mole` object.
'''
mol = Mole()
mol.__dict__.update(moldic)
return mol
[docs]
def dumps(mol):
'''Serialize Mole object to a JSON formatted str.
'''
exclude_keys = set(('output', 'stdout', '_keys',
# Constructing in function loads
'symm_orb', 'irrep_id', 'irrep_name'))
# FIXME: nparray and kpts for cell objects may need to be excluded
nparray_keys = set(('_atm', '_bas', '_env', '_ecpbas',
'_symm_orig', '_symm_axes'))
moldic = dict(mol.__dict__)
for k in exclude_keys:
if k in moldic:
del (moldic[k])
for k in nparray_keys:
if isinstance(moldic[k], numpy.ndarray):
moldic[k] = moldic[k].tolist()
moldic['atom'] = repr(mol.atom)
moldic['basis']= repr(mol.basis)
moldic['ecp' ] = repr(mol.ecp)
moldic['pseudo'] = repr(mol.pseudo)
try:
return json.dumps(moldic)
except TypeError:
def skip_value(dic):
dic1 = {}
for k,v in dic.items():
if (v is None or
isinstance(v, (str, bool, int, float))):
dic1[k] = v
elif isinstance(v, (list, tuple)):
dic1[k] = v # Should I recursively skip_vaule?
elif isinstance(v, set):
dic1[k] = list(v)
elif isinstance(v, dict):
dic1[k] = skip_value(v)
else:
msg =('Function mol.dumps drops attribute %s because '
'it is not JSON-serializable' % k)
warnings.warn(msg)
return dic1
return json.dumps(skip_value(moldic), skipkeys=True)
[docs]
def loads(molstr):
'''Deserialize a str containing a JSON document to a Mole object.
'''
# the numpy function array is used by eval function
from numpy import array # noqa
moldic = json.loads(molstr)
mol = Mole()
mol.__dict__.update(moldic)
mol.atom = eval(mol.atom)
mol.basis= eval(mol.basis)
mol.ecp = eval(mol.ecp)
mol.pseudo = eval(mol.pseudo)
mol._atm = numpy.array(mol._atm, dtype=numpy.int32)
mol._bas = numpy.array(mol._bas, dtype=numpy.int32)
mol._env = numpy.array(mol._env, dtype=numpy.double)
mol._ecpbas = numpy.array(mol._ecpbas, dtype=numpy.int32)
# Objects related to symmetry cannot be serialized by dumps function.
# Recreate it manually
if mol.symmetry and mol._symm_orig is not None:
from pyscf import symm
mol._symm_orig = numpy.array(mol._symm_orig)
mol._symm_axes = numpy.array(mol._symm_axes)
mol.symm_orb, mol.irrep_id = \
symm.symm_adapted_basis(mol, mol.groupname,
mol._symm_orig, mol._symm_axes)
mol.irrep_name = [symm.irrep_id2name(mol.groupname, ir)
for ir in mol.irrep_id]
elif mol.symmetry and mol.symm_orb is not None:
# Backward compatibility. To load symm_orb from chkfile of pyscf-1.6
# and earlier.
symm_orb = []
# decompress symm_orb
for val, x, y, shape in mol.symm_orb:
if isinstance(val[0], list):
# backward compatibility for chkfile of pyscf-1.4 in which val
# is an array of real floats. In pyscf-1.5, val can be a list
# of list, to include the imaginary part
val_real, val_imag = val
else:
val_real, val_imag = val, None
if val_imag is None:
c = numpy.zeros(shape)
c[numpy.array(x),numpy.array(y)] = numpy.array(val_real)
else:
c = numpy.zeros(shape, dtype=numpy.complex128)
val = numpy.array(val_real) + numpy.array(val_imag) * 1j
c[numpy.array(x),numpy.array(y)] = val
symm_orb.append(c)
mol.symm_orb = symm_orb
return mol
[docs]
def len_spinor(l, kappa):
'''The number of spinor associated with given angular momentum and kappa. If kappa is 0,
return 4l+2
'''
if kappa == 0:
n = (l * 4 + 2)
elif kappa < 0:
n = (l * 2 + 2)
else:
n = (l * 2)
return n
[docs]
def len_cart(l):
'''The number of Cartesian function associated with given angular momentum.
'''
return (l + 1) * (l + 2) // 2
[docs]
def npgto_nr(mol, cart=None):
'''Total number of primitive spherical GTOs for the given :class:`Mole` object'''
if cart is None:
cart = mol.cart
l = mol._bas[:,ANG_OF]
if cart:
return ((l+1)*(l+2)//2 * mol._bas[:,NPRIM_OF]).sum()
else:
return ((l*2+1) * mol._bas[:,NPRIM_OF]).sum()
[docs]
def nao_nr(mol, cart=None):
'''Total number of contracted GTOs for the given :class:`Mole` object'''
if cart is None:
cart = mol.cart
if cart:
return nao_cart(mol)
else:
return ((mol._bas[:,ANG_OF]*2+1) * mol._bas[:,NCTR_OF]).sum()
[docs]
def nao_cart(mol):
'''Total number of contracted cartesian GTOs for the given :class:`Mole` object'''
l = mol._bas[:,ANG_OF]
return ((l+1)*(l+2)//2 * mol._bas[:,NCTR_OF]).sum()
# nao_id0:nao_id1 corresponding to bas_id0:bas_id1
[docs]
def nao_nr_range(mol, bas_id0, bas_id1):
'''Lower and upper boundary of contracted spherical basis functions associated
with the given shell range
Args:
mol :
:class:`Mole` object
bas_id0 : int
start shell id
bas_id1 : int
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)
'''
ao_loc = moleintor.make_loc(mol._bas[:bas_id1], 'sph')
nao_id0 = ao_loc[bas_id0]
nao_id1 = ao_loc[-1]
return nao_id0, nao_id1
[docs]
def nao_2c(mol):
'''Total number of contracted spinor GTOs for the given :class:`Mole` object'''
l = mol._bas[:,ANG_OF]
kappa = mol._bas[:,KAPPA_OF]
dims = (l*4+2) * mol._bas[:,NCTR_OF]
dims[kappa<0] = (l[kappa<0] * 2 + 2) * mol._bas[kappa<0,NCTR_OF]
dims[kappa>0] = (l[kappa>0] * 2) * mol._bas[kappa>0,NCTR_OF]
return dims.sum()
# nao_id0:nao_id1 corresponding to bas_id0:bas_id1
[docs]
def nao_2c_range(mol, bas_id0, bas_id1):
'''Lower and upper boundary of contracted spinor basis functions associated
with the given shell range
Args:
mol :
:class:`Mole` object
bas_id0 : int
start shell id, 0-based
bas_id1 : int
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)
'''
ao_loc = moleintor.make_loc(mol._bas[:bas_id1], '')
nao_id0 = ao_loc[bas_id0]
nao_id1 = ao_loc[-1]
return nao_id0, nao_id1
[docs]
def ao_loc_nr(mol, 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]
'''
if cart is None:
cart = mol.cart
if cart:
return moleintor.make_loc(mol._bas, 'cart')
else:
return moleintor.make_loc(mol._bas, 'sph')
[docs]
def ao_loc_2c(mol):
'''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]
'''
return moleintor.make_loc(mol._bas, 'spinor')
[docs]
def time_reversal_map(mol):
r'''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 :math:`T|i\rangle = -|j\rangle`,
otherwise :math:`T|i\rangle = |j\rangle`
'''
tao = []
i = 0
for b in mol._bas:
l = b[ANG_OF]
if b[KAPPA_OF] == 0:
djs = (l * 2, l * 2 + 2)
elif b[KAPPA_OF] > 0:
djs = (l * 2,)
else:
djs = (l * 2 + 2,)
if l % 2 == 0:
for n in range(b[NCTR_OF]):
for dj in djs:
for m in range(0, dj, 2):
tao.append(-(i + dj - m))
tao.append( i + dj - m - 1)
i += dj
else:
for n in range(b[NCTR_OF]):
for dj in djs:
for m in range(0, dj, 2):
tao.append( i + dj - m)
tao.append(-(i + dj - m - 1))
i += dj
return numpy.asarray(tao, dtype=numpy.int32)
CHECK_GEOM = getattr(__config__, 'gto_mole_check_geom', True)
[docs]
def classical_coulomb_energy(mol, charges=None, coords=None):
'''Compute nuclear repulsion energy (AU) or static Coulomb energy
Returns
float
'''
if charges is None: charges = mol.atom_charges()
if len(charges) <= 1:
return 0
rr = inter_distance(mol, coords)
rr[numpy.diag_indices_from(rr)] = 1e200
if CHECK_GEOM and numpy.any(rr < 1e-5):
raise_err = False
for atm_idx in numpy.argwhere(rr<1e-5):
# Only raise error if atoms with charge != 0 have the same coordinates
if charges[atm_idx[0]] * charges[atm_idx[1]] != 0:
logger.warn(mol, 'Atoms %s have the same coordinates', atm_idx)
raise_err = True
# At least one of the atoms is a ghost atom; suppress divide by 0 warning
else:
rr[atm_idx[0], atm_idx[1]] = 1e200
if raise_err: raise RuntimeError('Ill geometry')
e = numpy.einsum('i,ij,j->', charges, 1./rr, charges) * .5
return e
energy_nuc = classical_coulomb_energy
[docs]
def inter_distance(mol, coords=None):
'''
Inter-particle distance array
'''
if coords is None: coords = mol.atom_coords()
rr = numpy.linalg.norm(coords.reshape(-1,1,3) - coords, axis=2)
