def numeric_forces(atoms,D=None,**opts):
"Compute numerical forces on atoms"
# D is ignored here.
dx = opts.get('dx',1e-6)
sym = opts.get('sym',True)
return_energy = opts.get('return_energy',False)
nat = len(atoms)
Forces = zeros((nat,3),'d')
E0 = scf(atoms)
for iat in range(nat):
for idir in range(3):
dr = zeros(3,'d')
dr[idir] = dx
atoms[iat].translate(dr)
Ep = scf(atoms)
atoms[iat].translate(-dr)
if sym:
atoms[iat].translate(-dr)
Em = scf(atoms)
atoms[iat].translate(dr)
Forces[iat,idir] = 0.5*(Ep-Em)/dx
else:
Forces[iat,idir] = (Ep-E0)/dx
if return_energy: return E0,Forces
return Forces
def numeric_forces(atoms,D=None,**kwargs):
"Compute numerical forces on atoms"
# D is ignored here.
dx = kwargs.get('dx',settings.NumericForceDx)
sym = kwargs.get('sym',settings.NumericForceSym)
return_energy = kwargs.get('return_energy')
nat = len(atoms)
Forces = zeros((nat,3),'d')
E0 = scf(atoms)
for iat in xrange(nat):
for idir in xrange(3):
dr = zeros(3,'d')
dr[idir] = dx
atoms[iat].translate(dr)
Ep = scf(atoms)
atoms[iat].translate(-dr)
if sym:
atoms[iat].translate(-dr)
Em = scf(atoms)
atoms[iat].translate(dr)
Forces[iat,idir] = 0.5*(Ep-Em)/dx
else:
Forces[iat,idir] = (Ep-E0)/dx
if return_energy: return E0,Forces
return Forces
def zero_density(self):
"""Initialize the density matrices for later. If nothing else,
this assures that I don't have to worry about an undefined
gamma matrix later on."""
self.density = zeros((self.ng,2),'d')
self.grada = zeros((self.ng,3),'d')
self.gradb = zeros((self.ng,3),'d')
self.gamma = zeros((self.ng,3),'d')
def zero_density(self):
"""Initialize the density matrices for later. If nothing else,
this assures that I don't have to worry about an undefined
gamma matrix later on."""
self.density = zeros((self.ng,2),'d')
self.grada = zeros((self.ng,3),'d')
self.gradb = zeros((self.ng,3),'d')
self.gamma = zeros((self.ng,3),'d')
def TransformInts(Ints,orbs):
"""O(N^5) 4-index transformation of the two-electron integrals. Not as
efficient as it could be, since it inflates to the full rectangular
matrices rather than keeping them compressed. But at least it gets the
correct result."""
from time import time
t0 = time()
nbf,nmo = orbs.shape
totlen = nmo*(nmo+1)*(nmo*nmo+nmo+2)/8
temp = zeros((nbf,nbf,nbf,nmo),'d')
tempvec = zeros(nbf,'d')
temp2 = zeros((nbf,nbf,nmo,nmo),'d')
mos = range(nmo) # preform so we don't form inside loops
bfs = range(nbf)
# Start with (mu,nu|sigma,eta)
# Unpack aoints and transform eta -> l
for mu in bfs:
for nu in bfs:
for sigma in bfs:
for l in mos:
for eta in bfs:
tempvec[eta] = Ints[ijkl2intindex(mu,nu,sigma,eta)]
temp[mu,nu,sigma,l] = dot(orbs[:,l],tempvec)
# Transform sigma -> k
for mu in bfs:
for nu in bfs:
for l in mos:
for k in mos:
temp2[mu,nu,k,l] = dot(orbs[:,k],temp[mu,nu,:,l])
# Transform nu -> j
for mu in bfs:
for k in mos:
for l in mos:
for j in mos:
temp[mu,j,k,l] = dot(orbs[:,j],temp2[mu,:,k,l])
# Transform mu -> i and repack integrals:
MOInts = zeros(totlen,'d')
for i in mos:
for j in xrange(i+1):
ij = i*(i+1)/2+j
for k in mos:
for l in xrange(k+1):
kl = k*(k+1)/2+l
if ij >= kl:
ijkl = ijkl2intindex(i,j,k,l)
MOInts[ijkl] = dot(orbs[:,i],temp[:,j,k,l])
del temp,temp2,tempvec #force garbage collection now
return MOInts
def TransformInts(Ints, orbs):
"""O(N^5) 4-index transformation of the two-electron integrals. Not as
efficient as it could be, since it inflates to the full rectangular
matrices rather than keeping them compressed. But at least it gets the
correct result."""
