def test_mgga_deriv1(self):
ng = 7
xctype = 'MGGA'
np.random.seed(8)
rho = np.random.rand(2, 5, ng)
weight = 1
exc, vxc, fxc, kxc = eval_xc(f'R-{xctype}', ng)
ref = v6to5(numint._rks_mgga_wv0(v5to6(rho[0]), vxc, weight))
ref[0] *= 2
ref[4] *= 4
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 = v6to5(np.array(numint._uks_mgga_wv0(v5to6(rho), vxc, weight)))
ref[:, 0] *= 2
ref[:, 4] *= 4
v1 = xc_deriv.transform_vxc(rho, vxc, xctype, spin=1)
self.assertAlmostEqual(abs(v1 - ref).max(), 0, 12)
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':
def lda_sum_(vmat, ao, wv, mask):
aow = numint._scale_ao(ao[0], wv)
for k in range(4):
vmat[k] += numint._dot_ao_ao(mol, ao[k], aow, mask, shls_slice,
ao_loc)
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,
xctype),
ni.eval_rho2(mol, ao[0], mo_coeff[1], mo_occ[1], mask,
xctype))
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, xctype)
rho1b = ni.eval_rho(mol, ao[0], dmvo[1], mask, xctype)
lda_sum_(f1vo[0], ao, u_u * rho1a + u_d * rho1b, mask)
lda_sum_(f1vo[1], ao, u_d * rho1a + d_d * rho1b, mask)
if dmoo is not None:
rho2a = ni.eval_rho(mol, ao[0], dmoo[0], mask, xctype)
rho2b = ni.eval_rho(mol, ao[0], dmoo[1], mask, xctype)
lda_sum_(f1oo[0], ao, u_u * rho2a + u_d * rho2b, mask)
lda_sum_(f1oo[1], ao, u_d * rho2a + d_d * rho2b, mask)
if with_vxc:
vrho = vxc[0].T * weight
lda_sum_(v1ao[0], ao, vrho[0], mask)
lda_sum_(v1ao[1], ao, vrho[1], mask)
if with_kxc:
u_u_u, u_u_d, u_d_d, d_d_d = kxc[0].T * weight
lda_sum_(
k1ao[0], ao, u_u_u * rho1a * rho1a +
u_u_d * rho1a * rho1b * 2 + u_d_d * rho1b * rho1b, mask)
lda_sum_(
k1ao[1], ao, u_u_d * rho1a * rho1a +
u_d_d * rho1a * rho1b * 2 + d_d_d * rho1b * rho1b, mask)
elif xctype == 'GGA':
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)
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, xctype),
ni.eval_rho2(mol, ao, mo_coeff[1], mo_occ[1], mask, xctype))
vxc, fxc, kxc = ni.eval_xc(xc_code, rho, 1, deriv=deriv)[1:]
rho1 = (ni.eval_rho(mol, ao, dmvo[0], mask, xctype),
ni.eval_rho(mol, ao, dmvo[1], mask, xctype))
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, xctype),
ni.eval_rho(mol, ao, dmoo[1], mask, xctype))
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
elif xctype == 'MGGA':
logger.warn(mol, 'More tests are needed for TD-MGGA')
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)
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, xctype),
ni.eval_rho2(mol, ao, mo_coeff[1], mo_occ[1], mask, xctype))
vxc, fxc, kxc = ni.eval_xc(xc_code, rho, 1, deriv=deriv)[1:]
rho1 = (ni.eval_rho(mol, ao, dmvo[0], mask, xctype),
ni.eval_rho(mol, ao, dmvo[1], mask, xctype))
wv = numint._uks_mgga_wv1(rho, rho1, vxc, fxc, weight)
mgga_sum_(f1vo[0], ao, wv[0], mask)
mgga_sum_(f1vo[1], ao, wv[1], mask)
if dmoo is not None:
rho2 = (ni.eval_rho(mol, ao, dmoo[0], mask, xctype),
ni.eval_rho(mol, ao, dmoo[1], mask, xctype))
wv = numint._uks_mgga_wv1(rho, rho2, vxc, fxc, weight)
mgga_sum_(f1oo[0], ao, wv[0], mask)
mgga_sum_(f1oo[1], ao, wv[1], mask)
if with_vxc:
wv = numint._uks_mgga_wv0(rho, vxc, weight)
mgga_sum_(v1ao[0], ao, wv[0], mask)
mgga_sum_(v1ao[1], ao, wv[1], mask)
if with_kxc:
wv = numint._uks_mgga_wv2(rho, rho1, fxc, kxc, weight)
mgga_sum_(k1ao[0], ao, wv[0], mask)
mgga_sum_(k1ao[1], ao, wv[1], mask)
vxc = fxc = kxc = rho = rho1 = None
elif xctype == 'HF':
pass
else:
raise NotImplementedError(f'td-uks for functional {xc_code}')