rr[numpy.diag_indices_from(rr)] = 0
return rr
[docs]
def sph_labels(mol, fmt=True, base=BASE):
'''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')]
'''
count = numpy.zeros((mol.natm, 9), dtype=int)
label = []
for ib in range(mol.nbas):
ia = mol.bas_atom(ib)
l = mol.bas_angular(ib)
strl = param.ANGULAR[l]
nc = mol.bas_nctr(ib)
symb = mol.atom_symbol(ia)
nelec_ecp = mol.atom_nelec_core(ia)
if nelec_ecp == 0 or l > 3:
shl_start = count[ia,l]+l+1
else:
coreshl = core_configuration(nelec_ecp, atom_symbol=_std_symbol(symb))
shl_start = coreshl[l]+count[ia,l]+l+1
count[ia,l] += nc
for n in range(shl_start, shl_start+nc):
for m in range(-l, l+1):
label.append((ia+base, symb, '%d%s' % (n, strl),
str(param.REAL_SPHERIC[l][l+m])))
if isinstance(fmt, str):
return [(fmt % x) for x in label]
elif fmt:
return ['%d %s %s%-4s' % x for x in label]
else:
return label
spheric_labels = spherical_labels = sph_labels
[docs]
def cart_labels(mol, fmt=True, base=BASE):
'''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"
'''
cartxyz = []
for l in range(max(mol._bas[:,ANG_OF])+1):
xyz = []
for x in range(l, -1, -1):
for y in range(l-x, -1, -1):
z = l-x-y
xyz.append('x'*x + 'y'*y + 'z'*z)
cartxyz.append(xyz)
count = numpy.zeros((mol.natm, 9), dtype=int)
label = []
for ib in range(len(mol._bas)):
ia = mol.bas_atom(ib)
l = mol.bas_angular(ib)
strl = param.ANGULAR[l]
nc = mol.bas_nctr(ib)
symb = mol.atom_symbol(ia)
nelec_ecp = mol.atom_nelec_core(ia)
if nelec_ecp == 0 or l > 3:
shl_start = count[ia,l]+l+1
else:
coreshl = core_configuration(nelec_ecp, atom_symbol=_std_symbol(symb))
shl_start = coreshl[l]+count[ia,l]+l+1
count[ia,l] += nc
ncart = (l + 1) * (l + 2) // 2
for n in range(shl_start, shl_start+nc):
for m in range(ncart):
label.append((ia+base, symb, '%d%s' % (n, strl), cartxyz[l][m]))
if isinstance(fmt, str):
return [(fmt % x) for x in label]
elif fmt:
return ['%d%3s %s%-4s' % x for x in label]
else:
return label
[docs]
def ao_labels(mol, fmt=True, base=BASE):
'''Labels of AO basis 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-AO-notation)]
or formatted strings based on the argument "fmt"
'''
if mol.cart:
return mol.cart_labels(fmt, base)
else:
return mol.sph_labels(fmt, base)
[docs]
def spinor_labels(mol, fmt=True, base=BASE):
'''
Labels of spinor GTO functions
'''
count = numpy.zeros((mol.natm, 9), dtype=int)
label = []
for ib in range(mol.nbas):
ia = mol.bas_atom(ib)
l = mol.bas_angular(ib)
kappa = mol.bas_kappa(ib)
strl = param.ANGULAR[l]
nc = mol.bas_nctr(ib)
symb = mol.atom_symbol(ia)
nelec_ecp = mol.atom_nelec_core(ia)
if nelec_ecp == 0 or l > 3:
shl_start = count[ia,l]+l+1
else:
coreshl = core_configuration(nelec_ecp, atom_symbol=_std_symbol(symb))
shl_start = coreshl[l]+count[ia,l]+l+1
count[ia,l] += nc
for n in range(shl_start, shl_start+nc):
if kappa >= 0:
for m in range(-l*2+1, l*2, 2):
label.append((ia+base, symb, '%d%s%d/2' % (n, strl, l*2-1),
'%d/2'%m))
if kappa <= 0:
for m in range(-l*2-1, l*2+2, 2):
label.append((ia+base, symb, '%d%s%d/2' % (n, strl, l*2+1),
'%d/2'%m))
if isinstance(fmt, str):
return [(fmt % x) for x in label]
elif fmt:
return ['%d %s %s,%-5s' % x for x in label]
else:
return label
[docs]
def search_ao_label(mol, label):
'''Find the index of the AO basis function based on the given ao_label
Args:
ao_label : string 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]
'''
return _aolabels2baslst(mol, label)
def _aolabels2baslst(mol, aolabels_or_baslst, base=BASE):
if callable(aolabels_or_baslst):
baslst = [i for i,x in enumerate(mol.ao_labels(base=base))
if aolabels_or_baslst(x)]
elif isinstance(aolabels_or_baslst, str):
aolabels = re.sub(' +', ' ', aolabels_or_baslst.strip(), count=1)
aolabels = re.compile(aolabels)
baslst = [i for i,s in enumerate(mol.ao_labels(base=base))
if re.search(aolabels, s)]
elif len(aolabels_or_baslst) > 0 and isinstance(aolabels_or_baslst[0], str):
aolabels = [re.compile(re.sub(' +', ' ', x.strip(), count=1))
for x in aolabels_or_baslst]
baslst = [i for i,t in enumerate(mol.ao_labels(base=base))
if any(re.search(x, t) for x in aolabels)]
else:
baslst = [i-base for i in aolabels_or_baslst]
return numpy.asarray(baslst, dtype=int)
[docs]
def search_shell_id(mol, atm_id, l):
'''Search the first basis/shell id (**not** the basis function id) which
matches the given atom-id and angular momentum
Args:
atm_id : int
atom id, 0-based
l : int
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
'''
for ib in range(len(mol._bas)):
ia = mol.bas_atom(ib)
l1 = mol.bas_angular(ib)
if ia == atm_id and l1 == l:
return ib
[docs]
def search_ao_nr(mol, 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_id : int
atom id, 0-based
l : int
angular momentum
m : int
magnetic angular momentum
atmshell : int
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
'''
ibf = 0
for ib in range(len(mol._bas)):
ia = mol.bas_atom(ib)
l1 = mol.bas_angular(ib)
if mol.cart:
degen = (l1 + 1) * (l1 + 2) // 2
else:
degen = l1 * 2 + 1
nc = mol.bas_nctr(ib)
if ia == atm_id and l1 == l:
if atmshell > nc+l1:
atmshell = atmshell - nc
else:
return ibf + (atmshell-l1-1)*degen + (l1+m)
ibf += degen * nc
raise RuntimeError('Required AO not found')
[docs]
def search_ao_r(mol, atm_id, l, j, m, atmshell):
raise RuntimeError('TODO')
#TODO: ibf = 0
#TODO: for ib in range(len(mol._bas)):
#TODO: ia = mol.bas_atom(ib)
#TODO: l1 = mol.bas_angular(ib)
#TODO: nc = mol.bas_nctr(ib)
#TODO: k = mol.bas_kappa(bas_id)
#TODO: degen = len_spinor(l1, k)
#TODO: if ia == atm_id and l1 == l and k == kappa:
#TODO: if atmshell > nc+l1:
#TODO: atmshell = atmshell - nc
#TODO: else:
#TODO: return ibf + (atmshell-l1-1)*degen + (degen+m)
#TODO: ibf += degen
[docs]
def offset_2c_by_atom(mol):
'''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)
'''
return aoslice_by_atom(mol, mol.ao_loc_2c())
[docs]
def aoslice_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)
'''
if ao_loc is None:
ao_loc = mol.ao_loc_nr()
aorange = numpy.empty((mol.natm,4), dtype=int)
if mol.natm == 0:
return aorange
bas_atom = mol._bas[:,ATOM_OF]
delimiter = numpy.where(bas_atom[0:-1] != bas_atom[1:])[0] + 1
if mol.natm == len(delimiter) + 1:
aorange[:,0] = shell_start = numpy.append(0, delimiter)
aorange[:,1] = shell_end = numpy.append(delimiter, mol.nbas)
else: # Some atoms miss basis
shell_start = numpy.empty(mol.natm, dtype=int)
shell_start[:] = -1
shell_start[0] = 0
shell_start[bas_atom[0]] = 0
shell_start[bas_atom[delimiter]] = delimiter
shell_end = numpy.empty(mol.natm, dtype=int)
shell_end[0] = 0
shell_end[bas_atom[delimiter-1]] = delimiter
shell_end[bas_atom[-1]] = mol.nbas
for i in range(1, mol.natm):
if shell_start[i] == -1:
shell_start[i] = shell_end[i] = shell_end[i-1]
aorange[:,0] = shell_start
aorange[:,1] = shell_end
aorange[:,2] = ao_loc[shell_start]
aorange[:,3] = ao_loc[shell_end]
return aorange
offset_nr_by_atom = aoslice_by_atom
[docs]
def same_basis_set(mol1, mol2):
'''Check whether two molecules use the same basis sets.
The two molecules can have different geometry.
'''
atomtypes1 = atom_types(mol1._atom, mol1._basis)
atomtypes2 = atom_types(mol2._atom, mol2._basis)
if set(atomtypes1.keys()) != set(atomtypes2.keys()):
return False
for k in atomtypes1:
if len(atomtypes1[k]) != len(atomtypes2[k]):
return False
elif mol1._basis.get(k, None) != mol2._basis.get(k, None):
return False
return True
[docs]
def same_mol(mol1, mol2, tol=1e-5, cmp_basis=True, ignore_chiral=False):
'''Compare the two molecules whether they have the same structure.