from time import time
t0 = time()
nbf, nmo = orbs.shape
totlen = nmo * (nmo + 1) * (nmo * nmo + nmo + 2) / 8
temp = zeros((nbf, nbf, nbf, nmo), 'd')
tempvec = zeros(nbf, 'd')
temp2 = zeros((nbf, nbf, nmo, nmo), 'd')
mos = range(nmo) # preform so we don't form inside loops
bfs = range(nbf)
# Start with (mu,nu|sigma,eta)
# Unpack aoints and transform eta -> l
for mu in bfs:
for nu in bfs:
for sigma in bfs:
for l in mos:
for eta in bfs:
tempvec[eta] = Ints[ijkl2intindex(mu, nu, sigma, eta)]
temp[mu, nu, sigma, l] = dot(orbs[:, l], tempvec)
# Transform sigma -> k
for mu in bfs:
for nu in bfs:
for l in mos:
for k in mos:
temp2[mu, nu, k, l] = dot(orbs[:, k], temp[mu, nu, :, l])
# Transform nu -> j
for mu in bfs:
for k in mos:
for l in mos:
for j in mos:
temp[mu, j, k, l] = dot(orbs[:, j], temp2[mu, :, k, l])
# Transform mu -> i and repack integrals:
MOInts = zeros(totlen, 'd')
for i in mos:
for j in xrange(i + 1):
ij = i * (i + 1) / 2 + j
for k in mos:
for l in xrange(k + 1):
kl = k * (k + 1) / 2 + l
if ij >= kl:
ijkl = ijkl2intindex(i, j, k, l)
MOInts[ijkl] = dot(orbs[:, i], temp[:, j, k, l])
del temp, temp2, tempvec #force garbage collection now
return MOInts
def TransformIntsMP2(Ints, orbs, nclosed):
"""\
O(N^5) 4-index transformation of the two-electron integrals.
Only transform the ones needed for MP2, which reduces the
scaling to O(nN^4), where n are the occs (<<N).
"""
from time import time
t0 = time()
nbf, nmo = orbs.shape
totlen = nmo * (nmo + 1) * (nmo * nmo + nmo + 2) / 8
occs = range(nclosed)
mos = range(nmo)
bfs = range(nbf)
# Start with (mu,nu|sigma,eta)
# Unpack aoints and transform sigma -> b
temp = zeros((nbf, nbf, nclosed, nbf), 'd')
tempvec = zeros(nbf, 'd')
for mu in bfs:
for nu in bfs:
for eta in bfs:
for b in occs:
for sigma in bfs:
tempvec[sigma] = Ints[ijkl2intindex(
mu, nu, sigma, eta)]
temp[mu, nu, b, eta] = dot(orbs[:, b], tempvec)
temp2 = zeros((nclosed, nbf, nclosed, nbf), 'd')
for nu in bfs:
for eta in bfs:
for b in occs:
for a in occs:
temp2[a, nu, b, eta] = dot(orbs[:, a], temp[:, nu, b, eta])
temp = zeros((nclosed, nbf, nclosed, nmo), 'd')
for a in occs:
for nu in bfs:
for b in occs:
for j in mos:
temp[a, nu, b, j] = dot(orbs[:, j], temp2[a, nu, b, :])
# Transform mu -> i and repack integrals:
MOInts = zeros(totlen, 'd')
for a in occs:
for j in mos:
for b in occs:
for i in mos:
aibj = ijkl2intindex(a, i, b, j)
MOInts[aibj] = dot(orbs[:, i], temp[a, :, b, j])
#print "Integral transform time = ",time()-t0
del temp, temp2, tempvec #force garbage collection now
return MOInts
def TransformIntsMP2(Ints,orbs,nclosed):
"""\
O(N^5) 4-index transformation of the two-electron integrals.
Only transform the ones needed for MP2, which reduces the
scaling to O(nN^4), where n are the occs (<<N).
