def gen_vind(self, mf):
wfnsym = self.wfnsym
singlet = self.singlet
mol = mf.mol
mo_coeff = mf.mo_coeff
assert (mo_coeff.dtype == numpy.double)
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
nao, nmo = mo_coeff.shape
occidx = numpy.where(mo_occ == 2)[0]
viridx = numpy.where(mo_occ == 0)[0]
nocc = len(occidx)
nvir = len(viridx)
orbv = mo_coeff[:, viridx]
orbo = mo_coeff[:, occidx]
if wfnsym is not None and mol.symmetry:
orbsym = hf_symm.get_orbsym(mol, mo_coeff)
sym_forbid = (orbsym[viridx].reshape(-1, 1)
^ orbsym[occidx]) != wfnsym
eai = mo_energy[viridx].reshape(-1, 1) - mo_energy[occidx]
if wfnsym is not None and mol.symmetry:
eai[sym_forbid] = 0
dai = numpy.sqrt(eai).ravel()
edai = eai.ravel() * dai
hdiag = eai.ravel()**2
vresp = _gen_rhf_response(mf, singlet=singlet, hermi=1)
def vind(zs):
nz = len(zs)
dmvo = numpy.empty((nz, nao, nao))
for i, z in enumerate(zs):
# *2 for double occupancy
dm = reduce(numpy.dot,
(orbv, (dai * z).reshape(nvir, nocc) * 2, orbo.T))
dmvo[
i] = dm + dm.T # +cc for A+B and K_{ai,jb} in A == K_{ai,bj} in B
v1ao = vresp(dmvo)
v1vo = _ao2mo.nr_e2(v1ao, mo_coeff,
(nocc, nmo, 0, nocc)).reshape(-1, nvir * nocc)
for i, z in enumerate(zs):
# numpy.sqrt(eai) * (eai*dai*z + v1vo)
v1vo[i] += edai * z
v1vo[i] *= dai
return v1vo.reshape(nz, -1)
return vind, hdiag
def gen_vind(self, mf):
'''Induced potential'''
vresp = _gen_rhf_response(mf, hermi=2)
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
occidx = mo_occ > 0
orbo = mo_coeff[:,occidx]
nocc = orbo.shape[1]
nao, nmo = mo_coeff.shape
def vind(mo1):
#direct_scf_bak, mf.direct_scf = mf.direct_scf, False
dm1 = [reduce(numpy.dot, (mo_coeff, x*2, orbo.T.conj()))
for x in mo1.reshape(3,nmo,nocc)]
dm1 = numpy.asarray([d1-d1.conj().T for d1 in dm1])
v1mo = numpy.asarray([reduce(numpy.dot, (mo_coeff.T.conj(), x, orbo))
for x in vresp(dm1)])
#mf.direct_scf = direct_scf_bak
return v1mo.ravel()
return vind
def gen_vind(self, mf, mo_coeff, mo_occ):
'''Induced potential associated with h1_PSO'''
vresp = _gen_rhf_response(mf, hermi=2)
occidx = mo_occ > 0
orbo = mo_coeff[:, occidx]
orbv = mo_coeff[:, ~occidx]
nocc = orbo.shape[1]
nao, nmo = mo_coeff.shape
nvir = nmo - nocc
def vind(mo1):
#direct_scf_bak, mf.direct_scf = mf.direct_scf, False
dm1 = [
reduce(numpy.dot, (orbv, x * 2, orbo.T.conj()))
for x in mo1.reshape(-1, nvir, nocc)
]
dm1 = numpy.asarray([d1 - d1.conj().T for d1 in dm1])
v1mo = numpy.asarray([
reduce(numpy.dot, (orbv.T.conj(), x, orbo)) for x in vresp(dm1)
])
#mf.direct_scf = direct_scf_bak
return v1mo.ravel()
return vind
def solve_mo1_fc(sscobj, h1):
cput1 = (time.clock(), time.time())
log = logger.Logger(sscobj.stdout, sscobj.verbose)
mol = sscobj.mol
mo_energy = sscobj._scf.mo_energy
mo_coeff = sscobj._scf.mo_coeff
mo_occ = sscobj._scf.mo_occ
nset = len(h1)
eai = 1. / lib.direct_sum('a-i->ai', mo_energy[mo_occ == 0],
mo_energy[mo_occ > 0])
mo1 = numpy.asarray(h1) * -eai
if not sscobj.cphf:
return mo1
orbo = mo_coeff[:, mo_occ > 0]
orbv = mo_coeff[:, mo_occ == 0]
nocc = orbo.shape[1]
nvir = orbv.shape[1]
nmo = nocc + nvir
vresp = _gen_rhf_response(mf, singlet=False, hermi=1)
mo_v_o = numpy.asarray(numpy.hstack((orbv, orbo)), order='F')
def vind(mo1):
dm1 = _dm1_mo2ao(mo1.reshape(nset, nvir, nocc), orbv,
