def get_energy(self, b):
self.iter += 1
ba = b[:self.nbf]
bb = b[self.nbf:]
self.Hoepa = get_Hoep(ba, self.H0, self.Gij)
self.Hoepb = get_Hoep(bb, self.H0, self.Gij)
self.orbea, self.orbsa = geigh(self.Hoepa, self.S)
self.orbeb, self.orbsb = geigh(self.Hoepb, self.S)
if self.etemp:
self.Da, entropya = mkdens_fermi(2 * self.nalpha, self.orbea,
self.orbsa, self.etemp)
self.Db, entropyb = mkdens_fermi(2 * self.nbeta, self.orbeb,
self.orbsb, self.etemp)
self.entropy = 0.5 * (entropya + entropyb)
else:
self.Da = mkdens(self.orbsa, 0, self.nalpha)
self.Db = mkdens(self.orbsb, 0, self.nbeta)
self.entropy = 0
J = getJ(self.Ints, self.Da + self.Db)
Ka = getK(self.Ints, self.Da)
Kb = getK(self.Ints, self.Db)
self.Fa = self.h + J - Ka
self.Fb = self.h + J - Kb
self.energy = 0.5*(trace2(self.h+self.Fa,self.Da) +
trace2(self.h+self.Fb,self.Db))\
+ self.Enuke + self.entropy
if self.iter == 1 or self.iter % 10 == 0:
logging.debug("%4d %10.5f %10.5f" %
(self.iter, self.energy, dot(b, b)))
return self.energy
def get_energy(self,b):
self.iter += 1
ba = b[:self.nbf]
bb = b[self.nbf:]
self.Hoepa = get_Hoep(ba,self.H0,self.Gij)
self.Hoepb = get_Hoep(bb,self.H0,self.Gij)
self.orbea,self.orbsa = geigh(self.Hoepa,self.S)
self.orbeb,self.orbsb = geigh(self.Hoepb,self.S)
if self.etemp:
self.Da,entropya = mkdens_fermi(2*self.nalpha,self.orbea,self.orbsa,
self.etemp)
self.Db,entropyb = mkdens_fermi(2*self.nbeta,self.orbeb,self.orbsb,
self.etemp)
self.entropy = 0.5*(entropya+entropyb)
else:
self.Da = mkdens(self.orbsa,0,self.nalpha)
self.Db = mkdens(self.orbsb,0,self.nbeta)
self.entropy=0
J = getJ(self.Ints,self.Da+self.Db)
Ka = getK(self.Ints,self.Da)
Kb = getK(self.Ints,self.Db)
self.Fa = self.h + J - Ka
self.Fb = self.h + J - Kb
self.energy = 0.5*(trace2(self.h+self.Fa,self.Da) +
trace2(self.h+self.Fb,self.Db))\
+ self.Enuke + self.entropy
if self.iter == 1 or self.iter % 10 == 0:
logging.debug("%4d %10.5f %10.5f" % (self.iter,self.energy,dot(b,b)))
return self.energy
def update(self,**opts):
from PyQuante.Ints import getJ,getK
from PyQuante.LA2 import geigh,mkdens
from PyQuante.rohf import ao2mo
from PyQuante.hartree_fock import get_energy
from PyQuante.NumWrap import eigh,matrixmultiply
if self.orbs is None:
self.orbe,self.orbs = geigh(self.h, self.S)
Da = mkdens(self.orbs,0,self.nalpha)
Db = mkdens(self.orbs,0,self.nbeta)
Ja = getJ(self.ERI,Da)
Jb = getJ(self.ERI,Db)
Ka = getK(self.ERI,Da)
Kb = getK(self.ERI,Db)
Fa = self.h+Ja+Jb-Ka
Fb = self.h+Ja+Jb-Kb
energya = get_energy(self.h,Fa,Da)
energyb = get_energy(self.h,Fb,Db)
self.energy = (energya+energyb)/2 + self.Enuke
Fa = ao2mo(Fa,self.orbs)
Fb = ao2mo(Fb,self.orbs)
# Building the approximate Fock matrices in the MO basis
F = 0.5*(Fa+Fb)
K = Fb-Fa
# The Fock matrix now looks like
# F-K | F + K/2 | F
# ---------------------------------
# F + K/2 | F | F - K/2
# ---------------------------------
# F | F - K/2 | F + K
# Make explicit slice objects to simplify this
do = slice(0,self.nbeta)
