def get_jk(self, u):
mo_coeff = numpy.dot(self.mo_coeff, u)
nmo = mo_coeff.shape[1]
dms = [numpy.einsum('i,j->ij', mo_coeff[:,i], mo_coeff[:,i]) for i in range(nmo)]
vj, vk = hf.get_jk(self.mol, dms, hermi=1)
vj = numpy.asarray([reduce(numpy.dot, (mo_coeff.T, v, mo_coeff)) for v in vj])
vk = numpy.asarray([reduce(numpy.dot, (mo_coeff.T, v, mo_coeff)) for v in vk])
return vj, vk
def get_jk(self, mol=None, dm=None, hermi=1):
if mol is None: mol = self.mol
if dm is None: dm = self.make_rdm1()
cpu0 = (time.clock(), time.time())
if self._eri is not None or self._is_mem_enough():
if self._eri is None:
self._eri = _vhf.int2e_sph(mol._atm, mol._bas, mol._env)
vj, vk = hf.dot_eri_dm(self._eri, dm, hermi)
else:
vj, vk = hf.get_jk(mol, dm, hermi, self.opt)
logger.timer(self, 'vj and vk', *cpu0)
return vj, vk
def get_jk_(self, mol=None, dm=None, hermi=1):
if mol is None: mol = self.mol
if dm is None: dm = self.make_rdm1()
dm = numpy.asarray(dm)
nao = dm.shape[-1]
cpu0 = (time.clock(), time.time())
if self._eri is not None or mol.incore_anyway or self._is_mem_enough():
if self._eri is None:
self._eri = _vhf.int2e_sph(mol._atm, mol._bas, mol._env)
vj, vk = hf.dot_eri_dm(self._eri, dm.reshape(-1,nao,nao), hermi)
else:
if self.direct_scf:
self.opt = self.init_direct_scf(mol)
vj, vk = hf.get_jk(mol, dm.reshape(-1,nao,nao), hermi, self.opt)
logger.timer(self, 'vj and vk', *cpu0)
return vj.reshape(dm.shape), vk.reshape(dm.shape)
def get_jk(self, mol=None, dm=None, hermi=1):
if mol is None: mol = self.mol
if dm is None: dm = self.make_rdm1()
dm = numpy.asarray(dm)
nao = dm.shape[-1]
cpu0 = (time.clock(), time.time())
if self._eri is not None or mol.incore_anyway or self._is_mem_enough():
if self._eri is None:
self._eri = _vhf.int2e_sph(mol._atm, mol._bas, mol._env)
vj, vk = hf.dot_eri_dm(self._eri, dm.reshape(-1, nao, nao), hermi)
else:
if self.direct_scf:
self.opt = self.init_direct_scf(mol)
vj, vk = hf.get_jk(mol, dm.reshape(-1, nao, nao), hermi, self.opt)
logger.timer(self, 'vj and vk', *cpu0)
return vj.reshape(dm.shape), vk.reshape(dm.shape)
def get_veff(mol, dm, dm_last=0, vhf_last=0, hermi=1, vhfopt=None):
r'''Unrestricted Hartree-Fock potential matrix of alpha and beta spins,
for the given density matrix
.. math::
V_{ij}^\alpha &= \sum_{kl} (ij|kl)(\gamma_{lk}^\alpha+\gamma_{lk}^\beta)
- \sum_{kl} (il|kj)\gamma_{lk}^\alpha \\
V_{ij}^\beta &= \sum_{kl} (ij|kl)(\gamma_{lk}^\alpha+\gamma_{lk}^\beta)
- \sum_{kl} (il|kj)\gamma_{lk}^\beta
Args:
mol : an instance of :class:`Mole`
dm : a list of ndarrays
A list of density matrices, stored as (alpha,alpha,...,beta,beta,...)
Kwargs:
dm_last : ndarray or a list of ndarrays or 0
The density matrix baseline. When it is 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.
hermi : int
Whether J, K matrix is hermitian
| 0 : no hermitian or symmetric
| 1 : hermitian
| 2 : anti-hermitian
vhfopt :
A class which holds precomputed quantities to optimize the
computation of J, K matrices
Returns:
:math:`V_{hf} = (V^\alpha, V^\beta)`. :math:`V^\alpha` (and :math:`V^\beta`)
can be a list matrices, corresponding to the input density matrices.
