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 pyq1_dft(atomtuples=[(2, (0, 0, 0))],
basis='6-31G**',
maxit=10,
xcname='SVWN'):
from PyQuante import Ints, settings, Molecule
from PyQuante.dft import getXC
from PyQuante.MG2 import MG2 as MolecularGrid
from PyQuante.LA2 import mkdens, geigh, trace2
from PyQuante.Ints import getJ
print("PyQ1 DFT run")
atoms = Molecule('Pyq1', atomlist=atomtuples)
bfs = Ints.getbasis(atoms, basis=basis)
S, h, Ints = Ints.getints(bfs, atoms)
nclosed, nopen = nel // 2, nel % 2
assert nopen == 0
enuke = atoms.get_enuke()
grid_nrad = settings.DFTGridRadii
grid_fineness = settings.DFTGridFineness
gr = MolecularGrid(atoms, grid_nrad, grid_fineness)
gr.set_bf_amps(bfs)
orbe, orbs = geigh(h, S)
eold = 0
for i in range(maxit):
D = mkdens(orbs, 0, nclosed)
gr.setdens(D)
J = getJ(Ints, D)
Exc, Vxc = getXC(gr, nel, functional=xcname)
F = h + 2 * J + Vxc
orbe, orbs = geigh(F, S)
Ej = 2 * trace2(D, J)
Eone = 2 * trace2(D, h)
energy = Eone + Ej + Exc + enuke
print(i, energy, Eone, Ej, Exc, enuke)
if np.isclose(energy, eold):
break
eold = energy
return energy
def solve(self, H, **kwargs):
from PyQuante.LA2 import geigh
from PyQuante.fermi_dirac import mkdens_fermi
self.orbe, self.orbs = geigh(H, self.S)
self.D, self.entropy = mkdens_fermi(self.nel, self.orbe, self.orbs,
self.etemp)
return self.D, self.entropy
def solve(self,H,**opts):
from PyQuante.LA2 import geigh
from PyQuante.fermi_dirac import mkdens_fermi
self.orbe,self.orbs = geigh(H,self.S)
self.D,self.entropy = mkdens_fermi(self.nel,self.orbe,
self.orbs,self.etemp)
return self.D,self.entropy
def get_exx_energy(b, nbf, nel, nocc, ETemp, Enuke, S, h, Ints, H0, Gij,
**opts):
"""Computes the energy for the OEP/HF functional
Options:
return_flag 0 Just return the energy
1 Return energy, orbe, orbs
2 Return energy, orbe, orbs, F
"""
return_flag = opts.get('return_flag', 0)
Hoep = get_Hoep(b, H0, Gij)
orbe, orbs = geigh(Hoep, S)
if ETemp:
efermi = get_efermi(nel, orbe, ETemp)
occs = get_fermi_occs(efermi, orbe, ETemp)
D = mkdens_occs(orbs, occs)
entropy = get_entropy(occs, ETemp)
else:
D = mkdens(orbs, 0, nocc)
F = get_fock(D, Ints, h)
energy = trace2(h + F, D) + Enuke
if ETemp: energy += entropy
iref = nel / 2
gap = 627.51 * (orbe[iref] - orbe[iref - 1])
logging.debug("EXX Energy, B, Gap: %10.5f %10.5f %10.5f" %
(energy, sqrt(dot(b, b)), gap))
#logging.debug("%s" % orbe)
if return_flag == 1:
return energy, orbe, orbs
elif return_flag == 2:
return energy, orbe, orbs, F
return energy
def rohf_wag(atoms,noccsh=None,f=None,a=None,b=None,**kwargs):
"""\
rohf(atoms,noccsh=None,f=None,a=None,b=None,**kwargs):
Restricted open shell HF driving routine
atoms A Molecule object containing the system of interest
"""
ConvCriteria = kwargs.get('ConvCriteria',settings.ConvergenceCriteria)
MaxIter = kwargs.get('MaxIter',settings.MaxIter)
DoAveraging = kwargs.get('DoAveraging',settings.Averaging)
verbose = kwargs.get('verbose')
bfs = getbasis(atoms,**kwargs)
S,h,Ints = getints(bfs,atoms,**kwargs)
nel = atoms.get_nel()
orbs = kwargs.get('orbs')
if orbs is None:
orbe,orbs = geigh(h,nS)
nclosed,nopen = atoms.get_closedopen()
nocc = nopen+nclosed
if not noccsh: noccsh = get_noccsh(nclosed,nopen)
nsh = len(noccsh)
nbf = norb = len(bfs)
if not f:
f,a,b = get_fab(nclosed,nopen)
if verbose:
print "ROHF calculation"
print "nsh = ",nsh
print "noccsh = ",noccsh
print "f = ",f
print "a_ij: "
for i in xrange(nsh):
for j in xrange(i+1):
print a[i,j],
print
print "b_ij: "
for i in xrange(nsh):
for j in xrange(i+1):
print b[i,j],
print
enuke = atoms.get_enuke()
energy = eold = 0.