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[0].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()
dm0a, dm0b = mf.make_rdm1(mo_coeff, mo_occ)
vmata = numpy.zeros((mol.natm, 3, nao, nao))
vmatb = numpy.zeros((mol.natm, 3, nao, nao))
max_memory = max(2000, max_memory - (vmata.size + vmatb.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):
rhoa = ni.eval_rho2(mol, ao[0], mo_coeff[0], mo_occ[0], mask,
xctype)
rhob = ni.eval_rho2(mol, ao[0], mo_coeff[1], mo_occ[1], mask,
xctype)
vxc, fxc = ni.eval_xc(mf.xc, (rhoa, rhob), 1, deriv=2)[1:3]
vrho = vxc[0]
u_u, u_d, d_d = fxc[0].T
ao_dm0a = numint._dot_ao_dm(mol, ao[0], dm0a, mask, shls_slice,
ao_loc)
ao_dm0b = numint._dot_ao_dm(mol, ao[0], dm0b, mask, shls_slice,
ao_loc)
aow1a = numpy.einsum('xpi,p->xpi', ao[1:], weight * vrho[:, 0])
aow1b = numpy.einsum('xpi,p->xpi', ao[1:], weight * vrho[:, 1])
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
rho1a = numpy.einsum('xpi,pi->xp', ao[1:, :, p0:p1],
ao_dm0a[:, p0:p1])
rho1b = numpy.einsum('xpi,pi->xp', ao[1:, :, p0:p1],
ao_dm0b[:, p0:p1])
wv = u_u * rho1a + u_d * rho1b
wv *= weight
aow = numpy.einsum('pi,xp->xpi', ao[0], wv)
aow[:, :, p0:p1] += aow1a[:, :, p0:p1]
rks_grad._d1_dot_(vmata[ia], mol, aow, ao[0], mask, ao_loc,
True)
wv = u_d * rho1a + d_d * rho1b
wv *= weight
aow = numpy.einsum('pi,xp->xpi', ao[0], wv)
aow[:, :, p0:p1] += aow1b[:, :, p0:p1]
rks_grad._d1_dot_(vmatb[ia], mol, aow, ao[0], mask, ao_loc,
True)
ao_dm0a = ao_dm0b = aow = aow1a = aow1b = None
for ia in range(mol.natm):
vmata[ia] = -vmata[ia] - vmata[ia].transpose(0, 2, 1)
vmatb[ia] = -vmatb[ia] - vmatb[ia].transpose(0, 2, 1)
elif xctype == 'GGA':
ao_deriv = 2
vipa = numpy.zeros((3, nao, nao))
vipb = numpy.zeros((3, nao, nao))
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,
xctype)
rhob = ni.eval_rho2(mol, ao[:4], mo_coeff[1], mo_occ[1], mask,
xctype)
vxc, fxc = ni.eval_xc(mf.xc, (rhoa, rhob), 1, deriv=2)[1:3]
wva, wvb = numint._uks_gga_wv0((rhoa, rhob), vxc, weight)
rks_grad._gga_grad_sum_(vipa, mol, ao, wva, mask, ao_loc)
rks_grad._gga_grad_sum_(vipb, mol, ao, wvb, mask, ao_loc)
ao_dm0a = [
numint._dot_ao_dm(mol, ao[i], dm0a, mask, shls_slice, ao_loc)
for i in range(4)
]
ao_dm0b = [
numint._dot_ao_dm(mol, ao[i], dm0b, mask, shls_slice, ao_loc)
for i in range(4)
]
for ia in range(mol.natm):
wva = dR_rho1a = rks_hess._make_dR_rho1(
ao, ao_dm0a, ia, aoslices)
wvb = dR_rho1b = rks_hess._make_dR_rho1(
ao, ao_dm0b, ia, aoslices)
wva[0], wvb[0] = numint._uks_gga_wv1(
(rhoa, rhob), (dR_rho1a[0], dR_rho1b[0]), vxc, fxc, weight)
wva[1], wvb[1] = numint._uks_gga_wv1(
(rhoa, rhob), (dR_rho1a[1], dR_rho1b[1]), vxc, fxc, weight)
wva[2], wvb[2] = numint._uks_gga_wv1(
(rhoa, rhob), (dR_rho1a[2], dR_rho1b[2]), vxc, fxc, weight)
aow = [numint._scale_ao(ao[:4], wva[i, :4]) for i in range(3)]
rks_grad._d1_dot_(vmata[ia], mol, aow, ao[0], mask, ao_loc,
True)
aow = [numint._scale_ao(ao[:4], wvb[i, :4]) for i in range(3)]
rks_grad._d1_dot_(vmatb[ia], mol, aow, ao[0], mask, ao_loc,
True)
ao_dm0a = ao_dm0b = aow = None
for ia in range(mol.natm):
p0, p1 = aoslices[ia][2:]
vmata[ia, :, p0:p1] += vipa[:, p0:p1]
vmatb[ia, :, p0:p1] += vipb[:, p0:p1]
vmata[ia] = -vmata[ia] - vmata[ia].transpose(0, 2, 1)
vmatb[ia] = -vmatb[ia] - vmatb[ia].transpose(0, 2, 1)
elif xctype == 'MGGA':
if grids.level < 5:
logger.warn(mol, 'MGGA Hessian is sensitive to dft grids.')
