def tda_grad(td, z):
'''ddcosmo TDA gradients'''
mol = td.mol
mf = td._scf
mo_coeff = mf.mo_coeff
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
nao, nmo = mo_coeff.shape
nocc = (mo_occ > 0).sum()
nvir = nmo - nocc
z = z[0].reshape(nocc, nvir).T * numpy.sqrt(2)
orbv = mo_coeff[:, nocc:]
orbo = mo_coeff[:, :nocc]
r_vdw = ddcosmo.get_atomic_radii(td.with_solvent)
fi = ddcosmo.make_fi(td.with_solvent, r_vdw)
ui = 1 - fi
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(
td.with_solvent.lebedev_order)
ylm_1sph = numpy.vstack(
sph.real_sph_vec(coords_1sph, td.with_solvent.lmax, True))
grids = td.with_solvent.grids
cached_pol = ddcosmo.cache_fake_multipoles(grids, r_vdw,
td.with_solvent.lmax)
L = ddcosmo.make_L(td.with_solvent, r_vdw, ylm_1sph, fi)
def fvind(x):
v_mo = numpy.einsum('iabj,xai->xbj', g[:nocc, nocc:, nocc:, :nocc], x)
v_mo += numpy.einsum('aibj,xai->xbj', g[nocc:, :nocc, nocc:, :nocc], x)
return v_mo
h1 = rhf_grad.get_hcore(mol)
s1 = rhf_grad.get_ovlp(mol)
eri1 = -mol.intor('int2e_ip1', aosym='s1', comp=3)
eri1 = eri1.reshape(3, nao, nao, nao, nao)
eri0 = ao2mo.kernel(mol, mo_coeff)
eri0 = ao2mo.restore(1, eri0, nmo).reshape(nmo, nmo, nmo, nmo)
g = eri0 * 2 - eri0.transpose(0, 3, 2, 1)
zeta = lib.direct_sum('i+j->ij', mo_energy, mo_energy) * .5
zeta[nocc:, :nocc] = mo_energy[:nocc]
zeta[:nocc, nocc:] = mo_energy[nocc:]
dielectric = td.with_solvent.eps
if dielectric > 0:
f_epsilon = (dielectric - 1.) / dielectric
else:
f_epsilon = 1
pcm_nuc = .5 * f_epsilon * nuc_part1(td.with_solvent, r_vdw, ui, ylm_1sph,
cached_pol, L)
B0 = .5 * f_epsilon * make_B(td.with_solvent, r_vdw, ui, ylm_1sph,
cached_pol, L)
B0 = lib.einsum('pqrs,pi,qj,rk,sl->ijkl', B0, mo_coeff, mo_coeff, mo_coeff,
mo_coeff)
g += B0 * 2
B1 = .5 * f_epsilon * make_B1(td.with_solvent, r_vdw, ui, ylm_1sph,
cached_pol, L)
offsetdic = mol.offset_nr_by_atom()
de = numpy.zeros((mol.natm, 3))
for ia in range(mol.natm):
shl0, shl1, p0, p1 = offsetdic[ia]
mol.set_rinv_origin(mol.atom_coord(ia))
h1ao = -mol.atom_charge(ia) * mol.intor('int1e_iprinv', comp=3)
h1ao[:, p0:p1] += h1[:, p0:p1]
h1ao = h1ao + h1ao.transpose(0, 2, 1)
h1ao += pcm_nuc[ia]
h1mo = numpy.einsum('pi,xpq,qj->xij', mo_coeff, h1ao, mo_coeff)
s1mo = numpy.einsum('pi,xpq,qj->xij', mo_coeff[p0:p1], s1[:, p0:p1],
mo_coeff)
s1mo = s1mo + s1mo.transpose(0, 2, 1)
f1 = h1mo - numpy.einsum('xpq,pq->xpq', s1mo, zeta)
