def get_vxc_full_response(ni, mol, grids, xc_code, dms, relativity=0, hermi=1,
max_memory=2000, verbose=None):
'''Full response including the response of the grids'''
xctype = ni._xc_type(xc_code)
make_rho, nset, nao = ni._gen_rho_evaluator(mol, dms, hermi)
ao_loc = mol.ao_loc_nr()
excsum = 0
vmat = numpy.zeros((3,nao,nao))
if xctype == 'LDA':
ao_deriv = 1
vtmp = numpy.empty((3,nao,nao))
for atm_id, (coords, weight, weight1) in enumerate(grids_response_cc(grids)):
ngrids = weight.size
mask = gen_grid.make_mask(mol, coords)
ao = ni.eval_ao(mol, coords, deriv=ao_deriv, non0tab=mask)
rho = make_rho(0, ao[0], mask, 'LDA')
exc, vxc = ni.eval_xc(xc_code, rho, 0, relativity, 1,
verbose=verbose)[:2]
vrho = vxc[0]
vtmp = numpy.zeros((3,nao,nao))
aow = numpy.einsum('pi,p->pi', ao[0], weight*vrho)
_d1_dot_(vtmp, mol, ao[1:4], aow, mask, ao_loc, True)
vmat += vtmp
# response of weights
excsum += numpy.einsum('r,r,nxr->nx', exc, rho, weight1)
# response of grids coordinates
excsum[atm_id] += numpy.einsum('xij,ji->x', vtmp, dms) * 2
rho = vxc = vrho = aow = None
elif xctype == 'GGA':
ao_deriv = 2
for atm_id, (coords, weight, weight1) in enumerate(grids_response_cc(grids)):
ngrids = weight.size
mask = gen_grid.make_mask(mol, coords)
ao = ni.eval_ao(mol, coords, deriv=ao_deriv, non0tab=mask)
rho = make_rho(0, ao[:4], mask, 'GGA')
exc, vxc = ni.eval_xc(xc_code, rho, 0, relativity, 1,
verbose=verbose)[:2]
vtmp = numpy.zeros((3,nao,nao))
wv = numint._rks_gga_wv0(rho, vxc, weight)
_gga_grad_sum_(vtmp, mol, ao, wv, mask, ao_loc)
vmat += vtmp
# response of weights
excsum += numpy.einsum('r,r,nxr->nx', exc, rho[0], weight1)
# response of grids coordinates
excsum[atm_id] += numpy.einsum('xij,ji->x', vtmp, dms) * 2
rho = vxc = vrho = vsigma = wv = mat = None
elif xctype == 'NLC':
raise NotImplementedError('NLC')
else:
raise NotImplementedError('meta-GGA')
# - sign because nabla_X = -nabla_x
return excsum, -vmat
def get_vxc_full_response(ni, mol, grids, xc_code, dms, relativity=0, hermi=1,
max_memory=2000, verbose=None):
'''Full response including the response of the grids'''
xctype = ni._xc_type(xc_code)
make_rho, nset, nao = ni._gen_rho_evaluator(mol, dms, hermi)
ao_loc = mol.ao_loc_nr()
excsum = 0
vmat = numpy.zeros((3,nao,nao))
if xctype == 'LDA':
ao_deriv = 1
vtmp = numpy.empty((3,nao,nao))
for atm_id, (coords, weight, weight1) in enumerate(grids_response_cc(grids)):
ngrids = weight.size
mask = gen_grid.make_mask(mol, coords)
ao = ni.eval_ao(mol, coords, deriv=ao_deriv, non0tab=mask)
rho = make_rho(0, ao[0], mask, 'LDA')
exc, vxc = ni.eval_xc(xc_code, rho, 0, relativity, 1, verbose)[:2]
vrho = vxc[0]
vtmp = numpy.zeros((3,nao,nao))
aow = numpy.einsum('pi,p->pi', ao[0], weight*vrho)
_d1_dot_(vtmp, mol, ao[1:4], aow, mask, ao_loc, True)
vmat += vtmp
# response of weights
excsum += numpy.einsum('r,r,nxr->nx', exc, rho, weight1)
# response of grids coordinates
excsum[atm_id] += numpy.einsum('xij,ji->x', vtmp, dms) * 2
rho = vxc = vrho = aow = None
elif xctype == 'GGA':
ao_deriv = 2
for atm_id, (coords, weight, weight1) in enumerate(grids_response_cc(grids)):
ngrids = weight.size
mask = gen_grid.make_mask(mol, coords)
ao = ni.eval_ao(mol, coords, deriv=ao_deriv, non0tab=mask)
rho = make_rho(0, ao[:4], mask, 'GGA')
exc, vxc = ni.eval_xc(xc_code, rho, 0, relativity, 1, verbose)[:2]
vtmp = numpy.zeros((3,nao,nao))
wv = numint._rks_gga_wv0(rho, vxc, weight)
_gga_grad_sum_(vtmp, mol, ao, wv, mask, ao_loc)
vmat += vtmp
# response of weights
excsum += numpy.einsum('r,r,nxr->nx', exc, rho[0], weight1)
# response of grids coordinates
excsum[atm_id] += numpy.einsum('xij,ji->x', vtmp, dms) * 2
rho = vxc = vrho = vsigma = wv = mat = None
elif xctype == 'NLC':
raise NotImplementedError('NLC')
else:
raise NotImplementedError('meta-GGA')
# - sign because nabla_X = -nabla_x
return excsum, -vmat
def get_vxc(ni,
mol,
grids,
xc_code,
dms,
relativity=0,
hermi=1,
max_memory=2000,
verbose=None):
xctype = ni._xc_type(xc_code)
make_rho, nset, nao = ni._gen_rho_evaluator(mol, dms, hermi)
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
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):
for idm in range(nset):
rho = make_rho(idm, ao[0], mask, 'LDA')
vxc = ni.eval_xc(xc_code,
rho,
0,
relativity,
1,
verbose=verbose)[1]
vrho = vxc[0]
aow = numpy.einsum('pi,p->pi', ao[0], weight * vrho)
_d1_dot_(vmat[idm], mol, ao[1:4], aow, mask, ao_loc, True)