so = slice(self.nbeta,self.nalpha)
uo = slice(self.nalpha,self.norbs)
F[do,do] -= K[do,do]
F[uo,uo] += K[uo,uo]
F[do,so] += 0.5*K[do,so]
F[so,do] += 0.5*K[so,do]
F[so,uo] -= 0.5*K[so,uo]
F[uo,so] -= 0.5*K[uo,so]
self.orbe,mo_orbs = eigh(F)
self.orbs = matrixmultiply(self.orbs,mo_orbs)
return
def update(self, **kwargs):
from PyQuante.Ints import getJ, getK
from PyQuante.LA2 import geigh, mkdens
from PyQuante.rohf import ao2mo
from PyQuante.hartree_fock import get_energy
from PyQuante.NumWrap import eigh, matrixmultiply
if self.orbs is None:
self.orbe, self.orbs = geigh(self.h, self.S)
Da = mkdens(self.orbs, 0, self.nalpha)
Db = mkdens(self.orbs, 0, self.nbeta)
Ja = getJ(self.ERI, Da)
Jb = getJ(self.ERI, Db)
Ka = getK(self.ERI, Da)
Kb = getK(self.ERI, Db)
Fa = self.h + Ja + Jb - Ka
Fb = self.h + Ja + Jb - Kb
energya = get_energy(self.h, Fa, Da)
energyb = get_energy(self.h, Fb, Db)
self.energy = (energya + energyb) / 2 + self.Enuke
Fa = ao2mo(Fa, self.orbs)
Fb = ao2mo(Fb, self.orbs)
# Building the approximate Fock matrices in the MO basis
F = 0.5 * (Fa + Fb)
K = Fb - Fa
# The Fock matrix now looks like
# F-K | F + K/2 | F
# ---------------------------------
# F + K/2 | F | F - K/2
# ---------------------------------
# F | F - K/2 | F + K
# Make explicit slice objects to simplify this
do = slice(0, self.nbeta)
so = slice(self.nbeta, self.nalpha)
uo = slice(self.nalpha, self.norbs)
F[do, do] -= K[do, do]
F[uo, uo] += K[uo, uo]
F[do, so] += 0.5 * K[do, so]
F[so, do] += 0.5 * K[so, do]
F[so, uo] -= 0.5 * K[so, uo]
F[uo, so] -= 0.5 * K[uo, so]
self.orbe, mo_orbs = eigh(F)
self.orbs = matrixmultiply(self.orbs, mo_orbs)
return
def test_mol(mol,**opts):
basis_data = opts.get('basis_data',None)
do_python_tests = opts.get('do_python_tests',True)
make_hf_driver(mol,basis_data=basis_data)
if do_python_tests:
bfs = getbasis(mol,basis_data)
S= getS(bfs)
T = getT(bfs)
V = getV(bfs,mol)
Ints = get2ints(bfs)
nclosed,nopen = mol.get_closedopen()
enuke = mol.get_enuke()
assert nopen==0
h = T+V
orbe,orbs = GHeigenvectors(h,S)
print "Eval of h: ",
print orbe
for i in range(10):
D = mkdens(orbs,0,nclosed)
J = getJ(Ints,D)
K = getK(Ints,D)
orbe,orbs = GHeigenvectors(h+2*J-K,S)
eone = TraceProperty(D,h)
ej = TraceProperty(D,J)
ek = TraceProperty(D,K)
energy = enuke+2*eone+2*ej-ek
print i,energy,enuke,eone,ej,ek
return
def test_mol(mol, **opts):
basis_data = opts.get('basis_data', None)
do_python_tests = opts.get('do_python_tests', True)
make_hf_driver(mol, basis_data=basis_data)
if do_python_tests:
bfs = getbasis(mol, basis_data)
S = getS(bfs)
T = getT(bfs)
V = getV(bfs, mol)
Ints = get2ints(bfs)
nclosed, nopen = mol.get_closedopen()
enuke = mol.get_enuke()
assert nopen == 0
h = T + V
orbe, orbs = GHeigenvectors(h, S)
print "Eval of h: ",
print orbe
for i in range(10):
D = mkdens(orbs, 0, nclosed)
J = getJ(Ints, D)
K = getK(Ints, D)