"""
from time import time
t0 = time()
nbf,nmo = orbs.shape
totlen = nmo*(nmo+1)*(nmo*nmo+nmo+2)/8
occs = range(nclosed)
mos = range(nmo)
bfs = range(nbf)
# Start with (mu,nu|sigma,eta)
# Unpack aoints and transform sigma -> b
temp = zeros((nbf,nbf,nclosed,nbf),'d')
tempvec = zeros(nbf,'d')
for mu in bfs:
for nu in bfs:
for eta in bfs:
for b in occs:
for sigma in bfs:
tempvec[sigma] = Ints[ijkl2intindex(mu,nu,sigma,eta)]
temp[mu,nu,b,eta] = dot(orbs[:,b],tempvec)
temp2 = zeros((nclosed,nbf,nclosed,nbf),'d')
for nu in bfs:
for eta in bfs:
for b in occs:
for a in occs:
temp2[a,nu,b,eta] = dot(orbs[:,a],temp[:,nu,b,eta])
temp = zeros((nclosed,nbf,nclosed,nmo),'d')
for a in occs:
for nu in bfs:
for b in occs:
for j in mos:
temp[a,nu,b,j] = dot(orbs[:,j],temp2[a,nu,b,:])
# Transform mu -> i and repack integrals:
MOInts = zeros(totlen,'d')
for a in occs:
for j in mos:
for b in occs:
for i in mos:
aibj = ijkl2intindex(a,i,b,j)
MOInts[aibj] = dot(orbs[:,i],temp[a,:,b,j])
#print "Integral transform time = ",time()-t0
del temp,temp2,tempvec #force garbage collection now
return MOInts
def EXXC1(dens, gamma):
"AEM's EXX compatible correlation #1 (note: no spin). AEM June 2006."
npts = len(dens)
ec = zeros(npts, 'd')
vc = zeros(npts, 'd')
for i in range(npts):
rho = float(dens[i]) # Density
gam = gamma[i]
ecpnt, dnedrho, dnedgamma = c1(rho, gam)
ec[i] = ecpnt
vc[i] = dnedrho # more derivatives need to be added
return ec, vc
def EXXC1(dens,gamma):
"AEM's EXX compatible correlation #1 (note: no spin). AEM June 2006."
npts = len(dens)
ec = zeros(npts,'d')
vc = zeros(npts,'d')
for i in range(npts):
rho = float(dens[i]) # Density
gam = gamma[i]
ecpnt,dnedrho,dnedgamma = c1(rho,gam)
ec[i] = ecpnt
vc[i] = dnedrho # more derivatives need to be added
return ec,vc
def CPBE(dens,gamma):
"PBE Correlation Functional"
npts = len(dens)
ec = zeros(npts,'d')
vc = zeros(npts,'d')
for i in xrange(npts):
rho = 0.5*float(dens[i]) # Density of the alpha spin
gam = 0.25*gamma[i]
ecab,vca,vcb = cpbe(rho,rho,gam,gam,gam)
ec[i] = ecab
vc[i] = vca
return ec,vc
def CPBE(dens,gamma):
"PBE Correlation Functional"
npts = len(dens)
ec = zeros(npts,'d')
vc = zeros(npts,'d')
for i in range(npts):
rho = 0.5*float(dens[i]) # Density of the alpha spin
gam = 0.25*gamma[i]
ecab,vca,vcb = cpbe(rho,rho,gam,gam,gam)
ec[i] = ecab
vc[i] = vca
return ec,vc
def XPBE(dens,gamma):
"PBE Exchange Functional"
npts = len(dens)
assert len(gamma) == npts
ex = zeros(npts,'d')
vx = zeros(npts,'d')
for i in xrange(npts):
rho = 0.5*float(dens[i]) # Density of the alpha spin
gam = 0.25*gamma[i]
exa,vxa = xpbe(rho,gam)
ex[i] = 2*exa
vx[i] = vxa
return ex,vx
def XPBE(dens,gamma):
"PBE Exchange Functional"
npts = len(dens)
assert len(gamma) == npts
ex = zeros(npts,'d')
vx = zeros(npts,'d')
for i in range(npts):
rho = 0.5*float(dens[i]) # Density of the alpha spin
gam = 0.25*gamma[i]
exa,vxa = xpbe(rho,gam)
ex[i] = 2*exa
vx[i] = vxa
return ex,vx
def TransformInts(Ints, orbs1, orbs2, nocc):