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):
for idm in range(nset):
rho = make_rho(idm, ao[:4], mask, 'GGA')
vxc = ni.eval_xc(xc_code,
rho,
0,
relativity,
1,
verbose=verbose)[1]
wv = numint._rks_gga_wv0(rho, vxc, weight)
_gga_grad_sum_(vmat[idm], mol, ao, wv, mask, ao_loc)
rho = vxc = vrho = vsigma = wv = None
elif xctype == 'NLC':
raise NotImplementedError('NLC')
else:
raise NotImplementedError('meta-GGA')
exc = None
if nset == 1:
vmat = vmat.reshape(3, nao, nao)
# - sign because nabla_X = -nabla_x
return exc, -vmat
def test_gga_deriv1(self):
ng = 7
xctype = 'GGA'
np.random.seed(8)
rho = np.random.rand(2, 4, ng)
weight = 1
exc, vxc, fxc, kxc = eval_xc(f'R-{xctype}', ng)
ref = numint._rks_gga_wv0(rho[0], vxc, weight)
ref[0] *= 2
v1 = xc_deriv.transform_vxc(rho[0], vxc, xctype, spin=0)
self.assertAlmostEqual(abs(v1 - ref).max(), 0, 12)
exc, vxc, fxc, kxc = eval_xc(f'U-{xctype}', ng)
ref = np.array(numint._uks_gga_wv0(rho, vxc, weight))
ref[:, 0] *= 2
v1 = xc_deriv.transform_vxc(rho, vxc, xctype, spin=1)
self.assertAlmostEqual(abs(v1 - ref).max(), 0, 12)
def get_vxc(ni, mol, grids, xc_code, dms, relativity=0, hermi=1,
max_memory=2000, verbose=None):
xctype = ni._xc_type(xc_code)
make_rho, nset, nao = ni._gen_rho_evaluator(mol, dms, hermi)
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
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):
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)
_d1_dot_(vmat[idm], mol, ao[1:4], aow, mask, ao_loc, True)
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):
for idm in range(nset):
rho = make_rho(idm, ao[:4], mask, 'GGA')
vxc = ni.eval_xc(xc_code, rho, 0, relativity, 1, verbose)[1]
wv = numint._rks_gga_wv0(rho, vxc, weight)
_gga_grad_sum_(vmat[idm], mol, ao, wv, mask, ao_loc)
rho = vxc = vrho = vsigma = wv = None
elif xctype == 'NLC':
raise NotImplementedError('NLC')
else:
raise NotImplementedError('meta-GGA')
exc = None
if nset == 1:
vmat = vmat.reshape(3,nao,nao)
# - sign because nabla_X = -nabla_x
return exc, -vmat
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_deriv1(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)
aoslices = mol.aoslice_by_atom()
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
dm0 = mf.make_rdm1(mo_coeff, mo_occ)
vmat = numpy.zeros((mol.natm, 3, nao, nao))
max_memory = max(2000, max_memory - vmat.size * 8 / 1e6)
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, mo_occ, mask, 'LDA')
vxc, fxc = ni.eval_xc(mf.xc, rho, 0, deriv=2)[1:3]
vrho = vxc[0]
frr = fxc[0]
ao_dm0 = numint._dot_ao_dm(mol, ao[0], dm0, mask, shls_slice,
ao_loc)
aow1 = numpy.einsum('xpi,p->xpi', ao[1:], weight * vrho)
for ia in range(mol.natm):
p0, p1 = aoslices[ia][2:]
# First order density = rho1 * 2. *2 is not applied because + c.c. in the end
rho1 = numpy.einsum('xpi,pi->xp', ao[1:, :, p0:p1],
ao_dm0[:, p0:p1])
aow = numpy.einsum('pi,xp->xpi', ao[0], weight * frr * rho1)
aow[:, :, p0:p1] += aow1[:, :, p0:p1]
rks_grad._d1_dot_(vmat[ia], mol, aow, ao[0], mask, ao_loc,
True)
ao_dm0 = aow = aow1 = None
for ia in range(mol.natm):
vmat[ia] = -vmat[ia] - vmat[ia].transpose(0, 2, 1)
elif xctype == 'GGA':
ao_deriv = 2
v_ip = numpy.zeros((3, nao, nao))
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, fxc = ni.eval_xc(mf.xc, rho, 0, deriv=2)[1:3]
wv = numint._rks_gga_wv0(rho, vxc, weight)
rks_grad._gga_grad_sum_(v_ip, mol, ao, wv, mask, ao_loc)
ao_dm0 = [
numint._dot_ao_dm(mol, ao[i], dm0, mask, shls_slice, ao_loc)
for i in range(4)
]
for ia in range(mol.natm):
wv = dR_rho1 = _make_dR_rho1(ao, ao_dm0, ia, aoslices)
wv[0] = numint._rks_gga_wv1(rho, dR_rho1[0], vxc, fxc, weight)
wv[1] = numint._rks_gga_wv1(rho, dR_rho1[1], vxc, fxc, weight)
wv[2] = numint._rks_gga_wv1(rho, dR_rho1[2], vxc, fxc, weight)
aow = numpy.einsum('npi,Xnp->Xpi', ao[:4], wv)
rks_grad._d1_dot_(vmat[ia], mol, aow, ao[0], mask, ao_loc,
True)
ao_dm0 = aow = None
for ia in range(mol.natm):
p0, p1 = aoslices[ia][2:]
vmat[ia, :, p0:p1] += v_ip[:, p0:p1]
vmat[ia] = -vmat[ia] - vmat[ia].transpose(0, 2, 1)
elif xctype == 'MGGA':
raise NotImplementedError('meta-GGA')
return vmat
def _get_vxc_deriv2(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)
aoslices = mol.aoslice_by_atom()
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
dm0 = mf.make_rdm1(mo_coeff, mo_occ)
vmat = numpy.zeros((mol.natm, 3, 3, nao, nao))
ipip = numpy.zeros((3, 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):