ao_deriv = 2
vipa = numpy.zeros((3, nao, nao))
vipb = numpy.zeros((3, nao, nao))
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
rhoa = ni.eval_rho2(mol, ao[:10], mo_coeff[0], mo_occ[0], mask,
xctype)
rhob = ni.eval_rho2(mol, ao[:10], mo_coeff[1], mo_occ[1], mask,
xctype)
vxc, fxc = ni.eval_xc(mf.xc, (rhoa, rhob), 1, deriv=2)[1:3]
wva, wvb = numint._uks_mgga_wv0((rhoa, rhob), vxc, weight)
rks_grad._gga_grad_sum_(vipa, mol, ao, wva, mask, ao_loc)
rks_grad._gga_grad_sum_(vipb, mol, ao, wvb, mask, ao_loc)
rks_grad._tau_grad_dot_(vipa, mol, ao, wva[5] * 2, mask, ao_loc,
True)
rks_grad._tau_grad_dot_(vipb, mol, ao, wvb[5] * 2, mask, ao_loc,
True)
ao_dm0a = [
numint._dot_ao_dm(mol, ao[i], dm0a, mask, shls_slice, ao_loc)
for i in range(4)
]
ao_dm0b = [
numint._dot_ao_dm(mol, ao[i], dm0b, mask, shls_slice, ao_loc)
for i in range(4)
]
for ia in range(mol.natm):
wva = dR_rho1a = rks_hess._make_dR_rho1(
ao, ao_dm0a, ia, aoslices, xctype)
wvb = dR_rho1b = rks_hess._make_dR_rho1(
ao, ao_dm0b, ia, aoslices, xctype)
wva[0], wvb[0] = numint._uks_mgga_wv1(
(rhoa, rhob), (dR_rho1a[0], dR_rho1b[0]), vxc, fxc, weight)
wva[1], wvb[1] = numint._uks_mgga_wv1(
(rhoa, rhob), (dR_rho1a[1], dR_rho1b[1]), vxc, fxc, weight)
wva[2], wvb[2] = numint._uks_mgga_wv1(
(rhoa, rhob), (dR_rho1a[2], dR_rho1b[2]), vxc, fxc, weight)
aow = [numint._scale_ao(ao[:4], wva[i, :4]) for i in range(3)]
rks_grad._d1_dot_(vmata[ia], mol, aow, ao[0], mask, ao_loc,
True)
aow = [numint._scale_ao(ao[:4], wvb[i, :4]) for i in range(3)]
rks_grad._d1_dot_(vmatb[ia], mol, aow, ao[0], mask, ao_loc,
True)
for j in range(1, 4):
aow = [
numint._scale_ao(ao[j], wva[i, 5]) for i in range(3)
]
rks_grad._d1_dot_(vmata[ia], mol, aow, ao[j], mask, ao_loc,
True)
aow = [
numint._scale_ao(ao[j], wvb[i, 5]) for i in range(3)
]
rks_grad._d1_dot_(vmatb[ia], mol, aow, ao[j], mask, ao_loc,
True)
for ia in range(mol.natm):
p0, p1 = aoslices[ia][2:]
vmata[ia, :, p0:p1] += vipa[:, p0:p1]
vmatb[ia, :, p0:p1] += vipb[:, p0:p1]
vmata[ia] = -vmata[ia] - vmata[ia].transpose(0, 2, 1)
vmatb[ia] = -vmatb[ia] - vmatb[ia].transpose(0, 2, 1)
return vmata, vmatb
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[0].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()
dm0a, dm0b = mf.make_rdm1(mo_coeff, mo_occ)
vmata = numpy.zeros((mol.natm, 3, 3, nao, nao))
vmatb = numpy.zeros((mol.natm, 3, 3, nao, nao))
ipipa = numpy.zeros((3, 3, nao, nao))
ipipb = 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):
rhoa = ni.eval_rho2(mol, ao[0], mo_coeff[0], mo_occ[0], mask,
xctype)
rhob = ni.eval_rho2(mol, ao[0], mo_coeff[1], mo_occ[1], mask,
xctype)
vxc, fxc = ni.eval_xc(mf.xc, (rhoa, rhob), 1, deriv=2)[1:3]
vrho = vxc[0]
u_u, u_d, d_d = fxc[0].T
aow = numpy.einsum('xpi,p->xpi', ao[1:4], weight * vrho[:, 0])
rks_hess._d1d2_dot_(ipipa, mol, aow, ao[1:4], mask, ao_loc, False)
aow = numpy.einsum('xpi,p->xpi', ao[1:4], weight * vrho[:, 1])
