def _col_lda_vxc_mat(mol,
ao,
weight,
rho,
vxc,
mask,
shls_slice,
ao_loc,
hermi,
on_LL=True):
'''Vxc matrix of collinear LDA'''
# NOTE vxc in u/d representation
aoa, aob = ao
wv = weight * vxc
if hermi:
wv *= .5
if on_LL:
wva, wvb = wv
else: # for SS block
# v_rho = (vxc_a + vxc_b) * .5
# v_mz = (vxc_a - vxc_b) * .5
# For small components, M = \beta\Sigma leads to
# (v_rho - sigma_z*v_mz) = [vxc_b, 0 ]
# [0 , vxc_a]
wvb, wva = wv
mat = _dot_ao_ao(mol, aoa, _scale_ao(aoa, wva[0]), mask, shls_slice,
ao_loc)
mat += _dot_ao_ao(mol, aob, _scale_ao(aob, wvb[0]), mask, shls_slice,
ao_loc)
return mat
def _col_gga_vxc_mat(mol,
ao,
weight,
rho,
vxc,
mask,
shls_slice,
ao_loc,
hermi,
on_LL=True):
'''Vxc matrix of collinear GGA'''
# NOTE vxc in u/d representation
aoa, aob = ao
wv = weight * vxc
if hermi:
wv[:, 0] *= .5
if on_LL:
wva, wvb = wv
else: # for SS block
wvb, wva = wv
aow = None
aow = _scale_ao(aoa[:4], wva[:4], out=aow)
mat = _dot_ao_ao(mol, aoa[0], aow, mask, shls_slice, ao_loc)
aow = _scale_ao(aob[:4], wvb[:4], out=aow)
mat += _dot_ao_ao(mol, aob[0], aow, mask, shls_slice, ao_loc)
if hermi != 1:
aow = _scale_ao(aoa[1:4], wva[1:4].conj(), out=aow)
mat += _dot_ao_ao(mol, aow, aoa[0], mask, shls_slice, ao_loc)
aow = _scale_ao(aob[1:4], wvb[1:4].conj(), out=aow)
mat += _dot_ao_ao(mol, aow, aob[0], mask, shls_slice, ao_loc)
return mat
def _mcol_lda_vxc_mat(mol, ao, weight, rho, vxc, mask, shls_slice, ao_loc, hermi):
'''Vxc matrix of multi-collinear LDA'''
wv = weight * vxc
if hermi:
wv *= .5 # * .5 because of v+v.conj().T in r_vxc
wr, wmx, wmy, wmz = wv
# einsum('g,g,xgi,xgj->ij', vxc, weight, ao, ao)
# + einsum('xy,g,g,xgi,ygj->ij', sx, vxc, weight, ao, ao)
# + einsum('xy,g,g,xgi,ygj->ij', sy, vxc, weight, ao, ao)
# + einsum('xy,g,g,xgi,ygj->ij', sz, vxc, weight, ao, ao)
aow = None
aow = _scale_ao(ao, wmx[0], out=aow) # Mx
tmpx = _dot_ao_ao(mol, ao, aow, mask, shls_slice, ao_loc)
aow = _scale_ao(ao, wmy[0], out=aow) # My
tmpy = _dot_ao_ao(mol, ao, aow, mask, shls_slice, ao_loc)
if hermi:
# conj(mx+my*1j) == mx-my*1j, tmpx and tmpy should be real
matba = (tmpx + tmpx.T) + (tmpy + tmpy.T) * 1j
matab = np.zeros_like(matba)
else:
# conj(mx+my*1j) != mx-my*1j, tmpx and tmpy should be complex
matba = tmpx + tmpy * 1j
matab = tmpx - tmpy * 1j
tmpx = tmpy = None
aow = _scale_ao(ao, wr[0]+wmz[0], out=aow) # Mz
mataa = _dot_ao_ao(mol, ao, aow, mask, shls_slice, ao_loc)
aow = _scale_ao(ao, wr[0]-wmz[0], out=aow) # Mz
matbb = _dot_ao_ao(mol, ao, aow, mask, shls_slice, ao_loc)
mat = np.block([[mataa, matab], [matba, matbb]])
return mat
def dot(ao1, ao2):
ao1_re = numpy.asarray(ao1.real, order='C')
ao1_im = numpy.asarray(ao1.imag, order='C')
ao2_re = numpy.asarray(ao2.real, order='C')
ao2_im = numpy.asarray(ao2.imag, order='C')
mat_re = _dot_ao_ao(cell, ao1_re, ao2_re, nao, ngrids, non0tab)
mat_re += _dot_ao_ao(cell, ao1_im, ao2_im, nao, ngrids, non0tab)
mat_im = _dot_ao_ao(cell, ao1_re, ao2_im, nao, ngrids, non0tab)
mat_im -= _dot_ao_ao(cell, ao1_im, ao2_re, nao, ngrids, non0tab)
return mat_re + 1j*mat_im
def dot(ao1, ao2):
ao1_re = numpy.asarray(ao1.real, order='C')
ao1_im = numpy.asarray(ao1.imag, order='C')
ao2_re = numpy.asarray(ao2.real, order='C')
ao2_im = numpy.asarray(ao2.imag, order='C')
mat_re = _dot_ao_ao(cell, ao1_re, ao2_re, nao, ngrids, non0tab)
mat_re += _dot_ao_ao(cell, ao1_im, ao2_im, nao, ngrids, non0tab)
mat_im = _dot_ao_ao(cell, ao1_re, ao2_im, nao, ngrids, non0tab)
mat_im -= _dot_ao_ao(cell, ao1_im, ao2_re, nao, ngrids, non0tab)
return mat_re + 1j * mat_im
def _d1d2_dot_(vmat, mol, ao1, ao2, mask, ao_loc, dR1_on_bra=True):
shls_slice = (0, mol.nbas)
if dR1_on_bra: # (d/dR1 bra) * (d/dR2 ket)
for d1 in range(3):
for d2 in range(3):
vmat[d1,d2] += numint._dot_ao_ao(mol, ao1[d1], ao2[d2], mask,
shls_slice, ao_loc)
else: # (d/dR2 bra) * (d/dR1 ket)
for d1 in range(3):
for d2 in range(3):
vmat[d1,d2] += numint._dot_ao_ao(mol, ao1[d2], ao2[d1], mask,
shls_slice, ao_loc)
def _d1d2_dot_(vmat, mol, ao1, ao2, mask, ao_loc, dR1_on_bra=True):
shls_slice = (0, mol.nbas)
if dR1_on_bra: # (d/dR1 bra) * (d/dR2 ket)
for d1 in range(3):
for d2 in range(3):
vmat[d1, d2] += numint._dot_ao_ao(mol, ao1[d1], ao2[d2], mask,
shls_slice, ao_loc)
else: # (d/dR2 bra) * (d/dR1 ket)
for d1 in range(3):
for d2 in range(3):
vmat[d1, d2] += numint._dot_ao_ao(mol, ao1[d2], ao2[d1], mask,
shls_slice, ao_loc)
def _gga_sum_(vmat, mol, ao, giao, wv, mask, shls_slice, ao_loc):
aow = numpy.einsum('pi,p->pi', giao[XX], wv[1])
aow += numpy.einsum('pi,p->pi', giao[YX], wv[2])
aow += numpy.einsum('pi,p->pi', giao[ZX], wv[3])
vmat[0] += numint._dot_ao_ao(mol, ao[0], aow, mask, shls_slice, ao_loc)
aow = numpy.einsum('pi,p->pi', giao[XY], wv[1])
aow += numpy.einsum('pi,p->pi', giao[YY], wv[2])
aow += numpy.einsum('pi,p->pi', giao[ZY], wv[3])
vmat[1] += numint._dot_ao_ao(mol, ao[0], aow, mask, shls_slice, ao_loc)
aow = numpy.einsum('pi,p->pi', giao[XZ], wv[1])
aow += numpy.einsum('pi,p->pi', giao[YZ], wv[2])
aow += numpy.einsum('pi,p->pi', giao[ZZ], wv[3])
vmat[2] += numint._dot_ao_ao(mol, ao[0], aow, mask, shls_slice, ao_loc)
def _gga_sum_(vmat, mol, ao, giao, wv, mask, shls_slice, ao_loc):
aow = numpy.einsum('pi,p->pi', giao[XX], wv[1])
aow+= numpy.einsum('pi,p->pi', giao[YX], wv[2])
aow+= numpy.einsum('pi,p->pi', giao[ZX], wv[3])
vmat[0] += numint._dot_ao_ao(mol, ao[0], aow, mask, shls_slice, ao_loc)
aow = numpy.einsum('pi,p->pi', giao[XY], wv[1])
aow+= numpy.einsum('pi,p->pi', giao[YY], wv[2])
aow+= numpy.einsum('pi,p->pi', giao[ZY], wv[3])
vmat[1] += numint._dot_ao_ao(mol, ao[0], aow, mask, shls_slice, ao_loc)
aow = numpy.einsum('pi,p->pi', giao[XZ], wv[1])
aow+= numpy.einsum('pi,p->pi', giao[YZ], wv[2])
aow+= numpy.einsum('pi,p->pi', giao[ZZ], wv[3])
vmat[2] += numint._dot_ao_ao(mol, ao[0], aow, mask, shls_slice, ao_loc)
def _ncol_lda_vxc_mat(mol,
ao,
weight,
rho_tm,
vxc,
mask,
shls_slice,
ao_loc,
hermi,
on_LL=True):
'''Vxc matrix of non-collinear LDA'''
# NOTE vxc in u/d representation
aoa, aob = ao
r, mx, my, mz = rho_tm
vxc = xc_deriv.ud2ts(vxc)
vr, vs = vxc[:, 0]
s = lib.norm(rho_tm[1:4], axis=0)
wv = weight * vr
with numpy.errstate(divide='ignore', invalid='ignore'):
ws = vs * weight / s
ws[s < 1e-20] = 0
if not on_LL:
# flip the sign for small components because
# M = \beta\Sigma = [sigma, 0 ]
# [0 , -sigma]
ws *= -1
# * .5 because of v+v.conj().T in r_vxc
if hermi:
wv *= .5
ws *= .5
# einsum('g,g,xgi,xgj->ij', vr, weight, ao, ao)
# + einsum('xy,g,g,xgi,ygj->ij', sx, vs*m[0]/s, weight, ao, ao)
# + einsum('xy,g,g,xgi,ygj->ij', sy, vs*m[1]/s, weight, ao, ao)
# + einsum('xy,g,g,xgi,ygj->ij', sz, vs*m[2]/s, weight, ao, ao)
aow = None
aow = _scale_ao(aoa, ws * (mx + my * 1j), out=aow)
mat = _dot_ao_ao(mol, aob, aow, mask, shls_slice, ao_loc)
if hermi:
mat = mat + mat.conj().T
else:
aow = _scale_ao(aob, ws * (mx - my * 1j), out=aow) # Mx
mat += _dot_ao_ao(mol, aoa, aow, mask, shls_slice, ao_loc)
aow = _scale_ao(aoa, wv + ws * mz, out=aow) # Mz
mat += _dot_ao_ao(mol, aoa, aow, mask, shls_slice, ao_loc)
aow = _scale_ao(aob, wv - ws * mz, out=aow) # Mz
mat += _dot_ao_ao(mol, aob, aow, mask, shls_slice, ao_loc)
return mat
def mgga_sum_(vmat, ao, wv, mask):
aow = numint._scale_ao(ao[:4], wv[:4])
tmp = numint._dot_ao_ao(mol, ao[0], aow, mask, shls_slice, ao_loc)
aow = numint._scale_ao(ao[1], wv[5], aow)
tmp += numint._dot_ao_ao(mol, ao[1], aow, mask, shls_slice, ao_loc)
aow = numint._scale_ao(ao[2], wv[5], aow)
tmp += numint._dot_ao_ao(mol, ao[2], aow, mask, shls_slice, ao_loc)
aow = numint._scale_ao(ao[3], wv[5], aow)
tmp += numint._dot_ao_ao(mol, ao[3], aow, mask, shls_slice, ao_loc)
vmat[0] += tmp + tmp.T
rks_grad._gga_grad_sum_(vmat[1:], mol, ao, wv[:4], mask, ao_loc)
rks_grad._tau_grad_dot_(vmat[1:], mol, ao, wv[5] * 2, mask, ao_loc,
True)
def _mcol_mgga_vxc_mat(mol,
ao,
weight,
rho,
vxc,
mask,
shls_slice,
ao_loc,
hermi,
on_LL=True):
'''Vxc matrix of multi-collinear MGGA'''
# NOTE vxc in t/m representation
aoa, aob = ao
wv = weight * vxc
tau_idx = 4
wv[:, tau_idx] *= .5 # *.5 for 1/2 in tau
if hermi:
wv[:, 0] *= .5
wv[:, tau_idx] *= .5
if not on_LL:
# flip the sign for small components because
# M = \beta\Sigma = [sigma, 0 ]
# [0 , -sigma]
wv[1:4] *= -1
wr, wmx, wmy, wmz = wv
aow = None
aow = _scale_ao(aoa[:4], wmx[:4] + wmy[:4] * 1j, out=aow)
mat = _dot_ao_ao(mol, aob[0], aow, mask, shls_slice, ao_loc)
mat += _tau_dot(mol, aob, aoa, wmx[tau_idx] + wmy[tau_idx] * 1j, mask,
shls_slice, ao_loc)
if hermi:
assert vxc.dtype == numpy.double
mat = mat + mat.conj().T
else:
aow = _scale_ao(aob[:4], wmx[:4] - wmy[:4] * 1j, out=aow)
mat += _dot_ao_ao(mol, aoa[0], aow, mask, shls_slice, ao_loc)
mat += _tau_dot(mol, aoa, aob, wmx[tau_idx] - wmy[tau_idx] * 1j, mask,
shls_slice, ao_loc)
aow = _scale_ao(aob[1:4], (wmx[1:4] + wmy[1:4] * 1j).conj(), out=aow)
mat += _dot_ao_ao(mol, aow, aoa[0], mask, shls_slice, ao_loc)
aow = _scale_ao(aoa[1:4], (wmx[1:4] - wmy[1:4] * 1j).conj(), out=aow)
mat += _dot_ao_ao(mol, aow, aob[0], mask, shls_slice, ao_loc)
aow = _scale_ao(aoa[1:4], (wr[1:4] + wmz[1:4]).conj(), out=aow) # Mz
mat += _dot_ao_ao(mol, aow, aoa[0], mask, shls_slice, ao_loc)
aow = _scale_ao(aob[1:4], (wr[1:4] - wmz[1:4]).conj(), out=aow) # Mz
mat += _dot_ao_ao(mol, aow, aob[0], mask, shls_slice, ao_loc)
aow = _scale_ao(aoa, wr[:4] + wmz[:4], out=aow) # Mz
mat += _dot_ao_ao(mol, aoa[0], aow, mask, shls_slice, ao_loc)
mat += _tau_dot(mol, aoa, aoa, wr[tau_idx] + wmz[tau_idx], mask,
shls_slice, ao_loc)
aow = _scale_ao(aob, wr[:4] - wmz[:4], out=aow) # Mz
mat += _dot_ao_ao(mol, aob[0], aow, mask, shls_slice, ao_loc)
mat += _tau_dot(mol, aob, aob, wr[tau_idx] - wmz[tau_idx], mask,
shls_slice, ao_loc)
return mat
def get_veff_nuc_epc(self, mol, dm, dm_last=None, vhf_last=None, hermi=1):
'''Add EPC contribution to nuclear veff'''
nao = mol.nao_nr()
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
nnuc = 0
excsum = 0
vmat = numpy.zeros((nao, nao))
grids = self.mf_elec.grids
ni = self.mf_elec._numint
aow = None
for ao, mask, weight, coords in ni.block_loop(mol, grids, nao):
aow = numpy.ndarray(ao.shape, order='F', buffer=aow)
ao_elec = eval_ao(self.mol.elec, coords)
if self.dm_elec.ndim > 2:
rho_elec = eval_rho(self.mol.elec, ao_elec, self.dm_elec[0] + self.dm_elec[1])
else:
rho_elec = eval_rho(self.mol.elec, ao_elec, self.dm_elec)
ao_nuc = eval_ao(mol, coords)
rho_nuc = eval_rho(mol, ao_nuc, dm)
exc, vxc = eval_xc_nuc(self.epc, rho_elec, rho_nuc)
den = rho_nuc * weight
nnuc += den.sum()
excsum += numpy.dot(den, exc)
# times 0.5 because vmat + vmat.T
aow = _scale_ao(ao_nuc, 0.5 * weight * vxc, out=aow)
vmat += _dot_ao_ao(mol, ao_nuc, aow, mask, shls_slice, ao_loc)
logger.debug(self, 'The number of nuclei: %.5f', nnuc)
vmat += vmat.conj().T
# attach E_ep to vmat to retrieve later
vmat = lib.tag_array(vmat, exc=excsum, ecoul=0, vj=0, vk=0)
return vmat
def get_veff_elec_epc(self, mol, dm, dm_last=None, vhf_last=None, hermi=1):
'''Add EPC contribution to electronic veff'''
nao = mol.nao_nr()
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
vmat = numpy.zeros((nao, nao))
grids = self.mf_elec.grids
ni = self.mf_elec._numint
aow = None
for i in range(self.mol.nuc_num):
ia = self.mol.nuc[i].atom_index
if self.mol.atom_symbol(ia) == 'H':
for ao, mask, weight, coords in ni.block_loop(mol, grids, nao):
aow = numpy.ndarray(ao.shape, order='F', buffer=aow)
ao_elec = eval_ao(mol, coords)
if dm.ndim > 2:
rho_elec = eval_rho(mol, ao_elec, dm[0] + dm[1])
else:
rho_elec = eval_rho(mol, ao_elec, dm)
ao_nuc = eval_ao(self.mol.nuc[i], coords)
rho_nuc = eval_rho(self.mol.nuc[i], ao_nuc, self.dm_nuc[i])
vxc_i = eval_xc_elec(self.epc, rho_elec, rho_nuc)
# times 0.5 because vmat + vmat.T
aow = _scale_ao(ao_elec, 0.5 * weight * vxc_i, out=aow)
vmat += _dot_ao_ao(mol, ao_elec, aow, mask, shls_slice, ao_loc)
vmat += vmat.conj().T
if dm.ndim > 2:
veff = dft.uks.get_veff(self.mf_elec, mol, dm, dm_last, vhf_last, hermi)
else:
veff = dft.rks.get_veff(self.mf_elec, mol, dm, dm_last, vhf_last, hermi)
vxc = lib.tag_array(veff + vmat, ecoul=veff.ecoul, exc=veff.exc, vj=veff.vj, vk=veff.vk)
return vxc
def gga_sum_(vmat, ao, wv, mask):
aow = numpy.einsum('pi,p->pi', ao[0], wv[0])
aow += numpy.einsum('npi,np->pi', ao[1:4], wv[1:])
tmp = numint._dot_ao_ao(mol, ao[0], aow, mask, shls_slice,
ao_loc)
vmat[0] += tmp + tmp.T
rks_grad._gga_grad_sum_(vmat[1:], mol, ao, wv, mask, ao_loc)
def _vxc2x2_to_mat(mol, ao, weight, rho, vrho, non0tab, shls_slice, ao_loc):
aoa, aob = ao
r, m = rho
vr, vm = vrho.T
aow = numpy.empty_like(aoa)