Kwargs:
tol : float
In Bohr
cmp_basis : bool
Whether to compare basis functions for the two molecules
'''
from pyscf import symm
if mol1._atom.__len__() != mol2._atom.__len__():
return False
chg1 = mol1._atm[:,CHARGE_OF]
chg2 = mol2._atm[:,CHARGE_OF]
if not numpy.all(numpy.sort(chg1) == numpy.sort(chg2)):
return False
if cmp_basis and not same_basis_set(mol1, mol2):
return False
def finger(mol, chgs, coord):
center = numpy.einsum('z,zr->r', chgs, coord) / chgs.sum()
im = inertia_moment(mol, chgs, coord)
# Divid im by chgs.sum(), to normalize im. Otherwise the input tol may
# not reflect the actual deviation.
im /= chgs.sum()
w, v = scipy.linalg.eigh(im)
axes = v.T
if numpy.linalg.det(axes) < 0:
axes *= -1
r = numpy.dot(coord-center, axes.T)
return w, r
coord1 = mol1.atom_coords()
coord2 = mol2.atom_coords()
w1, r1 = finger(mol1, chg1, coord1)
w2, r2 = finger(mol2, chg2, coord2)
if not (numpy.allclose(w1, w2, atol=tol)):
return False
rotate_xy = numpy.array([[-1., 0., 0.],
[ 0.,-1., 0.],
[ 0., 0., 1.]])
rotate_yz = numpy.array([[ 1., 0., 0.],
[ 0.,-1., 0.],
[ 0., 0.,-1.]])
rotate_zx = numpy.array([[-1., 0., 0.],
[ 0., 1., 0.],
[ 0., 0.,-1.]])
def inspect(z1, r1, z2, r2):
place = int(-numpy.log10(tol)) - 1
idx = symm.argsort_coords(r2, place)
z2 = z2[idx]
r2 = r2[idx]
for rot in (1, rotate_xy, rotate_yz, rotate_zx):
r1new = numpy.dot(r1, rot)
idx = symm.argsort_coords(r1new, place)
if (numpy.all(z1[idx] == z2) and
numpy.allclose(r1new[idx], r2, atol=tol)):
return True
return False
return (inspect(chg1, r1, chg2, r2) or
(ignore_chiral and inspect(chg1, r1, chg2, -r2)))
is_same_mol = same_mol
[docs]
def chiral_mol(mol1, mol2=None):
'''Detect whether the given molelcule is chiral molecule or two molecules
are chiral isomers.
'''
if mol2 is None:
mol2 = mol1.copy()
ptr_coord = mol2._atm[:,PTR_COORD]
mol2._env[ptr_coord ] *= -1
mol2._env[ptr_coord+1] *= -1
mol2._env[ptr_coord+2] *= -1
return (not same_mol(mol1, mol2, ignore_chiral=False) and
same_mol(mol1, mol2, ignore_chiral=True))
[docs]
def inertia_moment(mol, mass=None, coords=None):
if mass is None:
mass = mol.atom_mass_list()
if coords is None:
coords = mol.atom_coords()
mass_center = numpy.einsum('i,ij->j', mass, coords)/mass.sum()
coords = coords - mass_center
im = numpy.einsum('i,ij,ik->jk', mass, coords, coords)
im = numpy.eye(3) * im.trace() - im
return im
[docs]
def atom_mass_list(mol, isotope_avg=False):
'''A list of mass for all atoms in the molecule
Kwargs:
isotope_avg : boolean
Whether to use the isotope average mass as the atomic mass
'''
if isotope_avg:
mass_table = elements.MASSES
else:
mass_table = elements.ISOTOPE_MAIN
nucprop = mol.nucprop
if nucprop:
mass = []
for ia in range(mol.natm):
z = mol.atom_charge(ia)
symb = mol.atom_symbol(ia)
stdsymb = _std_symbol(symb)
if ia+1 in nucprop:
prop = nucprop[ia+1]
elif symb in nucprop:
prop = nucprop[symb]
else:
prop = nucprop.get(stdsymb, {})
mass.append(prop.get('mass', mass_table[z]))
else:
#mass = [mass_table[z] for z in mol.atom_charges()]
mass = []
for ia in range(mol.natm):
z = charge(mol.atom_symbol(ia))
mass.append(mass_table[z])
return numpy.array(mass)
[docs]
def condense_to_shell(mol, 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
'''
ao_loc = mol.ao_loc_nr()
if callable(compressor):
abstract = numpy.empty((mol.nbas, mol.nbas))
for i, i0 in enumerate(ao_loc[:mol.nbas]):
for j, j0 in enumerate(ao_loc[:mol.nbas]):
abstract[i,j] = compressor(mat[i0:ao_loc[i+1],j0:ao_loc[j+1]])
else:
abstract = lib.condense(compressor, mat, ao_loc)
return abstract
[docs]
def get_overlap_cond(mol, shls_slice=None):
'''Overlap magnitudes measured by -log(overlap) between two shells
Args:
mol : an instance of :class:`Mole`
Returns:
2D mask array of shape (nbas,nbas)
'''
nbas = mol.nbas
if shls_slice is None:
shls_slice = (0, nbas, 0, nbas)
cond = numpy.zeros((nbas, nbas))
moleintor.libcgto.GTOoverlap_cond(
cond.ctypes.data_as(ctypes.c_void_p), (ctypes.c_int * 4)(*shls_slice),
mol._atm.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(mol.natm),
mol._bas.ctypes.data_as(ctypes.c_void_p), ctypes.c_int(nbas),
mol._env.ctypes.data_as(ctypes.c_void_p))
return cond
[docs]
def tostring(mol, 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
'''
format = format.lower()
if format == 'xyz' or format == 'raw':
coords = mol.atom_coords() * param.BOHR
output = []
if format == 'xyz':
output.append('%d' % mol.natm)
output.append('XYZ from PySCF')
for i in range(mol.natm):
symb = mol.atom_pure_symbol(i)
x, y, z = coords[i]
output.append('%-4s %14.5f %14.5f %14.5f' %
(symb, x, y, z))
return '\n'.join(output)
elif format == 'zmat':
coords = mol.atom_coords() * param.BOHR
zmat = cart2zmat(coords).splitlines()
output = []
for i, line in enumerate(zmat):
symb = mol.atom_pure_symbol(i)
output.append('%-4s %s' % (symb, line))
return '\n'.join(output)
else:
raise NotImplementedError
[docs]
def tofile(mol, 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
'''
if format is None: # Guess format based on filename
format = os.path.splitext(filename)[1][1:]
string = tostring(mol, format)
with open(filename, 'w') as f:
f.write(string)
f.write('\n')
return string
[docs]
def fromfile(filename, format=None):
'''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
'''
if format is None: # Guess format based on filename
format = os.path.splitext(filename)[1][1:].lower()
if format not in ('xyz', 'zmat', 'sdf'):
format = 'raw'
with open(filename, 'r') as f:
return fromstring(f.read(), format)
[docs]
def fromstring(string, format='xyz'):
'''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
'''
format = format.lower()
if format == 'zmat':
return from_zmatrix(string)
elif format == 'xyz':
dat = string.splitlines()
natm = int(dat[0])
return '\n'.join(dat[2:natm+2])
elif format == 'sdf':
raw = string.splitlines()
natoms, nbonds = raw[3].split()[:2]
atoms = []
for line in raw[4:4+int(natoms)]:
d = line.split()
atoms.append('%s %s %s %s' % (d[3], d[0], d[1], d[2]))
return '\n'.join(atoms)
elif format == 'raw':
return string
else:
raise NotImplementedError
[docs]
def is_au(unit):
'''Return whether the unit is recognized as A.U. or not
'''
return unit.upper().startswith(('B', 'AU'))
#
# MoleBase handles three layers of basis data: input, internal format, libcint arguments.
# The relationship of the three layers are
# .atom (input) <=> ._atom (for python) <=> ._atm (for libcint)
# .basis (input) <=> ._basis (for python) <=> ._bas (for libcint)
# input layer does not talk to libcint directly. Data are held in python
# internal format layer. Most of methods defined in this class only operates
# on the internal format. Exceptions are make_env, make_atm_env, make_bas_env,
# set_common_orig_, set_rinv_orig_ which are used to manipulate the libcint arguments.
#
[docs]
class MoleBase(lib.StreamObject):
'''Basic class to hold molecular structure, integrals and global options
Attributes:
verbose : int
Print level
output : str or None
Output file, default is None which dumps msg to sys.stdout
max_memory : int, float
Allowed memory in MB
charge : int
Charge of molecule. It affects the electron numbers
spin : int 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.
symmetry : bool 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_subgroup : str
subgroup
atom : list or str
To define molecluar structure. The internal format is
| atom = [[atom1, (x, y, z)],
| [atom2, (x, y, z)],
| ...
| [atomN, (x, y, z)]]
unit : str
Angstrom or Bohr
basis : dict or str
To define basis set.
nucmod : dict 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.
nucprop : dict
Nuclear properties (like g-factor 'g', quadrupole moments 'Q').
It is needed by pyscf.prop module and submodules.
cart : boolean
Using Cartesian GTO basis and integrals (6d,10f,15g)
magmom : list
Collinear spin of each atom. Default is [0,]*natm
** Following attributes are generated by :func:`Mole.build` **
stdout : file object
Default is sys.stdout if :attr:`Mole.output` is not set
topgroup : str
Point group of the system.
groupname : str
The supported subgroup of the point group. It can be one of SO3,
Dooh, Coov, D2h, C2h, C2v, D2, Cs, Ci, C2, C1
nelectron : int
sum of nuclear charges - :attr:`Mole.charge`
symm_orb : a 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_id : a 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
:attr:`symm.param.IRREP_ID_TABLE`
irrep_name : a list of str
Each element is one irreducible representation symbol associated with the basis
stored in symm_orb. The irrep symbols are defined in
:attr:`symm.param.IRREP_ID_TABLE`
_built : bool
To label whether :func:`Mole.build` has been called. It is to
ensure certain functions being initialized only once.