nbf, nmo = orbs1.shape
totlen = nmo * nmo * nmo * nmo
occs = range(nocc)
mos = range(nmo)
bfs = range(nbf)
# Start with (mu,nu|sigma,eta)
# Unpack aoints and transform sigma -> b
# Here sigma, b, nu, j are of first same spin group,
# others of second same spin group
temp = zeros((nbf, nbf, nbf, nbf), 'd')
tempvec = zeros(nbf, 'd')
for mu in bfs:
for nu in bfs:
for eta in bfs:
for b in bfs:
for sigma in bfs:
tempvec[sigma] = Ints[ijkl2intindex(
mu, nu, sigma, eta)]
temp[mu, nu, b, eta] = dot(orbs1[b, :], tempvec)
temp2 = zeros((nbf, nbf, nbf, nbf), 'd')
for nu in bfs:
for eta in bfs:
for b in bfs:
for a in bfs:
temp2[a, nu, b, eta] = dot(orbs2[a, :], temp[:, nu, b,
eta])
temp = zeros((nbf, nbf, nbf, nbf), 'd')
for a in bfs:
for nu in bfs:
for b in bfs:
for j in bfs:
temp[a, nu, b, j] = dot(orbs1[j, :], temp2[a, nu, b, :])
# Transform mu -> i and repack integrals:
MOInts = zeros(totlen, 'd')
for a in bfs:
for j in bfs:
for b in bfs:
for i in bfs:
aibj = ijkl2intindex(a, i, b, j)
MOInts[aibj] = dot(orbs2[i, :], temp[a, :, b, j])
del temp, temp2, tempvec #force garbage collection now
return MOInts, nbf
def set_bf_amps(self, bfs):
x, y, z, w = self.xyzw()
nbf = len(bfs)
self.bfs = zeros(nbf, 'd')
for i in xrange(nbf):
self.bfs[i] = bfs[i].amp(x, y, z)
# This *if* statement is potentially slow. If it becomes
# a factor, pull it up to AtomicGrids and have two
# explicit cases here.
if self.do_grad_dens:
self.bfgrads = zeros((nbf, 3), 'd')
for i in xrange(nbf):
self.bfgrads[i, :] = bfs[i].grad(x, y, z)
return
def set_bf_amps(self,bfs):
x,y,z,w = self.xyzw()
nbf = len(bfs)
self.bfs = zeros(nbf,'d')
for i in xrange(nbf):
self.bfs[i] = bfs[i].amp(x,y,z)
# This *if* statement is potentially slow. If it becomes
# a factor, pull it up to AtomicGrids and have two
# explicit cases here.
if self.do_grad_dens:
self.bfgrads = zeros((nbf,3),'d')
for i in xrange(nbf):
self.bfgrads[i,:] = bfs[i].grad(x,y,z)
return
def add_basis(self,bfs):
# Compute the amplitudes of the basis functions over the grid
self.nbf = len(bfs)
self.bfgrid = zeros((self.ng,self.nbf),'d')
for ibf in xrange(self.nbf):
for ig in xrange(self.ng):
x,y,z,w = self.xyzw[ig,:]
self.bfgrid[ig,ibf] = bfs[ibf].amp(x,y,z)
if self.do_grad_dens:
self.bfgrads = zeros((self.ng,self.nbf,3),'d')
for ibf in xrange(self.nbf):
for ig in xrange(self.ng):
x,y,z,w = self.xyzw[ig,:]
self.bfgrads[ig,ibf,:] = bfs[ibf].grad(x,y,z)
return
def get1ints(bfs,atoms):
"Form the overlap S and h=t+vN one-electron Hamiltonian matrices"
nbf = len(bfs)
S = zeros((nbf,nbf),'d')
h = zeros((nbf,nbf),'d')
for i in xrange(nbf):
bfi = bfs[i]
for j in xrange(nbf):
bfj = bfs[j]
S[i,j] = bfi.overlap(bfj)
h[i,j] = bfi.kinetic(bfj)
for atom in atoms:
h[i,j] = h[i,j] + atom.atno*bfi.nuclear(bfj,atom.pos())
return S,h
def LYP(dens, gamma):
"""Transformed version of LYP. See 'Results obtained with correlation
energy density functionals of Becke and Lee, Yang, and Parr.' Miehlich,
Savin, Stoll and Preuss. CPL 157, 200 (1989).