orbo * 2) # *2 for double occupancy
dm1 = dm1 + dm1.transpose(0, 2, 1)
v1 = vresp(dm1)
v1 = _ao2mo.nr_e2(v1, mo_v_o,
(0, nvir, nvir, nmo)).reshape(nset, nvir, nocc)
v1 *= eai
return v1.ravel()
mo1 = lib.krylov(vind, mo1.ravel(), tol=1e-9, max_cycle=20, verbose=log)
log.timer('solving FC CPHF eqn', *cput1)
return mo1.reshape(nset, nvir, nocc)
def _gen_hop_rhf_external(mf, with_symmetry=True, verbose=None):
mol = mf.mol
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
occidx = numpy.where(mo_occ==2)[0]
viridx = numpy.where(mo_occ==0)[0]
nocc = len(occidx)
nvir = len(viridx)
orbv = mo_coeff[:,viridx]
orbo = mo_coeff[:,occidx]
if with_symmetry and mol.symmetry:
orbsym = hf_symm.get_orbsym(mol, mo_coeff)
sym_forbid = orbsym[viridx].reshape(-1,1) != orbsym[occidx]
h1e = mf.get_hcore()
dm0 = mf.make_rdm1(mo_coeff, mo_occ)
fock_ao = h1e + mf.get_veff(mol, dm0)
fock = reduce(numpy.dot, (mo_coeff.T, fock_ao, mo_coeff))
foo = fock[occidx[:,None],occidx]
fvv = fock[viridx[:,None],viridx]
hdiag = fvv.diagonal().reshape(-1,1) - foo.diagonal()
if with_symmetry and mol.symmetry:
hdiag[sym_forbid] = 0
hdiag = hdiag.ravel()
vrespz = _gen_rhf_response(mf, singlet=None, hermi=2)
def hop_real2complex(x1):
x1 = x1.reshape(nvir,nocc)
if with_symmetry and mol.symmetry:
x1 = x1.copy()
x1[sym_forbid] = 0
x2 = numpy.einsum('ps,sq->pq', fvv, x1)
x2-= numpy.einsum('ps,rp->rs', foo, x1)
d1 = reduce(numpy.dot, (orbv, x1*2, orbo.T.conj()))
dm1 = d1 - d1.T.conj()
# No Coulomb and fxc contribution for anti-hermitian DM
v1 = vrespz(dm1)
x2 += reduce(numpy.dot, (orbv.T.conj(), v1, orbo))
if with_symmetry and mol.symmetry:
x2[sym_forbid] = 0
return x2.ravel()
vresp1 = _gen_rhf_response(mf, singlet=False, hermi=1)
def hop_rhf2uhf(x1):
from pyscf.dft import numint
# See also rhf.TDA triplet excitation
x1 = x1.reshape(nvir,nocc)
if with_symmetry and mol.symmetry:
x1 = x1.copy()
x1[sym_forbid] = 0
x2 = numpy.einsum('ps,sq->pq', fvv, x1)
x2-= numpy.einsum('ps,rp->rs', foo, x1)
d1 = reduce(numpy.dot, (orbv, x1*2, orbo.T.conj()))
dm1 = d1 + d1.T.conj()
v1ao = vresp1(dm1)
x2 += reduce(numpy.dot, (orbv.T.conj(), v1ao, orbo))
if with_symmetry and mol.symmetry:
x2[sym_forbid] = 0
return x2.ravel()
return hop_real2complex, hdiag, hop_rhf2uhf, hdiag
def gen_vind(self, mf):
'''
[ A B][X]
[-B -A][Y]
'''
wfnsym = self.wfnsym
singlet = self.singlet
mol = mf.mol
mo_coeff = mf.mo_coeff
assert (mo_coeff.dtype == numpy.double)
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
nao, nmo = mo_coeff.shape
occidx = numpy.where(mo_occ == 2)[0]
viridx = numpy.where(mo_occ == 0)[0]
nocc = len(occidx)
nvir = len(viridx)
orbv = mo_coeff[:, viridx]
orbo = mo_coeff[:, occidx]
if wfnsym is not None and mol.symmetry:
orbsym = hf_symm.get_orbsym(mol, mo_coeff)
sym_forbid = (orbsym[viridx].reshape(-1, 1)
^ orbsym[occidx]) != wfnsym
#dm0 = mf.make_rdm1(mo_coeff, mo_occ)
#fock_ao = mf.get_hcore() + mf.get_veff(mol, dm0)
#fock = reduce(numpy.dot, (mo_coeff.T, fock_ao, mo_coeff))
#foo = fock[occidx[:,None],occidx]
#fvv = fock[viridx[:,None],viridx]
foo = numpy.diag(mo_energy[occidx])
fvv = numpy.diag(mo_energy[viridx])
e_ai = hdiag = fvv.diagonal().reshape(-1, 1) - foo.diagonal()
if wfnsym is not None and mol.symmetry:
hdiag[sym_forbid] = 0