# aow = numpy.einsum('pi,p->pi', aoa, weight*vr, out=aow)
# mat = _dot_ao_ao(mol, aoa, aow, non0tab, shls_slice, ao_loc)
# aow = numpy.einsum('pi,p->pi', aob, weight*vr, out=aow)
# mat+= _dot_ao_ao(mol, aob, aow, non0tab, shls_slice, ao_loc)
#
# s = lib.norm(m, axis=0)
# ws = vm * weight / (s+1e-300)
# aow = numpy.einsum('pi,p->pi', aoa, ws*m[0], out=aow) # Mx
# tmp = _dot_ao_ao(mol, aob, aow, non0tab, shls_slice, ao_loc)
# mat+= tmp + tmp.T.conj()
# aow = numpy.einsum('pi,p->pi', aoa, ws*m[1], out=aow) # My
# tmp = _dot_ao_ao(mol, aob, aow, non0tab, shls_slice, ao_loc)
# mat+= (tmp - tmp.T.conj()) * 1j
# aow = numpy.einsum('pi,p->pi', aoa, ws*m[2], out=aow) # Mz
# mat+= _dot_ao_ao(mol, aoa, aow, non0tab, shls_slice, ao_loc)
# aow = numpy.einsum('pi,p->pi', aob, ws*m[2], out=aow)
# mat-= _dot_ao_ao(mol, aob, aow, non0tab, shls_slice, ao_loc)
s = lib.norm(m, axis=0)
idx = s < 1e-20
with numpy.errstate(divide='ignore', invalid='ignore'):
ws = vm * weight / s
ws[idx] = 0
aow = numpy.einsum('pi,p->pi', aoa, ws * m[0], out=aow) # Mx
tmp = _dot_ao_ao(mol, aob, aow, non0tab, shls_slice, ao_loc)
mat = tmp + tmp.T.conj()
aow = numpy.einsum('pi,p->pi', aoa, ws * m[1], out=aow) # My
tmp = _dot_ao_ao(mol, aob, aow, non0tab, shls_slice, ao_loc)
mat += (tmp - tmp.T.conj()) * 1j
aow = numpy.einsum('pi,p->pi', aoa, weight * vr, out=aow)
aow += numpy.einsum('pi,p->pi', aoa, ws * m[2]) # Mz
mat += _dot_ao_ao(mol, aoa, aow, non0tab, shls_slice, ao_loc)
aow = numpy.einsum('pi,p->pi', aob, weight * vr, out=aow)
aow -= numpy.einsum('pi,p->pi', aob, ws * m[2]) # Mz
mat += _dot_ao_ao(mol, aob, aow, non0tab, shls_slice, ao_loc)
return mat
def _mcol_lda_vxc_mat(mol,
ao,
weight,
rho,
vxc,
mask,
shls_slice,
ao_loc,
hermi,
on_LL=True):
'''Vxc matrix of multi-collinear LDA'''
# NOTE vxc in t/m representation
aoa, aob = ao
wv = weight * vxc
if hermi:
wv *= .5 # * .5 because of v+v.conj().T in r_vxc
if not on_LL:
# flip the sign for small components because
# M = \beta\Sigma = [sigma, 0 ]
# [0 , -sigma]
wv[1:4] *= -1
wr, wmx, wmy, wmz = wv
# einsum('g,g,xgi,xgj->ij', vxc, weight, ao, ao)
# + einsum('xy,g,g,xgi,ygj->ij', sx, vxc, weight, ao, ao)
# + einsum('xy,g,g,xgi,ygj->ij', sy, vxc, weight, ao, ao)
# + einsum('xy,g,g,xgi,ygj->ij', sz, vxc, weight, ao, ao)
aow = None
aow = _scale_ao(aoa, wmx[0] + wmy[0] * 1j, out=aow)
mat = _dot_ao_ao(mol, aob, aow, mask, shls_slice, ao_loc)
if hermi:
assert vxc.dtype == numpy.double
mat = mat + mat.conj().T
else:
aow = _scale_ao(aob, wmx[0] - wmy[0] * 1j, out=aow)
mat += _dot_ao_ao(mol, aoa, aow, mask, shls_slice, ao_loc)
aow = _scale_ao(aoa, wr[0] + wmz[0], out=aow) # Mz
mat += _dot_ao_ao(mol, aoa, aow, mask, shls_slice, ao_loc)
aow = _scale_ao(aob, wr[0] - wmz[0], out=aow) # Mz
mat += _dot_ao_ao(mol, aob, aow, mask, shls_slice, ao_loc)
return mat
def _cross3x3_(out, mol, ao1, ao2, mask, shls_slice, ao_loc):
out[0] += numint._dot_ao_ao(mol, ao1[1], ao2[2], mask, shls_slice, ao_loc)
out[0] -= numint._dot_ao_ao(mol, ao1[2], ao2[1], mask, shls_slice, ao_loc)
out[1] += numint._dot_ao_ao(mol, ao1[2], ao2[0], mask, shls_slice, ao_loc)
out[1] -= numint._dot_ao_ao(mol, ao1[0], ao2[2], mask, shls_slice, ao_loc)
out[2] += numint._dot_ao_ao(mol, ao1[0], ao2[1], mask, shls_slice, ao_loc)
out[2] -= numint._dot_ao_ao(mol, ao1[1], ao2[0], mask, shls_slice, ao_loc)
return out
def _cross3x3_(out, mol, ao1, ao2, mask, shls_slice, ao_loc):
out[0] += numint._dot_ao_ao(mol, ao1[1], ao2[2], mask, shls_slice, ao_loc)
out[0] -= numint._dot_ao_ao(mol, ao1[2], ao2[1], mask, shls_slice, ao_loc)
out[1] += numint._dot_ao_ao(mol, ao1[2], ao2[0], mask, shls_slice, ao_loc)
out[1] -= numint._dot_ao_ao(mol, ao1[0], ao2[2], mask, shls_slice, ao_loc)
out[2] += numint._dot_ao_ao(mol, ao1[0], ao2[1], mask, shls_slice, ao_loc)
out[2] -= numint._dot_ao_ao(mol, ao1[1], ao2[0], mask, shls_slice, ao_loc)
return out
def _vxc2x2_to_mat(mol, ao, weight, rho, vrho, non0tab, shls_slice, ao_loc):
aoa, aob = ao
r, m = rho
vr, vm = vrho.T
aow = numpy.empty_like(aoa)
# aow = numpy.einsum('pi,p->pi', aoa, weight*vr, out=aow)
# mat = _dot_ao_ao(mol, aoa, aow, non0tab, shls_slice, ao_loc)
# aow = numpy.einsum('pi,p->pi', aob, weight*vr, out=aow)
# mat+= _dot_ao_ao(mol, aob, aow, non0tab, shls_slice, ao_loc)
#
# s = lib.norm(m, axis=0)
# ws = vm * weight / (s+1e-300)
# aow = numpy.einsum('pi,p->pi', aoa, ws*m[0], out=aow) # Mx
# tmp = _dot_ao_ao(mol, aob, aow, non0tab, shls_slice, ao_loc)
# mat+= tmp + tmp.T.conj()
# aow = numpy.einsum('pi,p->pi', aoa, ws*m[1], out=aow) # My
# tmp = _dot_ao_ao(mol, aob, aow, non0tab, shls_slice, ao_loc)
# mat+= (tmp - tmp.T.conj()) * 1j
# aow = numpy.einsum('pi,p->pi', aoa, ws*m[2], out=aow) # Mz
# mat+= _dot_ao_ao(mol, aoa, aow, non0tab, shls_slice, ao_loc)
# aow = numpy.einsum('pi,p->pi', aob, ws*m[2], out=aow)
# mat-= _dot_ao_ao(mol, aob, aow, non0tab, shls_slice, ao_loc)
s = lib.norm(m, axis=0)
ws = vm * weight / (s+1e-300)
aow = numpy.einsum('pi,p->pi', aoa, ws*m[0], out=aow) # Mx
tmp = _dot_ao_ao(mol, aob, aow, non0tab, shls_slice, ao_loc)
mat = tmp + tmp.T.conj()
aow = numpy.einsum('pi,p->pi', aoa, ws*m[1], out=aow) # My
tmp = _dot_ao_ao(mol, aob, aow, non0tab, shls_slice, ao_loc)
mat+= (tmp - tmp.T.conj()) * 1j
aow = numpy.einsum('pi,p->pi', aoa, weight*vr, out=aow)
aow+= numpy.einsum('pi,p->pi', aoa, ws*m[2]) # Mz
mat+= _dot_ao_ao(mol, aoa, aow, non0tab, shls_slice, ao_loc)
aow = numpy.einsum('pi,p->pi', aob, weight*vr, out=aow)
aow-= numpy.einsum('pi,p->pi', aob, ws*m[2]) # Mz
mat+= _dot_ao_ao(mol, aob, aow, non0tab, shls_slice, ao_loc)
return mat
def _ncol_lda_vxc_mat(mol, ao, weight, rho, vxc, mask, shls_slice, ao_loc, hermi):
'''Vxc matrix of non-collinear LDA'''
# NOTE vxc in u/d representation
r, mx, my, mz = rho
vxc = xc_deriv.ud2ts(vxc)
vr, vs = vxc[:,0]
s = lib.norm(rho[1:4], axis=0)
wv = weight * vr
with np.errstate(divide='ignore',invalid='ignore'):
ws = vs * weight / s
ws[s < 1e-20] = 0
# * .5 because of v+v.conj().T in r_vxc
if hermi:
wv *= .5
ws *= .5
aow = None
aow = _scale_ao(ao, ws*mx, out=aow) # Mx
tmpx = _dot_ao_ao(mol, ao, aow, mask, shls_slice, ao_loc)
aow = _scale_ao(ao, ws*my, out=aow) # My
tmpy = _dot_ao_ao(mol, ao, aow, mask, shls_slice, ao_loc)
if hermi:
# conj(mx+my*1j) == mx-my*1j, tmpx and tmpy should be real
matba = (tmpx + tmpx.T) + (tmpy + tmpy.T) * 1j
matab = np.zeros_like(matba)
else:
# conj(mx+my*1j) != mx-my*1j, tmpx and tmpy should be complex
matba = tmpx + tmpy * 1j
matab = tmpx - tmpy * 1j
tmpx = tmpy = None
aow = _scale_ao(ao, wv+ws*mz, out=aow) # Mz
mataa = _dot_ao_ao(mol, ao, aow, mask, shls_slice, ao_loc)
aow = _scale_ao(ao, wv-ws*mz, out=aow) # Mz
matbb = _dot_ao_ao(mol, ao, aow, mask, shls_slice, ao_loc)
mat = np.block([[mataa, matab], [matba, matbb]])
return mat
def _d1_dot_(vmat, mol, ao1, ao2, mask, ao_loc, dR1_on_bra=True):
shls_slice = (0, mol.nbas)
if dR1_on_bra:
vmat[0] += numint._dot_ao_ao(mol, ao1[0], ao2, mask, shls_slice, ao_loc)
vmat[1] += numint._dot_ao_ao(mol, ao1[1], ao2, mask, shls_slice, ao_loc)
vmat[2] += numint._dot_ao_ao(mol, ao1[2], ao2, mask, shls_slice, ao_loc)
else:
vmat[0] += numint._dot_ao_ao(mol, ao1, ao2[0], mask, shls_slice, ao_loc)
vmat[1] += numint._dot_ao_ao(mol, ao1, ao2[1], mask, shls_slice, ao_loc)
vmat[2] += numint._dot_ao_ao(mol, ao1, ao2[2], mask, shls_slice, ao_loc)
def _d1_dot_(vmat, mol, ao1, ao2, mask, ao_loc, dR1_on_bra=True):
shls_slice = (0, mol.nbas)
if dR1_on_bra:
vmat[0] += numint._dot_ao_ao(mol, ao1[0], ao2, mask, shls_slice, ao_loc)
vmat[1] += numint._dot_ao_ao(mol, ao1[1], ao2, mask, shls_slice, ao_loc)
vmat[2] += numint._dot_ao_ao(mol, ao1[2], ao2, mask, shls_slice, ao_loc)
else:
vmat[0] += numint._dot_ao_ao(mol, ao1, ao2[0], mask, shls_slice, ao_loc)
vmat[1] += numint._dot_ao_ao(mol, ao1, ao2[1], mask, shls_slice, ao_loc)
vmat[2] += numint._dot_ao_ao(mol, ao1, ao2[2], mask, shls_slice, ao_loc)
def _dot_ao_mo(mol,
ao,
mo,
non0tab=None,
shls_slice=None,
ao_loc=None,
hermi=0):
if hermi:
#print ("_dot_ao_mo punting to numint._dot_ao_ao")
return numint._dot_ao_ao(mol,
ao,
mo,
non0tab=non0tab,
shls_slice=shls_slice,
ao_loc=ao_loc,
hermi=hermi)
ngrids, nao = ao.shape
nmo = mo.shape[-1]
if nao < SWITCH_SIZE:
#print ("_dot_ao_mo punting to lib.dot")
return lib.dot(ao.T.conj(), mo)
#print ("_dot_ao_mo doing my own thing")
if not ao.flags.f_contiguous:
ao = lib.transpose(ao)
if not mo.flags.f_contiguous:
mo = lib.transpose(mo)
if ao.dtype == mo.dtype == np.double:
fn = libpdft.VOTdot_ao_mo
else:
raise NotImplementedError("Complex-orbital PDFT")
if non0tab is None or shls_slice is None or ao_loc is None:
pnon0tab = pshls_slice = pao_loc = lib.c_null_ptr()
else:
pnon0tab = non0tab.ctypes.data_as(ctypes.c_void_p)
pshls_slice = (ctypes.c_int * 2)(*shls_slice)
pao_loc = ao_loc.ctypes.data_as(ctypes.c_void_p)
vv = np.empty((nao, nmo), dtype=ao.dtype)
fn(vv.ctypes.data_as(ctypes.c_void_p), ao.ctypes.data_as(ctypes.c_void_p),
mo.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(nao), ctypes.c_int(nmo), ctypes.c_int(ngrids),
ctypes.c_int(mol.nbas), pnon0tab, pshls_slice, pao_loc)
return vv
def _mcol_mgga_vxc_mat(mol, ao, weight, rho, vxc, mask, shls_slice, ao_loc, hermi):
'''Vxc matrix of multi-collinear MGGA'''
wv = weight * vxc
tau_idx = 4
wv[:,tau_idx] *= .5 # *.5 for 1/2 in tau
if hermi:
wv[:,0] *= .5 # * .5 because of v+v.conj().T in r_vxc
wv[:,tau_idx] *= .5
wr, wmx, wmy, wmz = wv
aow = None
aow = _scale_ao(ao[:4], wr[:4]+wmz[:4], out=aow) # Mz
mataa = _dot_ao_ao(mol, ao[0], aow, mask, shls_slice, ao_loc)
mataa += _tau_dot(mol, ao, ao, wr[tau_idx]+wmz[tau_idx], mask, shls_slice, ao_loc)
aow = _scale_ao(ao[:4], wr[:4]-wmz[:4], out=aow) # Mz
matbb = _dot_ao_ao(mol, ao[0], aow, mask, shls_slice, ao_loc)
matbb += _tau_dot(mol, ao, ao, wr[tau_idx]-wmz[tau_idx], mask, shls_slice, ao_loc)
aow = _scale_ao(ao[:4], wmx[:4], out=aow) # Mx
tmpx = _dot_ao_ao(mol, ao[0], aow, mask, shls_slice, ao_loc)
tmpx += _tau_dot(mol, ao, ao, wmx[tau_idx], mask, shls_slice, ao_loc)
aow = _scale_ao(ao[:4], wmy[:4], out=aow) # My
tmpy = _dot_ao_ao(mol, ao[0], aow, mask, shls_slice, ao_loc)
tmpy += _tau_dot(mol, ao, ao, wmy[tau_idx], mask, shls_slice, ao_loc)
if hermi:
assert vxc.dtype == np.double
# conj(mx+my*1j) == mx-my*1j, tmpx and tmpy should be real
matba = (tmpx + tmpx.T) + (tmpy + tmpy.T) * 1j
matab = np.zeros_like(matba)
else:
# conj(mx+my*1j) != mx-my*1j, tmpx and tmpy should be complex
aow = _scale_ao(ao[1:4], wmx[1:4].conj(), out=aow) # Mx
tmpx += _dot_ao_ao(mol, aow, ao[0], mask, shls_slice, ao_loc)
aow = _scale_ao(ao[1:4], wmy[1:4].conj(), out=aow) # My
tmpy += _dot_ao_ao(mol, aow, ao[0], mask, shls_slice, ao_loc)
matba = tmpx + tmpy * 1j
matab = tmpx - tmpy * 1j
aow = _scale_ao(ao[1:4], (wr[1:4]+wmz[1:4]).conj(), out=aow) # Mz
mataa += _dot_ao_ao(mol, aow, ao[0], mask, shls_slice, ao_loc)
aow = _scale_ao(ao[1:4], (wr[1:4]-wmz[1:4]).conj(), out=aow) # Mz
matbb += _dot_ao_ao(mol, aow, ao[0], mask, shls_slice, ao_loc)
mat = np.block([[mataa, matab], [matba, matbb]])
return mat
def get_vxc_giao(ni, mol, grids, xc_code, dms, max_memory=2000, verbose=None):
xctype = ni._xc_type(xc_code)
make_rho, nset, nao = ni._gen_rho_evaluator(mol, dms, hermi=1)
ngrids = len(grids.weights)
BLKSIZE = numint.BLKSIZE
blksize = min(int(max_memory/12*1e6/8/nao/BLKSIZE)*BLKSIZE, ngrids)
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
vmat = numpy.zeros((3,nao,nao))
if xctype == 'LDA':
buf = numpy.empty((4,blksize,nao))
ao_deriv = 0
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory,
blksize=blksize, buf=buf):
rho = make_rho(0, ao, mask, 'LDA')
vxc = ni.eval_xc(xc_code, rho, 0, deriv=1)[1]
vrho = vxc[0]
aow = numpy.einsum('pi,p->pi', ao, weight*vrho)
giao = mol.eval_gto('GTOval_ig', coords, comp=3,
non0tab=mask, out=buf[1:])
vmat[0] += numint._dot_ao_ao(mol, aow, giao[0], mask, shls_slice, ao_loc)
vmat[1] += numint._dot_ao_ao(mol, aow, giao[1], mask, shls_slice, ao_loc)
vmat[2] += numint._dot_ao_ao(mol, aow, giao[2], mask, shls_slice, ao_loc)
rho = vxc = vrho = aow = None
elif xctype == 'GGA':
buf = numpy.empty((10,blksize,nao))
ao_deriv = 1
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory,
blksize=blksize, buf=buf):
rho = make_rho(0, ao, mask, 'GGA')
vxc = ni.eval_xc(xc_code, rho, 0, deriv=1)[1]
vrho, vsigma = vxc[:2]
wv = numpy.empty_like(rho)
wv[0] = weight * vrho
wv[1:] = rho[1:] * (weight * vsigma * 2)
aow = numpy.einsum('npi,np->pi', ao[:4], wv)
giao = mol.eval_gto('GTOval_ig', coords, 3, non0tab=mask, out=buf[4:])
vmat[0] += numint._dot_ao_ao(mol, aow, giao[0], mask, shls_slice, ao_loc)
vmat[1] += numint._dot_ao_ao(mol, aow, giao[1], mask, shls_slice, ao_loc)
vmat[2] += numint._dot_ao_ao(mol, aow, giao[2], mask, shls_slice, ao_loc)
giao = mol.eval_gto('GTOval_ipig', coords, 9, non0tab=mask, out=buf[1:])
_gga_sum_(vmat, mol, ao, giao, wv, mask, shls_slice, ao_loc)
rho = vxc = vrho = vsigma = wv = aow = None
elif xctype == 'MGGA':
raise NotImplementedError('meta-GGA')
return vmat - vmat.transpose(0,2,1)
def get_vxc_giao(ni, mol, grids, xc_code, dms, max_memory=2000, verbose=None):