rks_hess._d1d2_dot_(ipipb, mol, aow, ao[1:4], mask, ao_loc, False)
ao_dm0a = numint._dot_ao_dm(mol, ao[0], dm0a, mask, shls_slice,
ao_loc)
ao_dm0b = numint._dot_ao_dm(mol, ao[0], dm0b, mask, shls_slice,
ao_loc)
for ia in range(mol.natm):
p0, p1 = aoslices[ia][2:]
# *2 for \nabla|ket> in rho1
rho1a = numpy.einsum('xpi,pi->xp', ao[1:, :, p0:p1],
ao_dm0a[:, p0:p1]) * 2
rho1b = numpy.einsum('xpi,pi->xp', ao[1:, :, p0:p1],
ao_dm0b[:, p0:p1]) * 2
wv = u_u * rho1a + u_d * rho1b
wv *= weight
# aow ~ rho1 ~ d/dR1
aow = numpy.einsum('pi,xp->xpi', ao[0], wv)
rks_hess._d1d2_dot_(vmata[ia], mol, ao[1:4], aow, mask, ao_loc,
False)
wv = u_d * rho1a + d_d * rho1b
wv *= weight
aow = numpy.einsum('pi,xp->xpi', ao[0], wv)
rks_hess._d1d2_dot_(vmatb[ia], mol, ao[1:4], aow, mask, ao_loc,
False)
ao_dm0a = ao_dm0b = aow = None
for ia in range(mol.natm):
p0, p1 = aoslices[ia][2:]
vmata[ia, :, :, :, p0:p1] += ipipa[:, :, :, p0:p1]
vmatb[ia, :, :, :, p0:p1] += ipipb[:, :, :, p0:p1]
elif xctype == 'GGA':
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[:4], mo_coeff[0], mo_occ[0], mask,
xctype)
rhob = ni.eval_rho2(mol, ao[:4], mo_coeff[1], mo_occ[1], mask,
xctype)
vxc, fxc = ni.eval_xc(mf.xc, (rhoa, rhob), 1, deriv=2)[1:3]
wva, wvb = numint._uks_gga_wv0((rhoa, rhob), vxc, weight)
aow = rks_grad._make_dR_dao_w(ao, wva)
rks_hess._d1d2_dot_(ipipa, mol, aow, ao[1:4], mask, ao_loc, False)
aow = rks_grad._make_dR_dao_w(ao, wvb)
rks_hess._d1d2_dot_(ipipb, mol, aow, ao[1:4], mask, ao_loc, False)
ao_dm0a = [
numint._dot_ao_dm(mol, ao[i], dm0a, mask, shls_slice, ao_loc)
for i in range(4)
]
ao_dm0b = [
numint._dot_ao_dm(mol, ao[i], dm0b, mask, shls_slice, ao_loc)
for i in range(4)
]
for ia in range(mol.natm):
wva = dR_rho1a = rks_hess._make_dR_rho1(
ao, ao_dm0a, ia, aoslices)
wvb = dR_rho1b = rks_hess._make_dR_rho1(
ao, ao_dm0b, ia, aoslices)
wva[0], wvb[0] = numint._uks_gga_wv1(
(rhoa, rhob), (dR_rho1a[0], dR_rho1b[0]), vxc, fxc, weight)
wva[1], wvb[1] = numint._uks_gga_wv1(
(rhoa, rhob), (dR_rho1a[1], dR_rho1b[1]), vxc, fxc, weight)
wva[2], wvb[2] = numint._uks_gga_wv1(
(rhoa, rhob), (dR_rho1a[2], dR_rho1b[2]), vxc, fxc, weight)
aow = rks_grad._make_dR_dao_w(ao, wva[0])
rks_grad._d1_dot_(vmata[ia, 0], mol, aow, ao[0], mask, ao_loc,
True)
aow = rks_grad._make_dR_dao_w(ao, wva[1])
rks_grad._d1_dot_(vmata[ia, 1], mol, aow, ao[0], mask, ao_loc,
True)
aow = rks_grad._make_dR_dao_w(ao, wva[2])
rks_grad._d1_dot_(vmata[ia, 2], mol, aow, ao[0], mask, ao_loc,
True)
aow = [numint._scale_ao(ao[:4], wva[i, :4]) for i in range(3)]
rks_hess._d1d2_dot_(vmata[ia], mol, ao[1:4], aow, mask, ao_loc,
False)
aow = rks_grad._make_dR_dao_w(ao, wvb[0])
rks_grad._d1_dot_(vmatb[ia, 0], mol, aow, ao[0], mask, ao_loc,
True)
aow = rks_grad._make_dR_dao_w(ao, wvb[1])
rks_grad._d1_dot_(vmatb[ia, 1], mol, aow, ao[0], mask, ao_loc,
True)
aow = rks_grad._make_dR_dao_w(ao, wvb[2])
rks_grad._d1_dot_(vmatb[ia, 2], mol, aow, ao[0], mask, ao_loc,