hdiag = numpy.hstack((hdiag.ravel(), hdiag.ravel()))
mo_coeff = numpy.asarray(numpy.hstack((orbo, orbv)), order='F')
vresp = _gen_rhf_response(mf, singlet=singlet, hermi=0)
def vind(xys):
nz = len(xys)
if wfnsym is not None and mol.symmetry:
# shape(nz,2,nvir,nocc): 2 ~ X,Y
xys = numpy.copy(zs).reshape(nz, 2, nvir, nocc)
xys[:, :, sym_forbid] = 0
dms = numpy.empty((nz, nao, nao))
for i in range(nz):
x, y = xys[i].reshape(2, nvir, nocc)
# *2 for double occupancy
dmx = reduce(numpy.dot, (orbv, x * 2, orbo.T))
dmy = reduce(numpy.dot, (orbo, y.T * 2, orbv.T))
dms[i] = dmx + dmy # AX + BY
v1ao = vresp(dms)
v1vo = _ao2mo.nr_e2(v1ao, mo_coeff,
(nocc, nmo, 0, nocc)).reshape(-1, nvir, nocc)
v1ov = _ao2mo.nr_e2(v1ao, mo_coeff, (0, nocc, nocc, nmo))
v1ov = v1ov.reshape(-1, nocc, nvir).transpose(0, 2, 1)
hx = numpy.empty((nz, 2, nvir, nocc), dtype=v1vo.dtype)
for i in range(nz):
x, y = xys[i].reshape(2, nvir, nocc)
hx[i, 0] = v1vo[i]
hx[i, 0] += numpy.einsum('ps,sq->pq', fvv, x) # AX
hx[i, 0] -= numpy.einsum('ps,rp->rs', foo, x) # AX
hx[i, 1] = -v1ov[i]
hx[i, 1] -= numpy.einsum('ps,sq->pq', fvv, y) #-AY
hx[i, 1] += numpy.einsum('ps,rp->rs', foo, y) #-AY
if wfnsym is not None and mol.symmetry:
hx[:, :, sym_forbid] = 0
return hx.reshape(nz, -1)
return vind, hdiag
def gen_tda_hop(mf, fock_ao=None, singlet=True, wfnsym=None, max_memory=2000):
'''(A+B)x
Kwargs:
wfnsym : int
Point group symmetry for excited CIS wavefunction.
'''
mol = mf.mol
mo_coeff = mf.mo_coeff
assert (mo_coeff.dtype == numpy.double)
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
nao, nmo = mo_coeff.shape
occidx = numpy.where(mo_occ == 2)[0]
viridx = numpy.where(mo_occ == 0)[0]
nocc = len(occidx)
nvir = len(viridx)
orbv = mo_coeff[:, viridx]
orbo = mo_coeff[:, occidx]
if wfnsym is not None and mol.symmetry:
orbsym = hf_symm.get_orbsym(mol, mo_coeff)
sym_forbid = (orbsym[viridx].reshape(-1, 1) ^ orbsym[occidx]) != wfnsym
if fock_ao is None:
#dm0 = mf.make_rdm1(mo_coeff, mo_occ)
#fock_ao = mf.get_hcore() + mf.get_veff(mol, dm0)
foo = numpy.diag(mo_energy[occidx])
fvv = numpy.diag(mo_energy[viridx])
else:
fock = reduce(numpy.dot, (mo_coeff.T, fock_ao, mo_coeff))
foo = fock[occidx[:, None], occidx]
fvv = fock[viridx[:, None], viridx]
hdiag = fvv.diagonal().reshape(-1, 1) - foo.diagonal()
if wfnsym is not None and mol.symmetry:
hdiag[sym_forbid] = 0
hdiag = hdiag.ravel()
mo_coeff = numpy.asarray(numpy.hstack((orbo, orbv)), order='F')
vresp = _gen_rhf_response(mf, singlet=singlet, hermi=0)
def vind(zs):
nz = len(zs)
if wfnsym is not None and mol.symmetry:
zs = numpy.copy(zs).reshape(-1, nvir, nocc)
zs[:, sym_forbid] = 0
dmvo = numpy.empty((nz, nao, nao))
for i, z in enumerate(zs):
# *2 for double occupancy
dmvo[i] = reduce(numpy.dot,
(orbv, z.reshape(nvir, nocc) * 2, orbo.T))
v1ao = vresp(dmvo)
#v1vo = numpy.asarray([reduce(numpy.dot, (orbv.T, v, orbo)) for v in v1ao])
v1vo = _ao2mo.nr_e2(v1ao, mo_coeff,
(nocc, nmo, 0, nocc)).reshape(-1, nvir, nocc)
for i, z in enumerate(zs):
v1vo[i] += numpy.einsum('ps,sq->pq', fvv, z.reshape(nvir, nocc))
v1vo[i] -= numpy.einsum('ps,rp->rs', foo, z.reshape(nvir, nocc))
if wfnsym is not None and mol.symmetry:
v1vo[:, sym_forbid] = 0
return v1vo.reshape(nz, -1)
return vind, hdiag