orbe, orbs = GHeigenvectors(h + 2 * J - K, S)
eone = TraceProperty(D, h)
ej = TraceProperty(D, J)
ek = TraceProperty(D, K)
energy = enuke + 2 * eone + 2 * ej - ek
print i, energy, enuke, eone, ej, ek
return
def get_os_hams(Ints,Ds):
# GVB2P5 did this a little more efficiently; they stored
# 2J-K for the core, then J,K for each open shell. Didn't
# seem worth it here, so I'm jst storing J,K separately
Hs = []
for D in Ds:
Hs.append(getJ(Ints,D))
Hs.append(getK(Ints,D))
return Hs
def update(self,**opts):
from PyQuante.LA2 import trace2
from PyQuante.Ints import getJ,getK
self.amat,entropya = self.solvera.solve(self.Fa)
self.bmat,entropyb = self.solverb.solve(self.Fb)
Da = self.amat
Db = self.bmat
D = Da+Db
self.entropy = 0.5*(entropya+entropyb)
self.J = getJ(self.ERI,D)
self.Ej = 0.5*trace2(D,self.J)
self.Ka = getK(self.ERI,Da)
self.Kb = getK(self.ERI,Db)
self.Exc = -0.5*(trace2(Da,self.Ka)+trace2(Db,self.Kb))
self.Eone = trace2(D,self.h)
self.Fa = self.h + self.J - self.Ka
self.Fb = self.h + self.J - self.Kb
self.energy = self.Eone + self.Ej + self.Exc + self.Enuke + self.entropy
return
def update(self, **kwargs):
from PyQuante.LA2 import trace2
from PyQuante.Ints import getJ, getK
self.amat, entropya = self.solvera.solve(self.Fa)
self.bmat, entropyb = self.solverb.solve(self.Fb)
Da = self.amat
Db = self.bmat
D = Da + Db
self.entropy = 0.5 * (entropya + entropyb)
self.J = getJ(self.ERI, D)
self.Ej = 0.5 * trace2(D, self.J)
self.Ka = getK(self.ERI, Da)
self.Kb = getK(self.ERI, Db)
self.Exc = -0.5 * (trace2(Da, self.Ka) + trace2(Db, self.Kb))
self.Eone = trace2(D, self.h)
self.Fa = self.h + self.J - self.Ka
self.Fb = self.h + self.J - self.Kb
self.energy = self.Eone + self.Ej + self.Exc + self.Enuke + self.entropy
return
def update(self,**opts):
from PyQuante.LA2 import trace2
from PyQuante.Ints import getJ,getK
if self.DoAveraging and self.dmat is not None:
self.F = self.Averager.getF(self.F,self.dmat)
self.dmat,self.entropy = self.solver.solve(self.F,**opts)
D = self.dmat
self.J = getJ(self.ERI,D)
self.Ej = 2*trace2(D,self.J)
self.K = getK(self.ERI,D)
self.Exc = -trace2(D,self.K)
self.Eone = 2*trace2(D,self.h)
self.F = self.h + 2*self.J - self.K
self.energy = self.Eone + self.Ej + self.Exc + self.Enuke + self.entropy
return
def update(self, **kwargs):
from PyQuante.LA2 import trace2
from PyQuante.Ints import getJ, getK
if self.DoAveraging and self.dmat is not None:
self.F = self.Averager.getF(self.F, self.dmat)
self.dmat, self.entropy = self.solver.solve(self.F, **kwargs)
D = self.dmat
self.J = getJ(self.ERI, D)
self.Ej = 2 * trace2(D, self.J)
self.K = getK(self.ERI, D)
self.Exc = -trace2(D, self.K)
self.Eone = 2 * trace2(D, self.h)
self.F = self.h + 2 * self.J - self.K
self.energy = self.Eone + self.Ej + self.Exc + self.Enuke + self.entropy
return
def oep_uhf_an(atoms,orbsa,orbsb,**opts):
"""oep_hf - Form the optimized effective potential for HF exchange.
