def overlap_ni(me, sp1, R1, sp2, R2, **kw):
"""
Computes overlap for an atom pair. The atom pair is given by a pair of species indices
and the coordinates of the atoms.
Args:
sp1,sp2 : specie indices, and
R1,R2 : respective coordinates in Bohr, atomic units
Result:
matrix of orbital overlaps
The procedure uses the numerical integration in coordinate space.
"""
from pyscf.nao.m_ao_matelem import build_3dgrid
from pyscf.nao.m_ao_eval_libnao import ao_eval_libnao as ao_eval #_libnao
grids = build_3dgrid(me, sp1, R1, sp2, R2, **kw)
ao1 = ao_eval(me.ao1, R1, sp1, grids.coords)
ao1 = ao1 * grids.weights
ao2 = ao_eval(me.ao2, R2, sp2, grids.coords)
overlaps = np.einsum("ij,kj->ik", ao1,
ao2) # overlaps = np.matmul(ao1, ao2.T)
return overlaps
def xc_scalar_ni(me, sp1, R1, sp2, R2, xc_code, deriv, **kw):
from pyscf.dft.libxc import eval_xc
"""
Computes overlap for an atom pair. The atom pair is given by a pair of species indices
and the coordinates of the atoms.
Args:
sp1,sp2 : specie indices, and
R1,R2 : respective coordinates in Bohr, atomic units
Result:
matrix of orbital overlaps
The procedure uses the numerical integration in coordinate space.
"""
grids = build_3dgrid(me, sp1, R1, sp2, R2, **kw)
rho = dens_libnao(grids.coords, me.sv.nspin)
exc, vxc, fxc, kxc = libxc.eval_xc(xc_code,
rho.T,
spin=me.sv.nspin - 1,
deriv=deriv)
ao1 = ao_eval(me.ao1, R1, sp1, grids.coords)
if deriv == 1:
#print(' vxc[0].shape ', vxc[0].shape)
ao1 = ao1 * grids.weights * vxc[0]
elif deriv == 2:
ao1 = ao1 * grids.weights * fxc[0]
else:
print(' deriv ', deriv)
raise RuntimeError('!deriv!')
ao2 = ao_eval(me.ao2, R2, sp2, grids.coords)
overlaps = blas.dgemm(1.0, ao1, ao2.T)
return overlaps
def eri2c(me, sp1,R1,sp2,R2, **kvargs):
""" Computes two-center Electron Repulsion Integrals. This is normally done between product basis functions"""
from pyscf.nao.m_ao_matelem import build_3dgrid
from pyscf.nao.m_ao_eval_libnao import ao_eval_libnao as ao_eval
grids = build_3dgrid(me, sp1,np.array(R1), sp2,np.array(R2), **kvargs)
pf = grids.weights * ao_eval(me.ao2, np.array(R1), sp1, grids.coords)
qv = ao_eval(me.ao2_hartree, np.array(R2), sp2, grids.coords)
pq2eri = np.einsum('pr,qr->pq',pf,qv)
return pq2eri
def eri3c(me, sp1, sp2, R1, R2, sp3, R3, **kvargs):
""" Computes three-center Electron Repulsion Integrals.
atomic orbitals of second species must contain the Hartree potentials of radial functions (product orbitals)"""
from pyscf.nao.m_ao_matelem import build_3dgrid3c
from pyscf.nao.m_ao_eval_libnao import ao_eval_libnao as ao_eval
#from pyscf.nao.m_ao_eval import ao_eval as ao_eval
grids = build_3dgrid3c(me, sp1, sp2, R1, R2, sp3, R3, **kvargs)
ao1 = grids.weights * ao_eval(me.aos[0], R1, sp1, grids.coords)
ao2 = ao_eval(me.aos[0], R2, sp2, grids.coords)
aoao = np.einsum('ar,br->abr', ao1, ao2)
pbf = ao_eval(me.aos[1], R3, sp3, grids.coords)
abp2eri = np.einsum('abr,pr->abp', aoao, pbf)
return abp2eri
def eri3c(me, sp1,sp2,R1,R2, sp3,R3, **kvargs):
""" Computes three-center Electron Repulsion Integrals.
atomic orbitals of second species must contain the Hartree potentials of radial functions (product orbitals)"""
from pyscf.nao.m_ao_matelem import build_3dgrid3c
from pyscf.nao.m_ao_eval_libnao import ao_eval_libnao as ao_eval
#from pyscf.nao.m_ao_eval import ao_eval as ao_eval
grids = build_3dgrid3c(me, sp1,sp2,R1,R2, sp3,R3, **kvargs)
ao1 = grids.weights * ao_eval(me.aos[0], R1, sp1, grids.coords)
ao2 = ao_eval(me.aos[0], R2, sp2, grids.coords)
aoao = np.einsum('ar,br->abr', ao1, ao2)
pbf = ao_eval(me.aos[1], R3, sp3, grids.coords)
abp2eri = np.einsum('abr,pr->abp',aoao,pbf)
return abp2eri
def eval_ao(self, feval, coords, comp, shls_slice=None, non0tab=None, out=None):
""" Computes the values of all atomic orbitals for a set of given Cartesian coordinates.