True)
aow = [numint._scale_ao(ao[:4], wvb[i, :4]) for i in range(3)]
rks_hess._d1d2_dot_(vmatb[ia], mol, ao[1:4], aow, mask, ao_loc,
False)
ao_dm0a = ao_dm0b = aow = None
for ia in range(mol.natm):
p0, p1 = aoslices[ia][2:]
vmata[ia, :, :, :, p0:p1] += ipipa[:, :, :, p0:p1]
vmata[ia, :, :, :, p0:p1] += ipipa[:, :,
p0:p1].transpose(1, 0, 3, 2)
vmatb[ia, :, :, :, p0:p1] += ipipb[:, :, :, p0:p1]
vmatb[ia, :, :, :, p0:p1] += ipipb[:, :,
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):
rhoa = ni.eval_rho2(mol, ao[:10], mo_coeff[0], mo_occ[0], mask,
xctype)
rhob = ni.eval_rho2(mol, ao[:10], mo_coeff[1], mo_occ[1], mask,
xctype)
vxc, fxc = ni.eval_xc(mf.xc, (rhoa, rhob), 1, deriv=2)[1:3]
wva, wvb = numint._uks_mgga_wv0((rhoa, rhob), vxc, weight)
aow = rks_grad._make_dR_dao_w(ao, wva)
rks_hess._d1d2_dot_(ipipa, mol, aow, ao[1:4], mask, ao_loc, False)
aow = rks_grad._make_dR_dao_w(ao, wvb)
rks_hess._d1d2_dot_(ipipb, mol, aow, ao[1:4], mask, ao_loc, False)
aow = [numint._scale_ao(ao[i], wva[5]) for i in range(4, 10)]
rks_hess._d1d2_dot_(ipipa, mol, [aow[0], aow[1], aow[2]],
[ao[XX], ao[XY], ao[XZ]], mask, ao_loc, False)
rks_hess._d1d2_dot_(ipipa, mol, [aow[1], aow[3], aow[4]],
[ao[YX], ao[YY], ao[YZ]], mask, ao_loc, False)
rks_hess._d1d2_dot_(ipipa, mol, [aow[2], aow[4], aow[5]],
[ao[ZX], ao[ZY], ao[ZZ]], mask, ao_loc, False)
aow = [numint._scale_ao(ao[i], wvb[5]) for i in range(4, 10)]
rks_hess._d1d2_dot_(ipipb, mol, [aow[0], aow[1], aow[2]],
[ao[XX], ao[XY], ao[XZ]], mask, ao_loc, False)
rks_hess._d1d2_dot_(ipipb, mol, [aow[1], aow[3], aow[4]],
[ao[YX], ao[YY], ao[YZ]], mask, ao_loc, False)
rks_hess._d1d2_dot_(ipipb, mol, [aow[2], aow[4], aow[5]],
[ao[ZX], ao[ZY], ao[ZZ]], mask, ao_loc, False)
ao_dm0a = [
numint._dot_ao_dm(mol, ao[i], dm0a, mask, shls_slice, ao_loc)
for i in range(4)
]
ao_dm0b = [
numint._dot_ao_dm(mol, ao[i], dm0b, mask, shls_slice, ao_loc)
for i in range(4)
]
for ia in range(mol.natm):
wva = dR_rho1a = rks_hess._make_dR_rho1(
ao, ao_dm0a, ia, aoslices, xctype)
wvb = dR_rho1b = rks_hess._make_dR_rho1(
ao, ao_dm0b, ia, aoslices, xctype)
wva[0], wvb[0] = numint._uks_mgga_wv1(
(rhoa, rhob), (dR_rho1a[0], dR_rho1b[0]), vxc, fxc, weight)
wva[1], wvb[1] = numint._uks_mgga_wv1(
(rhoa, rhob), (dR_rho1a[1], dR_rho1b[1]), vxc, fxc, weight)
wva[2], wvb[2] = numint._uks_mgga_wv1(
(rhoa, rhob), (dR_rho1a[2], dR_rho1b[2]), vxc, fxc, weight)
aow = rks_grad._make_dR_dao_w(ao, wva[0])
rks_grad._d1_dot_(vmata[ia, 0], mol, aow, ao[0], mask, ao_loc,
True)
aow = rks_grad._make_dR_dao_w(ao, wva[1])
rks_grad._d1_dot_(vmata[ia, 1], mol, aow, ao[0], mask, ao_loc,
True)
aow = rks_grad._make_dR_dao_w(ao, wva[2])
rks_grad._d1_dot_(vmata[ia, 2], mol, aow, ao[0], mask, ao_loc,
True)
aow = [numint._scale_ao(ao[:4], wva[i, :4]) for i in range(3)]
rks_hess._d1d2_dot_(vmata[ia], mol, ao[1:4], aow, mask, ao_loc,
False)
aow = rks_grad._make_dR_dao_w(ao, wvb[0])