xctype = ni._xc_type(xc_code)
make_rho, nset, nao = ni._gen_rho_evaluator(mol, dms, hermi=1)
ngrids = len(grids.weights)
BLKSIZE = numint.BLKSIZE
blksize = min(int(max_memory/12*1e6/8/nao/BLKSIZE)*BLKSIZE, ngrids)
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
vmat = numpy.zeros((3,nao,nao))
if xctype == 'LDA':
buf = numpy.empty((4,blksize,nao))
ao_deriv = 0
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory,
blksize=blksize, buf=buf):
rho = make_rho(0, ao, mask, 'LDA')
vxc = ni.eval_xc(xc_code, rho, 0, deriv=1)[1]
vrho = vxc[0]
aow = numpy.einsum('pi,p->pi', ao, weight*vrho)
giao = mol.eval_gto('GTOval_ig', coords, comp=3,
non0tab=mask, out=buf[1:])
vmat[0] += numint._dot_ao_ao(mol, aow, giao[0], mask, shls_slice, ao_loc)
vmat[1] += numint._dot_ao_ao(mol, aow, giao[1], mask, shls_slice, ao_loc)
vmat[2] += numint._dot_ao_ao(mol, aow, giao[2], mask, shls_slice, ao_loc)
rho = vxc = vrho = aow = None
elif xctype == 'GGA':
buf = numpy.empty((10,blksize,nao))
ao_deriv = 1
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory,
blksize=blksize, buf=buf):
rho = make_rho(0, ao, mask, 'GGA')
vxc = ni.eval_xc(xc_code, rho, 0, deriv=1)[1]
vrho, vsigma = vxc[:2]
wv = numpy.empty_like(rho)
wv[0] = weight * vrho
wv[1:] = rho[1:] * (weight * vsigma * 2)
aow = numpy.einsum('npi,np->pi', ao[:4], wv)
giao = mol.eval_gto('GTOval_ig', coords, 3, non0tab=mask, out=buf[4:])
vmat[0] += numint._dot_ao_ao(mol, aow, giao[0], mask, shls_slice, ao_loc)
vmat[1] += numint._dot_ao_ao(mol, aow, giao[1], mask, shls_slice, ao_loc)
vmat[2] += numint._dot_ao_ao(mol, aow, giao[2], mask, shls_slice, ao_loc)
giao = mol.eval_gto('GTOval_ipig', coords, 9, non0tab=mask, out=buf[1:])
_gga_sum_(vmat, mol, ao, giao, wv, mask, shls_slice, ao_loc)
rho = vxc = vrho = vsigma = wv = aow = None
elif xctype == 'MGGA':
raise NotImplementedError('meta-GGA')
return vmat - vmat.transpose(0,2,1)
def _gga_grad_sum(mol, ao, wv, mask, shls_slice, ao_loc):
ngrid, nao = ao[0].shape
vmat = numpy.empty((3, nao, nao))
aow = numpy.einsum('npi,np->pi', ao[:4], wv)
vmat[0] = numint._dot_ao_ao(mol, ao[1], aow, mask, shls_slice, ao_loc)
vmat[1] = numint._dot_ao_ao(mol, ao[2], aow, mask, shls_slice, ao_loc)
vmat[2] = numint._dot_ao_ao(mol, ao[3], aow, mask, shls_slice, ao_loc)
# XX, XY, XZ = 4, 5, 6
# YX, YY, YZ = 5, 7, 8
# ZX, ZY, ZZ = 6, 8, 9
aow = numpy.einsum('pi,p->pi', ao[4], wv[1])
aow += numpy.einsum('pi,p->pi', ao[5], wv[2])
aow += numpy.einsum('pi,p->pi', ao[6], wv[3])
vmat[0] += numint._dot_ao_ao(mol, aow, ao[0], mask, shls_slice, ao_loc)
aow = numpy.einsum('pi,p->pi', ao[5], wv[1])
aow += numpy.einsum('pi,p->pi', ao[7], wv[2])
aow += numpy.einsum('pi,p->pi', ao[8], wv[3])
vmat[1] += numint._dot_ao_ao(mol, aow, ao[0], mask, shls_slice, ao_loc)
aow = numpy.einsum('pi,p->pi', ao[6], wv[1])
aow += numpy.einsum('pi,p->pi', ao[8], wv[2])
aow += numpy.einsum('pi,p->pi', ao[9], wv[3])
vmat[2] += numint._dot_ao_ao(mol, aow, ao[0], mask, shls_slice, ao_loc)
return vmat
def _gga_grad_sum(mol, ao, wv, mask):
ngrid, nao = ao[0].shape
vmat = numpy.empty((3,nao,nao))
aow = numpy.einsum('npi,np->pi', ao[:4], wv)
vmat[0] = numint._dot_ao_ao(mol, ao[1], aow, nao, ngrid, mask)
vmat[1] = numint._dot_ao_ao(mol, ao[2], aow, nao, ngrid, mask)
vmat[2] = numint._dot_ao_ao(mol, ao[3], aow, nao, ngrid, mask)
# XX, XY, XZ = 4, 5, 6
# YX, YY, YZ = 5, 7, 8
# ZX, ZY, ZZ = 6, 8, 9
aow = numpy.einsum('pi,p->pi', ao[4], wv[1])
aow+= numpy.einsum('pi,p->pi', ao[5], wv[2])
aow+= numpy.einsum('pi,p->pi', ao[6], wv[3])
vmat[0] += numint._dot_ao_ao(mol, aow, ao[0], nao, ngrid, mask)
aow = numpy.einsum('pi,p->pi', ao[5], wv[1])
aow+= numpy.einsum('pi,p->pi', ao[7], wv[2])
aow+= numpy.einsum('pi,p->pi', ao[8], wv[3])
vmat[1] += numint._dot_ao_ao(mol, aow, ao[0], nao, ngrid, mask)
aow = numpy.einsum('pi,p->pi', ao[6], wv[1])
aow+= numpy.einsum('pi,p->pi', ao[8], wv[2])
aow+= numpy.einsum('pi,p->pi', ao[9], wv[3])
vmat[2] += numint._dot_ao_ao(mol, aow, ao[0], nao, ngrid, mask)
return vmat
def _contract_xc_kernel(td_grad,
xc_code,
dmvo,
dmoo=None,
with_vxc=True,
with_kxc=True,
max_memory=2000):
mol = td_grad.mol
mf = td_grad.base._scf
grids = mf.grids
ni = mf._numint
xctype = ni._xc_type(xc_code)
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
nao = mo_coeff[0].shape[0]
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
# dmvo ~ reduce(numpy.dot, (orbv, Xai, orbo.T))
dmvo = [
(dmvo[0] + dmvo[0].T) * .5, # because K_{ia,jb} == K_{ia,jb}
(dmvo[1] + dmvo[1].T) * .5
]
f1vo = numpy.zeros((2, 4, nao, nao))
deriv = 2
if dmoo is not None:
f1oo = numpy.zeros((2, 4, nao, nao))
else:
f1oo = None
if with_vxc:
v1ao = numpy.zeros((2, 4, nao, nao))
else:
v1ao = None
if with_kxc:
k1ao = numpy.zeros((2, 4, nao, nao))
deriv = 3
else:
k1ao = None
if xctype == 'LDA':
ao_deriv = 1
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
rho = (ni.eval_rho2(mol, ao[0], mo_coeff[0], mo_occ[0], mask,
'LDA'),
ni.eval_rho2(mol, ao[0], mo_coeff[1], mo_occ[1], mask,
'LDA'))
vxc, fxc, kxc = ni.eval_xc(xc_code, rho, 1, deriv=deriv)[1:]
u_u, u_d, d_d = fxc[0].T * weight
rho1a = ni.eval_rho(mol, ao[0], dmvo[0], mask, 'LDA')
rho1b = ni.eval_rho(mol, ao[0], dmvo[1], mask, 'LDA')
aow = (numpy.einsum('pi,p,p->pi', ao[0], u_u, rho1a) +
numpy.einsum('pi,p,p->pi', ao[0], u_d, rho1b),
numpy.einsum('pi,p,p->pi', ao[0], u_d, rho1a) +
numpy.einsum('pi,p,p->pi', ao[0], d_d, rho1b))
for k in range(4):
f1vo[0, k] += numint._dot_ao_ao(mol, ao[k], aow[0], mask,
shls_slice, ao_loc)
f1vo[1, k] += numint._dot_ao_ao(mol, ao[k], aow[1], mask,
shls_slice, ao_loc)
if dmoo is not None:
rho2a = ni.eval_rho(mol, ao[0], dmoo[0], mask, 'LDA')
rho2b = ni.eval_rho(mol, ao[0], dmoo[1], mask, 'LDA')
aow = (numpy.einsum('pi,p,p->pi', ao[0], u_u, rho2a) +
numpy.einsum('pi,p,p->pi', ao[0], u_d, rho2b),
numpy.einsum('pi,p,p->pi', ao[0], u_d, rho2a) +
numpy.einsum('pi,p,p->pi', ao[0], d_d, rho2b))
for k in range(4):
f1oo[0, k] += numint._dot_ao_ao(mol, ao[k], aow[0], mask,
shls_slice, ao_loc)
f1oo[1, k] += numint._dot_ao_ao(mol, ao[k], aow[1], mask,
shls_slice, ao_loc)
if with_vxc:
vrho = vxc[0].T * weight
aow = (numpy.einsum('pi,p->pi', ao[0], vrho[0]),
numpy.einsum('pi,p->pi', ao[0], vrho[1]))
for k in range(4):
v1ao[0, k] += numint._dot_ao_ao(mol, ao[k], aow[0], mask,
shls_slice, ao_loc)
v1ao[1, k] += numint._dot_ao_ao(mol, ao[k], aow[1], mask,
shls_slice, ao_loc)
if with_kxc:
u_u_u, u_u_d, u_d_d, d_d_d = kxc[0].T * weight
aow = (
numpy.einsum('pi,p,p,p->pi', ao[0], u_u_u, rho1a, rho1a) +
numpy.einsum('pi,p,p,p->pi', ao[0], u_u_d, rho1a, rho1b) *
2 +
numpy.einsum('pi,p,p,p->pi', ao[0], u_d_d, rho1b, rho1b),
numpy.einsum('pi,p,p,p->pi', ao[0], u_u_d, rho1a, rho1a) +
numpy.einsum('pi,p,p,p->pi', ao[0], u_d_d, rho1a, rho1b) *
2 +
numpy.einsum('pi,p,p,p->pi', ao[0], d_d_d, rho1b, rho1b))
for k in range(4):
k1ao[0, k] += numint._dot_ao_ao(mol, ao[k], aow[0], mask,
shls_slice, ao_loc)
k1ao[1, k] += numint._dot_ao_ao(mol, ao[k], aow[1], mask,
shls_slice, ao_loc)
vxc = fxc = kxc = aow = rho = rho1 = rho2 = None
elif xctype == 'GGA':
def gga_sum_(vmat, ao, wv, mask):
aow = numpy.einsum('pi,p->pi', ao[0], wv[0])
aow += numpy.einsum('npi,np->pi', ao[1:4], wv[1:])
tmp = numint._dot_ao_ao(mol, ao[0], aow, mask, shls_slice, ao_loc)
vmat[0] += tmp + tmp.T
rks_grad._gga_grad_sum_(vmat[1:], mol, ao, wv, mask, ao_loc)
ao_deriv = 2
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
rho = (ni.eval_rho2(mol, ao, mo_coeff[0], mo_occ[0], mask, 'GGA'),
ni.eval_rho2(mol, ao, mo_coeff[1], mo_occ[1], mask, 'GGA'))
vxc, fxc, kxc = ni.eval_xc(xc_code, rho, 1, deriv=deriv)[1:]
rho1 = (ni.eval_rho(mol, ao, dmvo[0], mask, 'GGA'),
ni.eval_rho(mol, ao, dmvo[1], mask, 'GGA'))
wv = numint._uks_gga_wv1(rho, rho1, vxc, fxc, weight)
gga_sum_(f1vo[0], ao, wv[0], mask)
gga_sum_(f1vo[1], ao, wv[1], mask)
if dmoo is not None:
rho2 = (ni.eval_rho(mol, ao, dmoo[0], mask, 'GGA'),
ni.eval_rho(mol, ao, dmoo[1], mask, 'GGA'))
wv = numint._uks_gga_wv1(rho, rho2, vxc, fxc, weight)
gga_sum_(f1oo[0], ao, wv[0], mask)
gga_sum_(f1oo[1], ao, wv[1], mask)
if with_vxc:
wv = numint._uks_gga_wv0(rho, vxc, weight)
gga_sum_(v1ao[0], ao, wv[0], mask)
gga_sum_(v1ao[1], ao, wv[1], mask)
if with_kxc:
wv = numint._uks_gga_wv2(rho, rho1, fxc, kxc, weight)
gga_sum_(k1ao[0], ao, wv[0], mask)
gga_sum_(k1ao[1], ao, wv[1], mask)
vxc = fxc = kxc = rho = rho1 = None
else:
raise NotImplementedError('meta-GGA')
f1vo[:, 1:] *= -1
if f1oo is not None: f1oo[:, 1:] *= -1
if v1ao is not None: v1ao[:, 1:] *= -1
if k1ao is not None: k1ao[:, 1:] *= -1
return f1vo, f1oo, v1ao, k1ao
def _contract_xc_kernel(td_grad,
xc_code,
xai,
oovv=None,
with_vxc=True,
with_kxc=True,
singlet=True,
max_memory=2000):
mol = td_grad.mol
mf = td_grad._scf
grids = mf.grids
ni = mf._numint
xctype = ni._xc_type(xc_code)
mo_coeff = mf.mo_coeff
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
nao, nmo = mo_coeff.shape
nocc = (mo_occ > 0).sum()
orbv = mo_coeff[:, nocc:]
orbo = mo_coeff[:, :nocc]
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
# dmvo ~ reduce(numpy.dot, (orbv, Xai, orbo.T))
dmvo = (xai + xai.T) * .5 # because K_{ai,bj} == K_{ai,bj}
f1vo = numpy.zeros((4, nao, nao))
deriv = 2
if oovv is not None:
f1oo = numpy.zeros((4, nao, nao))
else:
f1oo = None
if with_vxc:
v1ao = numpy.zeros((4, nao, nao))
else:
v1ao = None
if with_kxc:
k1ao = numpy.zeros((4, nao, nao))
deriv = 3
else:
k1ao = None
if xctype == 'LDA':
ao_deriv = 1
if singlet:
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
rho = ni.eval_rho2(mol, ao[0], mo_coeff, mo_occ, mask, 'LDA')
vxc, fxc, kxc = ni.eval_xc(xc_code, rho, 0, deriv=deriv)[1:]
wfxc = fxc[0] * weight * 2 # *2 for alpha+beta
rho1 = ni.eval_rho(mol, ao[0], dmvo, mask, 'LDA')
aow = numpy.einsum('pi,p->pi', ao[0], wfxc * rho1)
for k in range(4):
f1vo[k] += numint._dot_ao_ao(mol, ao[k], aow, mask,
shls_slice, ao_loc)
if oovv is not None:
rho2 = ni.eval_rho(mol, ao[0], oovv, mask, 'LDA')
aow = numpy.einsum('pi,p->pi', ao[0], wfxc * rho2)
for k in range(4):
f1oo[k] += numint._dot_ao_ao(mol, ao[k], aow, mask,
shls_slice, ao_loc)
if with_vxc:
aow = numpy.einsum('pi,p->pi', ao[0], vxc[0] * weight)
for k in range(4):
v1ao[k] += numint._dot_ao_ao(mol, ao[k], aow, mask,
shls_slice, ao_loc)
if with_kxc:
aow = numpy.einsum('pi,p->pi', ao[0],
kxc[0] * weight * rho1**2)
for k in range(4):
k1ao[k] += numint._dot_ao_ao(mol, ao[k], aow, mask,
shls_slice, ao_loc)
vxc = fxc = kxc = aow = rho = rho1 = rho2 = None
if with_kxc: # for (rho1*2)^2, *2 for alpha+beta in singlet
k1ao *= 4
else:
raise NotImplementedError('LDA triplet')
elif xctype == 'GGA':
if singlet:
def gga_sum_(vmat, ao, wv, mask):
aow = numpy.einsum('pi,p->pi', ao[0], wv[0] * .5)
aow += numpy.einsum('npi,np->pi', ao[1:4], wv[1:])
tmp = numint._dot_ao_ao(mol, ao[0], aow, mask, shls_slice,
ao_loc)
vmat[0] += tmp + tmp.T
vmat[1:] += rks_grad._gga_grad_sum(mol, ao, wv, mask,
shls_slice, ao_loc)
ao_deriv = 2
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
rho = ni.eval_rho2(mol, ao, mo_coeff, mo_occ, mask, 'GGA')
vxc, fxc, kxc = ni.eval_xc(xc_code, rho, 0, deriv=deriv)[1:]
vrho, vgamma = vxc[:2]
frr, frg, fgg = fxc[:3]
rho1 = ni.eval_rho(mol, ao, dmvo, mask,
'GGA') * 2 # *2 for alpha + beta
sigma1 = numpy.einsum('xi,xi->i', rho[1:], rho1[1:])
wv = numpy.empty_like((rho))
wv[0] = frr * rho1[0]
wv[0] += frg * sigma1 * 2
wv[1:] = (fgg * sigma1 * 4 + frg * rho1[0] * 2) * rho[1:]
wv[1:] += vgamma * rho1[1:] * 2
wv *= weight
gga_sum_(f1vo, ao, wv, mask)
if oovv is not None:
rho2 = ni.eval_rho(mol, ao, oovv, mask, 'GGA') * 2
sigma2 = numpy.einsum('xi,xi->i', rho[1:], rho2[1:])
wv[0] = frr * rho2[0]
wv[0] += frg * sigma2 * 2
wv[1:] = (fgg * sigma2 * 4 + frg * rho2[0] * 2) * rho[1:]
wv[1:] += vgamma * rho2[1:] * 2
wv *= weight
gga_sum_(f1oo, ao, wv, mask)
if with_vxc:
wv[0] = vrho
wv[1:] = 2 * vgamma * rho[1:]
wv *= weight
gga_sum_(v1ao, ao, wv, mask)
if with_kxc:
frrr, frrg, frgg, fggg = kxc
r1r1 = rho1[0]**2
s1s1 = sigma1**2
r1s1 = rho1[0] * sigma1
sigma2 = numpy.einsum('xi,xi->i', rho1[1:], rho1[1:])
wv[0] = frrr * r1r1
wv[0] += 4 * frrg * r1s1
wv[0] += 4 * frgg * s1s1
wv[0] += 2 * frg * sigma2
wv[1:] = 2 * frrg * r1r1 * rho[1:]
wv[1:] += 8 * frgg * r1s1 * rho[1:]
wv[1:] += 4 * frg * rho1[0] * rho1[1:]
wv[1:] += 4 * fgg * sigma2 * rho[1:]
wv[1:] += 8 * fgg * sigma1 * rho1[1:]
wv[1:] += 8 * fggg * s1s1 * rho[1:]
wv *= weight
gga_sum_(k1ao, ao, wv, mask)
vxc = fxc = kxc = rho = rho1 = rho2 = sigma1 = sigma2 = None
else:
raise NotImplementedError('GGA triplet')
else:
raise NotImplementedError('meta-GGA')
f1vo[1:] *= -1
if f1oo is not None: f1oo[1:] *= -1
if v1ao is not None: v1ao[1:] *= -1
if k1ao is not None: k1ao[1:] *= -1
return f1vo, f1oo, v1ao, k1ao
def get_vxc_giao(ni, mol, grids, xc_code, dms, max_memory=2000, verbose=None):