_basis : dict
like :attr:`Mole.basis`, the internal format which is returned from the
parser :func:`format_basis`
** Following attributes are arguments used by ``libcint`` library **
_atm :
:code:`[[charge, ptr-of-coord, nuc-model, ptr-zeta, 0, 0], [...]]`
each element represents one atom
natm :
number of atoms
_bas :
:code:`[[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
''' # noqa: E501
output = None
max_memory = param.MAX_MEMORY
verbose = getattr(__config__, 'VERBOSE', logger.NOTE)
# the unit (angstrom/bohr) of the coordinates defined by the input self.atom
unit = getattr(__config__, 'UNIT', 'angstrom')
# Whether to hold everything in memory
incore_anyway = getattr(__config__, 'INCORE_ANYWAY', False)
# Using cartesian GTO (6d,10f,15g)
cart = getattr(__config__, 'gto_mole_Mole_cart', False)
charge = 0
spin = 0 # 2j == nelec_alpha - nelec_beta
symmetry = False
symmetry_subgroup = None
# Store the keys appeared in the module. It is used to check misinput attributes
_keys = {
'verbose', 'unit', 'incore_anyway', 'output', 'max_memory',
'cart', 'charge', 'spin', 'symmetry', 'symmetry_subgroup',
'atom', 'basis', 'nucmod', 'ecp', 'nucprop', 'magmom', 'pseudo',
'groupname', 'topgroup', 'symm_orb', 'irrep_id', 'irrep_name',
}
def __init__(self):
# self.atom = [(symb/nuc_charge, (coord(Angstrom):0.,0.,0.)), ...]
self.atom = []
# self.basis = {atom_type/nuc_charge: [l, kappa, (expnt, c_1, c_2,..),..]}
self.basis = 'sto-3g'
# self.nucmod = {atom_symbol: nuclear_model, atom_id: nuc_mod}, atom_id is 1-based
self.nucmod = {}
# self.ecp = {atom_symbol: [[l, (r_order, expnt, c),...]]}
self.ecp = {}
# Nuclear property. self.nucprop = {atom_symbol: {key: value}}
self.nucprop = {}
# Collinear spin of each atom. self.magmom = [0, ...]
self.magmom = []
self.pseudo = None
##################################################
# don't modify the following private variables, they are not input options
self._atm = numpy.zeros((0,6), dtype=numpy.int32)
self._bas = numpy.zeros((0,8), dtype=numpy.int32)
self._env = numpy.zeros(PTR_ENV_START)
self._ecpbas = numpy.zeros((0,8), dtype=numpy.int32)
self.stdout = sys.stdout
self.groupname = 'C1'
self.topgroup = 'C1'
self.symm_orb = None
self.irrep_id = None
self.irrep_name = None
self._symm_orig = None
self._symm_axes = None
self._nelectron = None
self._nao = None
self._enuc = None
self._atom = []
self._basis = {}
self._ecp = {}
self._pseudo = {}
self._built = False
# Some methods modify ._env. These method are executed in the context
# _TemporaryMoleContext which is protected by the _ctx_lock.
self._ctx_lock = None
@property
def natm(self):
return len(self._atm)
@property
def nbas(self):
return len(self._bas)
@property
def nelec(self):
ne = self.nelectron
nalpha = (ne + self.spin) // 2
nbeta = nalpha - self.spin
assert (nalpha >= 0 and nbeta >= 0)
if nalpha + nbeta != ne:
raise RuntimeError('Electron number %d and spin %d are not consistent\n'
'Note mol.spin = 2S = Nalpha - Nbeta, not 2S+1' %
(ne, self.spin))
return nalpha, nbeta
@nelec.setter
def nelec(self, neleca_nelecb):
neleca, nelecb = neleca_nelecb
self._nelectron = neleca + nelecb
self.spin = neleca - nelecb
@property
def nelectron(self):
if self._nelectron is None:
return self.tot_electrons()
else:
return self._nelectron
@nelectron.setter
def nelectron(self, n):
self._nelectron = n
@property
def multiplicity(self):
return self.spin + 1
@multiplicity.setter
def multiplicity(self, x):
if x is None:
self.spin = None
else:
self.spin = x - 1
@property
def ms(self):
'''Spin quantum number. multiplicity = ms*2+1'''
if self.spin % 2 == 0:
return self.spin // 2
else:
return self.spin * .5
@ms.setter
def ms(self, x):
if x is None:
self.spin = None
else:
self.spin = int(round(2*x, 4))
copy = copy
pack = pack
[docs]
@classmethod
@lib.with_doc(unpack.__doc__)
def unpack(cls, moldic):
return unpack(moldic)
[docs]
@lib.with_doc(unpack.__doc__)
def unpack_(self, moldic):
self.__dict__.update(moldic)
return self
dumps = dumps
[docs]
@classmethod
@lib.with_doc(loads.__doc__)
def loads(cls, molstr):
return loads(molstr)
[docs]
@lib.with_doc(loads.__doc__)
def loads_(self, molstr):
self.__dict__.update(loads(molstr).__dict__)
return self
# when pickling, serialize as a JSON-formatted string
__getstate__ = dumps
__setstate__ = loads_
[docs]
def build(self, dump_input=True, parse_arg=ARGPARSE,
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 :class:`Mole`, you need call
this function to refresh the internal data of Mole.
Kwargs:
dump_input : bool
whether to dump the contents of input file in the output file
parse_arg : bool
whether to read the sys.argv and overwrite the relevant parameters
verbose : int
Print level. If given, overwrite :attr:`Mole.verbose`
output : str or None
Output file. If given, overwrite :attr:`Mole.output`
max_memory : int, float
Allowd memory in MB. If given, overwrite :attr:`Mole.max_memory`
atom : list or str
To define molecluar structure.
basis : dict or str
To define basis set.
nucmod : dict or str
Nuclear model. If given, overwrite :attr:`Mole.nucmod`
charge : int
Charge of molecule. It affects the electron numbers
If given, overwrite :attr:`Mole.charge`
spin : int
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 :attr:`Mole.spin`
symmetry : bool or str
Whether to use symmetry. If given a string of point group
name, the given point group symmetry will be used.
magmom : list
Collinear spin of each atom. Default is [0.0,]*natm
'''
if isinstance(dump_input, str):
sys.stderr.write('Assigning the first argument %s to mol.atom\n' %
dump_input)
dump_input, atom = True, dump_input
if verbose is not None: self.verbose = verbose
if output is not None: self.output = output
if max_memory is not None: self.max_memory = max_memory
if atom is not None: self.atom = atom
if basis is not None: self.basis = basis
if unit is not None: self.unit = unit
if nucmod is not None: self.nucmod = nucmod
if ecp is not None: self.ecp = ecp
if pseudo is not None: self.pseudo = pseudo
if charge is not None: self.charge = charge
if spin != 0: self.spin = spin
if symmetry is not None: self.symmetry = symmetry
if symmetry_subgroup is not None: self.symmetry_subgroup = symmetry_subgroup
if cart is not None: self.cart = cart
if magmom is not None: self.magmom = magmom
if parse_arg:
_update_from_cmdargs_(self)
# avoid opening output file twice
if (self.output is not None
# StringIO() does not have attribute 'name'
and getattr(self.stdout, 'name', None) != self.output):
if self.verbose > logger.QUIET:
if os.path.isfile(self.output):
print('overwrite output file: %s' % self.output)
else:
print('output file: %s' % self.output)
if self.output == '/dev/null':
self.stdout = open(os.devnull, 'w')
else:
self.stdout = open(self.output, 'w')
if self.verbose >= logger.WARN:
self.check_sanity()
self._atom = self.format_atom(self.atom, unit=self.unit)
uniq_atoms = set([a[0] for a in self._atom])
_basis = _parse_default_basis(self.basis, uniq_atoms)
self._basis = self.format_basis(_basis)
env = self._env[:PTR_ENV_START]
self._atm, self._bas, self._env = \
self.make_env(self._atom, self._basis, env, self.nucmod,
self.nucprop)
if self.pseudo:
self.ecp, self.pseudo = classify_ecp_pseudo(self, self.ecp, self.pseudo)
if self.ecp:
# Unless explicitly input, ECP should not be assigned to ghost atoms
atoms_wo_ghost = [a for a in uniq_atoms if not is_ghost_atom(a)]
_ecp = _parse_default_basis(self.ecp, atoms_wo_ghost)
self._ecp = self.format_ecp(_ecp)
if self._ecp:
self._atm, self._ecpbas, self._env = \
self.make_ecp_env(self._atm, self._ecp, self._env)
if self.pseudo:
# Unless explicitly input, PP should not be assigned to ghost atoms
atoms_wo_ghost = [a for a in uniq_atoms if not is_ghost_atom(a)]
_pseudo = _parse_default_basis(self.pseudo, atoms_wo_ghost)
self._pseudo = _pseudo = self.format_pseudo(_pseudo)
if _pseudo:
conflicts = set(_pseudo).intersection(self._ecp)
if conflicts:
raise RuntimeError('Pseudo potential for atoms %s are defined '
'in both .ecp and .pseudo.' % list(conflicts))
for ia, atom in enumerate(self._atom):
symb = atom[0]
if (symb in _pseudo and
# skip ghost atoms
self._atm[ia,0] != 0):
self._atm[ia,0] = sum(_pseudo[symb][0])
if self.spin is None:
self.spin = self.nelectron % 2
else:
# Access self.nelec in which the code checks whether the spin and
# number of electrons are consistent.
self.nelec
if self.magmom is None or len(self.magmom) != self.natm:
self.magmom = [0,] * self.natm
if self.spin == 0 and abs(numpy.sum(self.magmom) - self.spin) > 1e-6:
#don't check for unrestricted calcs.
raise ValueError("mol.magmom is set incorrectly.")