"""
npts = len(dens)
ec = zeros(npts, 'd')
vc = zeros(npts, 'd')
for i in range(npts):
rho = 0.5 * float(dens[i]) # Density of the alpha spin
gam = 0.25 * gamma[i]
ecab, vca, vcb = clyp(rho, rho, gam, gam, gam)
ec[i] = ecab
vc[i] = vca
return ec, vc
def LYP(dens,gamma):
"""Transformed version of LYP. See 'Results obtained with correlation
energy density functionals of Becke and Lee, Yang, and Parr.' Miehlich,
Savin, Stoll and Preuss. CPL 157, 200 (1989).
"""
npts = len(dens)
ec = zeros(npts,'d')
vc = zeros(npts,'d')
for i in range(npts):
rho = 0.5*float(dens[i]) # Density of the alpha spin
gam = 0.25*gamma[i]
ecab,vca,vcb = clyp(rho,rho,gam,gam,gam)
ec[i] = ecab
vc[i] = vca
return ec,vc
def add_basis(self,bfs):
# Compute the amplitudes of the basis functions over the grid
self.nbf = len(bfs)
self.bfgrid = zeros((self.ng,self.nbf),'d')
for ibf in xrange(self.nbf):
for ig in xrange(self.ng):
x,y,z,w = self.xyzw[ig,:]
self.bfgrid[ig,ibf] = bfs[ibf].amp(x,y,z)
if self.do_grad_dens:
self.bfgrads = zeros((self.ng,self.nbf,3),'d')
for ibf in xrange(self.nbf):
for ig in xrange(self.ng):
x,y,z,w = self.xyzw[ig,:]
self.bfgrads[ig,ibf,:] = bfs[ibf].grad(x,y,z)
return
def get1ints(bfs, atoms):
"Form the overlap S and h=t+vN one-electron Hamiltonian matrices"
nbf = len(bfs)
S = zeros((nbf, nbf), 'd')
h = zeros((nbf, nbf), 'd')
for i in xrange(nbf):
bfi = bfs[i]
for j in xrange(nbf):
bfj = bfs[j]
S[i, j] = bfi.overlap(bfj)
h[i, j] = bfi.kinetic(bfj)
for atom in atoms:
h[i, j] = h[i, j] + atom.atno * bfi.nuclear(bfj, atom.pos())
return S, h
def TransformInts(Ints,orbs1,orbs2, nocc):
nbf,nmo = orbs1.shape
totlen = nmo*nmo*nmo*nmo
occs = range(nocc)
mos = range(nmo)
bfs = range(nbf)
# Start with (mu,nu|sigma,eta)
# Unpack aoints and transform sigma -> b
# Here sigma, b, nu, j are of first same spin group,
# others of second same spin group
temp = zeros((nbf,nbf,nbf,nbf),'d')
tempvec = zeros(nbf,'d')
for mu in bfs:
for nu in bfs:
for eta in bfs:
for b in bfs:
for sigma in bfs:
tempvec[sigma] = Ints[ijkl2intindex(mu,nu,sigma,eta)]
temp[mu,nu,b,eta] = dot(orbs1[b,:],tempvec)
temp2 = zeros((nbf,nbf,nbf,nbf),'d')
for nu in bfs:
for eta in bfs:
for b in bfs:
for a in bfs:
temp2[a,nu,b,eta] = dot(orbs2[a,:],temp[:,nu,b,eta])
temp = zeros((nbf,nbf,nbf,nbf),'d')
for a in bfs:
for nu in bfs:
for b in bfs:
for j in bfs:
temp[a,nu,b,j] = dot(orbs1[j,:],temp2[a,nu,b,:])
# Transform mu -> i and repack integrals:
MOInts = zeros(totlen,'d')
for a in bfs:
for j in bfs:
for b in bfs:
for i in bfs:
aibj = ijkl2intindex(a,i,b,j)
MOInts[aibj] = dot(orbs2[i,:],temp[a,:,b,j])
del temp,temp2,tempvec #force garbage collection now
return MOInts, nbf
def get_F1(atoms,D):
"One-center corrections to the core fock matrix"
nbf = get_nbf(atoms)
nat = len(atoms)
F1 = zeros((nbf,nbf),'d')
ibf = 0 # bf number of the first bfn on iat
for iat in xrange(nat):
atomi = atoms[iat]
for i in xrange(atomi.nbf):
bfi = atomi.basis[i]
gii = get_g(bfi,bfi)
qi = D[ibf+i,ibf+i]
F1[ibf+i,ibf+i] = 0.5*qi*gii
for j in xrange(atomi.nbf): # ij on same atom
if j != i:
bfj = atomi.basis[j]
qj = D[ibf+j,ibf+j]
gij = get_g(bfi,bfj)
pij = D[ibf+i,ibf+j]
hij = get_h(bfi,bfj)