rho = ni.eval_rho2(mol, ao[0], mo_coeff, mo_occ, mask, 'LDA')
vxc, fxc = ni.eval_xc(mf.xc, rho, 0, deriv=2)[1:3]
vrho = vxc[0]
frr = fxc[0]
aow = numpy.einsum('xpi,p->xpi', ao[1:4], weight * vrho)
_d1d2_dot_(ipip, mol, aow, ao[1:4], mask, ao_loc, False)
ao_dm0 = numint._dot_ao_dm(mol, ao[0], dm0, mask, shls_slice,
ao_loc)
for ia in range(mol.natm):
p0, p1 = aoslices[ia][2:]
# *2 for \nabla|ket> in rho1
rho1 = numpy.einsum('xpi,pi->xp', ao[1:, :, p0:p1],
ao_dm0[:, p0:p1]) * 2
# aow ~ rho1 ~ d/dR1
aow = numpy.einsum('pi,xp->xpi', ao[0], weight * frr * rho1)
_d1d2_dot_(vmat[ia], mol, ao[1:4], aow, mask, ao_loc, False)
ao_dm0 = aow = None
for ia in range(mol.natm):
p0, p1 = aoslices[ia][2:]
vmat[ia, :, :, :, p0:p1] += ipip[:, :, :, p0:p1]
elif xctype == 'GGA':
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[:4], mo_coeff, mo_occ, mask, 'GGA')
vxc, fxc = ni.eval_xc(mf.xc, rho, 0, deriv=2)[1:3]
wv = numint._rks_gga_wv0(rho, vxc, weight)
aow = rks_grad._make_dR_dao_w(ao, wv)
_d1d2_dot_(ipip, mol, aow, ao[1:4], mask, ao_loc, False)
ao_dm0 = [
numint._dot_ao_dm(mol, ao[i], dm0, mask, shls_slice, ao_loc)
for i in range(4)
]
for ia in range(mol.natm):
wv = dR_rho1 = _make_dR_rho1(ao, ao_dm0, ia, aoslices)
wv[0] = numint._rks_gga_wv1(rho, dR_rho1[0], vxc, fxc, weight)
wv[1] = numint._rks_gga_wv1(rho, dR_rho1[1], vxc, fxc, weight)
wv[2] = numint._rks_gga_wv1(rho, dR_rho1[2], vxc, fxc, weight)
aow = rks_grad._make_dR_dao_w(ao, wv[0])
rks_grad._d1_dot_(vmat[ia, 0], mol, aow, ao[0], mask, ao_loc,
True)
aow = rks_grad._make_dR_dao_w(ao, wv[1])
rks_grad._d1_dot_(vmat[ia, 1], mol, aow, ao[0], mask, ao_loc,
True)
aow = rks_grad._make_dR_dao_w(ao, wv[2])
rks_grad._d1_dot_(vmat[ia, 2], mol, aow, ao[0], mask, ao_loc,
True)
aow = numpy.einsum('npi,Xnp->Xpi', ao[:4], wv)
_d1d2_dot_(vmat[ia], mol, ao[1:4], aow, mask, ao_loc, False)
ao_dm0 = aow = None
for ia in range(mol.natm):
p0, p1 = aoslices[ia][2:]
vmat[ia, :, :, :, p0:p1] += ipip[:, :, :, p0:p1]
vmat[ia, :, :, :, p0:p1] += ipip[:, :, p0:p1].transpose(1, 0, 3, 2)
elif xctype == 'MGGA':
raise NotImplementedError('meta-GGA')
return vmat
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 _get_vxc_deriv1(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)
aoslices = mol.aoslice_by_atom()
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
dm0 = mf.make_rdm1(mo_coeff, mo_occ)
vmat = numpy.zeros((mol.natm,3,nao,nao))
max_memory = max(2000, max_memory-vmat.size*8/1e6)
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, mo_occ, mask, 'LDA')
vxc, fxc = ni.eval_xc(mf.xc, rho, 0, deriv=2)[1:3]
vrho = vxc[0]
frr = fxc[0]
ao_dm0 = numint._dot_ao_dm(mol, ao[0], dm0, mask, shls_slice, ao_loc)
aow1 = numpy.einsum('xpi,p->xpi', ao[1:], weight*vrho)
for ia in range(mol.natm):
p0, p1 = aoslices[ia][2:]
# First order density = rho1 * 2. *2 is not applied because + c.c. in the end
rho1 = numpy.einsum('xpi,pi->xp', ao[1:,:,p0:p1], ao_dm0[:,p0:p1])
aow = numpy.einsum('pi,xp->xpi', ao[0], weight*frr*rho1)
aow[:,:,p0:p1] += aow1[:,:,p0:p1]
rks_grad._d1_dot_(vmat[ia], mol, aow, ao[0], mask, ao_loc, True)
ao_dm0 = aow = aow1 = None
for ia in range(mol.natm):
vmat[ia] = -vmat[ia] - vmat[ia].transpose(0,2,1)
elif xctype == 'GGA':
ao_deriv = 2
v_ip = numpy.zeros((3,nao,nao))
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, fxc = ni.eval_xc(mf.xc, rho, 0, deriv=2)[1:3]
wv = numint._rks_gga_wv0(rho, vxc, weight)
rks_grad._gga_grad_sum_(v_ip, mol, ao, wv, mask, ao_loc)
ao_dm0 = [numint._dot_ao_dm(mol, ao[i], dm0, mask, shls_slice, ao_loc)
for i in range(4)]
for ia in range(mol.natm):
wv = dR_rho1 = _make_dR_rho1(ao, ao_dm0, ia, aoslices)
wv[0] = numint._rks_gga_wv1(rho, dR_rho1[0], vxc, fxc, weight)
wv[1] = numint._rks_gga_wv1(rho, dR_rho1[1], vxc, fxc, weight)
wv[2] = numint._rks_gga_wv1(rho, dR_rho1[2], vxc, fxc, weight)
aow = numpy.einsum('npi,Xnp->Xpi', ao[:4], wv)
rks_grad._d1_dot_(vmat[ia], mol, aow, ao[0], mask, ao_loc, True)
ao_dm0 = aow = None
for ia in range(mol.natm):
p0, p1 = aoslices[ia][2:]
vmat[ia,:,p0:p1] += v_ip[:,p0:p1]
vmat[ia] = -vmat[ia] - vmat[ia].transpose(0,2,1)
elif xctype == 'MGGA':
raise NotImplementedError('meta-GGA')
return vmat
def _get_vxc_deriv2(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)
aoslices = mol.aoslice_by_atom()
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
dm0 = mf.make_rdm1(mo_coeff, mo_occ)
vmat = numpy.zeros((mol.natm,3,3,nao,nao))
ipip = numpy.zeros((3,3,nao,nao))