if isinstance(max_memory, (list, tuple, numpy.ndarray)):
import warnings
xc_code = '%s, %s' % (xc_code, dms)
dms, max_memory = max_memory, 2000
with warnings.catch_warnings():
warnings.simplefilter("once")
warnings.warn('API updates: the 5th argument c_id is decoreated '
'and will be removed in future release.\n')
xctype = ni._xc_type(xc_code)
make_rho, nset, nao = ni._gen_rho_evaluator(mol, dms, hermi=1)
ngrids = len(grids.weights)
BLKSIZE = numint.BLKSIZE
blksize = min(int(max_memory/12*1e6/8/nao/BLKSIZE)*BLKSIZE, ngrids)
vmat = numpy.zeros((3,nao,nao))
if xctype == 'LDA':
buf = numpy.empty((4,blksize,nao))
ao_deriv = 0
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory,
ni.non0tab, blksize=blksize, buf=buf):
rho = make_rho(0, ao, mask, 'LDA')
vxc = ni.eval_xc(xc_code, rho, 0, deriv=1)[1]
vrho = vxc[0]
aow = numpy.einsum('pi,p->pi', ao, weight*vrho)
giao = mol.eval_gto('GTOval_ig_sph', coords, comp=3,
non0tab=mask, out=buf[1:])
vmat[0] += numint._dot_ao_ao(mol, aow, giao[0], nao, weight.size, mask)
vmat[1] += numint._dot_ao_ao(mol, aow, giao[1], nao, weight.size, mask)
vmat[2] += numint._dot_ao_ao(mol, aow, giao[2], nao, weight.size, mask)
rho = vxc = vrho = aow = None
elif xctype == 'GGA':
buf = numpy.empty((10,blksize,nao))
XX, XY, XZ = 0, 1, 2
YX, YY, YZ = 3, 4, 5
ZX, ZY, ZZ = 6, 7, 8
ao_deriv = 1
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory,
ni.non0tab, blksize=blksize, buf=buf):
rho = make_rho(0, ao, mask, 'GGA')
vxc = ni.eval_xc(xc_code, rho, 0, deriv=1)[1]
vrho, vsigma = vxc[:2]
wv = numpy.empty_like(rho)
wv[0] = weight * vrho
wv[1:] = rho[1:] * (weight * vsigma * 2)
aow = numpy.einsum('npi,np->pi', ao[:4], wv)
giao = mol.eval_gto('GTOval_ig_sph', coords, 3,
non0tab=mask, out=buf[4:])
vmat[0] += numint._dot_ao_ao(mol, aow, giao[0], nao, weight.size, mask)
vmat[1] += numint._dot_ao_ao(mol, aow, giao[1], nao, weight.size, mask)
vmat[2] += numint._dot_ao_ao(mol, aow, giao[2], nao, weight.size, mask)
giao = mol.eval_gto('GTOval_ipig_sph', coords, 9,
non0tab=mask, out=buf[1:])
aow = numpy.einsum('pi,p->pi', giao[XX], wv[1])
aow+= numpy.einsum('pi,p->pi', giao[YX], wv[2])
aow+= numpy.einsum('pi,p->pi', giao[ZX], wv[3])
vmat[0] += numint._dot_ao_ao(mol, ao[0], aow, nao, weight.size, mask)
aow = numpy.einsum('pi,p->pi', giao[XY], wv[1])
aow+= numpy.einsum('pi,p->pi', giao[YY], wv[2])
aow+= numpy.einsum('pi,p->pi', giao[ZY], wv[3])
vmat[1] += numint._dot_ao_ao(mol, ao[0], aow, nao, weight.size, mask)
aow = numpy.einsum('pi,p->pi', giao[XZ], wv[1])
aow+= numpy.einsum('pi,p->pi', giao[YZ], wv[2])
aow+= numpy.einsum('pi,p->pi', giao[ZZ], wv[3])
vmat[2] += numint._dot_ao_ao(mol, ao[0], aow, nao, weight.size, mask)
rho = vxc = vrho = vsigma = wv = aow = None
else:
raise NotImplementedError('meta-GGA')
return vmat - vmat.transpose(0,2,1)
def _get_vxc_diag(hessobj, mo_coeff, mo_occ, max_memory):
mol = hessobj.mol
mf = hessobj.base
if hessobj.grids is not None:
grids = hessobj.grids
else:
grids = mf.grids
if grids.coords is None:
grids.build(with_non0tab=True)
nao, nmo = mo_coeff.shape
ni = mf._numint
xctype = ni._xc_type(mf.xc)
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
vmat = numpy.zeros((6, nao, nao))
if xctype == 'LDA':
ao_deriv = 2
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
rho = ni.eval_rho2(mol, ao[0], mo_coeff, mo_occ, mask, 'LDA')
vxc = ni.eval_xc(mf.xc, rho, 0, deriv=1)[1]
vrho = vxc[0]
aow = numpy.einsum('pi,p->pi', ao[0], weight * vrho)
for i in range(6):
vmat[i] += numint._dot_ao_ao(mol, ao[i + 4], aow, mask,
shls_slice, ao_loc)
aow = None
elif xctype == 'GGA':
def contract_(mat, ao, aoidx, wv, mask):
aow = numpy.einsum('pi,p->pi', ao[aoidx[0]], wv[1])
aow += numpy.einsum('pi,p->pi', ao[aoidx[1]], wv[2])
aow += numpy.einsum('pi,p->pi', ao[aoidx[2]], wv[3])
mat += numint._dot_ao_ao(mol, aow, ao[0], mask, shls_slice, ao_loc)
ao_deriv = 3
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
rho = ni.eval_rho2(mol, ao[:4], mo_coeff, mo_occ, mask, 'GGA')
vxc = ni.eval_xc(mf.xc, rho, 0, deriv=1)[1]
wv = numint._rks_gga_wv0(rho, vxc, weight)
# *2 because v.T is not applied. Only v is computed in the next _dot_ao_ao
wv[0] *= 2
aow = numpy.einsum('npi,np->pi', ao[:4], wv)
for i in range(6):
vmat[i] += numint._dot_ao_ao(mol, ao[i + 4], aow, mask,
shls_slice, ao_loc)
contract_(vmat[0], ao, [XXX, XXY, XXZ], wv, mask)
contract_(vmat[1], ao, [XXY, XYY, XYZ], wv, mask)
contract_(vmat[2], ao, [XXZ, XYZ, XZZ], wv, mask)
contract_(vmat[3], ao, [XYY, YYY, YYZ], wv, mask)
contract_(vmat[4], ao, [XYZ, YYZ, YZZ], wv, mask)
contract_(vmat[5], ao, [XZZ, YZZ, ZZZ], wv, mask)
rho = vxc = wv = aow = None
elif xctype == 'MGGA':
raise NotImplementedError('meta-GGA')
vmat = vmat[[0, 1, 2, 1, 3, 4, 2, 4, 5]]
return vmat.reshape(3, 3, nao, nao)
def contract_(mat, ao, aoidx, wv, mask):
aow = numpy.einsum('pi,p->pi', ao[aoidx[0]], wv[1])
aow+= numpy.einsum('pi,p->pi', ao[aoidx[1]], wv[2])
aow+= numpy.einsum('pi,p->pi', ao[aoidx[2]], wv[3])
mat += numint._dot_ao_ao(mol, aow, ao[0], mask, shls_slice, ao_loc)
def make_psi_vmat(pcmobj, dm, r_vdw, ui, grids, ylm_1sph, cached_pol, L_X, L):
mol = pcmobj.mol
natm = mol.natm
lmax = pcmobj.lmax
nlm = (lmax+1)**2
i1 = 0
scaled_weights = numpy.empty(grids.weights.size)
for ia in range(natm):
fak_pol, leak_idx = cached_pol[mol.atom_symbol(ia)]
i0, i1 = i1, i1 + fak_pol[0].shape[1]
eta_nj = 0
p1 = 0
for l in range(lmax+1):
fac = 4*numpy.pi/(l*2+1)
p0, p1 = p1, p1 + (l*2+1)
eta_nj += fac * numpy.einsum('mn,m->n', fak_pol[l], L_X[ia,p0:p1])
scaled_weights[i0:i1] = eta_nj * grids.weights[i0:i1]
if not (isinstance(dm, numpy.ndarray) and dm.ndim == 2):
dm = dm[0] + dm[1]
ni = numint.NumInt()
max_memory = pcmobj.max_memory - lib.current_memory()[0]
make_rho, nset, nao = ni._gen_rho_evaluator(mol, dm)
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
den = numpy.empty(grids.weights.size)
vmat = numpy.zeros((nao,nao))
p1 = 0
aow = None
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, 0, max_memory):
p0, p1 = p1, p1 + weight.size
den[p0:p1] = weight * make_rho(0, ao, mask, 'LDA')
aow = numpy.ndarray(ao.shape, order='F', buffer=aow)
aow = numpy.einsum('pi,p->pi', ao, scaled_weights[p0:p1], out=aow)
vmat -= numint._dot_ao_ao(mol, ao, aow, mask, shls_slice, ao_loc)
ao = aow = scaled_weights = None
nelec_leak = 0
psi = numpy.empty((natm,nlm))
i1 = 0
for ia in range(natm):
fak_pol, leak_idx = cached_pol[mol.atom_symbol(ia)]
i0, i1 = i1, i1 + fak_pol[0].shape[1]
nelec_leak += den[i0:i1][leak_idx].sum()
p1 = 0
for l in range(lmax+1):
fac = 4*numpy.pi/(l*2+1)
p0, p1 = p1, p1 + (l*2+1)
psi[ia,p0:p1] = -fac * numpy.einsum('n,mn->m', den[i0:i1], fak_pol[l])
# Contribution of nuclear charge to the total density
# The factor numpy.sqrt(4*numpy.pi) is due to the product of 4*pi * Y_0^0
psi[ia,0] += numpy.sqrt(4*numpy.pi)/r_vdw[ia] * mol.atom_charge(ia)
logger.debug(pcmobj, 'electron leak %f', nelec_leak)
# <Psi, L^{-1}g> -> Psi = SL the adjoint equation to LX = g
L_S = numpy.linalg.solve(L.T.reshape(natm*nlm,-1), psi.ravel()).reshape(natm,-1)
coords_1sph, weights_1sph = make_grids_one_sphere(pcmobj.lebedev_order)
# JCP, 141, 184108, Eq (39)
xi_jn = numpy.einsum('n,jn,xn,jx->jn', weights_1sph, ui, ylm_1sph, L_S)
extern_point_idx = ui > 0
cav_coords = (mol.atom_coords().reshape(natm,1,3)
+ numpy.einsum('r,gx->rgx', r_vdw, coords_1sph))
cav_coords = cav_coords[extern_point_idx]
xi_jn = xi_jn[extern_point_idx]
max_memory = pcmobj.max_memory - lib.current_memory()[0]
blksize = int(max(max_memory*1e6/8/nao**2, 400))
cintopt = gto.moleintor.make_cintopt(mol._atm, mol._bas,
mol._env, 'int3c2e')
vmat_tril = 0
for i0, i1 in lib.prange(0, xi_jn.size, blksize):
fakemol = gto.fakemol_for_charges(cav_coords[i0:i1])
v_nj = df.incore.aux_e2(mol, fakemol, intor='int3c2e', aosym='s2ij',
cintopt=cintopt)
vmat_tril += numpy.einsum('xn,n->x', v_nj, xi_jn[i0:i1])
vmat += lib.unpack_tril(vmat_tril)
return psi, vmat, L_S
def _contract_xc_kernel(td_grad,
xc_code,
dmvo,
dmoo=None,
with_vxc=True,
with_kxc=True,
singlet=True,
max_memory=2000):
mol = td_grad.mol
mf = td_grad.base._scf
grids = mf.grids
ni = mf._numint
xctype = ni._xc_type(xc_code)
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
nao, nmo = mo_coeff.shape
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
# dmvo ~ reduce(numpy.dot, (orbv, Xai, orbo.T))
dmvo = (dmvo + dmvo.T) * .5 # because K_{ia,jb} == K_{ia,jb}
f1vo = numpy.zeros((4, nao, nao)) # 0th-order, d/dx, d/dy, d/dz
deriv = 2
if dmoo is not None:
f1oo = numpy.zeros((4, nao, nao))
else:
f1oo = None
if with_vxc:
v1ao = numpy.zeros((4, nao, nao))
else:
v1ao = None
if with_kxc:
k1ao = numpy.zeros((4, nao, nao))
deriv = 3
else:
k1ao = None
if xctype == 'LDA':
ao_deriv = 1
if singlet:
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
rho = ni.eval_rho2(mol, ao[0], mo_coeff, mo_occ, mask, 'LDA')
vxc, fxc, kxc = ni.eval_xc(xc_code, rho, 0, deriv=deriv)[1:]
wfxc = fxc[0] * weight * 2 # *2 for alpha+beta
rho1 = ni.eval_rho(mol, ao[0], dmvo, mask, 'LDA')
aow = numpy.einsum('pi,p,p->pi', ao[0], wfxc, rho1)
for k in range(4):
f1vo[k] += numint._dot_ao_ao(mol, ao[k], aow, mask,
shls_slice, ao_loc)
if dmoo is not None:
rho2 = ni.eval_rho(mol, ao[0], dmoo, mask, 'LDA')
aow = numpy.einsum('pi,p,p->pi', ao[0], wfxc, rho2)
for k in range(4):
f1oo[k] += numint._dot_ao_ao(mol, ao[k], aow, mask,
shls_slice, ao_loc)
if with_vxc:
aow = numpy.einsum('pi,p,p->pi', ao[0], vxc[0], weight)
for k in range(4):
v1ao[k] += numint._dot_ao_ao(mol, ao[k], aow, mask,
shls_slice, ao_loc)
if with_kxc:
aow = numpy.einsum('pi,p,p,p->pi', ao[0], kxc[0], weight,
rho1**2)
for k in range(4):
k1ao[k] += numint._dot_ao_ao(mol, ao[k], aow, mask,
shls_slice, ao_loc)
vxc = fxc = kxc = aow = rho = rho1 = rho2 = None
if with_kxc: # for (rho1*2)^2, *2 for alpha+beta in singlet
k1ao *= 4
else:
raise NotImplementedError('LDA triplet')
elif xctype == 'GGA':
if singlet:
def gga_sum_(vmat, ao, wv, mask):
aow = numpy.einsum('pi,p->pi', ao[0], wv[0])
aow += numpy.einsum('npi,np->pi', ao[1:4], wv[1:])
tmp = numint._dot_ao_ao(mol, ao[0], aow, mask, shls_slice,
ao_loc)
vmat[0] += tmp + tmp.T
rks_grad._gga_grad_sum_(vmat[1:], mol, ao, wv, mask, ao_loc)
ao_deriv = 2
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
rho = ni.eval_rho2(mol, ao, mo_coeff, mo_occ, mask, 'GGA')
vxc, fxc, kxc = ni.eval_xc(xc_code, rho, 0, deriv=deriv)[1:]
rho1 = ni.eval_rho(mol, ao, dmvo, mask,
'GGA') * 2 # *2 for alpha + beta
wv = numint._rks_gga_wv1(rho, rho1, vxc, fxc, weight)
gga_sum_(f1vo, ao, wv, mask)
if dmoo is not None:
rho2 = ni.eval_rho(mol, ao, dmoo, mask, 'GGA') * 2
wv = numint._rks_gga_wv1(rho, rho2, vxc, fxc, weight)
gga_sum_(f1oo, ao, wv, mask)
if with_vxc:
wv = numint._rks_gga_wv0(rho, vxc, weight)
gga_sum_(v1ao, ao, wv, mask)
if with_kxc:
wv = numint._rks_gga_wv2(rho, rho1, fxc, kxc, weight)
gga_sum_(k1ao, ao, wv, mask)
vxc = fxc = kxc = rho = rho1 = None
else:
raise NotImplementedError('GGA triplet')
else:
raise NotImplementedError('meta-GGA')
f1vo[1:] *= -1
if f1oo is not None: f1oo[1:] *= -1
if v1ao is not None: v1ao[1:] *= -1
if k1ao is not None: k1ao[1:] *= -1
return f1vo, f1oo, v1ao, k1ao
def _get_vxc_diag(hessobj, mo_coeff, mo_occ, max_memory):
mol = hessobj.mol
mf = hessobj.base
if hessobj.grids is not None:
grids = hessobj.grids
else:
grids = mf.grids
if grids.coords is None:
grids.build(with_non0tab=True)
nao, nmo = mo_coeff[0].shape
ni = mf._numint
xctype = ni._xc_type(mf.xc)
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
vmata = numpy.zeros((6,nao,nao))
vmatb = numpy.zeros((6,nao,nao))
if xctype == 'LDA':
ao_deriv = 2
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
rhoa = ni.eval_rho2(mol, ao[0], mo_coeff[0], mo_occ[0], mask, 'LDA')
rhob = ni.eval_rho2(mol, ao[0], mo_coeff[1], mo_occ[1], mask, 'LDA')
vxc = ni.eval_xc(mf.xc, (rhoa,rhob), 1, deriv=1)[1]
vrho = vxc[0]
aowa = numpy.einsum('pi,p->pi', ao[0], weight*vrho[:,0])
aowb = numpy.einsum('pi,p->pi', ao[0], weight*vrho[:,1])
for i in range(6):
vmata[i] += numint._dot_ao_ao(mol, ao[i+4], aowa, mask, shls_slice, ao_loc)
vmatb[i] += numint._dot_ao_ao(mol, ao[i+4], aowb, mask, shls_slice, ao_loc)
aowa = aowb = None
elif xctype == 'GGA':
def contract_(mat, ao, aoidx, wv, mask):
aow = numpy.einsum('pi,p->pi', ao[aoidx[0]], wv[1])
aow+= numpy.einsum('pi,p->pi', ao[aoidx[1]], wv[2])
aow+= numpy.einsum('pi,p->pi', ao[aoidx[2]], wv[3])
mat += numint._dot_ao_ao(mol, aow, ao[0], mask, shls_slice, ao_loc)
ao_deriv = 3
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
rhoa = ni.eval_rho2(mol, ao[:4], mo_coeff[0], mo_occ[0], mask, 'GGA')
rhob = ni.eval_rho2(mol, ao[:4], mo_coeff[1], mo_occ[1], mask, 'GGA')
vxc = ni.eval_xc(mf.xc, (rhoa,rhob), 1, deriv=1)[1]
wva, wvb = numint._uks_gga_wv0((rhoa,rhob), vxc, weight)