# the following 0.5 is something of a kludge to match
# the mopac results.
F1[ibf+i,ibf+i] += qj*gij - 0.5*qj*hij
F1[ibf+i,ibf+j] += 0.5*pij*(3*hij-gij)
ibf += atomi.nbf
return F1
def get_F0_old(atoms):
"Form the zero-iteration (density matrix independent) Fock matrix"
nbf = get_nbf(atoms)
nat = len(atoms)
F0 = zeros((nbf,nbf),'d')
ibf = 0 # bf number of the first bfn on iat
for iat in xrange(nat):
atomi = atoms[iat]
for i in xrange(atomi.nbf):
bfi = atomi.basis[i]
F0[ibf+i,ibf+i] = bfi.u
jbf = 0
for jat in xrange(nat):
atomj = atoms[jat]
if iat != jat:
gammaij = get_gamma(atomi,atomj)
betaij = get_beta0(atomi.atno,atomj.atno)
F0[ibf+i,ibf+i] -= gammaij*atomj.Z
for j in xrange(atomj.nbf):
bfj = atomj.basis[j]
Sij = bfi.cgbf.overlap(bfj.cgbf)
#Sij = mopac_overlap(bfi,bfj)
IPij = bfi.ip+bfj.ip
F0[ibf+i,jbf+j] = betaij*IPij*Sij
F0[jbf+j,ibf+i] = F0[ibf+i,jbf+j]
jbf += atomj.nbf
ibf += atomi.nbf
return F0
def grad_bf_prod(self,a,b):
"Form grad(chia,chib)."
B = zeros((self._length,3),'d')
for i in xrange(3):
B[:,i] = self.bfgrid[:,a]*self.bfgrads[:,b,i] \
+ self.bfgrid[:,b]*self.bfgrads[:,a,i]
return B
def get_F0_old(atoms):
"Form the zero-iteration (density matrix independent) Fock matrix"
nbf = get_nbf(atoms)
nat = len(atoms)
F0 = zeros((nbf,nbf),'d')
ibf = 0 # bf number of the first bfn on iat
for iat in range(nat):
atomi = atoms[iat]
for i in range(atomi.nbf):
bfi = atomi.basis[i]
F0[ibf+i,ibf+i] = bfi.u
jbf = 0
for jat in range(nat):
atomj = atoms[jat]
if iat != jat:
gammaij = get_gamma(atomi,atomj)
betaij = get_beta0(atomi.atno,atomj.atno)
F0[ibf+i,ibf+i] -= gammaij*atomj.Z
for j in range(atomj.nbf):
bfj = atomj.basis[j]
Sij = bfi.cgbf.overlap(bfj.cgbf)
#Sij = mopac_overlap(bfi,bfj)
IPij = bfi.ip+bfj.ip
F0[ibf+i,jbf+j] = betaij*IPij*Sij
F0[jbf+j,ibf+i] = F0[ibf+i,jbf+j]
jbf += atomj.nbf
ibf += atomi.nbf
return F0
def get_F2_open(atoms,Da,Db):
"Two-center corrections to the core fock matrix"
nbf = get_nbf(atoms)
nat = len(atoms)
F2 = zeros((nbf,nbf),'d')
ibf = 0 # bf number of the first bfn on iat
for iat in range(nat):
atomi = atoms[iat]
jbf = 0
for jat in range(nat):
atomj = atoms[jat]
if iat != jat:
gammaij = get_gamma(atomi,atomj)
for i in range(atomi.nbf):
for j in range(atomj.nbf):
pija = Da[ibf+i,jbf+j]
pijb = Db[ibf+i,jbf+j]
pij = pija+pijb
qja = Da[jbf+j,jbf+j]
qjb = Db[jbf+j,jbf+j]
qj = qja+qjb
qia = Da[ibf+i,ibf+i]
qib = Db[ibf+i,ibf+i]
qi = qia+qib
F2[ibf+i,jbf+j] -= 0.25*pij*gammaij
F2[jbf+j,ibf+i] = F2[ibf+i,jbf+j]
# The following 0.5 is a kludge
F2[ibf+i,ibf+i] += 0.5*qj*gammaij