if xctype == 'LDA':
ao_deriv = 1
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
rho = ni.eval_rho2(mol, ao[0], mo_coeff, mo_occ, mask, 'LDA')
vxc, fxc = ni.eval_xc(mf.xc, rho, 0, deriv=2)[1:3]
vrho = vxc[0]
frr = fxc[0]
aow = numpy.einsum('xpi,p->xpi', ao[1:4], weight*vrho)
_d1d2_dot_(ipip, mol, aow, ao[1:4], mask, ao_loc, False)
ao_dm0 = numint._dot_ao_dm(mol, ao[0], dm0, mask, shls_slice, ao_loc)
for ia in range(mol.natm):
p0, p1 = aoslices[ia][2:]
# *2 for \nabla|ket> in rho1
rho1 = numpy.einsum('xpi,pi->xp', ao[1:,:,p0:p1], ao_dm0[:,p0:p1]) * 2
# aow ~ rho1 ~ d/dR1
aow = numpy.einsum('pi,xp->xpi', ao[0], weight*frr*rho1)
_d1d2_dot_(vmat[ia], mol, ao[1:4], aow, mask, ao_loc, False)
ao_dm0 = aow = None
for ia in range(mol.natm):
p0, p1 = aoslices[ia][2:]
vmat[ia,:,:,:,p0:p1] += ipip[:,:,:,p0:p1]
elif xctype == 'GGA':
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[:4], mo_coeff, mo_occ, mask, 'GGA')
vxc, fxc = ni.eval_xc(mf.xc, rho, 0, deriv=2)[1:3]
wv = numint._rks_gga_wv0(rho, vxc, weight)
aow = rks_grad._make_dR_dao_w(ao, wv)
_d1d2_dot_(ipip, mol, aow, ao[1:4], mask, ao_loc, False)
ao_dm0 = [numint._dot_ao_dm(mol, ao[i], dm0, mask, shls_slice, ao_loc)
for i in range(4)]
for ia in range(mol.natm):
wv = dR_rho1 = _make_dR_rho1(ao, ao_dm0, ia, aoslices)
wv[0] = numint._rks_gga_wv1(rho, dR_rho1[0], vxc, fxc, weight)
wv[1] = numint._rks_gga_wv1(rho, dR_rho1[1], vxc, fxc, weight)
wv[2] = numint._rks_gga_wv1(rho, dR_rho1[2], vxc, fxc, weight)
aow = rks_grad._make_dR_dao_w(ao, wv[0])
rks_grad._d1_dot_(vmat[ia,0], mol, aow, ao[0], mask, ao_loc, True)
aow = rks_grad._make_dR_dao_w(ao, wv[1])
rks_grad._d1_dot_(vmat[ia,1], mol, aow, ao[0], mask, ao_loc, True)
aow = rks_grad._make_dR_dao_w(ao, wv[2])
rks_grad._d1_dot_(vmat[ia,2], mol, aow, ao[0], mask, ao_loc, True)
aow = numpy.einsum('npi,Xnp->Xpi', ao[:4], wv)
_d1d2_dot_(vmat[ia], mol, ao[1:4], aow, mask, ao_loc, False)
ao_dm0 = aow = None
for ia in range(mol.natm):
p0, p1 = aoslices[ia][2:]
vmat[ia,:,:,:,p0:p1] += ipip[:,:,:,p0:p1]
vmat[ia,:,:,:,p0:p1] += ipip[:,:,p0:p1].transpose(1,0,3,2)
elif xctype == 'MGGA':
raise NotImplementedError('meta-GGA')
return vmat
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 dia(magobj, gauge_orig=None):
mol = magobj.mol
mf = magobj._scf
mo_energy = mf.mo_energy
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
orbo = mo_coeff[:, mo_occ > 0]
dm0 = numpy.dot(orbo, orbo.T) * 2
dm0 = lib.tag_array(dm0, mo_coeff=mo_coeff, mo_occ=mo_occ)
dme0 = numpy.dot(orbo * mo_energy[mo_occ > 0], orbo.T) * 2
e2 = rhf_mag._get_dia_1e(magobj, gauge_orig, dm0, dme0)
if gauge_orig is not None:
return -e2
# Computing the 2nd order Vxc integrals from GIAO
grids = mf.grids
ni = mf._numint
xc_code = mf.xc
xctype = ni._xc_type(xc_code)
omega, alpha, hyb = ni.rsh_and_hybrid_coeff(xc_code, mol.spin)
make_rho, nset, nao = ni._gen_rho_evaluator(mol, dm0, hermi=1)
ngrids = len(grids.weights)
mem_now = lib.current_memory()[0]
max_memory = max(2000, mf.max_memory * .9 - mem_now)
BLKSIZE = numint.BLKSIZE
blksize = min(
int(max_memory / 12 * 1e6 / 8 / nao / BLKSIZE) * BLKSIZE, ngrids)
vmat = numpy.zeros((3, 3, nao, nao))
if xctype == 'LDA':
ao_deriv = 0
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory,
blksize=blksize):
rho = make_rho(0, ao, mask, 'LDA')
vxc = ni.eval_xc(xc_code, rho, 0, deriv=1)[1]
vrho = vxc[0]
r_ao = numpy.einsum('pi,px->pxi', ao, coords)
aow = numpy.einsum('pxi,p,p->pxi', r_ao, weight, vrho)
vmat += lib.einsum('pxi,pyj->xyij', r_ao, aow)
rho = vxc = vrho = aow = None
elif xctype == 'GGA':
ao_deriv = 1
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory,
blksize=blksize):
rho = make_rho(0, ao, mask, 'GGA')
vxc = ni.eval_xc(xc_code, rho, 0, deriv=1)[1]
wv = numint._rks_gga_wv0(rho, vxc, weight)
# Computing \nabla (r * AO) = r * \nabla AO + [\nabla,r]_- * AO
r_ao = numpy.einsum('npi,px->npxi', ao, coords)
r_ao[1, :, 0] += ao[0]
r_ao[2, :, 1] += ao[0]
r_ao[3, :, 2] += ao[0]
aow = numpy.einsum('npxi,np->pxi', r_ao, wv)
vmat += lib.einsum('pxi,pyj->xyij', r_ao[0], aow)
rho = vxc = vrho = vsigma = wv = aow = None
vmat = vmat + vmat.transpose(0, 1, 3, 2)
elif xctype == 'MGGA':
raise NotImplementedError('meta-GGA')
vmat = _add_giao_phase(mol, vmat)
e2 += numpy.einsum('qp,xypq->xy', dm0, vmat)
vmat = None
e2 = e2.ravel()
# Handle the hybrid functional and the range-separated functional
if abs(hyb) > 1e-10:
vs = jk.get_jk(mol, [dm0] * 3,
['ijkl,ji->s2kl', 'ijkl,jk->s1il', 'ijkl,li->s1kj'],
'int2e_gg1',
's4',
9,
hermi=1)
e2 += numpy.einsum('xpq,qp->x', vs[0], dm0)
e2 -= numpy.einsum('xpq,qp->x', vs[1], dm0) * .25 * hyb
e2 -= numpy.einsum('xpq,qp->x', vs[2], dm0) * .25 * hyb
vk = jk.get_jk(mol,
dm0,
'ijkl,jk->s1il',
'int2e_g1g2',
'aa4',
9,
hermi=0)
e2 -= numpy.einsum('xpq,qp->x', vk, dm0) * .5 * hyb
if abs(omega) > 1e-10:
with mol.with_range_coulomb(omega):
vs = jk.get_jk(mol, [dm0] * 2,
['ijkl,jk->s1il', 'ijkl,li->s1kj'],
'int2e_gg1',
's4',
9,
hermi=1)
e2 -= numpy.einsum('xpq,qp->x', vs[0],
dm0) * .25 * (alpha - hyb)
e2 -= numpy.einsum('xpq,qp->x', vs[1],
dm0) * .25 * (alpha - hyb)
vk = jk.get_jk(mol,
dm0,
'ijkl,jk->s1il',
'int2e_g1g2',
'aa4',
9,
hermi=0)
e2 -= numpy.einsum('xpq,qp->x', vk, dm0) * .5 * (alpha - hyb)
else:
vj = jk.get_jk(mol,
dm0,
'ijkl,ji->s2kl',
'int2e_gg1',
's4',
9,
hermi=1)
e2 += numpy.einsum('xpq,qp->x', vj, dm0)
return -e2.reshape(3, 3)
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(ni,
cell,
grids,
xc_code,
dms,
kpts,
kpts_band=None,
relativity=0,
hermi=1,
max_memory=2000,
verbose=None):
xctype = ni._xc_type(xc_code)
make_rho, nset, nao = ni._gen_rho_evaluator(cell, dms, hermi)
ao_loc = cell.ao_loc_nr()
nkpts = len(kpts)
vmat = np.zeros((3, nset, nkpts, nao, nao), dtype=dms.dtype)
if xctype == 'LDA':
ao_deriv = 1
for ao_k1, ao_k2, mask, weight, coords \
in ni.block_loop(cell, grids, nao, ao_deriv, kpts, kpts_band, max_memory):
ao_k1 = np.asarray(ao_k1)
ao_k2 = np.asarray(ao_k2)
for i in range(nset):
rho = make_rho(i, ao_k2[:, 0], mask, xctype)
vxc = ni.eval_xc(xc_code, rho, 0, relativity, 1)[1]
vrho = vxc[0]
aow = np.einsum('xpi,p->xpi', ao_k1[:, 0], weight * vrho)
for kn in range(nkpts):
rks_grad._d1_dot_(vmat[:, i, kn], cell, ao_k1[kn, 1:4],
aow[kn], mask, ao_loc, True)
rho = vrho = aow = None
elif xctype == 'GGA':
ao_deriv = 2
for ao_k1, ao_k2, mask, weight, coords \
in ni.block_loop(cell, grids, nao, ao_deriv, kpts, kpts_band, max_memory):
ao_k1 = np.asarray(ao_k1)
ao_k2 = np.asarray(ao_k2)
for i in range(nset):
rho = make_rho(i, ao_k2[:, :4], mask, xctype)
vxc = ni.eval_xc(xc_code,
rho,
0,
relativity,
1,
verbose=verbose)[1]
wv = numint._rks_gga_wv0(rho, vxc, weight)
for kn in range(nkpts):
rks_grad._gga_grad_sum_(vmat[:, i, kn], cell, ao_k1[kn],
wv, mask, ao_loc)
rho = vxc = wv = None
elif xctype == 'NLC':
raise NotImplementedError("NLC")
else:
raise NotImplementedError("metaGGA")
if nset == 1:
return -vmat[:, 0]
else:
return -vmat
def _get_vxc_deriv1(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)
aoslices = mol.aoslice_by_atom()
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
dm0 = mf.make_rdm1(mo_coeff, mo_occ)
v_ip = numpy.zeros((3, nao, nao))
vmat = numpy.zeros((mol.natm, 3, nao, nao))
max_memory = max(2000, max_memory - vmat.size * 8 / 1e6)
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, mo_occ, mask, xctype)
vxc, fxc = ni.eval_xc(mf.xc, rho, 0, deriv=2)[1:3]
vrho = vxc[0]
frr = fxc[0]
aow = numint._scale_ao(ao[0], weight * vrho)
rks_grad._d1_dot_(v_ip, mol, ao[1:4], aow, mask, ao_loc, True)
ao_dm0 = numint._dot_ao_dm(mol, ao[0], dm0, mask, shls_slice,
ao_loc)
for ia in range(mol.natm):
p0, p1 = aoslices[ia][2:]
# First order density = rho1 * 2. *2 is not applied because + c.c. in the end
rho1 = numpy.einsum('xpi,pi->xp', ao[1:, :, p0:p1],
ao_dm0[:, p0:p1])
wv = weight * frr * rho1
aow = [numint._scale_ao(ao[0], wv[i]) for i in range(3)]
rks_grad._d1_dot_(vmat[ia], mol, aow, ao[0], mask, ao_loc,
True)
ao_dm0 = aow = None
elif xctype == 'GGA':
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[:4], mo_coeff, mo_occ, mask, xctype)
vxc, fxc = ni.eval_xc(mf.xc, rho, 0, deriv=2)[1:3]
wv = numint._rks_gga_wv0(rho, vxc, weight)
rks_grad._gga_grad_sum_(v_ip, mol, ao, wv, mask, ao_loc)
ao_dm0 = [
numint._dot_ao_dm(mol, ao[i], dm0, mask, shls_slice, ao_loc)
for i in range(4)
]
for ia in range(mol.natm):
wv = dR_rho1 = _make_dR_rho1(ao, ao_dm0, ia, aoslices)
wv[0] = numint._rks_gga_wv1(rho, dR_rho1[0], vxc, fxc, weight)
wv[1] = numint._rks_gga_wv1(rho, dR_rho1[1], vxc, fxc, weight)
wv[2] = numint._rks_gga_wv1(rho, dR_rho1[2], vxc, fxc, weight)
aow = [numint._scale_ao(ao[:4], wv[i, :4]) for i in range(3)]
rks_grad._d1_dot_(vmat[ia], mol, aow, ao[0], mask, ao_loc,
True)
ao_dm0 = aow = None
elif xctype == 'MGGA':
if grids.level < 5:
logger.warn(mol, 'MGGA Hessian is sensitive to dft grids.')