if self.symmetry:
self._build_symmetry()
if dump_input and not self._built and self.verbose > logger.NOTE:
self.dump_input()
if self.verbose >= logger.DEBUG3:
logger.debug3(self, 'arg.atm = %s', self._atm)
logger.debug3(self, 'arg.bas = %s', self._bas)
logger.debug3(self, 'arg.env = %s', self._env)
logger.debug3(self, 'ecpbas = %s', self._ecpbas)
self._built = True
return self
kernel = build
def _build_symmetry(self, *args, **kwargs):
'''
Update symmetry related attributes: topgroup, groupname, _symm_orig,
_symm_axes, irrep_id, irrep_name, symm_orb
'''
from pyscf import symm
# TODO: Consider ECP info in point group symmetry initialization
self.topgroup, orig, axes = symm.detect_symm(self._atom, self._basis)
if isinstance(self.symmetry, str):
self.symmetry = str(symm.std_symb(self.symmetry))
groupname = None
if abs(axes - np.eye(3)).max() < symm.TOLERANCE:
if symm.check_symm(self.symmetry, self._atom, self._basis):
# Try to use original axes (issue #1209)
groupname = self.symmetry
axes = np.eye(3)
else:
logger.warn(self, 'Unable to to identify input symmetry using original axes.\n'
'Different symmetry axes will be used.')
if groupname is None:
try:
groupname, axes = symm.as_subgroup(self.topgroup, axes,
self.symmetry)
except PointGroupSymmetryError as e:
raise PointGroupSymmetryError(
'Unable to identify input symmetry %s. Try symmetry="%s"' %
(self.symmetry, self.topgroup)) from e
else:
groupname, axes = symm.as_subgroup(self.topgroup, axes,
self.symmetry_subgroup)
self._symm_orig = orig
self._symm_axes = axes
if self.cart and groupname in ('Dooh', 'Coov', 'SO3'):
if groupname == 'Coov':
groupname, lgroup = 'C2v', groupname
else:
groupname, lgroup = 'D2h', groupname
logger.warn(self, 'This version does not support symmetry %s '
'for cartesian GTO basis. Its subgroup %s is used',
lgroup, groupname)
self.groupname = groupname
self.symm_orb, self.irrep_id = \
symm.symm_adapted_basis(self, groupname, orig, axes)
self.irrep_name = [symm.irrep_id2name(groupname, ir)
for ir in self.irrep_id]
return self
[docs]
@lib.with_doc(expand_etb.__doc__)
def expand_etb(self, l, n, alpha, beta):
return expand_etb(l, n, alpha, beta)
[docs]
@lib.with_doc(expand_etbs.__doc__)
def expand_etbs(self, etbs):
return expand_etbs(etbs)
etbs = expand_etbs
[docs]
@lib.with_doc(make_env.__doc__)
def make_env(self, atoms, basis, pre_env=[], nucmod={}, nucprop=None):
if nucprop is None:
nucprop = self.nucprop
return make_env(atoms, basis, pre_env, nucmod, nucprop)
[docs]
@lib.with_doc(make_atm_env.__doc__)
def make_atm_env(self, atom, ptr=0, nucmod=NUC_POINT, nucprop=None):
if nucprop is None:
nucprop = self.nucprop.get(atom[0], {})
return make_atm_env(atom, ptr, nucmod, nucprop)
[docs]
@lib.with_doc(make_bas_env.__doc__)
def make_bas_env(self, basis_add, atom_id=0, ptr=0):
return make_bas_env(basis_add, atom_id, ptr)
[docs]
@lib.with_doc(make_ecp_env.__doc__)
def make_ecp_env(self, _atm, _ecp, pre_env=[]):
if _ecp:
_atm, _ecpbas, _env = make_ecp_env(self, _atm, _ecp, pre_env)
else:
_atm, _ecpbas, _env = _atm, numpy.zeros((0,BAS_SLOTS)), pre_env
return _atm, _ecpbas, _env
tot_electrons = tot_electrons
[docs]
@lib.with_doc(gto_norm.__doc__)
def gto_norm(self, l, expnt):
return gto_norm(l, expnt)
[docs]
def set_common_origin(self, 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))
'''
self._env[PTR_COMMON_ORIG:PTR_COMMON_ORIG+3] = coord
return self
set_common_orig = set_common_origin
set_common_orig_ = set_common_orig # for backward compatibility
set_common_origin_ = set_common_orig # for backward compatibility
[docs]
def with_common_origin(self, 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 :func:`mol.set_common_origin`
Examples:
>>> with mol.with_common_origin((1,0,0)):
... mol.intor('int1e_r', comp=3)
'''
coord0 = self._env[PTR_COMMON_ORIG:PTR_COMMON_ORIG+3].copy()
return self._TemporaryMoleContext(self.set_common_origin, (coord,), (coord0,))
with_common_orig = with_common_origin
[docs]
def set_rinv_origin(self, coord):
r'''Update origin for operator :math:`\frac{1}{|r-R_O|}`.
**Note** the unit is Bohr
Examples:
>>> mol.set_rinv_origin(0)
>>> mol.set_rinv_origin((0,1,0))
'''
self._env[PTR_RINV_ORIG:PTR_RINV_ORIG+3] = coord[:3]
return self
set_rinv_orig = set_rinv_origin
set_rinv_orig_ = set_rinv_orig # for backward compatibility
set_rinv_origin_ = set_rinv_orig # for backward compatibility
[docs]
def with_rinv_origin(self, 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 :func:`mol.set_rinv_origin`
Examples:
>>> with mol.with_rinv_origin((1,0,0)):
... mol.intor('int1e_rinv')
'''
coord0 = self._env[PTR_RINV_ORIG:PTR_RINV_ORIG+3].copy()
return self._TemporaryMoleContext(self.set_rinv_origin, (coord,), (coord0,))
with_rinv_orig = with_rinv_origin
[docs]
def set_range_coulomb(self, 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
'''
if omega is not None:
self._env[PTR_RANGE_OMEGA] = omega
set_range_coulomb_ = set_range_coulomb # for backward compatibility
@property
def omega(self):
return self._env[PTR_RANGE_OMEGA]
omega = omega.setter(set_range_coulomb)
[docs]
def with_range_coulomb(self, omega):
'''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 :func:`mol.set_range_coulomb`
Examples:
>>> with mol.with_range_coulomb(omega=1.5):
... mol.intor('int2e')
'''
if omega is None:
return contextlib.nullcontext()
omega0 = self._env[PTR_RANGE_OMEGA].copy()
return self._TemporaryMoleContext(self.set_range_coulomb, (omega,), (omega0,))
[docs]
def with_long_range_coulomb(self, omega):
'''Return a temporary mol context for long-range part of
range-separated Coulomb operator.
'''
if omega is None:
return contextlib.nullcontext()
return self.with_range_coulomb(abs(omega))
[docs]
def with_short_range_coulomb(self, omega):
'''Return a temporary mol context for short-range part of
range-separated Coulomb operator.
'''
if omega is None:
return contextlib.nullcontext()
return self.with_range_coulomb(-abs(omega))
[docs]
def set_f12_zeta(self, zeta):
'''Set zeta for YP exp(-zeta r12)/r12 or STG exp(-zeta r12) type integrals
'''
self._env[PTR_F12_ZETA] = zeta
[docs]
def set_nuc_mod(self, 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)
'''
ptr = self._atm[atm_id,PTR_ZETA]
self._env[ptr] = zeta
if zeta == 0:
self._atm[atm_id,NUC_MOD_OF] = NUC_POINT
else:
self._atm[atm_id,NUC_MOD_OF] = NUC_GAUSS
return self
set_nuc_mod_ = set_nuc_mod # for backward compatibility
[docs]
def set_rinv_zeta(self, 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!
'''
self._env[PTR_RINV_ZETA] = zeta
return self
set_rinv_zeta_ = set_rinv_zeta # for backward compatibility
[docs]
def with_rinv_zeta(self, zeta):
'''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 :func:`mol.set_rinv_zeta`
Examples:
>>> with mol.with_rinv_zeta(zeta=1.5), mol.with_rinv_origin((1.,0,0)):
... mol.intor('int1e_rinv')
'''
zeta0 = self._env[PTR_RINV_ZETA].copy()
return self._TemporaryMoleContext(self.set_rinv_zeta, (zeta,), (zeta0,))
[docs]
def with_rinv_at_nucleus(self, 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')
'''
zeta = self._env[self._atm[atm_id,PTR_ZETA]]
rinv = self.atom_coord(atm_id)
if zeta == 0:
self._env[AS_RINV_ORIG_ATOM] = atm_id # required by ecp gradients
return self.with_rinv_origin(rinv)
else:
self._env[AS_RINV_ORIG_ATOM] = atm_id # required by ecp gradients
rinv0 = self._env[PTR_RINV_ORIG:PTR_RINV_ORIG+3].copy()
zeta0 = self._env[PTR_RINV_ZETA].copy()
def set_rinv(z, r):
self._env[PTR_RINV_ZETA] = z
self._env[PTR_RINV_ORIG:PTR_RINV_ORIG+3] = r
return self._TemporaryMoleContext(set_rinv, (zeta,rinv), (zeta0,rinv0))
with_rinv_as_nucleus = with_rinv_at_nucleus # For backward compatibility
[docs]
def with_integral_screen(self, threshold):
'''Return a temporary mol context which has the required integral
screen threshold
'''
if threshold is None:
# This calls the default cutoff settings in cint library
expcutoff = 0
else:
expcutoff = abs(numpy.log(threshold))
expcutoff0 = self._env[PTR_EXPCUTOFF]
def set_cutoff(cut):
self._env[PTR_EXPCUTOFF] = cut
return self._TemporaryMoleContext(set_cutoff, (expcutoff,), (expcutoff0,))
[docs]
def set_geom_(self, atoms_or_coords, unit=None, symmetry=None,
inplace=True):
'''Update geometry
'''
if inplace:
mol = self
else:
mol = self.copy(deep=False)
mol._env = mol._env.copy()
if unit is None:
unit = mol.unit
else:
mol.unit = unit
if symmetry is None:
symmetry = mol.symmetry
if isinstance(atoms_or_coords, numpy.ndarray):
mol.atom = list(zip([x[0] for x in mol._atom],
atoms_or_coords.tolist()))
else:
mol.atom = atoms_or_coords
if isinstance(atoms_or_coords, numpy.ndarray) and not symmetry:
if isinstance(unit, str):
if is_au(unit):
unit = 1.