f1 -= numpy.einsum('klpq,xlk->xpq', g[:nocc, :nocc],
s1mo[:, :nocc, :nocc])
eri1a = eri1.copy()
eri1a[:, :p0] = 0
eri1a[:, p1:] = 0
eri1a = eri1a + eri1a.transpose(0, 2, 1, 3, 4)
eri1a = eri1a + eri1a.transpose(0, 3, 4, 1, 2)
g1 = lib.einsum('xpqrs,pi,qj,rk,sl->xijkl', eri1a, mo_coeff, mo_coeff,
mo_coeff, mo_coeff)
tmp1 = lib.einsum('xpqrs,pi,qj,rk,sl->xijkl', B1[ia], mo_coeff,
mo_coeff, mo_coeff, mo_coeff)
g1 = g1 * 2 - g1.transpose(0, 1, 4, 3, 2)
g1 += tmp1 * 2
f1 += numpy.einsum('xkkpq->xpq', g1[:, :nocc, :nocc])
f1ai = f1[:, nocc:, :nocc].copy()
c1 = s1mo * -.5
c1vo = cphf.solve(fvind, mo_energy, mo_occ, f1ai, max_cycle=50)[0]
c1[:, nocc:, :nocc] = c1vo
c1[:, :nocc,
nocc:] = -(s1mo[:, nocc:, :nocc] + c1vo).transpose(0, 2, 1)
f1 += numpy.einsum('kapq,xak->xpq', g[:nocc, nocc:], c1vo)
f1 += numpy.einsum('akpq,xak->xpq', g[nocc:, :nocc], c1vo)
e1 = numpy.einsum('xaijb,ai,bj->x', g1[:, nocc:, :nocc, :nocc, nocc:],
z, z)
e1 += numpy.einsum('xab,ai,bi->x', f1[:, nocc:, nocc:], z, z)
e1 -= numpy.einsum('xij,ai,aj->x', f1[:, :nocc, :nocc], z, z)
g1 = numpy.einsum('pjkl,xpi->xijkl', g, c1)
g1 += numpy.einsum('ipkl,xpj->xijkl', g, c1)
g1 += numpy.einsum('ijpl,xpk->xijkl', g, c1)
g1 += numpy.einsum('ijkp,xpl->xijkl', g, c1)
e1 += numpy.einsum('xaijb,ai,bj->x', g1[:, nocc:, :nocc, :nocc, nocc:],
z, z)
de[ia] = e1
return de
def kernel(tdgrad,
z,
atmlst=None,
mf_grad=None,
max_memory=2000,
verbose=logger.INFO):
mol = tdgrad.mol
mf = tdgrad.base._scf
mo_coeff = mf.mo_coeff
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
nao, nmo = mo_coeff.shape
nocc = (mo_occ > 0).sum()
nvir = nmo - nocc
#eai = lib.direct_sum('a-i->ai', mo_energy[nocc:], mo_energy[:nocc])
z = z[0].reshape(nocc, nvir).T
orbv = mo_coeff[:, nocc:]
orbo = mo_coeff[:, :nocc]
def fvind(x):
dm = numpy.einsum('pi,xij,qj->xpq', orbv, x, orbo)
v_ao = mf.get_veff(mol, (dm + dm.transpose(0, 2, 1))) * 2
return numpy.einsum('pi,xpq,qj->xij', orbv, v_ao, orbo).reshape(3, -1)
h1 = rhf_grad.get_hcore(mol)
s1 = rhf_grad.get_ovlp(mol)
eri1 = -mol.intor('int2e_ip1', aosym='s1', comp=3)
eri1 = eri1.reshape(3, nao, nao, nao, nao)
eri0 = ao2mo.kernel(mol, mo_coeff)
eri0 = ao2mo.restore(1, eri0, nmo).reshape(nmo, nmo, nmo, nmo)
g = eri0 * 2 - eri0.transpose(0, 3, 2, 1)
zeta = lib.direct_sum('i+j->ij', mo_energy, mo_energy) * .5
zeta[nocc:, :nocc] = mo_energy[:nocc]
zeta[:nocc, nocc:] = mo_energy[nocc:]
if atmlst is None:
atmlst = range(mol.natm)