for i in xrange(MaxIter):
Ds = get_os_dens(orbs,f,noccsh)
Hs = get_os_hams(Ints,Ds)
orbs = rotion(orbs,h,Hs,f,a,b,noccsh)
orbe,orbs = ocbse(orbs,h,Hs,f,a,b,noccsh)
orthogonalize(orbs,S)
# Compute the energy
eone = sum(f[ish]*trace2(Ds[ish],h) for ish in xrange(nsh))
energy = enuke+eone+sum(orbe[:nocc])
print energy,eone
if abs(energy-eold) < ConvCriteria: break
eold = energy
return energy,orbe,orbs
def get_exx_energy(b,nbf,nel,nocc,ETemp,Enuke,S,h,Ints,H0,Gij,**opts):
"""Computes the energy for the OEP/HF functional
Options:
return_flag 0 Just return the energy
1 Return energy, orbe, orbs
2 Return energy, orbe, orbs, F
"""
return_flag = opts.get('return_flag',0)
Hoep = get_Hoep(b,H0,Gij)
orbe,orbs = geigh(Hoep,S)
if ETemp:
efermi = get_efermi(nel,orbe,ETemp)
occs = get_fermi_occs(efermi,orbe,ETemp)
D = mkdens_occs(orbs,occs)
entropy = get_entropy(occs,ETemp)
else:
D = mkdens(orbs,0,nocc)
F = get_fock(D,Ints,h)
energy = trace2(h+F,D)+Enuke
if ETemp: energy += entropy
iref = nel/2
gap = 627.51*(orbe[iref]-orbe[iref-1])
logging.debug("EXX Energy, B, Gap: %10.5f %10.5f %10.5f"
% (energy,sqrt(dot(b,b)),gap))
#logging.debug("%s" % orbe)
if return_flag == 1:
return energy,orbe,orbs
elif return_flag == 2:
return energy,orbe,orbs,F
return energy
def rohf_wag(atoms, noccsh=None, f=None, a=None, b=None, **kwargs):
"""\
rohf(atoms,noccsh=None,f=None,a=None,b=None,**kwargs):
Restricted open shell HF driving routine
atoms A Molecule object containing the system of interest
"""
ConvCriteria = kwargs.get('ConvCriteria', settings.ConvergenceCriteria)
MaxIter = kwargs.get('MaxIter', settings.MaxIter)
DoAveraging = kwargs.get('DoAveraging', settings.Averaging)
verbose = kwargs.get('verbose')
bfs = getbasis(atoms, **kwargs)
S, h, Ints = getints(bfs, atoms, **kwargs)
nel = atoms.get_nel()
orbs = kwargs.get('orbs')
if orbs is None:
orbe, orbs = geigh(h, nS)
nclosed, nopen = atoms.get_closedopen()
nocc = nopen + nclosed
if not noccsh: noccsh = get_noccsh(nclosed, nopen)
nsh = len(noccsh)
nbf = norb = len(bfs)
if not f:
f, a, b = get_fab(nclosed, nopen)
if verbose:
print "ROHF calculation"
print "nsh = ", nsh
print "noccsh = ", noccsh
print "f = ", f
print "a_ij: "
for i in xrange(nsh):
for j in xrange(i + 1):
print a[i, j],
print
print "b_ij: "
for i in xrange(nsh):
for j in xrange(i + 1):
print b[i, j],
print
enuke = atoms.get_enuke()
energy = eold = 0.