This function should be similar to the pyscf's function eval_gto()... """
from pyscf.nao.m_ao_eval_libnao import ao_eval_libnao as ao_eval
assert feval=="GTOval_sph_deriv0"
assert shls_slice is None
assert non0tab is None
assert comp==1
aos = ao_eval(self.ao_log, np.zeros(3), 0, coords)
return aos
def dipole_ni(me, sp1, R1, sp2, R2, **kvargs):
"""
Computes overlap for an atom pair. The atom pair is given by a pair of species indices
and the coordinates of the atoms.
Args:
sp1,sp2 : specie indices, and
R1,R2 : respective coordinates in Bohr, atomic units
Result:
matrix of orbital overlaps
The procedure uses the numerical integration in coordinate space.
"""
from pyscf.nao.m_ao_matelem import build_3dgrid
from pyscf.nao.m_ao_eval_libnao import ao_eval_libnao as ao_eval
grids = build_3dgrid(me, sp1, R1, sp2, R2, **kvargs)
ao1 = ao_eval(me.ao1, R1, sp1, grids.coords)
ao1 = ao1 * grids.weights
ko1 = np.einsum('ik,oi->koi', grids.coords, ao1)
ao2 = ao_eval(me.ao1, R2, sp2, grids.coords)
koo2dip = np.einsum("koi,pi->kop", ko1, ao2)
return koo2dip
def dipole_ni(me, sp1, R1, sp2, R2, **kvargs):
"""
Computes overlap for an atom pair. The atom pair is given by a pair of species indices
and the coordinates of the atoms.
Args:
sp1,sp2 : specie indices, and
R1,R2 : respective coordinates in Bohr, atomic units
Result:
matrix of orbital overlaps
The procedure uses the numerical integration in coordinate space.
"""
from pyscf.nao.m_ao_matelem import build_3dgrid
from pyscf.nao.m_ao_eval_libnao import ao_eval_libnao as ao_eval
grids = build_3dgrid(me, sp1, R1, sp2, R2, **kvargs)
ao1 = ao_eval(me.ao1, R1, sp1, grids.coords)
ao1 = ao1 * grids.weights
ko1 = np.einsum('ik,oi->koi', grids.coords, ao1)
ao2 = ao_eval(me.ao1, R2, sp2, grids.coords)
koo2dip = np.einsum("koi,pi->kop", ko1, ao2)
return koo2dip
def overlap_ni(me, sp1,R1, sp2,R2, **kvargs):
"""
Computes overlap for an atom pair. The atom pair is given by a pair of species indices
and the coordinates of the atoms.
Args:
sp1,sp2 : specie indices, and
R1,R2 : respective coordinates in Bohr, atomic units
Result:
matrix of orbital overlaps
The procedure uses the numerical integration in coordinate space.
"""
from pyscf.nao.m_ao_matelem import build_3dgrid
from pyscf.nao.m_ao_eval_libnao import ao_eval_libnao as ao_eval #_libnao
grids = build_3dgrid(me, sp1, R1, sp2, R2, **kvargs)
ao1 = ao_eval(me.ao1, R1, sp1, grids.coords)
ao1 = ao1 * grids.weights
ao2 = ao_eval(me.ao2, R2, sp2, grids.coords)
overlaps = np.einsum("ij,kj->ik", ao1, ao2) # overlaps = np.matmul(ao1, ao2.T)
return overlaps
def eval_ao(self,
feval,
coords,
comp,
shls_slice=None,
non0tab=None,
out=None):
""" Computes the values of all atomic orbitals for a set of given Cartesian coordinates.
This function should be similar to the pyscf's function eval_gto()... """
from pyscf.nao.m_ao_eval_libnao import ao_eval_libnao as ao_eval
assert feval == "GTOval_sph_deriv0"
assert shls_slice is None
assert non0tab is None
assert comp == 1
aos = ao_eval(self.ao_log, np.zeros(3), 0, coords)
return aos