# *2 because v.T is not applied.
wva[0] *= 2
wvb[0] *= 2
aowa = numpy.einsum('npi,np->pi', ao[:4], wva)
aowb = numpy.einsum('npi,np->pi', ao[:4], wvb)
for i in range(6):
vmata[i] += numint._dot_ao_ao(mol, ao[i+4], aowa, mask, shls_slice, ao_loc)
vmatb[i] += numint._dot_ao_ao(mol, ao[i+4], aowb, mask, shls_slice, ao_loc)
contract_(vmata[0], ao, [XXX,XXY,XXZ], wva, mask)
contract_(vmata[1], ao, [XXY,XYY,XYZ], wva, mask)
contract_(vmata[2], ao, [XXZ,XYZ,XZZ], wva, mask)
contract_(vmata[3], ao, [XYY,YYY,YYZ], wva, mask)
contract_(vmata[4], ao, [XYZ,YYZ,YZZ], wva, mask)
contract_(vmata[5], ao, [XZZ,YZZ,ZZZ], wva, mask)
contract_(vmatb[0], ao, [XXX,XXY,XXZ], wvb, mask)
contract_(vmatb[1], ao, [XXY,XYY,XYZ], wvb, mask)
contract_(vmatb[2], ao, [XXZ,XYZ,XZZ], wvb, mask)
contract_(vmatb[3], ao, [XYY,YYY,YYZ], wvb, mask)
contract_(vmatb[4], ao, [XYZ,YYZ,YZZ], wvb, mask)
contract_(vmatb[5], ao, [XZZ,YZZ,ZZZ], wvb, mask)
vxc = aowa = aowb = None
elif xctype == 'MGGA':
raise NotImplementedError('meta-GGA')
vmata = vmata[[0,1,2, 1,3,4, 2,4,5]].reshape(3,3,nao,nao)
vmatb = vmatb[[0,1,2, 1,3,4, 2,4,5]].reshape(3,3,nao,nao)
return vmata, vmatb
def get_vxc(ni, mol, grids, xc_code, dms, relativity=0, hermi=1,
max_memory=2000, verbose=None):
if isinstance(relativity, (list, tuple, numpy.ndarray)):
import warnings
xc_code = '%s, %s' % (xc_code, dms)
dms = relativity
with warnings.catch_warnings():
warnings.simplefilter("once")
warnings.warn('API updates: the 5th argument c_id is decoreated '
'and will be removed in future release.\n')
natocc = []
natorb = []
if isinstance(dms, numpy.ndarray) and dms.ndim == 2:
e, c = scipy.linalg.eigh(dms)
natocc.append(e)
natorb.append(c)
nao = dms.shape[0]
else:
for dm in dms:
e, c = scipy.linalg.eigh(dm)
natocc.append(e)
natorb.append(c)
nao = dms[0].shape[0]
xctype = ni._xc_type(xc_code)
make_rho, nset, nao = ni._gen_rho_evaluator(mol, dms, hermi)
nset = len(natocc)
vmat = numpy.zeros((nset,3,nao,nao))
if xctype == 'LDA':
ao_deriv = 1
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory, ni.non0tab):
for idm in range(nset):
rho = make_rho(idm, ao[0], mask, 'LDA')
vxc = ni.eval_xc(xc_code, rho, 0, relativity, 1, verbose)[1]
vrho = vxc[0]
aow = numpy.einsum('pi,p->pi', ao[0], weight*vrho)
vmat[idm,0] += numint._dot_ao_ao(mol, ao[1], aow, nao, weight.size, mask)
vmat[idm,1] += numint._dot_ao_ao(mol, ao[2], aow, nao, weight.size, mask)
vmat[idm,2] += numint._dot_ao_ao(mol, ao[3], aow, nao, weight.size, mask)
rho = vxc = vrho = aow = None
elif xctype == 'GGA':
ao_deriv = 2
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory, ni.non0tab):
for idm in range(nset):
rho = make_rho(idm, ao, mask, 'GGA')
vxc = ni.eval_xc(xc_code, rho, 0, relativity, 1, verbose)[1]
vrho, vsigma = vxc[:2]
wv = numpy.empty_like(rho)
wv[0] = weight * vrho
wv[1:] = rho[1:] * (weight * vsigma * 2)
vmat[idm] += _gga_grad_sum(mol, ao, wv, mask)
else:
raise NotImplementedError('meta-GGA')
if nset == 1:
vmat = vmat.reshape(3,nao,nao)
# - sign because nabla_X = -nabla_x
return -vmat
def _contract_xc_kernel(td_grad, xc_code, dmvo, dmoo=None, with_vxc=True,
with_kxc=True, max_memory=2000):
mol = td_grad.mol
mf = td_grad.base._scf
grids = mf.grids
ni = mf._numint
xctype = ni._xc_type(xc_code)
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
nao = mo_coeff[0].shape[0]
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
# dmvo ~ reduce(numpy.dot, (orbv, Xai, orbo.T))
dmvo = [(dmvo[0] + dmvo[0].T) * .5, # because K_{ia,jb} == K_{ia,jb}
(dmvo[1] + dmvo[1].T) * .5]
f1vo = numpy.zeros((2,4,nao,nao))
deriv = 2
if dmoo is not None:
f1oo = numpy.zeros((2,4,nao,nao))
else:
f1oo = None
if with_vxc:
v1ao = numpy.zeros((2,4,nao,nao))
else:
v1ao = None
if with_kxc:
k1ao = numpy.zeros((2,4,nao,nao))
deriv = 3
else:
k1ao = None
if xctype == 'LDA':
ao_deriv = 1
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
rho = (ni.eval_rho2(mol, ao[0], mo_coeff[0], mo_occ[0], mask, 'LDA'),
ni.eval_rho2(mol, ao[0], mo_coeff[1], mo_occ[1], mask, 'LDA'))
vxc, fxc, kxc = ni.eval_xc(xc_code, rho, 1, deriv=deriv)[1:]
u_u, u_d, d_d = fxc[0].T * weight
rho1a = ni.eval_rho(mol, ao[0], dmvo[0], mask, 'LDA')
rho1b = ni.eval_rho(mol, ao[0], dmvo[1], mask, 'LDA')
aow = (numpy.einsum('pi,p,p->pi', ao[0], u_u, rho1a) +
numpy.einsum('pi,p,p->pi', ao[0], u_d, rho1b),
numpy.einsum('pi,p,p->pi', ao[0], u_d, rho1a) +
numpy.einsum('pi,p,p->pi', ao[0], d_d, rho1b))
for k in range(4):
f1vo[0,k] += numint._dot_ao_ao(mol, ao[k], aow[0], mask, shls_slice, ao_loc)
f1vo[1,k] += numint._dot_ao_ao(mol, ao[k], aow[1], mask, shls_slice, ao_loc)
if dmoo is not None:
rho2a = ni.eval_rho(mol, ao[0], dmoo[0], mask, 'LDA')
rho2b = ni.eval_rho(mol, ao[0], dmoo[1], mask, 'LDA')
aow = (numpy.einsum('pi,p,p->pi', ao[0], u_u, rho2a) +
numpy.einsum('pi,p,p->pi', ao[0], u_d, rho2b),
numpy.einsum('pi,p,p->pi', ao[0], u_d, rho2a) +
numpy.einsum('pi,p,p->pi', ao[0], d_d, rho2b))
for k in range(4):
f1oo[0,k] += numint._dot_ao_ao(mol, ao[k], aow[0], mask, shls_slice, ao_loc)
f1oo[1,k] += numint._dot_ao_ao(mol, ao[k], aow[1], mask, shls_slice, ao_loc)
if with_vxc:
vrho = vxc[0].T * weight
aow = (numpy.einsum('pi,p->pi', ao[0], vrho[0]),
numpy.einsum('pi,p->pi', ao[0], vrho[1]))
for k in range(4):
v1ao[0,k] += numint._dot_ao_ao(mol, ao[k], aow[0], mask, shls_slice, ao_loc)
v1ao[1,k] += numint._dot_ao_ao(mol, ao[k], aow[1], mask, shls_slice, ao_loc)
if with_kxc:
u_u_u, u_u_d, u_d_d, d_d_d = kxc[0].T * weight
aow = (numpy.einsum('pi,p,p,p->pi', ao[0], u_u_u, rho1a, rho1a) +
numpy.einsum('pi,p,p,p->pi', ao[0], u_u_d, rho1a, rho1b)*2 +
numpy.einsum('pi,p,p,p->pi', ao[0], u_d_d, rho1b, rho1b),
numpy.einsum('pi,p,p,p->pi', ao[0], u_u_d, rho1a, rho1a) +
numpy.einsum('pi,p,p,p->pi', ao[0], u_d_d, rho1a, rho1b)*2 +
numpy.einsum('pi,p,p,p->pi', ao[0], d_d_d, rho1b, rho1b))
for k in range(4):
k1ao[0,k] += numint._dot_ao_ao(mol, ao[k], aow[0], mask, shls_slice, ao_loc)
k1ao[1,k] += numint._dot_ao_ao(mol, ao[k], aow[1], mask, shls_slice, ao_loc)
vxc = fxc = kxc = aow = rho = rho1 = rho2 = None
elif xctype == 'GGA':
def gga_sum_(vmat, ao, wv, mask):
aow = numpy.einsum('pi,p->pi', ao[0], wv[0])
aow += numpy.einsum('npi,np->pi', ao[1:4], wv[1:])
tmp = numint._dot_ao_ao(mol, ao[0], aow, mask, shls_slice, ao_loc)
vmat[0] += tmp + tmp.T
rks_grad._gga_grad_sum_(vmat[1:], mol, ao, wv, mask, ao_loc)
ao_deriv = 2
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
rho = (ni.eval_rho2(mol, ao, mo_coeff[0], mo_occ[0], mask, 'GGA'),
ni.eval_rho2(mol, ao, mo_coeff[1], mo_occ[1], mask, 'GGA'))
vxc, fxc, kxc = ni.eval_xc(xc_code, rho, 1, deriv=deriv)[1:]
rho1 = (ni.eval_rho(mol, ao, dmvo[0], mask, 'GGA'),
ni.eval_rho(mol, ao, dmvo[1], mask, 'GGA'))
wv = numint._uks_gga_wv1(rho, rho1, vxc, fxc, weight)
gga_sum_(f1vo[0], ao, wv[0], mask)
gga_sum_(f1vo[1], ao, wv[1], mask)
if dmoo is not None:
rho2 = (ni.eval_rho(mol, ao, dmoo[0], mask, 'GGA'),
ni.eval_rho(mol, ao, dmoo[1], mask, 'GGA'))
wv = numint._uks_gga_wv1(rho, rho2, vxc, fxc, weight)
gga_sum_(f1oo[0], ao, wv[0], mask)
gga_sum_(f1oo[1], ao, wv[1], mask)
if with_vxc:
wv = numint._uks_gga_wv0(rho, vxc, weight)
gga_sum_(v1ao[0], ao, wv[0], mask)
gga_sum_(v1ao[1], ao, wv[1], mask)
if with_kxc:
wv = numint._uks_gga_wv2(rho, rho1, fxc, kxc, weight)
gga_sum_(k1ao[0], ao, wv[0], mask)
gga_sum_(k1ao[1], ao, wv[1], mask)
vxc = fxc = kxc = rho = rho1 = None
else:
raise NotImplementedError('meta-GGA')
f1vo[:,1:] *= -1
if f1oo is not None: f1oo[:,1:] *= -1
if v1ao is not None: v1ao[:,1:] *= -1
if k1ao is not None: k1ao[:,1:] *= -1
return f1vo, f1oo, v1ao, k1ao
def _contract_xc_kernel(td, xc_code, dmvo, singlet=True, max_memory=2000):
mf = td._scf
mol = td.mol
grids = mf.grids
if USE_XCFUN:
ni = copy.copy(mf._numint)
try:
ni.libxc = dft.xcfun
xctype = ni._xc_type(xc_code)
except (ImportError, KeyError, NotImplementedError):
ni.libxc = dft.libxc
xctype = ni._xc_type(xc_code)
else:
ni = mf._numint
xctype = ni._xc_type(xc_code)
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
nao, nmo = mo_coeff.shape
ndm = len(dmvo)
dmvo = numpy.asarray(dmvo)
dmvo = (dmvo + dmvo.transpose(0,2,1)) * .5
v1ao = numpy.zeros((ndm,nao,nao))
if xctype == 'LDA':
ao_deriv = 0
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory, ni.non0tab):
rho = ni.eval_rho2(mol, ao, mo_coeff, mo_occ, mask, 'LDA')
rho *= .5 # alpha density
fxc = ni.eval_xc(xc_code, (rho,rho), 1, deriv=2)[2]
u_u, u_d, d_d = v2rho2 = fxc[0].T
if singlet:
frho = u_u + u_d
else:
frho = u_u - u_d
for i, dm in enumerate(dmvo):
rho1 = ni.eval_rho(mol, ao, dm, mask, xctype)
aow = numpy.einsum('pi,p->pi', ao, weight*frho*rho1)
v1ao[i] += numint._dot_ao_ao(mol, aow, ao, nao, weight.size, mask)
rho1 = aow = None
for i in range(ndm):
v1ao[i] = (v1ao[i] + v1ao[i].T) * .5
elif xctype == 'GGA':
ao_deriv = 1
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory, ni.non0tab):
rho = ni.eval_rho2(mol, ao, mo_coeff, mo_occ, mask, 'GGA')
rho *= .5 # alpha density
vxc, fxc = ni.eval_xc(xc_code, (rho,rho), 1, deriv=2)[1:3]
vsigma = vxc[1].T
u_u, u_d, d_d = fxc[0].T # v2rho2
u_uu, u_ud, u_dd, d_uu, d_ud, d_dd = fxc[1].T # v2rhosigma
uu_uu, uu_ud, uu_dd, ud_ud, ud_dd, dd_dd = fxc[2].T # v2sigma2
if singlet:
fgamma = 2*vsigma[0] + vsigma[1]
frho = u_u + u_d
fgg = uu_uu + .5*ud_ud + 2*uu_ud + uu_dd
frhogamma = u_uu + u_dd + u_ud
else:
fgamma = 2*vsigma[0] - vsigma[1]
frho = u_u - u_d
fgg = uu_uu - uu_dd
frhogamma = u_uu - u_dd
ngrid = weight.size
wv = numpy.empty((4,ngrid))
for i, dm in enumerate(dmvo):
# rho1[0 ] = |b><j| z_{bj}
# rho1[1:] = \nabla(|b><j|) z_{bj}
rho1 = ni.eval_rho(mol, ao, dm, mask, 'GGA')
# sigma1 = \nabla(\rho_\alpha+\rho_\beta) dot \nabla(|b><j|) z_{bj}
# *2 for alpha + beta
sigma1 = numpy.einsum('xi,xi->i', rho[1:], rho1[1:]) * 2
wv[0 ] = frho * rho1[0]
wv[0 ] += frhogamma * sigma1
wv[1:] = (fgg * sigma1 + frhogamma * rho1[0]) * rho[1:]
wv[1:] *= 2 # because \nabla\rho = \nabla(\rho_\alpha+\rho_\beta)
wv[1:] += fgamma * rho1[1:]
wv[1:] *= 2 # because +h.c for (\nabla\mu) \nu, which are symmetrized at the end
wv *= weight
aow = numpy.einsum('nip,ni->ip', ao, wv)