else:
unit = 1./param.BOHR
else:
unit = 1./unit
mol._atom = list(zip([x[0] for x in mol._atom],
(atoms_or_coords * unit).tolist()))
ptr = mol._atm[:,PTR_COORD]
mol._env[ptr+0] = unit * atoms_or_coords[:,0]
mol._env[ptr+1] = unit * atoms_or_coords[:,1]
mol._env[ptr+2] = unit * atoms_or_coords[:,2]
else:
mol.symmetry = symmetry
mol.build(False, False)
if mol.verbose >= logger.INFO:
logger.info(mol, 'New geometry')
for ia, atom in enumerate(mol._atom):
coorda = tuple([x * param.BOHR for x in atom[1]])
coordb = tuple([x for x in atom[1]])
coords = coorda + coordb
logger.info(mol, ' %3d %-4s %16.12f %16.12f %16.12f AA '
'%16.12f %16.12f %16.12f Bohr\n',
ia+1, mol.atom_symbol(ia), *coords)
return mol
[docs]
def update(self, chkfile):
return self.update_from_chk(chkfile)
[docs]
def update_from_chk(self, chkfile):
with h5py.File(chkfile, 'r') as fh5:
mol = loads(fh5['mol'][()])
self.__dict__.update(mol.__dict__)
return self
[docs]
def has_ecp(self):
'''Whether pseudo potential is used in the system.'''
return len(self._ecpbas) > 0 or self._pseudo
[docs]
def has_ecp_soc(self):
'''Whether spin-orbit coupling is enabled in ECP.'''
return (len(self._ecpbas) > 0 and
numpy.any(self._ecpbas[:,SO_TYPE_OF] == 1))
[docs]
def atom_symbol(self, atm_id):
r'''For the given atom id, return the input symbol (without striping special characters)
Args:
atm_id : int
0-based
Examples:
>>> mol.build(atom='H^2 0 0 0; H 0 0 1.1')
>>> mol.atom_symbol(0)
H^2
'''
return _symbol(self._atom[atm_id][0])
[docs]
def atom_pure_symbol(self, atm_id):
r'''For the given atom id, return the standard symbol (striping special characters)
Args:
atm_id : int
0-based
Examples:
>>> mol.build(atom='H^2 0 0 0; H 0 0 1.1')
>>> mol.atom_symbol(0)
H
'''
return _std_symbol(self._atom[atm_id][0])
@property
def elements(self):
'''A list of elements in the molecule'''
return [self.atom_pure_symbol(i) for i in range(self.natm)]
[docs]
def atom_charge(self, atm_id):
r'''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_id : int
0-based
Examples:
>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1')
>>> mol.atom_charge(1)
17
'''
if self._atm[atm_id,NUC_MOD_OF] != NUC_FRAC_CHARGE:
# regular QM atoms
return self._atm[atm_id,CHARGE_OF]
else:
# MM atoms with fractional charges
return self._env[self._atm[atm_id,PTR_FRAC_CHARGE]]
[docs]
def atom_charges(self):
'''np.asarray([mol.atom_charge(i) for i in range(mol.natm)])'''
z = self._atm[:,CHARGE_OF]
if numpy.any(self._atm[:,NUC_MOD_OF] == NUC_FRAC_CHARGE):
# Create the integer nuclear charges first then replace the MM
# particles with the MM charges that saved in _env[PTR_FRAC_CHARGE]
z = numpy.array(z, dtype=numpy.double)
idx = self._atm[:,NUC_MOD_OF] == NUC_FRAC_CHARGE
# MM fractional charges can be positive or negative
z[idx] = self._env[self._atm[idx,PTR_FRAC_CHARGE]]
return z
[docs]
def atom_nelec_core(self, atm_id):
'''Number of core electrons for pseudo potential.
'''
return charge(self.atom_symbol(atm_id)) - self.atom_charge(atm_id)
[docs]
def atom_coord(self, atm_id, unit='Bohr'):
r'''Coordinates (ndarray) of the given atom id
Args:
atm_id : int
0-based
Examples:
>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1')
>>> mol.atom_coord(1)
[ 0. 0. 2.07869874]
'''
ptr = self._atm[atm_id,PTR_COORD]
if not is_au(unit):
return self._env[ptr:ptr+3] * param.BOHR
else:
return self._env[ptr:ptr+3].copy()
[docs]
def atom_coords(self, unit='Bohr'):
'''np.asarray([mol.atom_coords(i) for i in range(mol.natm)])'''
ptr = self._atm[:,PTR_COORD]
c = self._env[numpy.vstack((ptr,ptr+1,ptr+2)).T].copy()
if not is_au(unit):
c *= param.BOHR
return c
atom_mass_list = atom_mass_list
[docs]
def atom_nshells(self, atm_id):
r'''Number of basis/shells of the given atom
Args:
atm_id : int
0-based
Examples:
>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1')
>>> mol.atom_nshells(1)
5
'''
return (self._bas[:,ATOM_OF] == atm_id).sum()
[docs]
def atom_shell_ids(self, atm_id):
r'''A list of the shell-ids of the given atom
Args:
atm_id : int
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]
'''
return numpy.where(self._bas[:,ATOM_OF] == atm_id)[0]
[docs]
def bas_coord(self, bas_id):
r'''Coordinates (ndarray) associated with the given basis id
Args:
bas_id : int
0-based
Examples:
>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1')
>>> mol.bas_coord(1)
[ 0. 0. 2.07869874]
'''
atm_id = self.bas_atom(bas_id)
ptr = self._atm[atm_id,PTR_COORD]
return self._env[ptr:ptr+3].copy()
[docs]
def bas_atom(self, bas_id):
r'''The atom (0-based id) that the given basis sits on
Args:
bas_id : int
0-based
Examples:
>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_atom(7)
1
'''
return self._bas[bas_id,ATOM_OF].copy()
[docs]
def bas_angular(self, bas_id):
r'''The angular momentum associated with the given basis
Args:
bas_id : int
0-based
Examples:
>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_atom(7)
2
'''
return self._bas[bas_id,ANG_OF].copy()
[docs]
def bas_nctr(self, bas_id):
r'''The number of contracted GTOs for the given shell
Args:
bas_id : int
0-based
Examples:
>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_atom(3)
3
'''
return self._bas[bas_id,NCTR_OF].copy()
[docs]
def bas_nprim(self, bas_id):
r'''The number of primitive GTOs for the given shell
Args:
bas_id : int
0-based
Examples:
>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_atom(3)
11
'''
return self._bas[bas_id,NPRIM_OF].copy()
[docs]
def bas_kappa(self, bas_id):
r'''Kappa (if l < j, -l-1, else l) of the given shell
Args:
bas_id : int
0-based
Examples:
>>> mol.build(atom='H 0 0 0; Cl 0 0 1.1', basis='cc-pvdz')
>>> mol.bas_kappa(3)
0
'''
return self._bas[bas_id,KAPPA_OF].copy()
[docs]
def bas_exp(self, bas_id):
r'''exponents (ndarray) of the given shell
Args:
bas_id : int
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]
'''
nprim = self.bas_nprim(bas_id)
ptr = self._bas[bas_id,PTR_EXP]
return self._env[ptr:ptr+nprim].copy()
[docs]
def bas_exps(self):
'''exponents of all basis
return [mol.bas_exp(i) for i in range(self.nbas)]
'''
nprims = self._bas[:,NPRIM_OF]
pexps = self._bas[:,PTR_EXP]
exps = [self._env[i0:i1] for i0, i1 in zip(pexps, pexps + nprims)]
return exps
def _libcint_ctr_coeff(self, bas_id):
nprim = self.bas_nprim(bas_id)
nctr = self.bas_nctr(bas_id)
ptr = self._bas[bas_id,PTR_COEFF]
return self._env[ptr:ptr+nprim*nctr].reshape(nctr,nprim).T
[docs]
def bas_ctr_coeff(self, bas_id):
r'''Contract coefficients (ndarray) of the given shell
Args:
bas_id : int
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]]
'''
l = self.bas_angular(bas_id)
es = self.bas_exp(bas_id)
cs = self._libcint_ctr_coeff(bas_id)
cs = numpy.einsum('pi,p->pi', cs, 1/gto_norm(l, es))
return cs
[docs]
def bas_len_spinor(self, bas_id):
'''The number of spinor associated with given basis
If kappa is 0, return 4l+2
'''
l = self.bas_angular(bas_id)
k = self.bas_kappa(bas_id)
return len_spinor(l, k)
[docs]
def bas_len_cart(self, bas_id):
'''The number of Cartesian function associated with given basis
'''
return len_cart(self._bas[bas_id,ANG_OF])
npgto_nr = npgto_nr
nao_nr = nao_nr
nao_2c = nao_2c
nao_cart = nao_cart
nao_nr_range = nao_nr_range
nao_2c_range = nao_2c_range
ao_loc_nr = ao_loc_nr
ao_loc_2c = ao_loc_2c
@property
def nao(self):
if self._nao is None:
return self.nao_nr()
else:
return self._nao
@nao.setter
def nao(self, x):
self._nao = x
ao_loc = property(ao_loc_nr)
tmap = time_reversal_map = time_reversal_map
[docs]
def intor(self, intor, comp=None, hermi=0, aosym='s1', out=None,
shls_slice=None, grids=None):
'''Integral generator.