rks_grad._d1_dot_(vmatb[ia, 0], mol, aow, ao[0], mask, ao_loc,
True)
aow = rks_grad._make_dR_dao_w(ao, wvb[1])
rks_grad._d1_dot_(vmatb[ia, 1], mol, aow, ao[0], mask, ao_loc,
True)
aow = rks_grad._make_dR_dao_w(ao, wvb[2])
rks_grad._d1_dot_(vmatb[ia, 2], mol, aow, ao[0], mask, ao_loc,
True)
aow = [numint._scale_ao(ao[:4], wvb[i, :4]) for i in range(3)]
rks_hess._d1d2_dot_(vmatb[ia], mol, ao[1:4], aow, mask, ao_loc,
False)
# *2 because wv[5] is scaled by 0.5 in _rks_mgga_wv1
wv = wva[:, 5] * 2
aow = [numint._scale_ao(ao[1], wv[i]) for i in range(3)]
rks_hess._d1d2_dot_(vmata[ia], mol, [ao[XX], ao[XY], ao[XZ]],
aow, mask, ao_loc, False)
aow = [numint._scale_ao(ao[2], wv[i]) for i in range(3)]
rks_hess._d1d2_dot_(vmata[ia], mol, [ao[YX], ao[YY], ao[YZ]],
aow, mask, ao_loc, False)
aow = [numint._scale_ao(ao[3], wv[i]) for i in range(3)]
rks_hess._d1d2_dot_(vmata[ia], mol, [ao[ZX], ao[ZY], ao[ZZ]],
aow, mask, ao_loc, False)
wv = wvb[:, 5] * 2
aow = [numint._scale_ao(ao[1], wv[i]) for i in range(3)]
rks_hess._d1d2_dot_(vmatb[ia], mol, [ao[XX], ao[XY], ao[XZ]],
aow, mask, ao_loc, False)
aow = [numint._scale_ao(ao[2], wv[i]) for i in range(3)]
rks_hess._d1d2_dot_(vmatb[ia], mol, [ao[YX], ao[YY], ao[YZ]],
aow, mask, ao_loc, False)
aow = [numint._scale_ao(ao[3], wv[i]) for i in range(3)]
rks_hess._d1d2_dot_(vmatb[ia], mol, [ao[ZX], ao[ZY], ao[ZZ]],
aow, mask, ao_loc, False)
for ia in range(mol.natm):
p0, p1 = aoslices[ia][2:]
vmata[ia, :, :, :, p0:p1] += ipipa[:, :, :, p0:p1]
vmata[ia, :, :, :, p0:p1] += ipipa[:, :,
p0:p1].transpose(1, 0, 3, 2)
vmatb[ia, :, :, :, p0:p1] += ipipb[:, :, :, p0:p1]
vmatb[ia, :, :, :, p0:p1] += ipipb[:, :,
p0:p1].transpose(1, 0, 3, 2)
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[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,
xctype)
rhob = ni.eval_rho2(mol, ao[0], mo_coeff[1], mo_occ[1], mask,
xctype)
vxc = ni.eval_xc(mf.xc, (rhoa, rhob), 1, deriv=1)[1]
vrho = vxc[0]
aowa = numint._scale_ao(ao[0], weight * vrho[:, 0])
aowb = numint._scale_ao(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 = numint._scale_ao(ao[aoidx[0]], wv[1])
aow += numint._scale_ao(ao[aoidx[1]], wv[2])
aow += numint._scale_ao(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,
xctype)
rhob = ni.eval_rho2(mol, ao[:4], mo_coeff[1], mo_occ[1], mask,
xctype)
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 = numint._scale_ao(ao[:4], wva[:4])
aowb = numint._scale_ao(ao[:4], wvb[:4])
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':
def contract_(mat, ao, aoidx, wv, mask):
aow = numint._scale_ao(ao[aoidx[0]], wv[1])
aow += numint._scale_ao(ao[aoidx[1]], wv[2])
aow += numint._scale_ao(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[:10], mo_coeff[0], mo_occ[0], mask,
xctype)
rhob = ni.eval_rho2(mol, ao[:10], mo_coeff[1], mo_occ[1], mask,
xctype)
vxc = ni.eval_xc(mf.xc, (rhoa, rhob), 1, deriv=1)[1]
wva, wvb = numint._uks_mgga_wv0((rhoa, rhob), vxc, weight)
