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)
rho_a = make_rho(0, ao_k2[:, 0], mask, xctype)
rho_b = make_rho(1, ao_k2[:, 0], mask, xctype)
vxc = ni.eval_xc(xc_code, (rho_a, rho_b), 1, relativity, 1)[1]
vrho = vxc[0]
aowa = np.einsum('xpi,p->xpi', ao_k1[:, 0], weight * vrho[:, 0])
aowb = np.einsum('xpi,p->xpi', ao_k1[:, 0], weight * vrho[:, 1])
ao_k2 = rho_a = rho_b = vxc = None
for kn in range(nkpts):
rks_grad._d1_dot_(vmat[:, 0, kn], cell, ao_k1[kn, 1:4],
aowa[kn], mask, ao_loc, True)
rks_grad._d1_dot_(vmat[:, 1, kn], cell, ao_k1[kn, 1:4],
aowb[kn], mask, ao_loc, True)
ao_k1 = aowa = aowb = 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)
rho_a = make_rho(0, ao_k2[:, :4], mask, xctype)
rho_b = make_rho(1, ao_k2[:, :4], mask, xctype)
vxc = ni.eval_xc(xc_code, (rho_a, rho_b), 1, relativity, 1)[1]
wva, wvb = numint._uks_gga_wv0((rho_a, rho_b), vxc, weight)
ao_k2 = rho_a = rho_b = vxc = None
for kn in range(nkpts):
rks_grad._gga_grad_sum_(vmat[:, 0, kn], cell, ao_k1[kn], wva,
mask, ao_loc)
rks_grad._gga_grad_sum_(vmat[:, 1, kn], cell, ao_k1[kn], wvb,
mask, ao_loc)
ao_k1 = wva = wvb = None
elif xctype == 'NLC':
raise NotImplementedError("NLC")
else:
raise NotImplementedError("metaGGA")
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((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, 'LDA')
rho_b = make_rho(1, ao[0], mask, 'LDA')
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])
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])
rks_grad._d1_dot_(vmat[1], mol, ao[1:4], aow, mask, ao_loc, True)
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):
rho_a = make_rho(0, ao[:4], mask, 'GGA')
rho_b = make_rho(1, ao[:4], mask, 'GGA')
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)
rho_a = rho_b = vxc = wva = wvb = None
elif xctype == 'NLC':
raise NotImplementedError('NLC')
elif xctype == 'MGGA':
raise NotImplementedError('meta-GGA')
exc = numpy.zeros((mol.natm, 3))
# - sign because nabla_X = -nabla_x
return exc, -vmat
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)
shls_slice = (0, cell.nbas)
ao_loc = cell.ao_loc_nr()
nkpts = len(kpts)
vmat = np.zeros((3,nset,nkpts,nao,nao), dtype=dms.dtype)
excsum = np.zeros(nset)
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 = vc = 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 make_e_psi1(pcmobj, dm, r_vdw, ui, ylm_1sph, cached_pol, Xvec, L):
mol = pcmobj.mol
natm = mol.natm
lmax = pcmobj.lmax
nlm = (lmax + 1)**2
grids = pcmobj.grids
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)
den = numpy.empty((4, grids.weights.size))
ao_loc = mol.ao_loc_nr()
vmat = numpy.zeros((3, nao, nao))
psi1 = numpy.zeros((natm, 3))
i1 = 0
for ia, (coords, weight,
weight1) in enumerate(rks_grad.grids_response_cc(grids)):
i0, i1 = i1, i1 + weight.size
ao = ni.eval_ao(mol, coords, deriv=1)
mask = gen_grid.make_mask(mol, coords)
den[:, i0:i1] = make_rho(0, ao, mask, 'GGA')
fak_pol, leak_idx = cached_pol[mol.atom_symbol(ia)]
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], Xvec[ia,
p0:p1])
psi1 -= numpy.einsum('n,n,zxn->zx', den[0, i0:i1], eta_nj, weight1)
psi1[ia] -= numpy.einsum('xn,n,n->x', den[1:4, i0:i1], eta_nj, weight)
vtmp = numpy.zeros((3, nao, nao))
aow = numpy.einsum('pi,p->pi', ao[0], weight * eta_nj)
rks_grad._d1_dot_(vtmp, mol, ao[1:4], aow, mask, ao_loc, True)
vmat += vtmp
aoslices = mol.aoslice_by_atom()
for ia in range(natm):
shl0, shl1, p0, p1 = aoslices[ia]
psi1[ia] += numpy.einsum('xij,ij->x', vmat[:, p0:p1], dm[p0:p1]) * 2
return psi1
def make_e_psi1(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
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)
den = numpy.empty((4,grids.weights.size))
ao_loc = mol.ao_loc_nr()
vmat = numpy.zeros((3,nao,nao))
psi1 = numpy.zeros((natm,3))
i1 = 0
for ia, (coords, weight, weight1) in enumerate(rks_grad.grids_response_cc(grids)):
i0, i1 = i1, i1 + weight.size
ao = ni.eval_ao(mol, coords, deriv=1)
mask = gen_grid.make_mask(mol, coords)
den[:,i0:i1] = make_rho(0, ao, mask, 'GGA')
fak_pol, leak_idx = cached_pol[mol.atom_symbol(ia)]
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])
psi1 -= numpy.einsum('n,n,zxn->zx', den[0,i0:i1], eta_nj, weight1)
psi1[ia] -= numpy.einsum('xn,n,n->x', den[1:4,i0:i1], eta_nj, weight)
vtmp = numpy.zeros((3,nao,nao))
aow = numpy.einsum('pi,p->pi', ao[0], weight*eta_nj)
rks_grad._d1_dot_(vtmp, mol, ao[1:4], aow, mask, ao_loc, True)
vmat += vtmp
aoslices = mol.aoslice_by_atom()
for ia in range(natm):
shl0, shl1, p0, p1 = aoslices[ia]
psi1[ia] += numpy.einsum('xij,ij->x', vmat[:,p0:p1], dm[p0:p1]) * 2
return psi1
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, 'LDA')