Examples:
>>> import numpy
>>> from pyscf import gto, scf
>>> from pyscf.scf import _vhf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> dmsa = numpy.random.random((3,mol.nao_nr(),mol.nao_nr()))
>>> dmsb = numpy.random.random((3,mol.nao_nr(),mol.nao_nr()))
>>> dms = numpy.vstack((dmsa,dmsb))
>>> dms.shape
(6, 2, 2)
>>> vhfa, vhfb = scf.uhf.get_veff(mol, dms, hermi=0)
>>> vhfa.shape
(3, 2, 2)
>>> vhfb.shape
(3, 2, 2)
'''
if ((isinstance(dm, numpy.ndarray) and dm.ndim == 4) or
(isinstance(dm[0], numpy.ndarray) and dm[0].ndim == 3) or
(isinstance(dm[0][0], numpy.ndarray) and dm[0][0].ndim == 2)):
# remove first dim, compress (dma,dmb)
dm = numpy.vstack(dm)
ddm = numpy.array(dm, copy=False) - numpy.array(dm_last, copy=False)
vj, vk = hf.get_jk(mol, ddm, hermi=hermi, vhfopt=vhfopt)
nset = len(dm) // 2
vhf = _makevhf(vj, vk, nset) + numpy.array(vhf_last, copy=False)
return vhf
def get_veff(mol, dm, dm_last=0, vhf_last=0, hermi=1, vhfopt=None):
r'''Unrestricted Hartree-Fock potential matrix of alpha and beta spins,
for the given density matrix
.. math::
V_{ij}^\alpha &= \sum_{kl} (ij|kl)(\gamma_{lk}^\alpha+\gamma_{lk}^\beta)
- \sum_{kl} (il|kj)\gamma_{lk}^\alpha \\
V_{ij}^\beta &= \sum_{kl} (ij|kl)(\gamma_{lk}^\alpha+\gamma_{lk}^\beta)
- \sum_{kl} (il|kj)\gamma_{lk}^\beta
Args:
mol : an instance of :class:`Mole`
dm : a list of ndarrays
A list of density matrices, stored as (alpha,alpha,...,beta,beta,...)
Kwargs:
dm_last : ndarray or a list of ndarrays or 0
The density matrix baseline. When it is 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.
hermi : int
Whether J, K matrix is hermitian
| 0 : no hermitian or symmetric
| 1 : hermitian
| 2 : anti-hermitian
vhfopt :
A class which holds precomputed quantities to optimize the
computation of J, K matrices
Returns:
:math:`V_{hf} = (V^\alpha, V^\beta)`. :math:`V^\alpha` (and :math:`V^\beta`)
can be a list matrices, corresponding to the input density matrices.
Examples:
>>> import numpy
>>> from pyscf import gto, scf
>>> from pyscf.scf import _vhf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> dmsa = numpy.random.random((3,mol.nao_nr(),mol.nao_nr()))
>>> dmsb = numpy.random.random((3,mol.nao_nr(),mol.nao_nr()))
>>> dms = numpy.vstack((dmsa,dmsb))
>>> dms.shape
(6, 2, 2)
>>> vhfa, vhfb = scf.uhf.get_veff(mol, dms, hermi=0)
>>> vhfa.shape
(3, 2, 2)
>>> vhfb.shape
(3, 2, 2)
'''
dm = numpy.asarray(dm)
nao = dm.shape[-1]
ddm = dm - numpy.asarray(dm_last)
# dm.reshape(-1,nao,nao) to remove first dim, compress (dma,dmb)
vj, vk = hf.get_jk(mol,
ddm.reshape(-1, nao, nao),
hermi=hermi,
vhfopt=vhfopt)
vhf = _makevhf(vj.reshape(dm.shape), vk.reshape(dm.shape))
vhf += numpy.asarray(vhf_last)
return vhf
def dump(self, fname='mole.h5'):
# Effective
nbas = self.nbas - self.nfrozen
sbas = nbas * 2
print('\n[iface.dump] (self.nbas,nbas)=', (self.nbas, nbas))