offsetdic = mol.offset_nr_by_atom()
de = numpy.zeros((len(atmlst), 3))
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = offsetdic[ia]
mol.set_rinv_origin(mol.atom_coord(ia))
h1ao = -mol.atom_charge(ia) * mol.intor('int1e_iprinv', comp=3)
h1ao[:, p0:p1] += h1[:, p0:p1]
h1ao = h1ao + h1ao.transpose(0, 2, 1)
h1mo = numpy.einsum('pi,xpq,qj->xij', mo_coeff, h1ao, mo_coeff)
s1mo = numpy.einsum('pi,xpq,qj->xij', mo_coeff[p0:p1], s1[:, p0:p1],
mo_coeff)
s1mo = s1mo + s1mo.transpose(0, 2, 1)
f1 = h1mo - numpy.einsum('xpq,pq->xpq', s1mo, zeta)
f1 -= numpy.einsum('klpq,xlk->xpq', g[:nocc, :nocc],
s1mo[:, :nocc, :nocc])
eri1a = eri1.copy()
eri1a[:, :p0] = 0
eri1a[:, p1:] = 0
eri1a = eri1a + eri1a.transpose(0, 2, 1, 3, 4)
eri1a = eri1a + eri1a.transpose(0, 3, 4, 1, 2)
g1 = numpy.einsum('xpjkl,pi->xijkl', eri1a, mo_coeff)
g1 = numpy.einsum('xipkl,pj->xijkl', g1, mo_coeff)
g1 = numpy.einsum('xijpl,pk->xijkl', g1, mo_coeff)
g1 = numpy.einsum('xijkp,pl->xijkl', g1, mo_coeff)
g1 = g1 * 2 - g1.transpose(0, 1, 4, 3, 2)
f1 += numpy.einsum('xkkpq->xpq', g1[:, :nocc, :nocc])
f1ai = f1[:, nocc:, :nocc].copy()
c1 = s1mo * -.5
c1vo = cphf.solve(fvind, mo_energy, mo_occ, f1ai, max_cycle=50)[0]
c1[:, nocc:, :nocc] = c1vo
c1[:, :nocc,
nocc:] = -(s1mo[:, nocc:, :nocc] + c1vo).transpose(0, 2, 1)
f1 += numpy.einsum('kapq,xak->xpq', g[:nocc, nocc:], c1vo)
f1 += numpy.einsum('akpq,xak->xpq', g[nocc:, :nocc], c1vo)
e1 = numpy.einsum('xaijb,ai,bj->x', g1[:, nocc:, :nocc, :nocc, nocc:],
z, z)
e1 += numpy.einsum('xab,ai,bi->x', f1[:, nocc:, nocc:], z, z)
e1 -= numpy.einsum('xij,ai,aj->x', f1[:, :nocc, :nocc], z, z)
g1 = numpy.einsum('pjkl,xpi->xijkl', g, c1)
g1 += numpy.einsum('ipkl,xpj->xijkl', g, c1)
g1 += numpy.einsum('ijpl,xpk->xijkl', g, c1)
g1 += numpy.einsum('ijkp,xpl->xijkl', g, c1)
e1 += numpy.einsum('xaijb,ai,bj->x', g1[:, nocc:, :nocc, :nocc, nocc:],
z, z)
de[k] = e1
return de
def kernel(tdgrad, z, atmlst=None, mf_grad=None, max_memory=2000,
verbose=logger.INFO):
mol = tdgrad.mol
mf = tdgrad.base._scf
mo_coeff = mf.mo_coeff
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
nao, nmo = mo_coeff.shape
nocc = (mo_occ>0).sum()
nvir = nmo - nocc
#eai = lib.direct_sum('a-i->ai', mo_energy[nocc:], mo_energy[:nocc])
z = z[0].reshape(nocc,nvir).T
orbv = mo_coeff[:,nocc:]
orbo = mo_coeff[:,:nocc]
def fvind(x):
dm = numpy.einsum('pi,xij,qj->xpq', orbv, x, orbo)