Args:
intor : str
Name of the 1e or 2e AO integrals. Ref to :func:`getints` for the
complete list of available 1-electron integral names
Kwargs:
comp : int
Components of the integrals, e.g. int1e_ipovlp_sph has 3 components.
hermi : int
Symmetry of the integrals
| 0 : no symmetry assumed (default)
| 1 : hermitian
| 2 : anti-hermitian
grids : ndarray
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]]
'''
if not self._built:
logger.warn(self, 'Warning: intor envs of %s not initialized.', self)
# FIXME: Whether to check _built and call build? ._bas and .basis
# may not be consistent. calling .build() may leads to wrong intor env.
#self.build(False, False)
intor = self._add_suffix(intor)
bas = self._bas
env = self._env
if 'ECP' in intor:
assert (self._ecp is not None)
bas = numpy.vstack((self._bas, self._ecpbas))
env[AS_ECPBAS_OFFSET] = len(self._bas)
env[AS_NECPBAS] = len(self._ecpbas)
if shls_slice is None:
shls_slice = (0, self.nbas, 0, self.nbas)
elif '_grids' in intor:
assert grids is not None
env = numpy.append(env, grids.ravel())
env[NGRIDS] = grids.shape[0]
env[PTR_GRIDS] = env.size - grids.size
return moleintor.getints(intor, self._atm, bas, env,
shls_slice, comp, hermi, aosym, out=out)
def _add_suffix(self, intor, cart=None):
if not (intor[:4] == 'cint' or
intor.endswith(('_sph', '_cart', '_spinor', '_ssc'))):
if cart is None:
cart = self.cart
if cart:
intor = intor + '_cart'
else:
intor = intor + '_sph'
return intor
[docs]
def intor_symmetric(self, intor, comp=None, grids=None):
'''One-electron integral generator. The integrals are assumed to be hermitian
Args:
intor : str
Name of the 1-electron integral. Ref to :func:`getints` for the
complete list of available 1-electron integral names
Kwargs:
comp : int
Components of the integrals, e.g. int1e_ipovlp_sph has 3 components.
grids : ndarray
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]]
'''
return self.intor(intor, comp, 1, aosym='s4', grids=grids)
[docs]
def intor_asymmetric(self, intor, comp=None, grids=None):
'''One-electron integral generator. The integrals are assumed to be anti-hermitian
Args:
intor : str
Name of the 1-electron integral. Ref to :func:`getints` for the
complete list of available 1-electron integral names
Kwargs:
comp : int
Components of the integrals, e.g. int1e_ipovlp has 3 components.
grids : ndarray
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]]
'''
return self.intor(intor, comp, 2, aosym='a4', grids=grids)
[docs]
@lib.with_doc(moleintor.getints_by_shell.__doc__)
def intor_by_shell(self, intor, shells, comp=None, grids=None):
intor = self._add_suffix(intor)
if 'ECP' in intor:
assert (self._ecp is not None)
bas = numpy.vstack((self._bas, self._ecpbas))
self._env[AS_ECPBAS_OFFSET] = len(self._bas)
self._env[AS_NECPBAS] = len(self._ecpbas)
else:
bas = self._bas
return moleintor.getints_by_shell(intor, shells, self._atm, bas,
self._env, comp)
eval_ao = eval_gto = eval_gto
energy_nuc = get_enuc = energy_nuc
[docs]
def get_ao_indices(self, bas_list, ao_loc=None):
'''
Generate (dis-continued) AO indices for basis specified in bas_list
'''
if ao_loc is None:
ao_loc = self.ao_loc
return lib.locs_to_indices(ao_loc, bas_list)
sph_labels = spheric_labels = sph_labels
cart_labels = cart_labels
ao_labels = ao_labels
spinor_labels = spinor_labels
search_ao_label = search_ao_label
[docs]
def search_shell_id(self, atm_id, l):
return search_shell_id(self, atm_id, l)
search_ao_nr = search_ao_nr
search_ao_r = search_ao_r
aoslice_by_atom = aoslice_nr_by_atom = offset_ao_by_atom = offset_nr_by_atom = aoslice_by_atom
aoslice_2c_by_atom = offset_2c_by_atom = offset_2c_by_atom
condense_to_shell = condense_to_shell
get_overlap_cond = get_overlap_cond
to_uncontracted_cartesian_basis = to_uncontracted_cartesian_basis
decontract_basis = decontract_basis
ao_rotation_matrix = ao_rotation_matrix
[docs]
def cart2sph_coeff(self, normalized='sp'):
'''Transformation matrix that transforms Cartesian GTOs to spherical
GTOs for all basis functions
Kwargs:
normalized : string 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
'''
c2s_l = [cart2sph(l, normalized=normalized) for l in range(12)]
c2s = []
for ib in range(self.nbas):
l = self.bas_angular(ib)
for n in range(self.bas_nctr(ib)):
c2s.append(c2s_l[l])
return scipy.linalg.block_diag(*c2s)
[docs]
def sph2spinor_coeff(self):
'''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
'''
from pyscf.symm import sph
return sph.sph2spinor_coeff(self)
[docs]
def apply(self, fn, *args, **kwargs):
if callable(fn):
return lib.StreamObject.apply(self, fn, *args, **kwargs)
elif isinstance(fn, str):
method = getattr(self, fn.upper())
return method(*args, **kwargs)
else:
raise TypeError('First argument of .apply method must be a '
'function/class or a name (string) of a method.')
@contextlib.contextmanager
def _TemporaryMoleContext(self, method, args, args_bak):
'''Almost every method depends on the Mole environment. Ensure the
modification in temporary environment being thread safe
'''
haslock = self._ctx_lock
if haslock is None:
self._ctx_lock = threading.RLock()
with self._ctx_lock:
method(*args)
try:
yield
finally:
method(*args_bak)
if haslock is None:
self._ctx_lock = None
[docs]
class Mole(MoleBase):
'''A Mole object to hold the basic information of a molecule.
'''
__add__ = conc_mol
inertia_moment = inertia_moment
tostring = tostring
tofile = tofile
def __init__(self, **kwargs):
MoleBase.__init__(self)
for key, val in kwargs.items():
setattr(self, key, val)
[docs]
def fromstring(self, string, format='xyz'):
'''Update the Mole object based on the input geometry string'''
atom = self.format_atom(fromstring(string, format), unit=1)
self.set_geom_(atom, unit='Angstrom', inplace=True)
if format == 'sdf' and 'M CHG' in string:
raise NotImplementedError
#FIXME self.charge = 0
return self
[docs]
def fromfile(self, filename, format=None):
'''Update the Mole object based on the input geometry file'''
atom = self.format_atom(fromfile(filename, format), unit=1)
self.set_geom_(atom, unit='Angstrom', inplace=True)
if format == 'sdf':
raise NotImplementedError
return self
def __getattr__(self, key):
'''To support accessing methods (mol.HF, mol.KS, mol.CCSD, mol.CASSCF, ...)
from Mole object.
'''
if key[0] == '_': # Skip private attributes and Python builtins
raise AttributeError('Mole object does not have attribute %s' % key)
elif key in ('_ipython_canary_method_should_not_exist_',
'_repr_mimebundle_'):
# https://github.com/mewwts/addict/issues/26
# https://github.com/jupyter/notebook/issues/2014
raise AttributeError
# Import all available modules. Some methods are registered to other
# classes/modules when importing modules in __all__.
from pyscf import __all__ # noqa
from pyscf import scf, dft
for mod in (scf, dft):
method = getattr(mod, key, None)
if callable(method):
return method(self)
if 'TD' in key[:3]:
if key in ('TDHF', 'TDA'):
mf = scf.HF(self)
else:
mf = dft.KS(self)
xc = key.split('TD', 1)[1]
if xc in dft.XC:
mf.xc = xc
key = 'TDDFT'
else:
mf = scf.HF(self)
method = getattr(mf, key)
# Initialize SCF object for post-SCF methods if applicable
if self.nelectron != 0:
mf.run()
return method
[docs]
def ao2mo(self, mo_coeffs, erifile=None, dataname='eri_mo', intor='int2e',
**kwargs):
'''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.