rho_b = make_rho(1, ao[0], mask, 'LDA')
vxc = ni.eval_xc(xc_code, (rho_a,rho_b), 1, relativity, 1, verbose)[1]
vrho = vxc[0]
aow = numpy.einsum('pi,p->pi', 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])
rks_grad._d1_dot_(vmat[1], 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):
rho_a = make_rho(0, ao[:4], mask, 'GGA')
rho_b = make_rho(1, ao[:4], mask, 'GGA')
vxc = ni.eval_xc(xc_code, (rho_a,rho_b), 1, relativity, 1, 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)
rho_a = rho_b = vxc = wva = wvb = None
elif xctype == 'NLC':
raise NotImplementedError('NLC')
else:
raise NotImplementedError('meta-GGA')
exc = numpy.zeros((mol.natm,3))
# - sign because nabla_X = -nabla_x
return exc, -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_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 = numpy.einsum('npi,Xnp->Xpi', ao[:4], wva)
rks_grad._d1_dot_(vmata[ia], mol, aow, ao[0], mask, ao_loc, True)
aow = numpy.einsum('npi,Xnp->Xpi', ao[:4], wvb)
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]
vmata[ia] = -vmata[ia] - vmata[ia].transpose(0,2,1)
vmatb[ia,:,p0:p1] += vipb[:,p0:p1]
vmatb[ia] = -vmatb[ia] - vmatb[ia].transpose(0,2,1)
elif xctype == 'MGGA':
raise NotImplementedError('meta-GGA')
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 = numpy.einsum('npi,Xnp->Xpi', ao[:4], wva)
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 = numpy.einsum('npi,Xnp->Xpi', ao[:4], wvb)
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':
raise NotImplementedError('meta-GGA')
return vmata, vmatb
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)):
ngrids = weight.size
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, 'LDA')
rho_b = make_rho(1, ao[0], mask, 'LDA')
exc, vxc = ni.eval_xc(xc_code, (rho_a, rho_b), 1, relativity, 1,
verbose)[:2]
vrho = vxc[0]
vtmp = numpy.zeros((3, nao, nao))
aow = numpy.einsum('pi,p->pi', 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])
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
rho = vxc = vrho = aow = None
elif xctype == 'GGA':
ao_deriv = 2
for atm_id, (coords, weight, weight1) \
in enumerate(rks_grad.grids_response_cc(grids)):
ngrids = weight.size
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, 'GGA')
rho_b = make_rho(1, ao[:4], mask, 'GGA')
exc, vxc = ni.eval_xc(xc_code, (rho_a, rho_b), 1, relativity, 1,
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
rho_a = rho_b = vxc = wva = wvb = None
elif xctype == 'NLC':
raise NotImplementedError('NLC')
else:
raise NotImplementedError('meta-GGA')
# - sign because nabla_X = -nabla_x
return excsum, -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[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 = numpy.einsum('npi,Xnp->Xpi', ao[:4], wva)
rks_grad._d1_dot_(vmata[ia], mol, aow, ao[0], mask, ao_loc, True)
aow = numpy.einsum('npi,Xnp->Xpi', ao[:4], wvb)
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]
vmata[ia] = -vmata[ia] - vmata[ia].transpose(0,2,1)
vmatb[ia,:,p0:p1] += vipb[:,p0:p1]
vmatb[ia] = -vmatb[ia] - vmatb[ia].transpose(0,2,1)
elif xctype == 'MGGA':
raise NotImplementedError('meta-GGA')
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 = numpy.einsum('npi,Xnp->Xpi', ao[:4], wva)
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 = numpy.einsum('npi,Xnp->Xpi', ao[:4], wvb)
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':
raise NotImplementedError('meta-GGA')
return vmata, vmatb
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_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[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_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)):
ngrids = weight.size
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, 'LDA')
rho_b = make_rho(1, ao[0], mask, 'LDA')
exc, vxc = ni.eval_xc(xc_code, (rho_a,rho_b), 1, relativity, 1, verbose)[:2]
vrho = vxc[0]
vtmp = numpy.zeros((3,nao,nao))
aow = numpy.einsum('pi,p->pi', 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])
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
rho = vxc = vrho = aow = None
elif xctype == 'GGA':
ao_deriv = 2
for atm_id, (coords, weight, weight1) \
in enumerate(rks_grad.grids_response_cc(grids)):
ngrids = weight.size
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, 'GGA')
rho_b = make_rho(1, ao[:4], mask, 'GGA')
exc, vxc = ni.eval_xc(xc_code, (rho_a,rho_b), 1, relativity, 1, 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
rho_a = rho_b = vxc = wva = wvb = None
elif xctype == 'NLC':
raise NotImplementedError('NLC')
else:
raise NotImplementedError('meta-GGA')
# - sign because nabla_X = -nabla_x
return excsum, -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