Implementation of Wu and Yang's Approximate Newton Scheme
from J. Theor. Comp. Chem. 2, 627 (2003).
oep_uhf(atoms,orbs,**opts)
atoms A Molecule object containing a list of the atoms
orbs A matrix of guess orbitals
Options
-------
bfs None The basis functions to use for the wfn
pbfs None The basis functions to use for the pot
basis_data None The basis data to use to construct bfs
integrals None The one- and two-electron integrals to use
If not None, S,h,Ints
"""
maxiter = opts.get('maxiter',100)
tol = opts.get('tol',1e-5)
ETemp = opts.get('ETemp',False)
bfs = opts.get('bfs',None)
if not bfs:
basis = opts.get('basis',None)
bfs = getbasis(atoms,basis)
# The basis set for the potential can be set different from
# that used for the wave function
pbfs = opts.get('pbfs',None)
if not pbfs: pbfs = bfs
npbf = len(pbfs)
integrals = opts.get('integrals',None)
if integrals:
S,h,Ints = integrals
else:
S,h,Ints = getints(bfs,atoms)
nel = atoms.get_nel()
nclosed,nopen = atoms.get_closedopen()
nalpha,nbeta = nclosed+nopen,nclosed
Enuke = atoms.get_enuke()
# Form the OEP using Yang/Wu, PRL 89 143002 (2002)
nbf = len(bfs)
norb = nbf
ba = zeros(npbf,'d')
bb = zeros(npbf,'d')
# Form and store all of the three-center integrals
# we're going to need.
# These are <ibf|gbf|jbf> (where 'bf' indicates basis func,
# as opposed to MO)
# N^3 storage -- obviously you don't want to do this for
# very large systems
Gij = []
for g in range(npbf):
gmat = zeros((nbf,nbf),'d')
Gij.append(gmat)
gbf = pbfs[g]
for i in range(nbf):
ibf = bfs[i]
for j in range(i+1):
jbf = bfs[j]
gij = three_center(ibf,gbf,jbf)
gmat[i,j] = gij
gmat[j,i] = gij
# Compute the Fermi-Amaldi potential based on the LDA density.
# We're going to form this matrix from the Coulombic matrix that
# arises from the input orbitals. D0 and J0 refer to the density
# matrix and corresponding Coulomb matrix
D0 = mkdens(orbsa,0,nalpha)+mkdens(orbsb,0,nbeta)
J0 = getJ(Ints,D0)
Vfa = ((nel-1.)/nel)*J0
H0 = h + Vfa
eold = 0
for iter in range(maxiter):
Hoepa = get_Hoep(ba,H0,Gij)
Hoepb = get_Hoep(ba,H0,Gij)
orbea,orbsa = geigh(Hoepa,S)
orbeb,orbsb = geigh(Hoepb,S)
if ETemp:
efermia = get_efermi(2*nalpha,orbea,ETemp)
occsa = get_fermi_occs(efermia,orbea,ETemp)
Da = mkdens_occs(orbsa,occsa)
efermib = get_efermi(2*nbeta,orbeb,ETemp)
occsb = get_fermi_occs(efermib,orbeb,ETemp)
Db = mkdens_occs(orbsb,occsb)
entropy = 0.5*(get_entropy(occsa,ETemp)+get_entropy(occsb,ETemp))
else:
Da = mkdens(orbsa,0,nalpha)
Db = mkdens(orbsb,0,nbeta)
J = getJ(Ints,Da) + getJ(Ints,Db)
Ka = getK(Ints,Da)
Kb = getK(Ints,Db)
energy = (trace2(2*h+J-Ka,Da)+trace2(2*h+J-Kb,Db))/2\
+Enuke
if ETemp: energy += entropy
if abs(energy-eold) < tol:
break
else:
eold = energy
logging.debug("OEP AN Opt: %d %f" % (iter,energy))
# Do alpha and beta separately
# Alphas
dV_ao = J-Ka-Vfa
dV = matrixmultiply(orbsa,matrixmultiply(dV_ao,transpose(orbsa)))
X = zeros((nbf,nbf),'d')
c = zeros(nbf,'d')
for k in range(nbf):
Gk = matrixmultiply(orbsa,matrixmultiply(Gij[k],
transpose(orbsa)))
for i in range(nalpha):
for a in range(nalpha,norb):
c[k] += dV[i,a]*Gk[i,a]/(orbea[i]-orbea[a])
for l in range(nbf):
Gl = matrixmultiply(orbsa,matrixmultiply(Gij[l],
transpose(orbsa)))
for i in range(nalpha):
for a in range(nalpha,norb):
X[k,l] += Gk[i,a]*Gl[i,a]/(orbea[i]-orbea[a])
