def gen_g_hop_rhf(mf, mo_coeff, mo_occ, fock_ao=None):
mol = mf.mol
occidx = numpy.where(mo_occ==2)[0]
viridx = numpy.where(mo_occ==0)[0]
nocc = len(occidx)
nvir = len(viridx)
if fock_ao is None:
dm1 = mf.make_rdm1(mo_coeff, mo_occ)
fock_ao = mf.get_hcore() + mf.get_veff(mol, dm1)
fock = reduce(numpy.dot, (mo_coeff.T, fock_ao, mo_coeff))
g = fock[viridx[:,None],occidx] * 2
foo = fock[occidx[:,None],occidx]
fvv = fock[viridx[:,None],viridx]
h_diag = (fvv.diagonal().reshape(-1,1)-foo.diagonal()) * 2
if hasattr(mf, 'xc'):
if APPROX_XC_HESSIAN:
from pyscf.dft import vxc
x_code = vxc.parse_xc_name(mf.xc)[0]
hyb = vxc.hybrid_coeff(x_code, spin=(mol.spin>0)+1)
else:
save_for_dft = [None, None] # (dm, veff)
def h_op(x):
x = x.reshape(nvir,nocc)
x2 =-numpy.einsum('sq,ps->pq', foo, x) * 2
x2+= numpy.einsum('pr,rq->pq', fvv, x) * 2
d1 = reduce(numpy.dot, (mo_coeff[:,viridx], x, mo_coeff[:,occidx].T))
if hasattr(mf, 'xc'):
if APPROX_XC_HESSIAN:
vj, vk = mf.get_jk(mol, d1+d1.T)
if abs(hyb) < 1e-10:
dvhf = vj
else:
dvhf = vj - vk * hyb * .5
else:
if save_for_dft[0] is None:
save_for_dft[0] = mf.make_rdm1(mo_coeff, mo_occ)
save_for_dft[1] = mf.get_veff(mol, save_for_dft[0])
dm1 = save_for_dft[0] + d1 + d1.T
vhf1 = mf.get_veff(mol, dm1, dm_last=save_for_dft[0],
vhf_last=save_for_dft[1])
dvhf = vhf1 - save_for_dft[1]
save_for_dft[0] = dm1
save_for_dft[1] = vhf1
else:
dvhf = mf.get_veff(mol, d1+d1.T)
x2 += reduce(numpy.dot, (mo_coeff[:,viridx].T, dvhf,
mo_coeff[:,occidx])) * 4
return x2.reshape(-1)
return g.reshape(-1), h_op, h_diag.reshape(-1)
def get_veff_(ks, mol, dm, dm_last=0, vhf_last=0, hermi=1):
'''Coulomb + XC functional for UKS. See pyscf/dft/rks.py
:func:`get_veff_` fore more details'''
if isinstance(dm, numpy.ndarray) and dm.ndim == 2:
dm = numpy.array((dm*.5,dm*.5))
nset = len(dm) // 2
t0 = (time.clock(), time.time())
if ks.grids.coords is None:
ks.grids.setup_grids_()
t0 = logger.timer(ks, 'seting up grids', *t0)
x_code, c_code = vxc.parse_xc_name(ks.xc)
n, ks._exc, vx = \
ks._numint.nr_uks(mol, ks.grids, x_code, c_code,
dm, verbose=ks.verbose)
logger.debug(ks, 'nelec by numeric integration = %s', n)
t0 = logger.timer(ks, 'vxc', *t0)
hyb = vxc.hybrid_coeff(x_code, spin=(mol.spin>0)+1)
if abs(hyb) < 1e-10:
vj = ks.get_j(mol, dm, hermi)
elif (ks._eri is not None or ks._is_mem_enough() or not ks.direct_scf):
vj, vk = ks.get_jk(mol, dm, hermi)
else:
if (ks.direct_scf and isinstance(vhf_last, numpy.ndarray) and
hasattr(ks, '_dm_last')):
ddm = numpy.asarray(dm) - numpy.asarray(ks._dm_last)
vj, vk = ks.get_jk(mol, ddm, hermi=hermi)
vj += ks._vj_last
vk += ks._vk_last
else:
vj, vk = ks.get_jk(mol, dm, hermi)
ks._dm_last = dm
ks._vj_last, ks._vk_last = vj, vk
if abs(hyb) > 1e-10:
if nset == 1:
ks._exc -=(numpy.einsum('ij,ji', dm[0], vk[0])
+numpy.einsum('ij,ji', dm[1], vk[1])) * .5 * hyb