v_ao = mf.get_veff(mol, (dm+dm.transpose(0,2,1)))*2
return numpy.einsum('pi,xpq,qj->xij', orbv, v_ao, orbo).reshape(3,-1)
h1 = rhf_grad.get_hcore(mol)
s1 = rhf_grad.get_ovlp(mol)
eri1 = -mol.intor('int2e_ip1', aosym='s1', comp=3)
eri1 = eri1.reshape(3,nao,nao,nao,nao)
eri0 = ao2mo.kernel(mol, mo_coeff)
eri0 = ao2mo.restore(1, eri0, nmo).reshape(nmo,nmo,nmo,nmo)
g = eri0 * 2 - eri0.transpose(0,3,2,1)
zeta = lib.direct_sum('i+j->ij', mo_energy, mo_energy) * .5
zeta[nocc:,:nocc] = mo_energy[:nocc]
zeta[:nocc,nocc:] = mo_energy[nocc:]
if atmlst is None:
atmlst = range(mol.natm)
offsetdic = mol.offset_nr_by_atom()
de = numpy.zeros((len(atmlst),3))
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = offsetdic[ia]
mol.set_rinv_origin(mol.atom_coord(ia))
h1ao = -mol.atom_charge(ia) * mol.intor('int1e_iprinv', comp=3)
h1ao[:,p0:p1] += h1[:,p0:p1]
h1ao = h1ao + h1ao.transpose(0,2,1)
h1mo = numpy.einsum('pi,xpq,qj->xij', mo_coeff, h1ao, mo_coeff)
s1mo = numpy.einsum('pi,xpq,qj->xij', mo_coeff[p0:p1], s1[:,p0:p1], mo_coeff)
s1mo = s1mo + s1mo.transpose(0,2,1)
f1 = h1mo - numpy.einsum('xpq,pq->xpq', s1mo, zeta)
f1-= numpy.einsum('klpq,xlk->xpq', g[:nocc,:nocc], s1mo[:,:nocc,:nocc])
eri1a = eri1.copy()
eri1a[:,:p0] = 0
eri1a[:,p1:] = 0
eri1a = eri1a + eri1a.transpose(0,2,1,3,4)
eri1a = eri1a + eri1a.transpose(0,3,4,1,2)
g1 = numpy.einsum('xpjkl,pi->xijkl', eri1a, mo_coeff)
g1 = numpy.einsum('xipkl,pj->xijkl', g1, mo_coeff)
g1 = numpy.einsum('xijpl,pk->xijkl', g1, mo_coeff)
g1 = numpy.einsum('xijkp,pl->xijkl', g1, mo_coeff)
g1 = g1 * 2 - g1.transpose(0,1,4,3,2)
f1 += numpy.einsum('xkkpq->xpq', g1[:,:nocc,:nocc])
f1ai = f1[:,nocc:,:nocc].copy()
c1 = s1mo * -.5
c1vo = cphf.solve(fvind, mo_energy, mo_occ, f1ai, max_cycle=50)[0]
c1[:,nocc:,:nocc] = c1vo
c1[:,:nocc,nocc:] = -(s1mo[:,nocc:,:nocc]+c1vo).transpose(0,2,1)
f1 += numpy.einsum('kapq,xak->xpq', g[:nocc,nocc:], c1vo)
f1 += numpy.einsum('akpq,xak->xpq', g[nocc:,:nocc], c1vo)
e1 = numpy.einsum('xaijb,ai,bj->x', g1[:,nocc:,:nocc,:nocc,nocc:], z, z)
e1 += numpy.einsum('xab,ai,bi->x', f1[:,nocc:,nocc:], z, z)
e1 -= numpy.einsum('xij,ai,aj->x', f1[:,:nocc,:nocc], z, z)
g1 = numpy.einsum('pjkl,xpi->xijkl', g, c1)
g1 += numpy.einsum('ipkl,xpj->xijkl', g, c1)
g1 += numpy.einsum('ijpl,xpk->xijkl', g, c1)
g1 += numpy.einsum('ijkp,xpl->xijkl', g, c1)
e1 += numpy.einsum('xaijb,ai,bj->x', g1[:,nocc:,:nocc,:nocc,nocc:], z, z)
de[k] = e1
return de