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[:10], mo_coeff, mo_occ, mask, xctype)
vxc, fxc = ni.eval_xc(mf.xc, rho, 0, deriv=2)[1:3]
wv = numint._rks_mgga_wv0(rho, vxc, weight)
rks_grad._gga_grad_sum_(v_ip, mol, ao, wv, mask, ao_loc)
# *2 because wv[5] is scaled by 0.5 in _rks_mgga_wv0
rks_grad._tau_grad_dot_(v_ip, mol, ao, wv[5] * 2, mask, ao_loc,
True)
ao_dm0 = [
numint._dot_ao_dm(mol, ao[i], dm0, mask, shls_slice, ao_loc)
for i in range(4)
]
for ia in range(mol.natm):
wv = dR_rho1 = _make_dR_rho1(ao, ao_dm0, ia, aoslices, xctype)
wv[0] = numint._rks_mgga_wv1(rho, dR_rho1[0], vxc, fxc, weight)
wv[1] = numint._rks_mgga_wv1(rho, dR_rho1[1], vxc, fxc, weight)
wv[2] = numint._rks_mgga_wv1(rho, dR_rho1[2], vxc, fxc, weight)
aow = [numint._scale_ao(ao[:4], wv[i, :4]) for i in range(3)]
rks_grad._d1_dot_(vmat[ia], mol, aow, ao[0], mask, ao_loc,
True)
for j in range(1, 4):
aow = [numint._scale_ao(ao[j], wv[i, 5]) for i in range(3)]
rks_grad._d1_dot_(vmat[ia], mol, aow, ao[j], mask, ao_loc,
True)
ao_dm0 = aow = None
for ia in range(mol.natm):
p0, p1 = aoslices[ia][2:]
vmat[ia, :, p0:p1] += v_ip[:, p0:p1]
vmat[ia] = -vmat[ia] - vmat[ia].transpose(0, 2, 1)
return vmat
def _get_vxc_deriv2(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)
aoslices = mol.aoslice_by_atom()
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
dm0 = mf.make_rdm1(mo_coeff, mo_occ)
vmat = numpy.zeros((mol.natm, 3, 3, nao, nao))
ipip = numpy.zeros((3, 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):
rho = ni.eval_rho2(mol, ao[0], mo_coeff, mo_occ, mask, xctype)
vxc, fxc = ni.eval_xc(mf.xc, rho, 0, deriv=2)[1:3]
vrho = vxc[0]
frr = fxc[0]
wv = weight * vrho
aow = [numint._scale_ao(ao[i], wv) for i in range(1, 4)]
_d1d2_dot_(ipip, mol, aow, ao[1:4], mask, ao_loc, False)
ao_dm0 = numint._dot_ao_dm(mol, ao[0], dm0, mask, shls_slice,
ao_loc)
for ia in range(mol.natm):
p0, p1 = aoslices[ia][2:]
# *2 for \nabla|ket> in rho1
rho1 = numpy.einsum('xpi,pi->xp', ao[1:, :, p0:p1],
ao_dm0[:, p0:p1]) * 2
# aow ~ rho1 ~ d/dR1
wv = weight * frr * rho1
aow = [numint._scale_ao(ao[0], wv[i]) for i in range(3)]
_d1d2_dot_(vmat[ia], mol, ao[1:4], aow, mask, ao_loc, False)
ao_dm0 = aow = None
for ia in range(mol.natm):
p0, p1 = aoslices[ia][2:]
vmat[ia, :, :, :, p0:p1] += ipip[:, :, :, p0:p1]
elif xctype == 'GGA':
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[:4], mo_coeff, mo_occ, mask, xctype)
vxc, fxc = ni.eval_xc(mf.xc, rho, 0, deriv=2)[1:3]
wv = numint._rks_gga_wv0(rho, vxc, weight)
aow = rks_grad._make_dR_dao_w(ao, wv)
_d1d2_dot_(ipip, mol, aow, ao[1:4], mask, ao_loc, False)
ao_dm0 = [
numint._dot_ao_dm(mol, ao[i], dm0, mask, shls_slice, ao_loc)
for i in range(4)
]
for ia in range(mol.natm):
wv = dR_rho1 = _make_dR_rho1(ao, ao_dm0, ia, aoslices)
for i in range(3):
wv[i] = numint._rks_gga_wv1(rho, dR_rho1[i], vxc, fxc,
weight)
aow = rks_grad._make_dR_dao_w(ao, wv[i])
rks_grad._d1_dot_(vmat[ia, i], mol, aow, ao[0], mask,
ao_loc, True)
aow = [numint._scale_ao(ao[:4], wv[i, :4]) for i in range(3)]
_d1d2_dot_(vmat[ia], mol, ao[1:4], aow, mask, ao_loc, False)
ao_dm0 = aow = None
for ia in range(mol.natm):
p0, p1 = aoslices[ia][2:]
vmat[ia, :, :, :, p0:p1] += ipip[:, :, :, p0:p1]
vmat[ia, :, :, :, p0:p1] += ipip[:, :, p0:p1].transpose(1, 0, 3, 2)
elif xctype == 'MGGA':
XX, XY, XZ = 4, 5, 6
YX, YY, YZ = 5, 7, 8
ZX, ZY, ZZ = 6, 8, 9
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[:10], mo_coeff, mo_occ, mask, xctype)
vxc, fxc = ni.eval_xc(mf.xc, rho, 0, deriv=2)[1:3]
wv = numint._rks_mgga_wv0(rho, vxc, weight)
aow = rks_grad._make_dR_dao_w(ao, wv)
_d1d2_dot_(ipip, mol, aow, ao[1:4], mask, ao_loc, False)
aow = [numint._scale_ao(ao[i], wv[5]) for i in range(4, 10)]
_d1d2_dot_(ipip, mol, [aow[0], aow[1], aow[2]],
[ao[XX], ao[XY], ao[XZ]], mask, ao_loc, False)
_d1d2_dot_(ipip, mol, [aow[1], aow[3], aow[4]],
[ao[YX], ao[YY], ao[YZ]], mask, ao_loc, False)
_d1d2_dot_(ipip, mol, [aow[2], aow[4], aow[5]],
[ao[ZX], ao[ZY], ao[ZZ]], mask, ao_loc, False)
ao_dm0 = [
numint._dot_ao_dm(mol, ao[i], dm0, mask, shls_slice, ao_loc)
for i in range(4)
]
for ia in range(mol.natm):
wv = dR_rho1 = _make_dR_rho1(ao, ao_dm0, ia, aoslices, xctype)
for i in range(3):
wv[i] = numint._rks_mgga_wv1(rho, dR_rho1[i], vxc, fxc,
weight)
aow = rks_grad._make_dR_dao_w(ao, wv[i])
rks_grad._d1_dot_(vmat[ia, i], mol, aow, ao[0], mask,
ao_loc, True)
aow = [numint._scale_ao(ao[:4], wv[i, :4]) for i in range(3)]
_d1d2_dot_(vmat[ia], mol, ao[1:4], aow, mask, ao_loc, False)