# This should actually be a pseudoinverse...
ba = solve(X,c)
# Betas
dV_ao = J-Kb-Vfa
dV = matrixmultiply(orbsb,matrixmultiply(dV_ao,transpose(orbsb)))
X = zeros((nbf,nbf),'d')
c = zeros(nbf,'d')
for k in range(nbf):
Gk = matrixmultiply(orbsb,matrixmultiply(Gij[k],
transpose(orbsb)))
for i in range(nbeta):
for a in range(nbeta,norb):
c[k] += dV[i,a]*Gk[i,a]/(orbeb[i]-orbeb[a])
for l in range(nbf):
Gl = matrixmultiply(orbsb,matrixmultiply(Gij[l],
transpose(orbsb)))
for i in range(nbeta):
for a in range(nbeta,norb):
X[k,l] += Gk[i,a]*Gl[i,a]/(orbeb[i]-orbeb[a])
# This should actually be a pseudoinverse...
bb = solve(X,c)
logging.info("Final OEP energy = %f" % energy)
return energy,(orbea,orbeb),(orbsa,orbsb)
def rohf(atoms,**opts):
"""\
rohf(atoms,**opts) - Restriced Open Shell Hartree Fock
atoms A Molecule object containing the molecule
"""
ConvCriteria = opts.get('ConvCriteria',1e-5)
MaxIter = opts.get('MaxIter',40)
DoAveraging = opts.get('DoAveraging',True)
averaging = opts.get('averaging',0.95)
verbose = opts.get('verbose',True)
bfs = opts.get('bfs',None)
if not bfs:
basis_data = opts.get('basis_data',None)
bfs = getbasis(atoms,basis_data)
nbf = len(bfs)
integrals = opts.get('integrals', None)
if integrals:
S,h,Ints = integrals
else:
S,h,Ints = getints(bfs,atoms)
nel = atoms.get_nel()
nalpha,nbeta = atoms.get_alphabeta()
S,h,Ints = getints(bfs,atoms)
orbs = opts.get('orbs',None)
if orbs is None:
orbe,orbs = geigh(h,S)
norbs = nbf
enuke = atoms.get_enuke()
eold = 0.
if verbose: print "ROHF calculation on %s" % atoms.name
if verbose: print "Nbf = %d" % nbf
if verbose: print "Nalpha = %d" % nalpha
if verbose: print "Nbeta = %d" % nbeta
if verbose: print "Averaging = %s" % DoAveraging
print "Optimization of HF orbitals"
for i in xrange(MaxIter):
if verbose: print "SCF Iteration:",i,"Starting Energy:",eold
Da = mkdens(orbs,0,nalpha)
Db = mkdens(orbs,0,nbeta)
if DoAveraging:
if i:
Da = averaging*Da + (1-averaging)*Da0
Db = averaging*Db + (1-averaging)*Db0
Da0 = Da
Db0 = Db
Ja = getJ(Ints,Da)
Jb = getJ(Ints,Db)
Ka = getK(Ints,Da)
Kb = getK(Ints,Db)
Fa = h+Ja+Jb-Ka
Fb = h+Ja+Jb-Kb
energya = get_energy(h,Fa,Da)
energyb = get_energy(h,Fb,Db)
eone = (trace2(Da,h) + trace2(Db,h))/2
etwo = (trace2(Da,Fa) + trace2(Db,Fb))/2
energy = (energya+energyb)/2 + enuke
print i,energy,eone,etwo,enuke
if abs(energy-eold) < ConvCriteria: break
eold = energy
Fa = ao2mo(Fa,orbs)
Fb = ao2mo(Fb,orbs)