for i in xrange(MaxIter):
Ds = get_os_dens(orbs, f, noccsh)
Hs = get_os_hams(Ints, Ds)
orbs = rotion(orbs, h, Hs, f, a, b, noccsh)
orbe, orbs = ocbse(orbs, h, Hs, f, a, b, noccsh)
orthogonalize(orbs, S)
# Compute the energy
eone = sum(f[ish] * trace2(Ds[ish], h) for ish in xrange(nsh))
energy = enuke + eone + sum(orbe[:nocc])
print energy, eone
if abs(energy - eold) < ConvCriteria: break
eold = energy
return energy, orbe, orbs
def pyq1_dft(atomtuples=[(2,(0,0,0))],basis = '6-31G**',maxit=10,
xcname='SVWN'):
from PyQuante import Ints,settings,Molecule
from PyQuante.dft import getXC
from PyQuante.MG2 import MG2 as MolecularGrid
from PyQuante.LA2 import mkdens,geigh,trace2
from PyQuante.Ints import getJ
print ("PyQ1 DFT run")
atoms = Molecule('Pyq1',atomlist=atomtuples)
bfs = Ints.getbasis(atoms,basis=basis)
S,h,Ints = Ints.getints(bfs,atoms)
nclosed,nopen = nel//2,nel%2
assert nopen==0
enuke = atoms.get_enuke()
grid_nrad = settings.DFTGridRadii
grid_fineness = settings.DFTGridFineness
gr = MolecularGrid(atoms,grid_nrad,grid_fineness)
gr.set_bf_amps(bfs)
orbe,orbs = geigh(h,S)
eold = 0
for i in range(maxit):
D = mkdens(orbs,0,nclosed)
gr.setdens(D)
J = getJ(Ints,D)
Exc,Vxc = getXC(gr,nel,functional=xcname)
F = h+2*J+Vxc
orbe,orbs = geigh(F,S)
Ej = 2*trace2(D,J)
Eone = 2*trace2(D,h)
energy = Eone + Ej + Exc + enuke
print (i,energy,Eone,Ej,Exc,enuke)
if np.isclose(energy,eold):
break
eold = energy
return energy
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 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 get_energy(self,b):
self.iter += 1
self.Hoep = get_Hoep(b,self.H0,self.Gij)
self.orbe,self.orbs = geigh(self.Hoep,self.S)
if self.etemp:
self.D,self.entropy = mkdens_fermi(self.nel,self.orbe,self.orbs,
self.etemp)
else:
self.D = mkdens(self.orbs,0,self.nclosed)
self.entropy=0
self.F = get_fock(self.D,self.Ints,self.h)
self.energy = trace2(self.h+self.F,self.D)+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 solve(self,H,**opts):
from PyQuante.LA2 import mkdens_spinavg,simx,geigh
from PyQuante.NumWrap import matrixmultiply,eigh
if self.first_iteration:
self.first_iteration = False
self.orbe,self.orbs = geigh(H,self.S)
else:
Ht = simx(H,self.orbs)
if self.pass_nroots:
self.orbe,orbs = self.solver(Ht,self.nroots)
else:
self.orbe,orbs = self.solver(Ht)
self.orbs = matrixmultiply(self.orbs,orbs)
self.D = mkdens_spinavg(self.orbs,self.nclosed,self.nopen)
self.entropy = 0
return self.D,self.entropy
def solve(self, H, **kwargs):
from PyQuante.LA2 import mkdens_spinavg, simx, geigh
from PyQuante.NumWrap import matrixmultiply, eigh
if self.first_iteration:
self.first_iteration = False
self.orbe, self.orbs = geigh(H, self.S)
else:
Ht = simx(H, self.orbs)
if self.pass_nroots:
self.orbe, orbs = self.solver(Ht, self.nroots)
else:
self.orbe, orbs = self.solver(Ht)
self.orbs = matrixmultiply(self.orbs, orbs)
self.D = mkdens_spinavg(self.orbs, self.nclosed, self.nopen)
self.entropy = 0
return self.D, self.entropy
def get_energy(self, b):
self.iter += 1
self.Hoep = get_Hoep(b, self.H0, self.Gij)
self.orbe, self.orbs = geigh(self.Hoep, self.S)
if self.etemp:
self.D, self.entropy = mkdens_fermi(self.nel, self.orbe, self.orbs,
self.etemp)
else:
self.D = mkdens(self.orbs, 0, self.nclosed)
self.entropy = 0
self.F = get_fock(self.D, self.Ints, self.h)
self.energy = trace2(self.h + self.F,
self.D) + 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 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 oep_hf_an(atoms,orbs,**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_hf(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)
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()
nocc,nopen = atoms.get_closedopen()
Enuke = atoms.get_enuke()
# Form the OEP using Yang/Wu, PRL 89 143002 (2002)
nbf = len(bfs)
norb = nbf
bp = zeros(nbf,'d')
bvec = opts.get('bvec',None)
if bvec:
assert len(bvec) == npbf
b = array(bvec)
else:
b = 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(orbs,0,nocc)
J0 = getJ(Ints,D0)
Vfa = (2*(nel-1.)/nel)*J0
H0 = h + Vfa
b = zeros(nbf,'d')
eold = 0
for iter in range(maxiter):
Hoep = get_Hoep(b,H0,Gij)
orbe,orbs = geigh(Hoep,S)
D = mkdens(orbs,0,nocc)
Vhf = get2JmK(Ints,D)
energy = trace2(2*h+Vhf,D)+Enuke
if abs(energy-eold) < tol:
break
else:
eold = energy
logging.debug("OEP AN Opt: %d %f" % (iter,energy))
dV_ao = Vhf-Vfa
dV = matrixmultiply(transpose(orbs),matrixmultiply(dV_ao,orbs))
X = zeros((nbf,nbf),'d')
c = zeros(nbf,'d')
Gkt = zeros((nbf,nbf),'d')
for k in range(nbf):
# This didn't work; in fact, it made things worse:
Gk = matrixmultiply(transpose(orbs),matrixmultiply(Gij[k],orbs))
for i in range(nocc):
for a in range(nocc,norb):
c[k] += dV[i,a]*Gk[i,a]/(orbe[i]-orbe[a])
for l in range(nbf):
Gl = matrixmultiply(transpose(orbs),matrixmultiply(Gij[l],orbs))
for i in range(nocc):
for a in range(nocc,norb):
X[k,l] += Gk[i,a]*Gl[i,a]/(orbe[i]-orbe[a])