# *2 because v.T is not applied.
wva[0] *= 2
wvb[0] *= 2
wva[5] *= 2
wvb[5] *= 2
aowa = numint._scale_ao(ao[:4], wva[:4])
aowb = numint._scale_ao(ao[:4], wvb[:4])
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)
aowa = [numint._scale_ao(ao[i], wva[5]) for i in range(1, 4)]
aowb = [numint._scale_ao(ao[i], wvb[5]) for i in range(1, 4)]
for i, j in enumerate([XXX, XXY, XXZ, XYY, XYZ, XZZ]):
vmata[i] += numint._dot_ao_ao(mol, ao[j], aowa[0], mask,
shls_slice, ao_loc)
vmatb[i] += numint._dot_ao_ao(mol, ao[j], aowb[0], mask,
shls_slice, ao_loc)
for i, j in enumerate([XXY, XYY, XYZ, YYY, YYZ, YZZ]):
vmata[i] += numint._dot_ao_ao(mol, ao[j], aowa[1], mask,
shls_slice, ao_loc)
vmatb[i] += numint._dot_ao_ao(mol, ao[j], aowb[1], mask,
shls_slice, ao_loc)
for i, j in enumerate([XXZ, XYZ, XZZ, YYZ, YZZ, ZZZ]):
vmata[i] += numint._dot_ao_ao(mol, ao[j], aowa[2], mask,
shls_slice, ao_loc)
vmatb[i] += numint._dot_ao_ao(mol, ao[j], aowb[2], mask,
shls_slice, ao_loc)
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):
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((2, 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_a = make_rho(0, ao[0], mask, xctype)
rho_b = make_rho(1, ao[0], mask, xctype)
vxc = ni.eval_xc(xc_code, (rho_a, rho_b),
1,
relativity,
1,
verbose=verbose)[1]
vrho = vxc[0]
#:aow = numpy.einsum('pi,p->pi', ao[0], weight*vrho[:,0])
aow = numint._scale_ao(ao[0], weight * vrho[:, 0])
rks_grad._d1_dot_(vmat[0], mol, ao[1:4], aow, mask, ao_loc, True)
#:aow = numpy.einsum('pi,p->pi', ao[0], weight*vrho[:,1])
aow = numint._scale_ao(ao[0], weight * vrho[:, 1])
rks_grad._d1_dot_(vmat[1], 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):
rho_a = make_rho(0, ao[:4], mask, xctype)
rho_b = make_rho(1, ao[:4], mask, xctype)
vxc = ni.eval_xc(xc_code, (rho_a, rho_b),
1,
relativity,
1,
verbose=verbose)[1]
wva, wvb = numint._uks_gga_wv0((rho_a, rho_b), vxc, weight)
rks_grad._gga_grad_sum_(vmat[0], mol, ao, wva, mask, ao_loc)
rks_grad._gga_grad_sum_(vmat[1], mol, ao, wvb, 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):
rho_a = make_rho(0, ao[:10], mask, xctype)
rho_b = make_rho(1, ao[:10], mask, xctype)
vxc = ni.eval_xc(xc_code, (rho_a, rho_b),
1,
relativity,
1,
verbose=verbose)[1]
wva, wvb = numint._uks_mgga_wv0((rho_a, rho_b), vxc, weight)
rks_grad._gga_grad_sum_(vmat[0], mol, ao, wva, mask, ao_loc)
rks_grad._gga_grad_sum_(vmat[1], mol, ao, wvb, mask, ao_loc)
# *2 because wv[5] is scaled by 0.5 in _uks_mgga_wv0
rks_grad._tau_grad_dot_(vmat[0], mol, ao, wva[5] * 2, mask, ao_loc,
True)
rks_grad._tau_grad_dot_(vmat[1], mol, ao, wvb[5] * 2, mask, ao_loc,
True)
exc = numpy.zeros((mol.natm, 3))
# - sign because nabla_X = -nabla_x
return exc, -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()
aoslices = mol.aoslice_by_atom()
excsum = 0
vmat = numpy.zeros((2, 3, nao, nao))
if xctype == 'LDA':
ao_deriv = 1
for atm_id, (coords, weight, weight1) \
in enumerate(rks_grad.grids_response_cc(grids)):
sh0, sh1 = aoslices[atm_id][:2]