# *2 because wv[5] is scaled by 0.5 in _rks_mgga_wv1
wv[:, 5] *= 2
aow = [numint._scale_ao(ao[1], wv[i, 5]) for i in range(3)]
_d1d2_dot_(vmat[ia], mol, [ao[XX], ao[XY], ao[XZ]], aow, mask,
ao_loc, False)
aow = [numint._scale_ao(ao[2], wv[i, 5]) for i in range(3)]
_d1d2_dot_(vmat[ia], mol, [ao[YX], ao[YY], ao[YZ]], aow, mask,
ao_loc, False)
aow = [numint._scale_ao(ao[3], wv[i, 5]) for i in range(3)]
_d1d2_dot_(vmat[ia], mol, [ao[ZX], ao[ZY], ao[ZZ]], aow, mask,
ao_loc, False)
for ia in range(mol.natm):
p0, p1 = aoslices[ia][2:]
vmat[ia, :, :, :, p0:p1] += ipip[:, :, :, p0:p1]
vmat[ia, :, :, :, p0:p1] += ipip[:, :, p0:p1].transpose(1, 0, 3, 2)
return vmat
def _get_vxc_deriv1(hessobj, mo_coeff, mo_occ, max_memory):
"""" This functions is slightly different from hessian.rks._get_vxc_deriv1 in that <\nabla u|Vxc|v> is removed"""
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)
aoslices = mol.aoslice_by_atom()
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
dm0 = mf.make_rdm1(mo_coeff, mo_occ)
vmat = np.zeros((mol.natm,3,nao,nao))
max_memory = max(2000, max_memory-vmat.size*8/1e6)
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, mo_occ, mask, 'LDA')
vxc, fxc = ni.eval_xc(mf.xc, rho, 0, deriv=2)[1:3]
frr = fxc[0]
ao_dm0 = numint._dot_ao_dm(mol, ao[0], dm0, mask, shls_slice, ao_loc)
for ia in range(mol.natm):
p0, p1 = aoslices[ia][2:]
rho1 = np.einsum('xpi,pi->xp', ao[1:,:,p0:p1], ao_dm0[:,p0:p1])
aow = np.einsum('pi,xp->xpi', ao[0], weight*frr*rho1)
rks_grad._d1_dot_(vmat[ia], mol, aow, ao[0], mask, ao_loc, True)
ao_dm0 = aow = None
for ia in range(mol.natm):
vmat[ia] = -vmat[ia] - vmat[ia].transpose(0,2,1)
elif xctype == 'GGA':
ao_deriv = 2
# v_ip = np.zeros((3,nao,nao))
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, fxc = ni.eval_xc(mf.xc, rho, 0, deriv=2)[1:3]
wv = numint._rks_gga_wv0(rho, vxc, weight)
# rks_grad._gga_grad_sum_(v_ip, mol, ao, wv, mask, ao_loc)
ao_dm0 = [numint._dot_ao_dm(mol, ao[i], dm0, mask, shls_slice, ao_loc)
for i in range(4)]
for ia in range(mol.natm):
wv = dR_rho1 = rks_hess._make_dR_rho1(ao, ao_dm0, ia, aoslices)
wv[0] = numint._rks_gga_wv1(rho, dR_rho1[0], vxc, fxc, weight)
wv[1] = numint._rks_gga_wv1(rho, dR_rho1[1], vxc, fxc, weight)
wv[2] = numint._rks_gga_wv1(rho, dR_rho1[2], vxc, fxc, weight)
aow = np.einsum('npi,Xnp->Xpi', ao[:4], wv)
rks_grad._d1_dot_(vmat[ia], mol, aow, ao[0], mask, ao_loc, True)
ao_dm0 = aow = None
for ia in range(mol.natm):
vmat[ia] = -vmat[ia] - vmat[ia].transpose(0,2,1)
elif xctype == 'MGGA':
raise NotImplementedError('meta-GGA')
return vmat
def get_vxc(ni,
mol,
grids,
xc_code,
dms,
relativity=0,
hermi=1,
max_memory=2000,
verbose=None):
xctype = ni._xc_type(xc_code)
make_rho, nset, nao = ni._gen_rho_evaluator(mol, dms, hermi)
ao_loc = mol.ao_loc_nr()
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):
for idm in range(nset):
rho = make_rho(idm, ao[0], mask, xctype)
vxc = ni.eval_xc(xc_code,
rho,
0,
relativity,
1,
verbose=verbose)[1]
vrho = vxc[0]
#:aow = numpy.einsum('pi,p->pi', ao[0], weight*vrho)
aow = numint._scale_ao(ao[0], weight * vrho)
_d1_dot_(vmat[idm], mol, ao[1:4], aow, mask, ao_loc, True)
elif xctype == 'GGA':
ao_deriv = 2
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
for idm in range(nset):
rho = make_rho(idm, ao[:4], mask, xctype)
vxc = ni.eval_xc(xc_code,
rho,
0,
relativity,
1,
verbose=verbose)[1]
wv = numint._rks_gga_wv0(rho, vxc, weight)
_gga_grad_sum_(vmat[idm], mol, ao, wv, mask, ao_loc)
elif xctype == 'NLC':
raise NotImplementedError('NLC')
elif xctype == 'MGGA':
ao_deriv = 2
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
for idm in range(nset):
rho = make_rho(idm, ao[:10], mask, xctype)
vxc = ni.eval_xc(xc_code,
rho,
0,
relativity,
1,
verbose=verbose)[1]
wv = numint._rks_mgga_wv0(rho, vxc, weight)
_gga_grad_sum_(vmat[idm], mol, ao, wv, mask, ao_loc)
# *2 because wv[5] is scaled by 0.5 in _rks_mgga_wv0
_tau_grad_dot_(vmat[idm], mol, ao, wv[5] * 2, mask, ao_loc,
True)
exc = None
if nset == 1:
vmat = vmat[0]
# - sign because nabla_X = -nabla_x
return exc, -vmat
def exc_rks(mf,
emb_dm,
dm,
relativity=0,
hermi=0,
max_memory=2000,
verbose=None):
ni = mf._numint
mol = mf.mol
grids = mf.grids
xc_code = mf.xc
xctype = ni._xc_type(xc_code)
make_rho_emb, nset, nao = ni._gen_rho_evaluator(mol, emb_dm, hermi)
make_rho_sub, nset_2, nao_2 = ni._gen_rho_evaluator(mol, dm, hermi)
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
nelec = np.zeros(nset)
excsum = np.zeros(nset)