# This should actually be a pseudoinverse...
b = solve(X,c)
logging.info("Final OEP energy = %f" % energy)
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
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 oep_hf_an(atoms, orbs, **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_hf(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)
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()
nocc, nopen = atoms.get_closedopen()
Enuke = atoms.get_enuke()
# Form the OEP using Yang/Wu, PRL 89 143002 (2002)
nbf = len(bfs)
norb = nbf
bp = zeros(nbf, 'd')
bvec = opts.get('bvec', None)
if bvec:
assert len(bvec) == npbf
b = array(bvec)
else:
b = 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(orbs, 0, nocc)
J0 = getJ(Ints, D0)
Vfa = (2 * (nel - 1.) / nel) * J0
H0 = h + Vfa
b = zeros(nbf, 'd')
eold = 0
for iter in xrange(maxiter):
Hoep = get_Hoep(b, H0, Gij)
orbe, orbs = geigh(Hoep, S)
D = mkdens(orbs, 0, nocc)
Vhf = get2JmK(Ints, D)
energy = trace2(2 * h + Vhf, D) + Enuke
if abs(energy - eold) < tol:
break
else:
eold = energy
logging.debug("OEP AN Opt: %d %f" % (iter, energy))
dV_ao = Vhf - Vfa
dV = matrixmultiply(transpose(orbs), matrixmultiply(dV_ao, orbs))
X = zeros((nbf, nbf), 'd')
c = zeros(nbf, 'd')
Gkt = zeros((nbf, nbf), 'd')
for k in xrange(nbf):
# This didn't work; in fact, it made things worse:
Gk = matrixmultiply(transpose(orbs), matrixmultiply(Gij[k], orbs))
for i in xrange(nocc):
for a in xrange(nocc, norb):
c[k] += dV[i, a] * Gk[i, a] / (orbe[i] - orbe[a])
for l in xrange(nbf):
Gl = matrixmultiply(transpose(orbs),
matrixmultiply(Gij[l], orbs))
for i in xrange(nocc):
for a in xrange(nocc, norb):
X[k, l] += Gk[i, a] * Gl[i, a] / (orbe[i] - orbe[a])
# This should actually be a pseudoinverse...
b = solve(X, c)
logger.info("Final OEP energy = %f" % energy)
return energy, orbe, orbs
def solve(self,H,**opts):
from PyQuante.LA2 import geigh,mkdens_spinavg
self.orbe,self.orbs = geigh(H,self.S)
self.D = mkdens_spinavg(self.orbs,self.nclosed,self.nopen)
self.entropy = 0
return self.D,self.entropy
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 solve(self, H, **kwargs):
from PyQuante.LA2 import geigh, mkdens_spinavg
self.orbe, self.orbs = geigh(H, self.S)
self.D = mkdens_spinavg(self.orbs, self.nclosed, self.nopen)
self.entropy = 0
return self.D, self.entropy
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
from PyQuante.TestMolecules import h2
from PyQuante.LA2 import geigh,mkdens
from PyQuante.Ints import get2JmK,getbasis,getints
from PyQuante.Convergence import DIIS
from PyQuante.hartree_fock import get_energy
bfs = getbasis(h2,basis="3-21g")
nclosed,nopen = h2.get_closedopen()
nocc = nclosed
nel = h2.get_nel()
S,h,Ints = getints(bfs,h2)
orbe,orbs = geigh(h,S)
enuke = h2.get_enuke()
eold = 0
avg = DIIS(S)
for i in range(20):
D = mkdens(orbs,0,nocc)
G = get2JmK(Ints,D)
F = h+G
F = avg.getF(F,D)
orbe,orbs = geigh(F,S)
energy = get_energy(h,F,D,enuke)
print i,energy,energy-eold
if abs(energy-eold)<1e-5:
break
eold = energy
print "Converged"