vhf = pyscf.scf.uhf._makevhf(vj, vk*hyb, nset)
else:
if nset == 1:
vhf = vj[0] + vj[1]
else:
vhf = vj[:nset] + vj[nset:]
vhf = numpy.array((vhf,vhf))
if nset == 1:
ks._ecoul = numpy.einsum('ij,ji', dm[0]+dm[1], vj[0]+vj[1]) * .5
return vhf + vx
def get_veff_(ks, mol, dm, dm_last=0, vhf_last=0, hermi=1):
'''Coulomb + XC functional'''
t0 = (time.clock(), time.time())
if ks.grids.coords is None:
ks.grids.setup_grids_()
t0 = logger.timer(ks, 'seting up grids', *t0)
x_code, c_code = vxc.parse_xc_name(ks.xc)
#n, ks._exc, vx = vxc.nr_vxc(mol, ks.grids, x_code, c_code,
# dm, spin=1, relativity=0)
if ks._numint is None:
n, ks._exc, vx = numint.nr_vxc(mol, ks.grids, x_code, c_code,
dm, spin=mol.spin, relativity=0)
else:
n, ks._exc, vx = \
ks._numint.nr_vxc(mol, ks.grids, x_code, c_code,
dm, spin=mol.spin, relativity=0)
logger.debug(ks, 'nelec by numeric integration = %s', n)
t0 = logger.timer(ks, 'vxc', *t0)
hyb = vxc.hybrid_coeff(x_code, spin=1)
if abs(hyb) < 1e-10:
vj = ks.get_j(mol, dm, hermi)
elif (ks._eri is not None or ks._is_mem_enough() or
not ks.direct_scf):
vj, vk = ks.get_jk(mol, dm, hermi)
else:
if isinstance(vhf_last, numpy.ndarray):
ddm = numpy.asarray(dm) - numpy.asarray(dm_last)
vj, vk = ks.get_jk(mol, ddm, hermi=hermi)
vj += ks._vj_last
vk += ks._vk_last
else:
vj, vk = ks.get_jk(mol, dm, hermi)
ks._vj_last, ks._vk_last = vj, vk
if abs(hyb) > 1e-10:
if isinstance(dm, numpy.ndarray) and dm.ndim == 2:
ks._exc -= numpy.einsum('ij,ji', dm, vk) * .5 * hyb*.5
vhf = vj - vk * (hyb * .5)
else:
vhf = vj
if isinstance(dm, numpy.ndarray) and dm.ndim == 2:
ks._ecoul = numpy.einsum('ij,ji', dm, vj) * .5
return vhf + vx
def gen_g_hop_rohf(mf, mo_coeff, mo_occ, fock_ao=None):
mol = mf.mol
occidxa = numpy.where(mo_occ>0)[0]
occidxb = numpy.where(mo_occ==2)[0]
viridxa = numpy.where(mo_occ==0)[0]
viridxb = numpy.where(mo_occ<2)[0]
mask = pyscf.scf.hf.uniq_var_indices(mo_occ)
if fock_ao is None:
dm1 = mf.make_rdm1(mo_coeff, mo_occ)
fock_ao = mf.get_hcore() + mf.get_veff(mol, dm1)
focka = reduce(numpy.dot, (mo_coeff.T, fock_ao[0], mo_coeff))
fockb = reduce(numpy.dot, (mo_coeff.T, fock_ao[1], mo_coeff))
g = numpy.zeros_like(focka)
g[viridxa[:,None],occidxa] = focka[viridxa[:,None],occidxa]
g[viridxb[:,None],occidxb] += fockb[viridxb[:,None],occidxb]
g = g[mask]
h_diag = numpy.zeros_like(focka)
h_diag[viridxa[:,None],occidxa] -= focka[occidxa,occidxa]
h_diag[viridxa[:,None],occidxa] += focka[viridxa,viridxa].reshape(-1,1)
h_diag[viridxb[:,None],occidxb] -= fockb[occidxb,occidxb]
h_diag[viridxb[:,None],occidxb] += fockb[viridxb,viridxb].reshape(-1,1)
h_diag = h_diag[mask]
if hasattr(mf, 'xc'):
if APPROX_XC_HESSIAN:
from pyscf.dft import vxc
x_code = vxc.parse_xc_name(mf.xc)[0]
hyb = vxc.hybrid_coeff(x_code, spin=(mol.spin>0)+1)
else:
save_for_dft = [None, None] # (dm, veff)
def h_op(x):
x1 = numpy.zeros_like(focka)
x1[mask] = x
x1 = x1 - x1.T
x2 = numpy.zeros_like(focka)
#: x2[nb:,:na] = numpy.einsum('sp,qs->pq', focka[:na,nb:], x1[:na,:na])
#: x2[nb:,:na] += numpy.einsum('rq,rp->pq', focka[:na,:na], x1[:na,nb:])
#: x2[na:,:na] -= numpy.einsum('sp,rp->rs', focka[:na,:na], x1[na:,:na])
#: x2[na:,:na] -= numpy.einsum('ps,qs->pq', focka[na:], x1[:na]) * 2
#: x2[nb:na,:nb] += numpy.einsum('qr,pr->pq', focka[:nb], x1[nb:na])
#: x2[nb:na,:nb] -= numpy.einsum('rq,sq->rs', focka[nb:na], x1[:nb])
#: x2[nb:,:na] += numpy.einsum('sp,qs->pq', fockb[:nb,nb:], x1[:na,:nb])
#: x2[nb:,:na] += numpy.einsum('rq,rp->pq', fockb[:nb,:na], x1[:nb,nb:])
#: x2[nb:,:nb] -= numpy.einsum('sp,rp->rs', fockb[:nb], x1[nb:])
#: x2[nb:,:nb] -= numpy.einsum('rq,sq->rs', fockb[nb:], x1[:nb]) * 2
x2[viridxb[:,None],occidxa] = \
(numpy.einsum('sp,qs->pq', focka[occidxa[:,None],viridxb], x1[occidxa[:,None],occidxa])
+numpy.einsum('rq,rp->pq', focka[occidxa[:,None],occidxa], x1[occidxa[:,None],viridxb]))
x2[viridxa[:,None],occidxa] -= \
(numpy.einsum('sp,rp->rs', focka[occidxa[:,None],occidxa], x1[viridxa[:,None],occidxa])
+numpy.einsum('ps,qs->pq', focka[viridxa], x1[occidxa]) * 2)
x2[occidxa[:,None],occidxb] += \
(numpy.einsum('qr,pr->pq', focka[occidxb], x1[occidxa])
-numpy.einsum('rq,sq->rs', focka[occidxa], x1[occidxb]))
x2[viridxb[:,None],occidxa] += \
(numpy.einsum('sp,qs->pq', fockb[occidxb[:,None],viridxb], x1[occidxa[:,None],occidxb])
+numpy.einsum('rq,rp->pq', fockb[occidxb[:,None],occidxa], x1[occidxb[:,None],viridxb]))
x2[viridxb[:,None],occidxb] -= \
(numpy.einsum('sp,rp->rs', fockb[occidxb], x1[viridxb])
+numpy.einsum('rq,sq->rs', fockb[viridxb], x1[occidxb]) * 2)
x2 *= .5
d1a = reduce(numpy.dot, (mo_coeff[:,viridxa], x1[viridxa[:,None],occidxa], mo_coeff[:,occidxa].T))
d1b = reduce(numpy.dot, (mo_coeff[:,viridxb], x1[viridxb[:,None],occidxb], mo_coeff[:,occidxb].T))
if hasattr(mf, 'xc'):
if APPROX_XC_HESSIAN:
vj, vk = mf.get_jk(mol, numpy.array((d1a+d1a.T,d1b+d1b.T)))
if abs(hyb) < 1e-10:
dvhf = vj[0] + vj[1]
else:
dvhf = (vj[0] + vj[1]) - vk * hyb
else:
from pyscf.dft import uks
if save_for_dft[0] is None:
save_for_dft[0] = mf.make_rdm1(mo_coeff, mo_occ)
save_for_dft[1] = mf.get_veff(mol, save_for_dft[0])
dm1 = numpy.array((save_for_dft[0][0]+d1a+d1a.T,
save_for_dft[0][1]+d1b+d1b.T))
vhf1 = uks.get_veff_(mf, mol, dm1, dm_last=save_for_dft[0],
vhf_last=save_for_dft[1])
dvhf = (vhf1[0]-save_for_dft[1][0], vhf1[1]-save_for_dft[1][1])
save_for_dft[0] = dm1
save_for_dft[1] = vhf1
else:
dvhf = mf.get_veff(mol, numpy.array((d1a+d1a.T,d1b+d1b.T)))
x2[viridxa[:,None],occidxa] += reduce(numpy.dot, (mo_coeff[:,viridxa].T, dvhf[0], mo_coeff[:,occidxa]))
x2[viridxb[:,None],occidxb] += reduce(numpy.dot, (mo_coeff[:,viridxb].T, dvhf[1], mo_coeff[:,occidxb]))