mask = gen_grid.make_mask(mol, coords)
ao = ni.eval_ao(mol, coords, deriv=ao_deriv, non0tab=mask)
rho_a = make_rho(0, ao[0], mask, xctype)
rho_b = make_rho(1, ao[0], mask, xctype)
exc, vxc = ni.eval_xc(xc_code, (rho_a, rho_b),
1,
relativity,
1,
verbose=verbose)[:2]
vrho = vxc[0]
vtmp = numpy.zeros((3, nao, nao))
#:aow = numpy.einsum('pi,p->pi', ao[0], weight*vrho[:,0])
aow = numint._scale_ao(ao[0], weight * vrho[:, 0])
rks_grad._d1_dot_(vtmp, mol, ao[1:4], aow, mask, ao_loc, True)
vmat[0] += vtmp
excsum += numpy.einsum('r,r,nxr->nx', exc, rho_a + rho_b, weight1)
excsum[atm_id] += numpy.einsum('xij,ji->x', vtmp, dms[0]) * 2
vtmp = numpy.zeros((3, nao, nao))
#:aow = numpy.einsum('pi,p->pi', ao[0], weight*vrho[:,1])
aow = numint._scale_ao(ao[0], weight * vrho[:, 1])
rks_grad._d1_dot_(vtmp, mol, ao[1:4], aow, mask, ao_loc, True)
vmat[1] += vtmp
excsum[atm_id] += numpy.einsum('xij,ji->x', vtmp, dms[1]) * 2
elif xctype == 'GGA':
ao_deriv = 2
for atm_id, (coords, weight, weight1) \
in enumerate(rks_grad.grids_response_cc(grids)):
sh0, sh1 = aoslices[atm_id][:2]
mask = gen_grid.make_mask(mol, coords)
ao = ni.eval_ao(mol, coords, deriv=ao_deriv, non0tab=mask)
rho_a = make_rho(0, ao[:4], mask, xctype)
rho_b = make_rho(1, ao[:4], mask, xctype)
exc, vxc = ni.eval_xc(xc_code, (rho_a, rho_b),
1,
relativity,
1,
verbose=verbose)[:2]
wva, wvb = numint._uks_gga_wv0((rho_a, rho_b), vxc, weight)
vtmp = numpy.zeros((3, nao, nao))
rks_grad._gga_grad_sum_(vtmp, mol, ao, wva, mask, ao_loc)
vmat[0] += vtmp
excsum += numpy.einsum('r,r,nxr->nx', exc, rho_a[0] + rho_b[0],
weight1)
excsum[atm_id] += numpy.einsum('xij,ji->x', vtmp, dms[0]) * 2
vtmp = numpy.zeros((3, nao, nao))
rks_grad._gga_grad_sum_(vtmp, mol, ao, wvb, mask, ao_loc)
vmat[1] += vtmp
excsum[atm_id] += numpy.einsum('xij,ji->x', vtmp, dms[1]) * 2
elif xctype == 'NLC':
raise NotImplementedError('NLC')
elif xctype == 'MGGA':
ao_deriv = 2
for atm_id, (coords, weight, weight1) \
in enumerate(rks_grad.grids_response_cc(grids)):
sh0, sh1 = aoslices[atm_id][:2]
mask = gen_grid.make_mask(mol, coords)
ao = ni.eval_ao(mol, coords, deriv=ao_deriv, non0tab=mask)
rho_a = make_rho(0, ao[:10], mask, xctype)
rho_b = make_rho(1, ao[:10], mask, xctype)
exc, vxc = ni.eval_xc(xc_code, (rho_a, rho_b),
1,
relativity,
1,
verbose=verbose)[:2]
wva, wvb = numint._uks_mgga_wv0((rho_a, rho_b), vxc, weight)
vtmp = numpy.zeros((3, nao, nao))
rks_grad._gga_grad_sum_(vtmp, mol, ao, wva, mask, ao_loc)
# *2 because wv[5] is scaled by 0.5 in _uks_mgga_wv0
rks_grad._tau_grad_dot_(vtmp, mol, ao, wva[5] * 2, mask, ao_loc,
True)
vmat[0] += vtmp
excsum += numpy.einsum('r,r,nxr->nx', exc, rho_a[0] + rho_b[0],
weight1)
excsum[atm_id] += numpy.einsum('xij,ji->x', vtmp, dms[0]) * 2
vtmp = numpy.zeros((3, nao, nao))
rks_grad._gga_grad_sum_(vtmp, mol, ao, wvb, mask, ao_loc)
rks_grad._tau_grad_dot_(vtmp, mol, ao, wvb[5] * 2, mask, ao_loc,
True)
vmat[1] += vtmp
excsum[atm_id] += numpy.einsum('xij,ji->x', vtmp, dms[1]) * 2
# - sign because nabla_X = -nabla_x
return excsum, -vmat