# Building the approximate Fock matrices in the MO basis
F = 0.5*(Fa+Fb)
K = Fb-Fa
# The Fock matrix now looks like
# F-K | F + K/2 | F
# ---------------------------------
# F + K/2 | F | F - K/2
# ---------------------------------
# F | F - K/2 | F + K
# Make explicit slice objects to simplify this
do = slice(0,nbeta)
so = slice(nbeta,nalpha)
uo = slice(nalpha,norbs)
F[do,do] -= K[do,do]
F[uo,uo] += K[uo,uo]
F[do,so] += 0.5*K[do,so]
F[so,do] += 0.5*K[so,do]
F[so,uo] -= 0.5*K[so,uo]
F[uo,so] -= 0.5*K[uo,so]
orbe,mo_orbs = eigh(F)
orbs = matrixmultiply(orbs,mo_orbs)
if verbose:
print "Final ROHF energy for system %s is %f" % (atoms.name,energy)
return energy,orbe,orbs
def oep_uhf_an(atoms, orbsa, orbsb, **opts):
"""oep_hf - Form the optimized effective potential for HF exchange.
Implementation of Wu and Yang's Approximate Newton Scheme
from J. Theor. Comp. Chem. 2, 627 (2003).
oep_uhf(atoms,orbs,**opts)
atoms A Molecule object containing a list of the atoms
orbs A matrix of guess orbitals
Options
-------
bfs None The basis functions to use for the wfn
pbfs None The basis functions to use for the pot
basis_data None The basis data to use to construct bfs
integrals None The one- and two-electron integrals to use
If not None, S,h,Ints
"""
maxiter = opts.get('maxiter', 100)
tol = opts.get('tol', 1e-5)
ETemp = opts.get('ETemp', False)
bfs = opts.get('bfs', None)
if not bfs:
basis = opts.get('basis', None)
bfs = getbasis(atoms, basis)
# The basis set for the potential can be set different from
# that used for the wave function
pbfs = opts.get('pbfs', None)
if not pbfs: pbfs = bfs
npbf = len(pbfs)
integrals = opts.get('integrals', None)
if integrals:
S, h, Ints = integrals
else:
S, h, Ints = getints(bfs, atoms)
nel = atoms.get_nel()
nclosed, nopen = atoms.get_closedopen()
nalpha, nbeta = nclosed + nopen, nclosed
Enuke = atoms.get_enuke()
# Form the OEP using Yang/Wu, PRL 89 143002 (2002)
nbf = len(bfs)
norb = nbf
ba = zeros(npbf, 'd')
bb = zeros(npbf, 'd')
# Form and store all of the three-center integrals
# we're going to need.
# These are <ibf|gbf|jbf> (where 'bf' indicates basis func,
# as opposed to MO)
# N^3 storage -- obviously you don't want to do this for
# very large systems
Gij = []
for g in xrange(npbf):
gmat = zeros((nbf, nbf), 'd')
Gij.append(gmat)
gbf = pbfs[g]
for i in xrange(nbf):
ibf = bfs[i]
for j in xrange(i + 1):
jbf = bfs[j]
gij = three_center(ibf, gbf, jbf)