v1ao[i] += numint._dot_ao_ao(mol, ao[0], aow, nao, ngrid, mask)
for i in range(ndm):
v1ao[i] = (v1ao[i] + v1ao[i].T) * .5
else:
raise NotImplementedError('meta-GGA')
return v1ao
def _contract_xc_kernel(mf, xc_code, dms, max_memory=2000):
mol = mf.mol
grids = mf.grids
ni = copy.copy(mf._numint)
if USE_XCFUN:
try:
ni.libxc = dft.xcfun
xctype = ni._xc_type(xc_code)
except (ImportError, KeyError, NotImplementedError):
ni.libxc = dft.libxc
xctype = ni._xc_type(xc_code)
else:
xctype = ni._xc_type(xc_code)
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
nao, nmo = mo_coeff.shape
ndm = len(dms)
dms = numpy.asarray(dms)
dms = (dms + dms.transpose(0,2,1)) * .5
v1ao = numpy.zeros((ndm,nao,nao))
if xctype == 'LDA':
ao_deriv = 0
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory, ni.non0tab):
rho = ni.eval_rho2(mol, ao, mo_coeff, mo_occ, mask, 'LDA')
fxc = ni.eval_xc(xc_code, rho, 0, deriv=2)[2]
frho = fxc[0]
for i, dm in enumerate(dms):
rho1 = ni.eval_rho(mol, ao, dm, mask, xctype)
aow = numpy.einsum('pi,p->pi', ao, weight*frho*rho1)
v1ao[i] += numint._dot_ao_ao(mol, aow, ao, nao, weight.size, mask)
rho1 = aow = None
elif xctype == 'GGA':
ao_deriv = 1
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory, ni.non0tab):
rho = ni.eval_rho2(mol, ao[:4], mo_coeff, mo_occ, mask, 'GGA')
vxc, fxc = ni.eval_xc(xc_code, rho, 0, deriv=2)[1:3]
vgamma = vxc[1]
frr, frg, fgg = fxc[:3]
for i, dm in enumerate(dms):
rho1 = ni.eval_rho(mol, ao, dm, mask, 'GGA')
sigma1 = numpy.einsum('xi,xi->i', rho[1:], rho1[1:])
ngrid = weight.size
wv = numpy.empty((4,ngrid))
wv[0] = frr * rho1[0]
wv[0] += frg * sigma1 * 2
wv[1:] = (fgg * sigma1 * 4 + frg * rho1[0] * 2) * rho[1:]
wv[1:] += vgamma * rho1[1:] * 2
wv[1:] *= 2 # for (\nabla\mu) \nu + \mu (\nabla\nu)
wv *= weight
aow = numpy.einsum('npi,np->pi', ao, wv)
v1ao[i] += numint._dot_ao_ao(mol, aow, ao[0], nao, ngrid, mask)
else:
raise NotImplementedError('meta-GGA')
for i in range(ndm):
v1ao[i] = (v1ao[i] + v1ao[i].T) * .5
return v1ao
def get_vxc_giao(ni, mol, grids, xc_code, dms, max_memory=2000, verbose=None):
xctype = ni._xc_type(xc_code)
make_rhoa, nset, nao = ni._gen_rho_evaluator(mol, dms[0], hermi=1)
make_rhob = ni._gen_rho_evaluator(mol, dms[1], hermi=1)[0]
ngrids = len(grids.weights)
BLKSIZE = numint.BLKSIZE
blksize = min(
int(max_memory / 12 * 1e6 / 8 / nao / BLKSIZE) * BLKSIZE, ngrids)
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
vmat = numpy.zeros((2, 3, nao, nao))
if xctype == 'LDA':
buf = numpy.empty((4, blksize, nao))
ao_deriv = 0
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory,
blksize=blksize, buf=buf):
rho_a = make_rhoa(0, ao, mask, 'LDA')
rho_b = make_rhob(0, ao, mask, 'LDA')
vxc = ni.eval_xc(xc_code, (rho_a, rho_b), 1, deriv=1)[1]
vrho = vxc[0]
giao = mol.eval_gto('GTOval_ig',
coords,
comp=3,
non0tab=mask,
out=buf[1:])
aow = numpy.einsum('pi,p->pi', ao, weight * vrho[:, 0])
vmat[0, 0] += numint._dot_ao_ao(mol, aow, giao[0], mask,
shls_slice, ao_loc)
vmat[0, 1] += numint._dot_ao_ao(mol, aow, giao[1], mask,
shls_slice, ao_loc)
vmat[0, 2] += numint._dot_ao_ao(mol, aow, giao[2], mask,
shls_slice, ao_loc)
aow = numpy.einsum('pi,p->pi', ao, weight * vrho[:, 1])
vmat[1, 0] += numint._dot_ao_ao(mol, aow, giao[0], mask,
shls_slice, ao_loc)
vmat[1, 1] += numint._dot_ao_ao(mol, aow, giao[1], mask,
shls_slice, ao_loc)
vmat[1, 2] += numint._dot_ao_ao(mol, aow, giao[2], mask,
shls_slice, ao_loc)
rho = vxc = vrho = aow = None
elif xctype == 'GGA':
buf = numpy.empty((10, blksize, nao))
ao_deriv = 1
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory,
blksize=blksize, buf=buf):
rho_a = make_rhoa(0, ao, mask, 'GGA')
rho_b = make_rhob(0, ao, mask, 'GGA')
vxc = ni.eval_xc(xc_code, (rho_a, rho_b), 1, deriv=1)[1]
vrho, vsigma = vxc[:2]
giao = mol.eval_gto('GTOval_ig',
coords,
3,
non0tab=mask,
out=buf[4:])
wva = numpy.empty_like(rho_a)
wva[0] = weight * vrho[:, 0]
wva[1:] = rho_a[1:] * (weight * vsigma[:, 0] * 2) # sigma_uu
wva[1:] += rho_b[1:] * (weight * vsigma[:, 1]) # sigma_ud
wvb = numpy.empty_like(rho_b)
wvb[0] = weight * vrho[:, 1]
wvb[1:] = rho_b[1:] * (weight * vsigma[:, 2] * 2) # sigma_dd
wvb[1:] += rho_a[1:] * (weight * vsigma[:, 1]) # sigma_ud
aow = numpy.einsum('npi,np->pi', ao[:4], wva)
vmat[0, 0] += numint._dot_ao_ao(mol, aow, giao[0], mask,
shls_slice, ao_loc)
vmat[0, 1] += numint._dot_ao_ao(mol, aow, giao[1], mask,
shls_slice, ao_loc)
vmat[0, 2] += numint._dot_ao_ao(mol, aow, giao[2], mask,
shls_slice, ao_loc)
aow = numpy.einsum('npi,np->pi', ao[:4], wvb)
vmat[1, 0] += numint._dot_ao_ao(mol, aow, giao[0], mask,
shls_slice, ao_loc)
vmat[1, 1] += numint._dot_ao_ao(mol, aow, giao[1], mask,
shls_slice, ao_loc)
vmat[1, 2] += numint._dot_ao_ao(mol, aow, giao[2], mask,
shls_slice, ao_loc)
giao = mol.eval_gto('GTOval_ipig',
coords,
9,
non0tab=mask,
out=buf[1:])
rks_nmr._gga_sum_(vmat[0], mol, ao, giao, wva, mask, shls_slice,
ao_loc)
rks_nmr._gga_sum_(vmat[1], mol, ao, giao, wvb, mask, shls_slice,
ao_loc)
rho = vxc = vrho = vsigma = wv = aow = None
else:
raise NotImplementedError('meta-GGA')
return vmat - vmat.transpose(0, 1, 3, 2)
def gga_sum_(vmat, ao, wv, mask):
aow = numpy.einsum('pi,p->pi', ao[0], wv[0])
aow += numpy.einsum('npi,np->pi', ao[1:4], wv[1:])
tmp = numint._dot_ao_ao(mol, ao[0], aow, mask, shls_slice, ao_loc)
vmat[0] += tmp + tmp.T
rks_grad._gga_grad_sum_(vmat[1:], mol, ao, wv, mask, ao_loc)
def gga_sum_(vmat, ao, wv, mask):
aow = numint._scale_ao(ao[:4], wv[:4])
tmp = numint._dot_ao_ao(mol, ao[0], aow, mask, shls_slice,
ao_loc)
vmat[0] += tmp + tmp.T
rks_grad._gga_grad_sum_(vmat[1:], mol, ao, wv, mask, ao_loc)
def _get_vxc(ni, mol, grids, x_id, c_id, dms, relativity=0, hermi=1,
max_memory=2000, verbose=None):
natocc = []
natorb = []
if isinstance(dms, numpy.ndarray) and dms.ndim == 2:
e, c = scipy.linalg.eigh(dms)
natocc.append(e)
natorb.append(c)
nao = dms.shape[0]
else:
for dm in dms:
e, c = scipy.linalg.eigh(dm)
natocc.append(e)
natorb.append(c)
nao = dms[0].shape[0]
xctype = numint._xc_type(x_id, c_id)
ngrids = len(grids.weights)
BLKSIZE = numint.BLKSIZE
blksize = min(int(max_memory/6*1e6/8/nao/BLKSIZE)*BLKSIZE, ngrids)
nset = len(natocc)
nelec = numpy.zeros(nset)
excsum = numpy.zeros(nset)
vmat = numpy.zeros((nset,3,nao,nao))
if xctype == 'LDA':
buf = numpy.empty((4,blksize,nao))
for ip0, ip1 in numint.prange(0, ngrids, blksize):
coords = grids.coords[ip0:ip1]
weight = grids.weights[ip0:ip1]
non0tab = ni.non0tab[ip0//BLKSIZE:]
ao = ni.eval_ao(mol, coords, deriv=1, non0tab=non0tab, out=buf)
for idm in range(nset):
rho = ni.eval_rho2(mol, ao[0], natorb[idm], natocc[idm], non0tab, xctype)
exc, vxc = ni.eval_xc(x_id, c_id, rho, 0, relativity, 1, verbose)[:2]
vrho = vxc[0]
den = rho * weight
nelec[idm] += den.sum()
excsum[idm] += (den * exc).sum()
aow = numpy.einsum('pi,p->pi', ao[0], weight*vrho)
vmat[idm,0] += numint._dot_ao_ao(mol, ao[1], aow, nao, ip1-ip0, non0tab)
vmat[idm,1] += numint._dot_ao_ao(mol, ao[2], aow, nao, ip1-ip0, non0tab)
vmat[idm,2] += numint._dot_ao_ao(mol, ao[3], aow, nao, ip1-ip0, non0tab)
rho = exc = vxc = vrho = aow = None
elif xctype == 'GGA':
buf = numpy.empty((10,blksize,nao))
XX, XY, XZ = 4, 5, 6
YX, YY, YZ = 5, 7, 8
ZX, ZY, ZZ = 6, 8, 9
for ip0, ip1 in numint.prange(0, ngrids, blksize):
coords = grids.coords[ip0:ip1]
weight = grids.weights[ip0:ip1]
non0tab = ni.non0tab[ip0//BLKSIZE:]
ao = ni.eval_ao(mol, coords, deriv=2, non0tab=non0tab, out=buf)
for idm in range(nset):
rho = ni.eval_rho2(mol, ao, natorb[idm], natocc[idm], non0tab, xctype)
exc, vxc = ni.eval_xc(x_id, c_id, rho, 0, relativity, 1, verbose)[:2]
vrho, vsigma = vxc[:2]
den = rho[0] * weight
nelec[idm] += den.sum()
excsum[idm] += (den * exc).sum()
wv = numpy.empty_like(rho)
# *.5 because vmat + vmat.T implicitly
wv[0] = weight * vrho * .5
wv[1:] = rho[1:] * (weight * vsigma * 2)
aow = numpy.einsum('npi,np->pi', ao[:4], wv)
vmat[idm,0] += numint._dot_ao_ao(mol, ao[1], aow, nao, ip1-ip0, non0tab)
vmat[idm,1] += numint._dot_ao_ao(mol, ao[2], aow, nao, ip1-ip0, non0tab)
vmat[idm,2] += numint._dot_ao_ao(mol, ao[3], aow, nao, ip1-ip0, non0tab)
aow = numpy.einsum('pi,p->pi', ao[1] , wv[0])
aow+= numpy.einsum('pi,p->pi', ao[XX], wv[1])
aow+= numpy.einsum('pi,p->pi', ao[XY], wv[2])
aow+= numpy.einsum('pi,p->pi', ao[XZ], wv[3])
vmat[idm,0] += numint._dot_ao_ao(mol, aow, ao[0], nao, ip1-ip0, non0tab)
aow = numpy.einsum('pi,p->pi', ao[2] , wv[0])
aow+= numpy.einsum('pi,p->pi', ao[YX], wv[1])
aow+= numpy.einsum('pi,p->pi', ao[YY], wv[2])
aow+= numpy.einsum('pi,p->pi', ao[YZ], wv[3])
vmat[idm,1] += numint._dot_ao_ao(mol, aow, ao[0], nao, ip1-ip0, non0tab)
aow = numpy.einsum('pi,p->pi', ao[3] , wv[0])
aow+= numpy.einsum('pi,p->pi', ao[ZX], wv[1])
aow+= numpy.einsum('pi,p->pi', ao[ZY], wv[2])
aow+= numpy.einsum('pi,p->pi', ao[ZZ], wv[3])
vmat[idm,2] += numint._dot_ao_ao(mol, aow, ao[0], nao, ip1-ip0, non0tab)
rho = exc = vxc = vrho = vsigma = wv = aow = None
else:
raise NotImplementedError('meta-GGA')
if nset == 1:
vmat = vmat.reshape(3,nao,nao)
return vmat
def gga_sum_(vmat, ao, wv, mask):
aow = numpy.einsum('pi,p->pi', ao[0], wv[0]*.5)
aow += numpy.einsum('npi,np->pi', ao[1:4], wv[1:])
tmp = numint._dot_ao_ao(mol, ao[0], aow, nao, weight.size, mask)
vmat[0] += tmp + tmp.T
vmat[1:] += rks_grad._gga_grad_sum(mol, ao, wv, mask)
def contract_(mat, ao, aoidx, wv, mask):
aow = numpy.einsum('pi,p->pi', ao[aoidx[0]], wv[1])
aow+= numpy.einsum('pi,p->pi', ao[aoidx[1]], wv[2])
aow+= numpy.einsum('pi,p->pi', ao[aoidx[2]], wv[3])
mat += numint._dot_ao_ao(mol, aow, ao[0], mask, shls_slice, ao_loc)
def eval_mat(mol, ao, weight, rho, vrho, vsigma=None, non0tab=None,
xctype='LDA', verbose=None):
'''Calculate the XC potential AO matrix.
Args:
mol : instance of :class:`Mole` or :class:`Cell`
ao : ([4,] nx*ny*nz, nao=cell.nao_nr()) ndarray
The value of the AO crystal orbitals on the real-space grid by default.
If xctype='GGA', also contains the value of the gradient in the x, y,
and z directions.
rho : ([4,] nx*ny*nz) ndarray
The value of the density on the real-space grid. If xctype='GGA',
also contains the value of the gradient in the x, y, and z
directions.