return x2[mask]
return g, h_op, h_diag
def gen_g_hop_uhf(mf, mo_coeff, mo_occ, fock_ao=None):
mol = mf.mol
occidxa = numpy.where(mo_occ[0]>0)[0]
occidxb = numpy.where(mo_occ[1]>0)[0]
viridxa = numpy.where(mo_occ[0]==0)[0]
viridxb = numpy.where(mo_occ[1]==0)[0]
nocca = len(occidxa)
noccb = len(occidxb)
nvira = len(viridxa)
nvirb = len(viridxb)
if fock_ao is None:
dm1 = mf.make_rdm1(mo_coeff, mo_occ)
fock_ao = mf.get_hcore() + mf.get_veff(mol, dm1)
focka = reduce(numpy.dot, (mo_coeff[0].T, fock_ao[0], mo_coeff[0]))
fockb = reduce(numpy.dot, (mo_coeff[1].T, fock_ao[1], mo_coeff[1]))
g = numpy.hstack((focka[viridxa[:,None],occidxa].reshape(-1),
fockb[viridxb[:,None],occidxb].reshape(-1)))
h_diaga =(focka[viridxa,viridxa].reshape(-1,1) - focka[occidxa,occidxa])
h_diagb =(fockb[viridxb,viridxb].reshape(-1,1) - fockb[occidxb,occidxb])
h_diag = numpy.hstack((h_diaga.reshape(-1), h_diagb.reshape(-1)))
if hasattr(mf, 'xc'):
if APPROX_XC_HESSIAN:
from pyscf.dft import vxc
x_code = vxc.parse_xc_name(mf.xc)[0]
hyb = vxc.hybrid_coeff(x_code, spin=(mol.spin>0)+1)
else:
save_for_dft = [None, None] # (dm, veff)
def h_op(x):
x1a = x[:nvira*nocca].reshape(nvira,nocca)
x1b = x[nvira*nocca:].reshape(nvirb,noccb)
x2a = numpy.zeros((nvira,nocca))
x2b = numpy.zeros((nvirb,noccb))
x2a -= numpy.einsum('sq,ps->pq', focka[occidxa[:,None],occidxa], x1a)
x2a += numpy.einsum('rp,rq->pq', focka[viridxa[:,None],viridxa], x1a)
x2b -= numpy.einsum('sq,ps->pq', fockb[occidxb[:,None],occidxb], x1b)
x2b += numpy.einsum('rp,rq->pq', fockb[viridxb[:,None],viridxb], x1b)
d1a = reduce(numpy.dot, (mo_coeff[0][:,viridxa], x1a,
mo_coeff[0][:,occidxa].T))
d1b = reduce(numpy.dot, (mo_coeff[1][:,viridxb], x1b,
mo_coeff[1][:,occidxb].T))
if hasattr(mf, 'xc'):
if APPROX_XC_HESSIAN:
vj, vk = mf.get_jk(mol, numpy.array((d1a+d1a.T,d1b+d1b.T)))
if abs(hyb) < 1e-10:
dvhf = vj[0] + vj[1]
dvhf = (dvhf, dvhf)
else:
dvhf = (vj[0] + vj[1]) - vk * hyb
else:
if save_for_dft[0] is None:
save_for_dft[0] = mf.make_rdm1(mo_coeff, mo_occ)
save_for_dft[1] = mf.get_veff(mol, save_for_dft[0])
dm1 = numpy.array((save_for_dft[0][0]+d1a+d1a.T,
save_for_dft[0][1]+d1b+d1b.T))
vhf1 = mf.get_veff(mol, dm1, dm_last=save_for_dft[0],
vhf_last=save_for_dft[1])
dvhf = (vhf1[0]-save_for_dft[1][0], vhf1[1]-save_for_dft[1][1])
save_for_dft[0] = dm1
save_for_dft[1] = vhf1
else:
dvhf = mf.get_veff(mol, numpy.array((d1a+d1a.T,d1b+d1b.T)))
x2a += reduce(numpy.dot, (mo_coeff[0][:,viridxa].T, dvhf[0],
mo_coeff[0][:,occidxa]))
x2b += reduce(numpy.dot, (mo_coeff[1][:,viridxb].T, dvhf[1],
mo_coeff[1][:,occidxb]))
return numpy.hstack((x2a.ravel(), x2b.ravel()))
return g, h_op, h_diag
def get_veff_(ks, mol, dm, dm_last=0, vhf_last=0, hermi=1):
'''Coulomb + XC functional
.. note::
This function will change the ks object.