dataname : str
*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 :func:`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')
'''
from pyscf import ao2mo
return ao2mo.kernel(self, mo_coeffs, erifile, dataname, intor, **kwargs)
[docs]
def to_cell(self, a, dimension=3):
'''Put a molecule in a cell with periodic boundary condictions
Args:
a : (3,3) ndarray
Lattice primitive vectors. Each row is a lattice vector
'''
from pyscf.pbc.gto import Cell
cell = Cell()
cell.__dict__.update(self.__dict__)
cell.dimension = dimension
cell.build(False, False)
return cell
def _parse_default_basis(basis, uniq_atoms):
if isinstance(basis, (str, tuple, list)):
# default basis for all atoms
_basis = {a: basis for a in uniq_atoms}
elif 'default' in basis:
default_basis = basis['default']
_basis = {a: default_basis for a in uniq_atoms}
_basis.update(basis)
del _basis['default']
else:
_basis = basis
return _basis
def _parse_nuc_mod(str_or_int_or_fn):
nucmod = NUC_POINT
if callable(str_or_int_or_fn):
nucmod = str_or_int_or_fn
elif (isinstance(str_or_int_or_fn, str) and
str_or_int_or_fn[0].upper() == 'G'): # 'gauss_nuc'
nucmod = NUC_GAUSS
elif str_or_int_or_fn != 0:
nucmod = NUC_GAUSS
return nucmod
def _update_from_cmdargs_(mol):
try:
# Detect whether in Ipython shell
__IPYTHON__ # noqa:
return
except Exception:
pass
if not mol._built: # parse cmdline args only once
opts = cmd_args.cmd_args()
if opts.verbose:
mol.verbose = opts.verbose
if opts.max_memory:
mol.max_memory = opts.max_memory
if opts.output:
mol.output = opts.output
[docs]
def from_zmatrix(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])]
'''
from pyscf.symm import rotation_mat
atomstr = atomstr.replace(';','\n').replace(',',' ')
symbols = []
coord = []
min_items_per_line = 1
for line_id, line in enumerate(atomstr.splitlines()):
line = line.strip()
if line and line[0] != '#':
rawd = line.split()
if len(rawd) < min_items_per_line:
raise ValueError('Zmatrix format error at L%d %s' % (line_id, line))
symbols.append(rawd[0])
if len(rawd) < 3:
coord.append(numpy.zeros(3))
min_items_per_line = 3
elif len(rawd) == 3:
if DISABLE_EVAL:
coord.append(numpy.array((float(rawd[2]), 0, 0)))
else:
coord.append(numpy.array((eval(rawd[2]), 0, 0)))
min_items_per_line = 5
elif len(rawd) == 5:
if DISABLE_EVAL:
vals = rawd[1:]
else:
vals = eval(','.join(rawd[1:]))
bonda = int(vals[0]) - 1
bond = float(vals[1])
anga = int(vals[2]) - 1
ang = float(vals[3])/180*numpy.pi
assert (ang >= 0)
v1 = coord[anga] - coord[bonda]
if not numpy.allclose(v1[:2], 0):
vecn = numpy.cross(v1, numpy.array((0.,0.,1.)))
else: # on z
vecn = numpy.array((0.,0.,1.))
rmat = rotation_mat(vecn, ang)
c = numpy.dot(rmat, v1) * (bond/numpy.linalg.norm(v1))
coord.append(coord[bonda]+c)
min_items_per_line = 7
else:
if DISABLE_EVAL:
vals = rawd[1:]
else:
vals = eval(','.join(rawd[1:]))
bonda = int(vals[0]) - 1
bond = float(vals[1])
anga = int(vals[2]) - 1
ang = float(vals[3])/180*numpy.pi
assert (ang >= 0 and ang <= numpy.pi)
v1 = coord[anga] - coord[bonda]
v1 /= numpy.linalg.norm(v1)
if ang < 1e-7:
c = v1 * bond
elif numpy.pi-ang < 1e-7:
c = -v1 * bond
else:
diha = int(vals[4]) - 1
dih = float(vals[5])/180*numpy.pi
v2 = coord[diha] - coord[anga]
vecn = numpy.cross(v2, -v1)
vecn_norm = numpy.linalg.norm(vecn)
if vecn_norm < 1e-7:
if not numpy.allclose(v1[:2], 0):
vecn = numpy.cross(v1, numpy.array((0.,0.,1.)))
else: # on z
vecn = numpy.array((0.,0.,1.))
rmat = rotation_mat(vecn, ang)
c = numpy.dot(rmat, v1) * bond
else:
rmat = rotation_mat(v1, -dih)
vecn = numpy.dot(rmat, vecn) / vecn_norm
rmat = rotation_mat(vecn, ang)
c = numpy.dot(rmat, v1) * bond
coord.append(coord[bonda]+c)
atoms = list(zip([_atom_symbol(x) for x in symbols], coord))
return atoms
zmat2cart = zmat = from_zmatrix
[docs]
def cart2zmat(coord):
'''>>> 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
'''
zstr = []
zstr.append('1')
if len(coord) > 1:
r1 = coord[1] - coord[0]
nr1 = numpy.linalg.norm(r1)
zstr.append('1 %.15g' % nr1)
if len(coord) > 2:
r2 = coord[2] - coord[0]
nr2 = numpy.linalg.norm(r2)
a = numpy.arccos(numpy.dot(r1,r2)/(nr1*nr2))
zstr.append('1 %.15g 2 %.15g' % (nr2, a*180/numpy.pi))
if len(coord) > 3:
o0, o1, o2 = coord[:3]
p0, p1, p2 = 1, 2, 3
for k, c in enumerate(coord[3:]):
r0 = c - o0
nr0 = numpy.linalg.norm(r0)
r1 = o1 - o0
nr1 = numpy.linalg.norm(r1)
a1 = numpy.arccos(numpy.dot(r0,r1)/(nr0*nr1))
b0 = numpy.cross(r0, r1)
nb0 = numpy.linalg.norm(b0)
if abs(nb0) < 1e-7: # o0, o1, c in line
a2 = 0
zstr.append('%d %.15g %d %.15g %d %.15g' %
(p0, nr0, p1, a1*180/numpy.pi, p2, a2))
else:
b1 = numpy.cross(o2-o0, r1)
nb1 = numpy.linalg.norm(b1)
if abs(nb1) < 1e-7: # o0 o1 o2 in line
a2 = 0
zstr.append('%d %.15g %d %.15g %d %.15g' %
(p0, nr0, p1, a1*180/numpy.pi, p2, a2))
o2 = c
p2 = 4 + k
else:
if numpy.dot(numpy.cross(b1, b0), r1) < 0:
a2 = numpy.arccos(numpy.dot(b1, b0) / (nb0*nb1))
else:
a2 =-numpy.arccos(numpy.dot(b1, b0) / (nb0*nb1))
zstr.append('%d %.15g %d %.15g %d %.15g' %
(p0, nr0, p1, a1*180/numpy.pi, p2, a2*180/numpy.pi))
return '\n'.join(zstr)
[docs]
def dyall_nuc_mod(nuc_charge, nucprop={}):
''' 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)
'''
mass = nucprop.get('mass', elements.ISOTOPE_MAIN[nuc_charge])
r = (0.836 * mass**(1./3) + 0.570) / 52917.7249
zeta = 1.5 / (r**2)
return zeta
[docs]
def filatov_nuc_mod(nuc_charge, nucprop={}):
''' 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)
M. Filatov and D. Cremer, Chem. Phys. Lett. 351, 259 (2002)
'''
c = param.LIGHT_SPEED
nuc_charge = charge(nuc_charge)
r = (-0.263188*nuc_charge + 106.016974 + 138.985999/nuc_charge) / c**2
zeta = 1 / (r**2)
return zeta
[docs]
def fakemol_for_charges(coords, expnt=1e16):
'''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).
'''
nbas = coords.shape[0]
expnt = numpy.asarray(expnt).ravel()
fakeatm = numpy.zeros((nbas,ATM_SLOTS), dtype=numpy.int32)
fakebas = numpy.zeros((nbas,BAS_SLOTS), dtype=numpy.int32)
fakeenv = [0] * PTR_ENV_START
ptr = PTR_ENV_START
fakeatm[:,PTR_COORD] = numpy.arange(ptr, ptr+nbas*3, 3)
fakeenv.append(coords.ravel())
ptr += nbas*3
fakebas[:,ATOM_OF] = numpy.arange(nbas)
fakebas[:,NPRIM_OF] = 1
fakebas[:,NCTR_OF] = 1
if expnt.size == 1:
expnt = expnt[0]
# approximate point charge with gaussian distribution exp(-1e16*r^2)
fakebas[:,PTR_EXP] = ptr
fakebas[:,PTR_COEFF] = ptr+1
fakeenv.append([expnt, 1/(2*numpy.sqrt(numpy.pi)*gaussian_int(2,expnt))])
ptr += 2
else:
assert expnt.size == nbas
# approximate point charge with gaussian distribution exp(-expnt*r^2)
fakebas[:,PTR_EXP] = ptr + numpy.arange(nbas) * 2
fakebas[:,PTR_COEFF] = ptr + numpy.arange(nbas) * 2 + 1
coeff = 1 / (2 * numpy.sqrt(numpy.pi) * gaussian_int(2, expnt))
fakeenv.append(numpy.vstack((expnt, coeff)).T.ravel())
fakemol = Mole()
fakemol._atm = fakeatm
fakemol._bas = fakebas
fakemol._env = numpy.hstack(fakeenv)
fakemol._built = True
return fakemol
[docs]
def classify_ecp_pseudo(mol, ecp, pp):
'''
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.
'''
def classify(ecp, pp_alias):
if isinstance(ecp, str):
if basis._format_pseudo_name(ecp)[0] in pp_alias:
return {}, {'default': str(ecp)}
elif isinstance(ecp, dict):
ecp_as_pp = {}
for atom in ecp:
key = ecp[atom]
if (isinstance(key, str) and
basis._format_pseudo_name(key)[0] in pp_alias):
ecp_as_pp[atom] = str(key)
if ecp_as_pp:
ecp_left = dict(ecp)
for atom in ecp_as_pp:
ecp_left.pop(atom)
return ecp_left, ecp_as_pp
return ecp, {}
ecp_left, ecp_as_pp = classify(ecp, basis.PP_ALIAS)
pp_left , pp_as_ecp = classify(pp, basis.ALIAS)
# ecp = ecp_left + pp_as_ecp
# pp = pp_left + ecp_as_pp
ecp = ecp_left
if pp_as_ecp and not isinstance(ecp_left, str):
# If ecp is a str, all atoms have ecp definition.
# The misplaced ecp has no effects.
logger.info(mol, 'pseudo-potentials keywords for %s found in .ecp',
pp_as_ecp.keys())
if ecp_left:
pp_as_ecp.update(ecp_left)
ecp = pp_as_ecp
pp = pp_left
if ecp_as_pp and not isinstance(pp_left, str):
logger.info(mol, 'ECP keywords for %s found in .pseudo',
ecp_as_pp.keys())
if pp_left:
ecp_as_pp.update(pp_left)
pp = ecp_as_pp
return ecp, pp