# Basic information
f = h5py.File(fname, "w")
cal = f.create_dataset("cal", (1, ), dtype='i')
enuc = self.mol.energy_nuc()
nelecA = self.nelec - self.nfrozen * 2
cal.attrs["nelec"] = nelecA
cal.attrs["sbas"] = sbas
cal.attrs["enuc"] = enuc
cal.attrs["escf"] = 0. # Not useful at all
# Intergrals
flter = 'lzf'
mcoeffC = self.mo_coeff[:, :self.nfrozen].copy()
mcoeffA = self.mo_coeff[:, self.nfrozen:].copy()
# Core part
pCore = 2.0 * mcoeffC.dot(mcoeffC.T)
vj, vk = hf.get_jk(self.mol, pCore)
h = self.mf.get_hcore()
fock = h + vj - 0.5 * vk
fmo = reduce(numpy.dot, (mcoeffA.T, fock, mcoeffA))
ecore = 0.5 * numpy.trace(pCore.dot(h + fock))
# Active part
nact = mcoeffA.shape[1]
eri = ao2mo.general(self.mol, (mcoeffA, mcoeffA, mcoeffA, mcoeffA),
compact=0)
eri = eri.reshape(nact, nact, nact, nact)
# Reorder
if self.ifreorder:
order = fielder.orbitalOrdering(eri, 'kij')
else:
order = list(range(mcoeffA.shape[1]))
# Sort
mcoeffA = mcoeffA[:, numpy.array(order)].copy()
fmo = fmo[numpy.ix_(order, order)].copy()
eri = eri[numpy.ix_(order, order, order, order)].copy()
#========================
# Spin orbital integrals
#========================
gmo_coeff = numpy.hstack((mcoeffC, mcoeffA))
print('gmo_coeff.shape=', gmo_coeff.shape)
f.create_dataset("mo_coeff_spatialAll", data=gmo_coeff)
# INT1e:
h1e = numpy.zeros((sbas, sbas))
h1e[0::2, 0::2] = fmo # AA
h1e[1::2, 1::2] = fmo # BB
# INT2e:
h2e = numpy.zeros((sbas, sbas, sbas, sbas))
h2e[0::2, 0::2, 0::2, 0::2] = eri # AAAA
h2e[1::2, 1::2, 1::2, 1::2] = eri # BBBB
h2e[0::2, 0::2, 1::2, 1::2] = eri # AABB
h2e[1::2, 1::2, 0::2, 0::2] = eri # BBAA
# <ij|kl> = [ik|jl]
h2e = h2e.transpose(0, 2, 1, 3)
# Antisymmetrize V[pqrs]=-1/2*<pq||rs> - In MPO construnction, only r<s part is used.
h2e = -0.5 * (h2e - h2e.transpose(0, 1, 3, 2))
print('E[core]=', ecore)
cal.attrs["ecor"] = ecore
int1e = f.create_dataset("int1e", data=h1e, compression=flter)
int2e = f.create_dataset("int2e", data=h2e, compression=flter)
# Occupation
occun = numpy.zeros(sbas)
for i in range(self.nalpha - self.nfrozen):
occun[2 * i] = 1.0
for i in range(self.nbeta - self.nfrozen):
occun[2 * i + 1] = 1.0
print()
print('initial occun for', len(occun), ' spin orbitals:\n', occun)
sorder = numpy.array([[2 * i, 2 * i + 1] for i in order]).flatten()
occun = occun[sorder].copy()
assert abs(numpy.sum(occun) - nelecA) < 1.e-10
print("sorder:", sorder)
print("occun :", occun)
orbsym = numpy.array([0] * sbas)
spinsym = numpy.array([[0, 1] for i in range(nbas)]).flatten()
print("orbsym :", orbsym)
print("spinsym:", spinsym)
f.create_dataset("occun", data=occun)
f.create_dataset("orbsym", data=orbsym)
f.create_dataset("spinsym", data=spinsym)
f.close()
print('Successfully dump information for HS-DMRG calculations! fname=',
fname)
self.check(fname)
return 0