Args:
ks : an instance of :class:`RKS`
XC functional are controlled by ks.xc attribute. Attribute
ks.grids might be initialized. The ._exc and ._ecoul attributes
will be updated after return. Attributes ._dm_last, ._vj_last and
._vk_last might be changed if direct SCF method is applied.
dm : ndarray or list of ndarrays
A density matrix or a list of density matrices
Kwargs:
dm_last : ndarray or a list of ndarrays or 0
The density matrix baseline. If not 0, this function computes the
increment of HF potential w.r.t. the reference HF potential matrix.
vhf_last : ndarray or a list of ndarrays or 0
The reference HF potential matrix. If vhf_last is not given,
the function will not call direct_scf and attacalites ._dm_last,
._vj_last and ._vk_last will not be updated.
hermi : int
Whether J, K matrix is hermitian
| 0 : no hermitian or symmetric
| 1 : hermitian
| 2 : anti-hermitian
Returns:
matrix Veff = J + Vxc. Veff can be a list matrices, if the input
dm is a list of density matrices.
'''
t0 = (time.clock(), time.time())
if ks.grids.coords is None:
ks.grids.setup_grids_()
t0 = logger.timer(ks, 'seting up grids', *t0)
x_code, c_code = vxc.parse_xc_name(ks.xc)
hyb = vxc.hybrid_coeff(x_code, spin=(mol.spin>0)+1)
if hermi == 2: # because rho = 0
n, ks._exc, vx = 0, 0, 0
else:
if ks._numint is None:
n, ks._exc, vx = numint.nr_rks_vxc(mol, ks.grids, x_code, c_code,
dm, hermi=hermi)
else:
n, ks._exc, vx = ks._numint.nr_rks(mol, ks.grids, x_code, c_code,
dm, hermi=hermi)
logger.debug(ks, 'nelec by numeric integration = %s', n)
t0 = logger.timer(ks, 'vxc', *t0)
if abs(hyb) < 1e-10:
vj = ks.get_j(mol, dm, hermi)
elif (ks._eri is not None or ks._is_mem_enough() or not ks.direct_scf):
vj, vk = ks.get_jk(mol, dm, hermi)
else:
if (ks.direct_scf and isinstance(vhf_last, numpy.ndarray) and
hasattr(ks, '_dm_last')):
ddm = numpy.asarray(dm) - numpy.asarray(ks._dm_last)
vj, vk = ks.get_jk(mol, ddm, hermi=hermi)
vj += ks._vj_last
vk += ks._vk_last
else:
vj, vk = ks.get_jk(mol, dm, hermi)
ks._dm_last = dm
ks._vj_last, ks._vk_last = vj, vk
if abs(hyb) > 1e-10:
if isinstance(dm, numpy.ndarray) and dm.ndim == 2:
ks._exc -= numpy.einsum('ij,ji', dm, vk) * .5 * hyb*.5
vhf = vj - vk * (hyb * .5)
else:
vhf = vj
if isinstance(dm, numpy.ndarray) and dm.ndim == 2:
ks._ecoul = numpy.einsum('ij,ji', dm, vj) * .5
return vhf + vx