vmat = np.zeros((nset, nao, nao))
aow = None
if xctype == 'LDA':
ao_deriv = 0
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
aow = np.ndarray(ao.shape, order='F', buffer=aow)
for idm in range(nset):
rho_emb = make_rho_emb(idm, ao, mask, 'LDA')
rho_sub = make_rho_sub(idm, ao, mask, 'LDA')
exc, vxc = ni.eval_xc(xc_code, rho_emb, 0, relativity, 1,
verbose)[:2]
vrho = vxc[0]
den = rho_sub * weight
nelec[idm] += den.sum()
excsum[idm] += np.dot(den, exc)
# *.5 because vmat + vmat.T
aow = np.einsum('pi,p->pi', ao, .5 * weight * vrho, out=aow)
vmat[idm] += numint._dot_ao_ao(mol, ao, aow, mask, shls_slice,
ao_loc)
rho_emb = rho_sub = exc = vxc = vrho = None
elif xctype == 'GGA':
ao_deriv = 1
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
ngrid = weight.size
aow = np.ndarray(ao[0].shape, order='F', buffer=aow)
for idm in range(nset):
rho_emb = make_rho_emb(idm, ao, mask, 'GGA')
rho_sub = make_rho_sub(idm, ao, mask, 'GGA')
exc, vxc = ni.eval_xc(xc_code, rho_emb, 0, relativity, 1,
verbose)[:2]
den = rho_sub[0] * weight
nelec[idm] += den.sum()
excsum[idm] += np.dot(den, exc)
# ref eval_mat function
wv = numint._rks_gga_wv0(rho_sub, vxc, weight)
aow = np.einsum('npi,np->pi', ao, wv, out=aow)
vmat[idm] += numint._dot_ao_ao(mol, ao[0], aow, mask,
shls_slice, ao_loc)
rho_emb = rho_sub = exc = vxc = wv = None
elif xctype == 'NLC':
nlc_pars = ni.nlc_coeff(xc_code[:-6])
if nlc_pars == [0, 0]:
raise NotImplementedError('VV10 cannot be used with %s. '
'The supported functionals are %s' %
(xc_code[:-6], ni.libxc.VV10_XC))
ao_deriv = 1
vvrho = np.empty([nset, 4, 0])
vvweight = np.empty([nset, 0])
vvcoords = np.empty([nset, 0, 3])
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
rhotmp = np.empty([0, 4, weight.size])
weighttmp = np.empty([0, weight.size])
coordstmp = np.empty([0, weight.size, 3])
for idm in range(nset):
rho_emb = make_rho_emb(idm, ao, mask, 'GGA')
rho_sub = make_rho_sub(idm, ao, mask, 'GGA')
rho_emb = np.expand_dims(rho, axis=0)
rhotmp = np.concatenate((rhotmp, rho_emb), axis=0)
weighttmp = np.concatenate(
(weighttmp, np.expand_dims(weight, axis=0)), axis=0)
coordstmp = np.concatenate(
(coordstmp, np.expand_dims(coords, axis=0)), axis=0)
rho = None
vvrho = np.concatenate((vvrho, rhotmp), axis=2)
vvweight = np.concatenate((vvweight, weighttmp), axis=1)
vvcoords = np.concatenate((vvcoords, coordstmp), axis=1)
rhotmp = weighttmp = coordstmp = None
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
ngrid = weight.size
aow = np.ndarray(ao[0].shape, order='F', buffer=aow)
for idm in range(nset):
rho_emb = make_rho_emb(idm, ao, mask, 'GGA')
rho_sub = make_rho_sub(idm, ao, mask, 'GGA')
exc, vxc = numint._vv10nlc(rho_emb, coords, vvrho[idm],
vvweight[idm], vvcoords[idm],
nlc_pars)
den = rho_sub[0] * weight
nelec[idm] += den.sum()
excsum[idm] += np.dot(den, exc)
# ref eval_mat function
wv = numint._rks_gga_wv0(rho_emb, vxc, weight)
aow = np.einsum('npi,np->pi', ao, wv, out=aow)
vmat[idm] += numint._dot_ao_ao(mol, ao[0], aow, mask,
shls_slice, ao_loc)
rho = exc = vxc = wv = None
vvrho = vvweight = vvcoords = None
elif xctype == 'MGGA':
if (any(x in xc_code.upper() for x in ('CC06', 'CS', 'BR89', 'MK00'))):
raise NotImplementedError('laplacian in meta-GGA method')
ao_deriv = 2
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
ngrid = weight.size
aow = np.ndarray(ao[0].shape, order='F', buffer=aow)
for idm in range(nset):
rho_emb = make_rho_emb(idm, ao, mask, 'MGGA')
rho_sub = make_rho_sub(idm, ao, mask, 'MGGA')
exc, vxc = ni.eval_xc(xc_code, rho_emb, 0, relativity, 1,
verbose)[:2]
vrho, vsigma, vlapl, vtau = vxc[:4]
den = rho_sub[0] * weight
nelec[idm] += den.sum()
excsum[idm] += np.dot(den, exc)
wv = numint._rks_gga_wv0(rho_emb, vxc, weight)
aow = np.einsum('npi,np->pi', ao[:4], wv, out=aow)
vmat[idm] += numint._dot_ao_ao(mol, ao[0], aow, mask,
shls_slice, ao_loc)
# FIXME: .5 * .5 First 0.5 for v+v.T symmetrization.
# Second 0.5 is due to the Libxc convention tau = 1/2 \nabla\phi\dot\nabla\phi
wv = (.5 * .5 * weight * vtau).reshape(-1, 1)
vmat[idm] += numint._dot_ao_ao(mol, ao[1], wv * ao[1], mask,
shls_slice, ao_loc)
vmat[idm] += numint._dot_ao_ao(mol, ao[2], wv * ao[2], mask,
shls_slice, ao_loc)
vmat[idm] += numint._dot_ao_ao(mol, ao[3], wv * ao[3], mask,
shls_slice, ao_loc)
rho_emb = rho_sub = exc = vxc = vrho = vsigma = wv = None
for i in range(nset):
vmat[i] = vmat[i] + vmat[i].T
if nset == 1:
nelec = nelec[0]
excsum = excsum[0]
vmat = vmat.reshape(nao, nao)
return nelec, excsum, vmat