def compute_F(P, Hcore, X, Ints, mu=0):
# get the matrix of 2J-K for a given fixed P
# P is here given in the non- orthonormal basis
G = get2JmK(Ints, P)
# pass the G matrix in the orthonormal basis
Gp = simx(G, X, 'T')
# form the Fock matrix in the orthonomral basis
F = Hcore + _ee_inter_ * Gp + mu
return F
def simple_hf(atoms,S,h,Ints):
from PyQuante.LA2 import mkdens
from PyQuante.hartree_fock import get_energy
orbe,orbs = geigh(h,S)
nclosed,nopen = atoms.get_closedopen()
enuke = atoms.get_enuke()
nocc = nclosed
eold = 0
for i in range(15):
D = mkdens(orbs,0,nocc)
G = get2JmK(Ints,D)
F = h+G
orbe,orbs = geigh(F,S)
energy = get_energy(h,F,D,enuke)
print "%d %f" % (i,energy)
if abs(energy-eold) < 1e-4: break
eold = energy
print "Final HF energy for system %s is %f" % (atoms.name,energy)
return energy,orbe,orbs
def simple_hf(atoms, S, h, Ints):
from PyQuante.LA2 import mkdens
from PyQuante.hartree_fock import get_energy
orbe, orbs = geigh(h, S)
nclosed, nopen = atoms.get_closedopen()
enuke = atoms.get_enuke()
nocc = nclosed
eold = 0
for i in range(15):
D = mkdens(orbs, 0, nocc)
G = get2JmK(Ints, D)
F = h + G
orbe, orbs = geigh(F, S)
energy = get_energy(h, F, D, enuke)
print "%d %f" % (i, energy)
if abs(energy - eold) < 1e-4: break
eold = energy
print "Final HF energy for system %s is %f" % (atoms.name, energy)
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 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 rhf(mol,
bfs,
S,
Hcore,
Ints,
mu=0,
MaxIter=100,
eps_SCF=1E-4,
_diis_=True):
##########################################################
## Get the system information
##########################################################
# size
nbfs = len(bfs)
# get the nuclear energy
enuke = mol.get_enuke()
# determine the number of electrons
# and occupation numbers
nelec = mol.get_nel()
nclosed, nopen = mol.get_closedopen()
nocc = nclosed
# orthogonalization matrix
X = SymOrthCutoff(S)
if _ee_inter_ == 0:
print '\t\t ==================================================='
print '\t\t == Electrons-Electrons interactions desactivated =='
print '\t\t ==================================================='
if nopen != 0:
print '\t\t ================================================================='
print '\t\t Warning : using restricted HF with open shell is not recommended'
print "\t\t Use only if you know what you're doing"
print '\t\t ================================================================='
# get a first DM
#D = np.zeros((nbfs,nbfs))
L, C = scla.eigh(Hcore, b=S)
D = mkdens(C, 0, nocc)
# initialize the old energy
eold = 0.
# initialize the DIIS
if _diis_:
avg = DIIS(S)
#print '\t SCF Calculations'
for iiter in range(MaxIter):
# form the G matrix from the
# density matrix and the 2electron integrals
G = get2JmK(Ints, D)
# form the Fock matrix
F = Hcore + _ee_inter_ * G + mu
# if DIIS
if _diis_:
F = avg.getF(F, D)
# orthogonalize the Fock matrix
Fp = np.dot(X.T, np.dot(F, X))
# diagonalize the Fock matrix
Lp, Cp = scla.eigh(Fp)
# form the density matrix in the OB
if nopen == 0:
Dp = mkdens(Cp, 0, nocc)
else:
Dp = mkdens_spinavg(Cp, nclosed, nopen)
# pass the eigenvector back to the AO
C = np.dot(X, Cp)
# form the density matrix in the AO
if nopen == 0:
D = mkdens(C, 0, nocc)
#else:
# D = mkdens_spinavg(C,nclosed,nopen)
# compute the total energy
e = np.sum(D * (Hcore + F)) + enuke
print "\t\t Iteration: %d Energy: %f EnergyVar: %f" % (
iiter, e.real, np.abs((e - eold).real))
# stop if done
if (np.abs(e - eold) < eps_SCF):
break
else:
eold = e
if iiter < MaxIter:
print(
"\t\t SCF for HF has converged in %d iterations, Final energy %1.3f Ha\n"
% (iiter, e.real))
else:
print("\t\t SCF for HF has failed to converge after %d iterations")
# compute the density matrix in the
# eigenbasis of F
P = np.dot(Cp.T, np.dot(Dp, Cp))
#print D
return Lp, C, Cp, F, Fp, D, Dp, P, X
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"
print energy, "(benchmark = -1.122956)"
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