gmat[i, j] = gij
gmat[j, i] = gij
# Compute the Fermi-Amaldi potential based on the LDA density.
# We're going to form this matrix from the Coulombic matrix that
# arises from the input orbitals. D0 and J0 refer to the density
# matrix and corresponding Coulomb matrix
D0 = mkdens(orbsa, 0, nalpha) + mkdens(orbsb, 0, nbeta)
J0 = getJ(Ints, D0)
Vfa = ((nel - 1.) / nel) * J0
H0 = h + Vfa
eold = 0
for iter in xrange(maxiter):
Hoepa = get_Hoep(ba, H0, Gij)
Hoepb = get_Hoep(ba, H0, Gij)
orbea, orbsa = geigh(Hoepa, S)
orbeb, orbsb = geigh(Hoepb, S)
if ETemp:
efermia = get_efermi(2 * nalpha, orbea, ETemp)
occsa = get_fermi_occs(efermia, orbea, ETemp)
Da = mkdens_occs(orbsa, occsa)
efermib = get_efermi(2 * nbeta, orbeb, ETemp)
occsb = get_fermi_occs(efermib, orbeb, ETemp)
Db = mkdens_occs(orbsb, occsb)
entropy = 0.5 * (get_entropy(occsa, ETemp) +
get_entropy(occsb, ETemp))
else:
Da = mkdens(orbsa, 0, nalpha)
Db = mkdens(orbsb, 0, nbeta)
J = getJ(Ints, Da) + getJ(Ints, Db)
Ka = getK(Ints, Da)
Kb = getK(Ints, Db)
energy = (trace2(2*h+J-Ka,Da)+trace2(2*h+J-Kb,Db))/2\
+Enuke
if ETemp: energy += entropy
if abs(energy - eold) < tol:
break
else:
eold = energy
logging.debug("OEP AN Opt: %d %f" % (iter, energy))
# Do alpha and beta separately
# Alphas
dV_ao = J - Ka - Vfa
dV = matrixmultiply(orbsa, matrixmultiply(dV_ao, transpose(orbsa)))
X = zeros((nbf, nbf), 'd')
c = zeros(nbf, 'd')
for k in xrange(nbf):
Gk = matrixmultiply(orbsa, matrixmultiply(Gij[k],
transpose(orbsa)))
for i in xrange(nalpha):
for a in xrange(nalpha, norb):
c[k] += dV[i, a] * Gk[i, a] / (orbea[i] - orbea[a])
for l in xrange(nbf):
Gl = matrixmultiply(orbsa,
matrixmultiply(Gij[l], transpose(orbsa)))
for i in xrange(nalpha):
for a in xrange(nalpha, norb):
X[k, l] += Gk[i, a] * Gl[i, a] / (orbea[i] - orbea[a])
# This should actually be a pseudoinverse...
ba = solve(X, c)
# Betas
dV_ao = J - Kb - Vfa
dV = matrixmultiply(orbsb, matrixmultiply(dV_ao, transpose(orbsb)))
X = zeros((nbf, nbf), 'd')
c = zeros(nbf, 'd')
for k in xrange(nbf):
Gk = matrixmultiply(orbsb, matrixmultiply(Gij[k],
transpose(orbsb)))
for i in xrange(nbeta):
for a in xrange(nbeta, norb):
c[k] += dV[i, a] * Gk[i, a] / (orbeb[i] - orbeb[a])
for l in xrange(nbf):
Gl = matrixmultiply(orbsb,
matrixmultiply(Gij[l], transpose(orbsb)))
for i in xrange(nbeta):
for a in xrange(nbeta, norb):
X[k, l] += Gk[i, a] * Gl[i, a] / (orbeb[i] - orbeb[a])
# This should actually be a pseudoinverse...
bb = solve(X, c)
logger.info("Final OEP energy = %f" % energy)
return energy, (orbea, orbeb), (orbsa, orbsb)
def pyq1_rohf(atomtuples=[(2,(0,0,0))],basis = '6-31G**',maxit=10,mult=3):
from PyQuante import Ints,settings,Molecule
from PyQuante.hartree_fock import get_energy
from PyQuante.MG2 import MG2 as MolecularGrid
from PyQuante.LA2 import mkdens,geigh,trace2,simx
from PyQuante.Ints import getJ,getK
print ("PyQ1 ROHF run")
atoms = Molecule('Pyq1',atomlist=atomtuples,multiplicity=mult)
bfs = Ints.getbasis(atoms,basis=basis)
S,h,I2e = Ints.getints(bfs,atoms)