See Also:
pyscf.dft.numint.eval_mat
'''
if xctype == 'GGA':
ngrids, nao = ao[0].shape
else:
ngrids, nao = ao.shape
if non0tab is None:
non0tab = numpy.ones(((ngrids+BLKSIZE-1)//BLKSIZE,mol.nbas),
dtype=numpy.int8)
if numpy.iscomplexobj(ao):
if xctype == 'GGA':
assert(vsigma is not None and rho.ndim==2)
#wv = weight * vsigma * 2
#aow = numpy.einsum('pi,p->pi', ao[1], rho[1]*wv)
#aow += numpy.einsum('pi,p->pi', ao[2], rho[2]*wv)
#aow += numpy.einsum('pi,p->pi', ao[3], rho[3]*wv)
#aow += numpy.einsum('pi,p->pi', ao[0], .5*weight*vrho)
wv = numpy.empty_like(rho)
wv[0] = weight * vrho * .5
wv[1:] = rho[1:] * (weight * vsigma * 2)
aow = numpy.einsum('npi,np->pi', ao, wv)
ao_re = numpy.ascontiguousarray(ao[0].real)
ao_im = numpy.ascontiguousarray(ao[0].imag)
aow_re = numpy.ascontiguousarray(aow.real)
aow_im = numpy.ascontiguousarray(aow.imag)
else:
# *.5 because return mat + mat.T
#:aow = numpy.einsum('pi,p->pi', ao, .5*weight*vrho)
ao_re = numpy.ascontiguousarray(ao.real)
ao_im = numpy.ascontiguousarray(ao.imag)
aow_re = ao_re * (.5*weight*vrho).reshape(-1,1)
aow_im = ao_im * (.5*weight*vrho).reshape(-1,1)
#mat = pyscf.lib.dot(ao.T, aow)
mat_re = _dot_ao_ao(mol, ao_re, aow_re, nao, ngrids, non0tab)
mat_re += _dot_ao_ao(mol, ao_im, aow_im, nao, ngrids, non0tab)
mat_im = _dot_ao_ao(mol, ao_re, aow_im, nao, ngrids, non0tab)
mat_im -= _dot_ao_ao(mol, ao_im, aow_re, nao, ngrids, non0tab)
mat = mat_re + 1j*mat_im
return (mat + mat.T.conj())
else:
return pyscf.dft.numint.eval_mat(mol, ao, weight, rho, vrho,
vsigma=None, non0tab=None,
xctype='LDA', verbose=None)
def _contract_xc_kernel(td, x_id, c_id, dmvo, singlet=True, max_memory=2000):
mf = td._scf
mol = td.mol
ni = mf._numint
grids = mf.grids
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
nao, nmo = mo_coeff.shape
ndm = len(dmvo)
dmvo = numpy.asarray(dmvo)
dmvo = (dmvo + dmvo.transpose(0,2,1)) * .5
xctype = numint._xc_type(x_id, c_id)
ngrids = len(grids.weights)
BLKSIZE = numint.BLKSIZE
blksize = min(int(max_memory*1e6/8/nao/BLKSIZE)*BLKSIZE, ngrids)
v1ao = numpy.zeros((ndm,nao,nao))
if xctype == 'LDA':
buf = numpy.empty((blksize,nao))
if singlet:
for ip0, ip1 in numint.prange(0, ngrids, blksize):
coords = grids.coords[ip0:ip1]
weight = grids.weights[ip0:ip1]
non0tab = ni.non0tab[ip0//BLKSIZE:]
ao = ni.eval_ao(mol, coords, deriv=0, non0tab=non0tab, out=buf)
rho = ni.eval_rho2(mol, ao, mo_coeff, mo_occ, non0tab, 'LDA')
rho *= .5 # alpha density
fxc = ni.eval_xc(x_id, c_id, (rho,rho), 1, deriv=2)[2]
u_u, u_d, d_d = v2rho2 = fxc[0].T
frho = u_u + u_d
for i, dm in enumerate(dmvo):
rho1 = ni.eval_rho(mol, ao, dm, non0tab, xctype)
aow = numpy.einsum('pi,p->pi', ao, weight*frho*rho1)
v1ao[i] += numint._dot_ao_ao(mol, aow, ao, nao, ip1-ip0, non0tab)
rho1 = aow = None
for i in range(ndm):
v1ao[i] = (v1ao[i] + v1ao[i].T) * .5
else:
# because frho = u_u - u_d = 0
pass
elif xctype == 'GGA':
buf = numpy.empty((4,blksize,nao))
for ip0, ip1 in numint.prange(0, ngrids, blksize):
coords = grids.coords[ip0:ip1]
weight = grids.weights[ip0:ip1]
non0tab = ni.non0tab[ip0//BLKSIZE:]
ao = ni.eval_ao(mol, coords, deriv=1, non0tab=non0tab, out=buf)
rho = ni.eval_rho2(mol, ao, mo_coeff, mo_occ, non0tab, 'GGA')
rho *= .5 # alpha density
vxc, fxc = ni.eval_xc(x_id, c_id, (rho,rho), 1, deriv=2)[1:3]
vsigma = vxc[1].T
u_u, u_d, d_d = fxc[0].T # v2rho2
u_uu, u_ud, u_dd, d_uu, d_ud, d_dd = fxc[1].T # v2rhosigma
uu_uu, uu_ud, uu_dd, ud_ud, ud_dd, dd_dd = fxc[2].T # v2sigma2
if singlet:
fgamma = 2*vsigma[0] + vsigma[1]
frho = u_u + u_d
fgg = uu_uu + .5*ud_ud + 2*uu_ud + uu_dd
frhogamma = u_uu + u_dd + u_ud
else:
fgamma = 2*vsigma[0] - vsigma[1]
frho = u_u - u_d
fgg = uu_uu - uu_dd
frhogamma = u_uu - u_dd
for i, dm in enumerate(dmvo):
# rho1[0 ] = |b><j| z_{bj}
# rho1[1:] = \nabla(|b><j|) z_{bj}
rho1 = ni.eval_rho(mol, ao, dm, non0tab, 'GGA')
# sigma1 = \nabla(\rho_\alpha+\rho_\beta) dot \nabla(|b><j|) z_{bj}
# *2 for alpha + beta
sigma1 = numpy.einsum('xi,xi->i', rho[1:], rho1[1:]) * 2
wv = frho * rho1[0]
wv += frhogamma * sigma1
wv *= weight
if c_id == 131 or x_id in (402, 404, 411, 416, 419):
# second derivative of LYP functional in libxc library diverge
wv[rho[0] < 4.57e-11] = 0
aow = numpy.einsum('pi,p->pi', ao[0], wv)
v1ao[i] += numint._dot_ao_ao(mol, aow, ao[0], nao, ip1-ip0, non0tab)
for k in range(3):
wv = fgg * sigma1 * rho[1+k]
wv += frhogamma * rho1[0] * rho[1+k]
wv *= 2 # *2 because \nabla\rho = \nabla(\rho_\alpha+\rho_\beta)
wv += fgamma * rho1[1+k]
wv *= weight
if c_id == 131 or x_id in (402, 404, 411, 416, 419):
# second derivative of LYP functional in libxc library diverge
wv[rho[0] < 4.57e-11] = 0
aow = numpy.einsum('ip,i->ip', ao[0], wv)
#v1ao += numint._dot_ao_ao(mol, aow, ao[1+k], nao, ip1-ip0, non0tab)
#v1ao += numint._dot_ao_ao(mol, ao[1+k], aow, nao, ip1-ip0, non0tab)
# v1ao+v1ao.T at the end
v1ao[i] += 2*numint._dot_ao_ao(mol, aow, ao[1+k], nao, ip1-ip0, non0tab)
aow = None
for i in range(ndm):
v1ao[i] = (v1ao[i] + v1ao[i].T) * .5
else:
raise NotImplementedError('meta-GGA')
return v1ao
def _contract_xc_kernel(td_grad, x_id, c_id, xai, oovv=None, with_vxc=True,
with_kxc=True, singlet=True, max_memory=4000):
mol = td_grad.mol
mf = td_grad._scf
ni = mf._numint
grids = mf.grids
mo_coeff = mf.mo_coeff
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
nao, nmo = mo_coeff.shape
nocc = (mo_occ>0).sum()
orbv = mo_coeff[:,nocc:]
orbo = mo_coeff[:,:nocc]
# dmvo ~ reduce(numpy.dot, (orbv, Xai, orbo.T))
dmvo = (xai + xai.T) * .5 # because K_{ai,bj} == K_{ai,bj}
f1vo = numpy.zeros((4,nao,nao))
deriv = 2
if oovv is not None:
f1oo = numpy.zeros((4,nao,nao))
else:
f1oo = None
if with_vxc:
v1ao = numpy.zeros((4,nao,nao))
else:
v1ao = None
if with_kxc:
k1ao = numpy.zeros((4,nao,nao))
deriv = 3
else:
k1ao = None
xctype = numint._xc_type(x_id, c_id)
ngrids = len(grids.weights)
BLKSIZE = numint.BLKSIZE
max_memory = max_memory - 4*nao**2*8/1e6
blksize = min(int(max_memory/6*1e6/8/nao/BLKSIZE)*BLKSIZE, ngrids)
if xctype == 'LDA':
buf = numpy.empty((4,blksize,nao))
for ip0, ip1 in numint.prange(0, ngrids, blksize):
coords = grids.coords[ip0:ip1]
weight = grids.weights[ip0:ip1]
non0tab = ni.non0tab[ip0//BLKSIZE:]
ao = ni.eval_ao(mol, coords, deriv=1, non0tab=non0tab, out=buf)
rho = ni.eval_rho2(mol, ao[0], mo_coeff, mo_occ, non0tab, 'LDA')
vxc, fxc, kxc = ni.eval_xc(x_id, c_id, rho, 0, deriv=deriv)[1:]
wfxc = fxc[0] * weight * 2 # *2 for alpha+beta
if singlet:
rho1 = ni.eval_rho(mol, ao[0], dmvo, non0tab, 'LDA')
aow = numpy.einsum('pi,p->pi', ao[0], wfxc*rho1)
for k in range(4):
f1vo[k] += numint._dot_ao_ao(mol, ao[k], aow, nao, ip1-ip0, non0tab)
if oovv is not None:
rho2 = ni.eval_rho(mol, ao[0], oovv, non0tab, 'LDA')
aow = numpy.einsum('pi,p->pi', ao[0], wfxc*rho2)
for k in range(4):
f1oo[k] += numint._dot_ao_ao(mol, ao[k], aow, nao, ip1-ip0, non0tab)
if with_vxc:
aow = numpy.einsum('pi,p->pi', ao[0], vxc[0]*weight)
for k in range(4):
v1ao[k] += numint._dot_ao_ao(mol, ao[k], aow, nao, ip1-ip0, non0tab)
if singlet and with_kxc:
aow = numpy.einsum('pi,p->pi', ao[0], kxc[0]*weight*rho1**2)
for k in range(4):
k1ao[k] += numint._dot_ao_ao(mol, ao[k], aow, nao, ip1-ip0, non0tab)
vxc = fxc = kxc = aow = rho = rho1 = rho2 = None
if singlet and with_kxc:
k1ao *= 4
elif xctype == 'GGA':
raise NotImplementedError('GGA')
else:
raise NotImplementedError('meta-GGA')
f1vo[1:] *= -1
if f1oo is not None: f1oo[1:] *= -1
if v1ao is not None: v1ao[1:] *= -1
if k1ao is not None: k1ao[1:] *= -1
return f1vo, f1oo, v1ao, k1ao
def _get_vxc_diag(hessobj, mo_coeff, mo_occ, max_memory):
mol = hessobj.mol
mf = hessobj.base
if hessobj.grids is not None:
grids = hessobj.grids
else:
grids = mf.grids
if grids.coords is None:
grids.build(with_non0tab=True)
nao, nmo = mo_coeff[0].shape
ni = mf._numint
xctype = ni._xc_type(mf.xc)
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
vmata = numpy.zeros((6,nao,nao))
vmatb = numpy.zeros((6,nao,nao))
if xctype == 'LDA':
ao_deriv = 2
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
rhoa = ni.eval_rho2(mol, ao[0], mo_coeff[0], mo_occ[0], mask, 'LDA')
rhob = ni.eval_rho2(mol, ao[0], mo_coeff[1], mo_occ[1], mask, 'LDA')
vxc = ni.eval_xc(mf.xc, (rhoa,rhob), 1, deriv=1)[1]
vrho = vxc[0]
aowa = numpy.einsum('pi,p->pi', ao[0], weight*vrho[:,0])
aowb = numpy.einsum('pi,p->pi', ao[0], weight*vrho[:,1])
for i in range(6):
vmata[i] += numint._dot_ao_ao(mol, ao[i+4], aowa, mask, shls_slice, ao_loc)
vmatb[i] += numint._dot_ao_ao(mol, ao[i+4], aowb, mask, shls_slice, ao_loc)
aowa = aowb = None
elif xctype == 'GGA':
def contract_(mat, ao, aoidx, wv, mask):
aow = numpy.einsum('pi,p->pi', ao[aoidx[0]], wv[1])
aow+= numpy.einsum('pi,p->pi', ao[aoidx[1]], wv[2])
aow+= numpy.einsum('pi,p->pi', ao[aoidx[2]], wv[3])
mat += numint._dot_ao_ao(mol, aow, ao[0], mask, shls_slice, ao_loc)
ao_deriv = 3
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
rhoa = ni.eval_rho2(mol, ao[:4], mo_coeff[0], mo_occ[0], mask, 'GGA')
rhob = ni.eval_rho2(mol, ao[:4], mo_coeff[1], mo_occ[1], mask, 'GGA')
vxc = ni.eval_xc(mf.xc, (rhoa,rhob), 1, deriv=1)[1]
wva, wvb = numint._uks_gga_wv0((rhoa,rhob), vxc, weight)
# *2 because v.T is not applied.
wva[0] *= 2
wvb[0] *= 2
aowa = numpy.einsum('npi,np->pi', ao[:4], wva)
aowb = numpy.einsum('npi,np->pi', ao[:4], wvb)
for i in range(6):
vmata[i] += numint._dot_ao_ao(mol, ao[i+4], aowa, mask, shls_slice, ao_loc)
vmatb[i] += numint._dot_ao_ao(mol, ao[i+4], aowb, mask, shls_slice, ao_loc)
contract_(vmata[0], ao, [XXX,XXY,XXZ], wva, mask)
contract_(vmata[1], ao, [XXY,XYY,XYZ], wva, mask)
contract_(vmata[2], ao, [XXZ,XYZ,XZZ], wva, mask)
contract_(vmata[3], ao, [XYY,YYY,YYZ], wva, mask)
contract_(vmata[4], ao, [XYZ,YYZ,YZZ], wva, mask)
contract_(vmata[5], ao, [XZZ,YZZ,ZZZ], wva, mask)
contract_(vmatb[0], ao, [XXX,XXY,XXZ], wvb, mask)
contract_(vmatb[1], ao, [XXY,XYY,XYZ], wvb, mask)
contract_(vmatb[2], ao, [XXZ,XYZ,XZZ], wvb, mask)
contract_(vmatb[3], ao, [XYY,YYY,YYZ], wvb, mask)
contract_(vmatb[4], ao, [XYZ,YYZ,YZZ], wvb, mask)
contract_(vmatb[5], ao, [XZZ,YZZ,ZZZ], wvb, mask)
rho = vxc = aowa = aowb = None
elif xctype == 'MGGA':
raise NotImplementedError('meta-GGA')
vmata = vmata[[0,1,2, 1,3,4, 2,4,5]].reshape(3,3,nao,nao)
vmatb = vmatb[[0,1,2, 1,3,4, 2,4,5]].reshape(3,3,nao,nao)
return vmata, vmatb
def _get_vxc_diag(hessobj, mo_coeff, mo_occ, max_memory):
mol = hessobj.mol
mf = hessobj.base
if hessobj.grids is not None:
grids = hessobj.grids
else:
grids = mf.grids
if grids.coords is None:
grids.build(with_non0tab=True)
nao, nmo = mo_coeff.shape
ni = mf._numint
xctype = ni._xc_type(mf.xc)
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
vmat = numpy.zeros((6,nao,nao))
if xctype == 'LDA':
ao_deriv = 2
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
rho = ni.eval_rho2(mol, ao[0], mo_coeff, mo_occ, mask, 'LDA')
vxc = ni.eval_xc(mf.xc, rho, 0, deriv=1)[1]
vrho = vxc[0]
aow = numpy.einsum('pi,p->pi', ao[0], weight*vrho)
for i in range(6):
vmat[i] += numint._dot_ao_ao(mol, ao[i+4], aow, mask, shls_slice, ao_loc)
aow = None
elif xctype == 'GGA':
def contract_(mat, ao, aoidx, wv, mask):
aow = numpy.einsum('pi,p->pi', ao[aoidx[0]], wv[1])
aow+= numpy.einsum('pi,p->pi', ao[aoidx[1]], wv[2])
aow+= numpy.einsum('pi,p->pi', ao[aoidx[2]], wv[3])
mat += numint._dot_ao_ao(mol, aow, ao[0], mask, shls_slice, ao_loc)
ao_deriv = 3
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
rho = ni.eval_rho2(mol, ao[:4], mo_coeff, mo_occ, mask, 'GGA')
vxc = ni.eval_xc(mf.xc, rho, 0, deriv=1)[1]
wv = numint._rks_gga_wv0(rho, vxc, weight)
# *2 because v.T is not applied. Only v is computed in the next _dot_ao_ao
wv[0] *= 2
aow = numpy.einsum('npi,np->pi', ao[:4], wv)
for i in range(6):
vmat[i] += numint._dot_ao_ao(mol, ao[i+4], aow, mask, shls_slice, ao_loc)
contract_(vmat[0], ao, [XXX,XXY,XXZ], wv, mask)
contract_(vmat[1], ao, [XXY,XYY,XYZ], wv, mask)
contract_(vmat[2], ao, [XXZ,XYZ,XZZ], wv, mask)
contract_(vmat[3], ao, [XYY,YYY,YYZ], wv, mask)
contract_(vmat[4], ao, [XYZ,YYZ,YZZ], wv, mask)
contract_(vmat[5], ao, [XZZ,YZZ,ZZZ], wv, mask)
rho = vxc = wv = aow = None
elif xctype == 'MGGA':
raise NotImplementedError('meta-GGA')
vmat = vmat[[0,1,2,
1,3,4,
2,4,5]]
return vmat.reshape(3,3,nao,nao)
def make_psi_vmat(pcmobj, dm, r_vdw, ui, grids, ylm_1sph, cached_pol, L_X, L):
mol = pcmobj.mol
natm = mol.natm
lmax = pcmobj.lmax
nlm = (lmax+1)**2
i1 = 0
scaled_weights = numpy.empty(grids.weights.size)
for ia in range(natm):
fak_pol, leak_idx = cached_pol[mol.atom_symbol(ia)]
i0, i1 = i1, i1 + fak_pol[0].shape[1]
eta_nj = 0
p1 = 0
for l in range(lmax+1):
fac = 4*numpy.pi/(l*2+1)
p0, p1 = p1, p1 + (l*2+1)
eta_nj += fac * numpy.einsum('mn,m->n', fak_pol[l], L_X[ia,p0:p1])