nbf = norbs = len(bfs)
nel = atoms.get_nel()
nalpha,nbeta = atoms.get_alphabeta()
enuke = atoms.get_enuke()
orbe,orbs = geigh(h,S)
eold = 0
for i in range(maxit):
Da = mkdens(orbs,0,nalpha)
Db = mkdens(orbs,0,nbeta)
Ja = getJ(I2e,Da)
Jb = getJ(I2e,Db)
Ka = getK(I2e,Da)
Kb = getK(I2e,Db)
Fa = h+Ja+Jb-Ka
Fb = h+Ja+Jb-Kb
energya = get_energy(h,Fa,Da)
energyb = get_energy(h,Fb,Db)
eone = (trace2(Da,h) + trace2(Db,h))/2
etwo = (trace2(Da,Fa) + trace2(Db,Fb))/2
energy = (energya+energyb)/2 + enuke
print (i,energy,eone,etwo,enuke)
if abs(energy-eold) < 1e-5: break
eold = energy
Fa = simx(Fa,orbs)
Fb = simx(Fb,orbs)
# Building the approximate Fock matrices in the MO basis
F = 0.5*(Fa+Fb)
K = Fb-Fa
# The Fock matrix now looks like
# F-K | F + K/2 | F
# ---------------------------------
# F + K/2 | F | F - K/2
# ---------------------------------
# F | F - K/2 | F + K
# Make explicit slice objects to simplify this
do = slice(0,nbeta)
so = slice(nbeta,nalpha)
uo = slice(nalpha,norbs)
F[do,do] -= K[do,do]
F[uo,uo] += K[uo,uo]
F[do,so] += 0.5*K[do,so]
F[so,do] += 0.5*K[so,do]
F[so,uo] -= 0.5*K[so,uo]
F[uo,so] -= 0.5*K[uo,so]
orbe,mo_orbs = np.linalg.eigh(F)
orbs = np.dot(orbs,mo_orbs)
return energy,orbe,orbs
def pyq1_rohf(atomtuples=[(2, (0, 0, 0))], basis='6-31G**', maxit=10, mult=3):
from PyQuante import Ints, settings, Molecule
from PyQuante.hartree_fock import get_energy
from PyQuante.MG2 import MG2 as MolecularGrid
from PyQuante.LA2 import mkdens, geigh, trace2, simx
from PyQuante.Ints import getJ, getK
print("PyQ1 ROHF run")
atoms = Molecule('Pyq1', atomlist=atomtuples, multiplicity=mult)
bfs = Ints.getbasis(atoms, basis=basis)
S, h, I2e = Ints.getints(bfs, atoms)
nbf = norbs = len(bfs)
nel = atoms.get_nel()
nalpha, nbeta = atoms.get_alphabeta()
enuke = atoms.get_enuke()
orbe, orbs = geigh(h, S)
eold = 0
for i in range(maxit):
Da = mkdens(orbs, 0, nalpha)
Db = mkdens(orbs, 0, nbeta)
Ja = getJ(I2e, Da)
Jb = getJ(I2e, Db)
Ka = getK(I2e, Da)
Kb = getK(I2e, Db)
Fa = h + Ja + Jb - Ka
Fb = h + Ja + Jb - Kb
energya = get_energy(h, Fa, Da)
energyb = get_energy(h, Fb, Db)
eone = (trace2(Da, h) + trace2(Db, h)) / 2
etwo = (trace2(Da, Fa) + trace2(Db, Fb)) / 2
energy = (energya + energyb) / 2 + enuke
print(i, energy, eone, etwo, enuke)
if abs(energy - eold) < 1e-5: break
eold = energy
Fa = simx(Fa, orbs)
Fb = simx(Fb, orbs)
# Building the approximate Fock matrices in the MO basis
F = 0.5 * (Fa + Fb)
K = Fb - Fa
# The Fock matrix now looks like
# F-K | F + K/2 | F
# ---------------------------------
# F + K/2 | F | F - K/2
# ---------------------------------
# F | F - K/2 | F + K
# Make explicit slice objects to simplify this
do = slice(0, nbeta)
so = slice(nbeta, nalpha)
uo = slice(nalpha, norbs)
F[do, do] -= K[do, do]
F[uo, uo] += K[uo, uo]
F[do, so] += 0.5 * K[do, so]
F[so, do] += 0.5 * K[so, do]
F[so, uo] -= 0.5 * K[so, uo]
F[uo, so] -= 0.5 * K[uo, so]
orbe, mo_orbs = np.linalg.eigh(F)
orbs = np.dot(orbs, mo_orbs)
return energy, orbe, orbs