scaled_weights[i0:i1] = eta_nj * grids.weights[i0:i1]
if not (isinstance(dm, numpy.ndarray) and dm.ndim == 2):
dm = dm[0] + dm[1]
ni = numint.NumInt()
max_memory = pcmobj.max_memory - lib.current_memory()[0]
make_rho, nset, nao = ni._gen_rho_evaluator(mol, dm)
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
den = numpy.empty(grids.weights.size)
vmat = numpy.zeros((nao,nao))
p1 = 0
aow = None
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, 0, max_memory):
p0, p1 = p1, p1 + weight.size
den[p0:p1] = weight * make_rho(0, ao, mask, 'LDA')
aow = numpy.ndarray(ao.shape, order='F', buffer=aow)
aow = numpy.einsum('pi,p->pi', ao, scaled_weights[p0:p1], out=aow)
vmat -= numint._dot_ao_ao(mol, ao, aow, mask, shls_slice, ao_loc)
ao = aow = scaled_weights = None
nelec_leak = 0
psi = numpy.empty((natm,nlm))
i1 = 0
for ia in range(natm):
fak_pol, leak_idx = cached_pol[mol.atom_symbol(ia)]
i0, i1 = i1, i1 + fak_pol[0].shape[1]
nelec_leak += den[i0:i1][leak_idx].sum()
p1 = 0
for l in range(lmax+1):
fac = 4*numpy.pi/(l*2+1)
p0, p1 = p1, p1 + (l*2+1)
psi[ia,p0:p1] = -fac * numpy.einsum('n,mn->m', den[i0:i1], fak_pol[l])
# Contribution of nuclear charge to the total density
# The factor numpy.sqrt(4*numpy.pi) is due to the product of 4*pi * Y_0^0
psi[ia,0] += numpy.sqrt(4*numpy.pi)/r_vdw[ia] * mol.atom_charge(ia)
logger.debug(pcmobj, 'electron leak %f', nelec_leak)
# <Psi, L^{-1}g> -> Psi = SL the adjoint equation to LX = g
L_S = numpy.linalg.solve(L.T.reshape(natm*nlm,-1), psi.ravel()).reshape(natm,-1)
coords_1sph, weights_1sph = make_grids_one_sphere(pcmobj.lebedev_order)
# JCP, 141, 184108, Eq (39)
xi_jn = numpy.einsum('n,jn,xn,jx->jn', weights_1sph, ui, ylm_1sph, L_S)
extern_point_idx = ui > 0
cav_coords = (mol.atom_coords().reshape(natm,1,3)
+ numpy.einsum('r,gx->rgx', r_vdw, coords_1sph))
cav_coords = cav_coords[extern_point_idx]
xi_jn = xi_jn[extern_point_idx]
max_memory = pcmobj.max_memory - lib.current_memory()[0]
blksize = int(max(max_memory*1e6/8/nao**2, 400))
vmat_tril = 0
for i0, i1 in lib.prange(0, xi_jn.size, blksize):
fakemol = gto.fakemol_for_charges(cav_coords[i0:i1])
v_nj = df.incore.aux_e2(mol, fakemol, intor='int3c2e', aosym='s2ij')
vmat_tril += numpy.einsum('xn,n->x', v_nj, xi_jn[i0:i1])
vmat += lib.unpack_tril(vmat_tril)
return psi, vmat, L_S
def _contract_xc_kernel(td_grad, xc_code, xai, oovv=None, with_vxc=True,
with_kxc=True, singlet=True, max_memory=2000):
mol = td_grad.mol
mf = td_grad._scf
grids = mf.grids
ni = copy.copy(mf._numint)
if rks.USE_XCFUN:
try:
ni.libxc = dft.xcfun
xctype = ni._xc_type(xc_code)
except (ImportError, KeyError, NotImplementedError):
ni.libxc = dft.libxc
xctype = ni._xc_type(xc_code)
else:
xctype = ni._xc_type(xc_code)
mo_coeff = mf.mo_coeff
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
nao, nmo = mo_coeff.shape
nocc = (mo_occ>0).sum()
orbv = mo_coeff[:,nocc:]
orbo = mo_coeff[:,:nocc]
# dmvo ~ reduce(numpy.dot, (orbv, Xai, orbo.T))
dmvo = (xai + xai.T) * .5 # because K_{ai,bj} == K_{ai,bj}
f1vo = numpy.zeros((4,nao,nao))
deriv = 2
if oovv is not None:
f1oo = numpy.zeros((4,nao,nao))
else:
f1oo = None
if with_vxc:
v1ao = numpy.zeros((4,nao,nao))
else:
v1ao = None
if with_kxc:
k1ao = numpy.zeros((4,nao,nao))
deriv = 3
else:
k1ao = None
if xctype == 'LDA':
ao_deriv = 1
if singlet:
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory, ni.non0tab):
rho = ni.eval_rho2(mol, ao[0], mo_coeff, mo_occ, mask, 'LDA')
vxc, fxc, kxc = ni.eval_xc(xc_code, rho, 0, deriv=deriv)[1:]
wfxc = fxc[0] * weight * 2 # *2 for alpha+beta
rho1 = ni.eval_rho(mol, ao[0], dmvo, mask, 'LDA')
aow = numpy.einsum('pi,p->pi', ao[0], wfxc*rho1)
for k in range(4):
f1vo[k] += numint._dot_ao_ao(mol, ao[k], aow, nao, weight.size, mask)
if oovv is not None:
rho2 = ni.eval_rho(mol, ao[0], oovv, mask, 'LDA')
aow = numpy.einsum('pi,p->pi', ao[0], wfxc*rho2)
for k in range(4):
f1oo[k] += numint._dot_ao_ao(mol, ao[k], aow, nao, weight.size, mask)
if with_vxc:
aow = numpy.einsum('pi,p->pi', ao[0], vxc[0]*weight)
for k in range(4):
v1ao[k] += numint._dot_ao_ao(mol, ao[k], aow, nao, weight.size, mask)
if with_kxc:
aow = numpy.einsum('pi,p->pi', ao[0], kxc[0]*weight*rho1**2)
for k in range(4):
k1ao[k] += numint._dot_ao_ao(mol, ao[k], aow, nao, weight.size, mask)
vxc = fxc = kxc = aow = rho = rho1 = rho2 = None
if with_kxc: # for (rho1*2)^2, *2 for alpha+beta in singlet
k1ao *= 4
else:
raise NotImplementedError('LDA triplet')
elif xctype == 'GGA':
if singlet:
def gga_sum_(vmat, ao, wv, mask):
aow = numpy.einsum('pi,p->pi', ao[0], wv[0]*.5)
aow += numpy.einsum('npi,np->pi', ao[1:4], wv[1:])
tmp = numint._dot_ao_ao(mol, ao[0], aow, nao, weight.size, mask)
vmat[0] += tmp + tmp.T
vmat[1:] += rks_grad._gga_grad_sum(mol, ao, wv, mask)
ao_deriv = 2
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory, ni.non0tab):
rho = ni.eval_rho2(mol, ao, mo_coeff, mo_occ, mask, 'GGA')
vxc, fxc, kxc = ni.eval_xc(xc_code, rho, 0, deriv=deriv)[1:]
vrho, vgamma = vxc[:2]
frr, frg, fgg = fxc[:3]
rho1 = ni.eval_rho(mol, ao, dmvo, mask, 'GGA') * 2 # *2 for alpha + beta
sigma1 = numpy.einsum('xi,xi->i', rho[1:], rho1[1:])
wv = numpy.empty_like((rho))
wv[0] = frr * rho1[0]
wv[0] += frg * sigma1 * 2
wv[1:] = (fgg * sigma1 * 4 + frg * rho1[0] * 2) * rho[1:]
wv[1:] += vgamma * rho1[1:] * 2
wv *= weight
gga_sum_(f1vo, ao, wv, mask)
if oovv is not None:
rho2 = ni.eval_rho(mol, ao, oovv, mask, 'GGA') * 2
sigma2 = numpy.einsum('xi,xi->i', rho[1:], rho2[1:])
wv[0] = frr * rho2[0]
wv[0] += frg * sigma2 * 2
wv[1:] = (fgg * sigma2 * 4 + frg * rho2[0] * 2) * rho[1:]
wv[1:] += vgamma * rho2[1:] * 2
wv *= weight
gga_sum_(f1oo, ao, wv, mask)
if with_vxc:
wv[0] = vrho
wv[1:] = 2 * vgamma * rho[1:]
wv *= weight
gga_sum_(v1ao, ao, wv, mask)
if with_kxc:
frrr, frrg, frgg, fggg = kxc
r1r1 = rho1[0]**2
s1s1 = sigma1**2
r1s1 = rho1[0] * sigma1
sigma2 = numpy.einsum('xi,xi->i', rho1[1:], rho1[1:])
wv[0] = frrr * r1r1
wv[0] += 4 * frrg * r1s1
wv[0] += 4 * frgg * s1s1
wv[0] += 2 * frg * sigma2
wv[1:] = 2 * frrg * r1r1 * rho[1:]
wv[1:] += 8 * frgg * r1s1 * rho[1:]
wv[1:] += 4 * frg * rho1[0] * rho1[1:]
wv[1:] += 4 * fgg * sigma2 * rho[1:]
wv[1:] += 8 * fgg * sigma1 * rho1[1:]
wv[1:] += 8 * fggg * s1s1 * rho[1:]
wv *= weight
gga_sum_(k1ao, ao, wv, mask)
vxc = fxc = kxc = rho = rho1 = rho2 = sigma1 = sigma2 = None
else:
raise NotImplementedError('GGA triplet')
else:
raise NotImplementedError('meta-GGA')
f1vo[1:] *= -1
if f1oo is not None: f1oo[1:] *= -1
if v1ao is not None: v1ao[1:] *= -1
if k1ao is not None: k1ao[1:] *= -1
return f1vo, f1oo, v1ao, k1ao
def _contract_xc_kernel(td_grad, xc_code, dmvo, dmoo=None, with_vxc=True,
with_kxc=True, singlet=True, max_memory=2000):
mol = td_grad.mol
mf = td_grad.base._scf
grids = mf.grids
ni = mf._numint
xctype = ni._xc_type(xc_code)
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
nao, nmo = mo_coeff.shape
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
# dmvo ~ reduce(numpy.dot, (orbv, Xai, orbo.T))
dmvo = (dmvo + dmvo.T) * .5 # because K_{ia,jb} == K_{ia,jb}
f1vo = numpy.zeros((4,nao,nao)) # 0th-order, d/dx, d/dy, d/dz
deriv = 2
if dmoo is not None:
f1oo = numpy.zeros((4,nao,nao))
else:
f1oo = None
if with_vxc:
v1ao = numpy.zeros((4,nao,nao))
else:
v1ao = None
if with_kxc:
k1ao = numpy.zeros((4,nao,nao))
deriv = 3
else:
k1ao = None
if xctype == 'LDA':
ao_deriv = 1
if singlet:
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
rho = ni.eval_rho2(mol, ao[0], mo_coeff, mo_occ, mask, 'LDA')
vxc, fxc, kxc = ni.eval_xc(xc_code, rho, 0, deriv=deriv)[1:]
wfxc = fxc[0] * weight * 2 # *2 for alpha+beta
rho1 = ni.eval_rho(mol, ao[0], dmvo, mask, 'LDA')
aow = numpy.einsum('pi,p,p->pi', ao[0], wfxc, rho1)
for k in range(4):
f1vo[k] += numint._dot_ao_ao(mol, ao[k], aow, mask, shls_slice, ao_loc)
if dmoo is not None:
rho2 = ni.eval_rho(mol, ao[0], dmoo, mask, 'LDA')
aow = numpy.einsum('pi,p,p->pi', ao[0], wfxc, rho2)
for k in range(4):
f1oo[k] += numint._dot_ao_ao(mol, ao[k], aow, mask, shls_slice, ao_loc)
if with_vxc:
aow = numpy.einsum('pi,p,p->pi', ao[0], vxc[0], weight)
for k in range(4):
v1ao[k] += numint._dot_ao_ao(mol, ao[k], aow, mask, shls_slice, ao_loc)
if with_kxc:
aow = numpy.einsum('pi,p,p,p->pi', ao[0], kxc[0], weight, rho1**2)
for k in range(4):
k1ao[k] += numint._dot_ao_ao(mol, ao[k], aow, mask, shls_slice, ao_loc)
vxc = fxc = kxc = aow = rho = rho1 = rho2 = None
if with_kxc: # for (rho1*2)^2, *2 for alpha+beta in singlet
k1ao *= 4
else:
raise NotImplementedError('LDA triplet')
elif xctype == 'GGA':
if singlet:
def gga_sum_(vmat, ao, wv, mask):
aow = numpy.einsum('pi,p->pi', ao[0], wv[0])
aow += numpy.einsum('npi,np->pi', ao[1:4], wv[1:])
tmp = numint._dot_ao_ao(mol, ao[0], aow, mask, shls_slice, ao_loc)
vmat[0] += tmp + tmp.T
rks_grad._gga_grad_sum_(vmat[1:], mol, ao, wv, mask, ao_loc)
ao_deriv = 2
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
rho = ni.eval_rho2(mol, ao, mo_coeff, mo_occ, mask, 'GGA')
vxc, fxc, kxc = ni.eval_xc(xc_code, rho, 0, deriv=deriv)[1:]
rho1 = ni.eval_rho(mol, ao, dmvo, mask, 'GGA') * 2 # *2 for alpha + beta
wv = numint._rks_gga_wv1(rho, rho1, vxc, fxc, weight)
gga_sum_(f1vo, ao, wv, mask)
if dmoo is not None:
rho2 = ni.eval_rho(mol, ao, dmoo, mask, 'GGA') * 2
wv = numint._rks_gga_wv1(rho, rho2, vxc, fxc, weight)
gga_sum_(f1oo, ao, wv, mask)
if with_vxc:
wv = numint._rks_gga_wv0(rho, vxc, weight)
gga_sum_(v1ao, ao, wv, mask)
if with_kxc:
wv = numint._rks_gga_wv2(rho, rho1, fxc, kxc, weight)
gga_sum_(k1ao, ao, wv, mask)
vxc = fxc = kxc = rho = rho1 = None
else:
raise NotImplementedError('GGA triplet')
else:
raise NotImplementedError('meta-GGA')
f1vo[1:] *= -1
if f1oo is not None: f1oo[1:] *= -1
if v1ao is not None: v1ao[1:] *= -1
if k1ao is not None: k1ao[1:] *= -1
return f1vo, f1oo, v1ao, k1ao
def _get_vxc_giao(ni, mol, grids, x_id, c_id, dm,
max_memory=2000, verbose=None):
natocc, natorb = scipy.linalg.eigh(dm)
nao = dm.shape[0]
xctype = numint._xc_type(x_id, c_id)
ngrids = len(grids.weights)
BLKSIZE = numint.BLKSIZE
blksize = min(int(max_memory/6*1e6/12/nao/BLKSIZE)*BLKSIZE, ngrids)
vmat = numpy.zeros((3,nao,nao))
if xctype == 'LDA':
buf = numpy.empty((4,blksize,nao))
for ip0, ip1 in numint.prange(0, ngrids, blksize):
coords = grids.coords[ip0:ip1]
weight = grids.weights[ip0:ip1]
non0tab = ni.non0tab[ip0//BLKSIZE:]
ao = ni.eval_ao(mol, coords, deriv=0, non0tab=non0tab, out=buf)
rho = ni.eval_rho2(mol, ao, natorb, natocc, non0tab, xctype)
vxc = ni.eval_xc(x_id, c_id, rho, 0, deriv=1)[1]
vrho = vxc[0]
aow = numpy.einsum('pi,p->pi', ao, weight*vrho)
giao = mol.eval_gto('GTOval_ig_sph', coords, comp=3,
non0tab=non0tab, out=buf[1:])
vmat[0] += numint._dot_ao_ao(mol, aow, giao[0], nao, ip1-ip0, non0tab)
vmat[1] += numint._dot_ao_ao(mol, aow, giao[1], nao, ip1-ip0, non0tab)
vmat[2] += numint._dot_ao_ao(mol, aow, giao[2], nao, ip1-ip0, non0tab)
rho = vxc = vrho = aow = giao = None
elif xctype == 'GGA':
buf = numpy.empty((10,blksize,nao))
XX, XY, XZ = 0, 1, 2
YX, YY, YZ = 3, 4, 5
ZX, ZY, ZZ = 6, 7, 8
for ip0, ip1 in numint.prange(0, ngrids, blksize):
coords = grids.coords[ip0:ip1]
weight = grids.weights[ip0:ip1]
non0tab = ni.non0tab[ip0//BLKSIZE:]
ao = ni.eval_ao(mol, coords, deriv=1, non0tab=non0tab, out=buf)
rho = ni.eval_rho2(mol, ao, natorb, natocc, non0tab, xctype)
vxc = ni.eval_xc(x_id, c_id, rho, 0, deriv=1)[1]
vrho, vsigma = vxc[:2]
wv = numpy.empty_like(rho)
wv[0] = weight * vrho
wv[1:] = rho[1:] * (weight * vsigma * 2)
aow = numpy.einsum('npi,np->pi', ao[:4], wv)
giao = mol.eval_gto('GTOval_ig_sph', coords, 3,
non0tab=non0tab, out=buf[4:])
vmat[0] += numint._dot_ao_ao(mol, aow, giao[0], nao, ip1-ip0, non0tab)
vmat[1] += numint._dot_ao_ao(mol, aow, giao[1], nao, ip1-ip0, non0tab)
vmat[2] += numint._dot_ao_ao(mol, aow, giao[2], nao, ip1-ip0, non0tab)
giao = mol.eval_gto('GTOval_ipig_sph', coords, 9,
non0tab=non0tab, out=buf[1:])
aow = numpy.einsum('pi,p->pi', giao[XX], wv[1])
aow+= numpy.einsum('pi,p->pi', giao[YX], wv[2])
aow+= numpy.einsum('pi,p->pi', giao[ZX], wv[3])
vmat[0] += numint._dot_ao_ao(mol, ao[0], aow, nao, ip1-ip0, non0tab)
aow = numpy.einsum('pi,p->pi', giao[XY], wv[1])
aow+= numpy.einsum('pi,p->pi', giao[YY], wv[2])
aow+= numpy.einsum('pi,p->pi', giao[ZY], wv[3])
vmat[1] += numint._dot_ao_ao(mol, ao[0], aow, nao, ip1-ip0, non0tab)
aow = numpy.einsum('pi,p->pi', giao[XZ], wv[1])
aow+= numpy.einsum('pi,p->pi', giao[YZ], wv[2])
aow+= numpy.einsum('pi,p->pi', giao[ZZ], wv[3])
vmat[2] += numint._dot_ao_ao(mol, ao[0], aow, nao, ip1-ip0, non0tab)
rho = vxc = vrho = vsigma = wv = aow = giao = None
else:
raise NotImplementedError('meta-GGA')
return vmat - vmat.transpose(0,2,1)