F2[jbf+j,jbf+j] += 0.5*qi*gammaij
jbf += atomj.nbf
ibf += atomi.nbf
return F2
def Ffunc_num(cnew):
E0 = Efunc(cnew)
F = zeros(3*nat,'d')
ei = zeros(3*nat,'d')
dx = 1e-7
for i in range(nat):
for j in range(3):
ei[3*i+j] = 1.0
E1 = Efunc(cnew+ei*dx)
ei[3*i+j] = 0.0
F[3*i+j] = (E1-E0)/dx
if verbose_level > 0:
print "MINDO3 gradient calculation requested:"
print atoms
print Hf
return F
def get_F1(atoms,D):
"One-center corrections to the core fock matrix"
nbf = get_nbf(atoms)
nat = len(atoms)
F1 = zeros((nbf,nbf),'d')
ibf = 0 # bf number of the first bfn on iat
for iat in range(nat):
atomi = atoms[iat]
for i in range(atomi.nbf):
bfi = atomi.basis[i]
gii = get_g(bfi,bfi)
qi = D[ibf+i,ibf+i]
F1[ibf+i,ibf+i] = 0.5*qi*gii
for j in range(atomi.nbf): # ij on same atom
if j != i:
bfj = atomi.basis[j]
qj = D[ibf+j,ibf+j]
gij = get_g(bfi,bfj)
pij = D[ibf+i,ibf+j]
hij = get_h(bfi,bfj)
# the following 0.5 is something of a kludge to match
# the mopac results.
F1[ibf+i,ibf+i] += qj*gij - 0.5*qj*hij
F1[ibf+i,ibf+j] += 0.5*pij*(3*hij-gij)
ibf += atomi.nbf
return F1
def Ffunc_num(cnew):
E0 = Efunc(cnew)
F = zeros(3*nat,'d')
ei = zeros(3*nat,'d')
dx = 1e-7
for i in xrange(nat):
for j in xrange(3):
ei[3*i+j] = 1.0
E1 = Efunc(cnew+ei*dx)
ei[3*i+j] = 0.0
F[3*i+j] = (E1-E0)/dx
if verbose:
print "MINDO3 gradient calculation requested:"
print atoms
print Hf
return F
def grad_bf_prod(self, a, b):
"Form grad(chia,chib)."
B = zeros((self._length, 3), 'd')
for i in xrange(3):
B[:,i] = self.bfgrid[:,a]*self.bfgrads[:,b,i] \
+ self.bfgrid[:,b]*self.bfgrads[:,a,i]
return B
def grad_bf_prod(self,a,b):
"Form grad(chia,chib)."
gab = zeros((self.ng,3),'d')
for i in xrange(3):
gab[:,i] = self.bfgrid[:,a]*self.bfgrads[:,b,i] \
+ self.bfgrid[:,b]*self.bfgrads[:,a,i]
return gab
def MP2(aoints, orbs, orbe, nclosed, nvirt):
#moints = TransformInts(aoints,orbs)
moints = TransformIntsMP2(aoints, orbs, nclosed)
occs = range(nclosed)
unoccs = range(nclosed, nclosed + nvirt)
nocc = len(occs)
Epairs = zeros((nocc, nocc), 'd')
Emp2 = 0
for a in occs:
for b in occs:
for r in unoccs:
for s in unoccs:
arbs = moints[ijkl2intindex(a, r, b, s)]
asbr = moints[ijkl2intindex(a, s, b, r)]
Epairs[a,b] += arbs*(2*arbs-asbr)/\
(orbe[a]+orbe[b]-orbe[r]-orbe[s])
if VERBOSE:
print "MP2 pair energies"
for a in xrange(nocc):
for b in xrange(a):
print a, b, Epairs[a, b] + Epairs[b, a]
print a, a, Epairs[a, a]
return sum(sum(Epairs))
def get_gamma(self):
"Return the density gradient gamma for each point in the grid"
if not self.do_grad_dens: return None
gamma = zeros(len(self.points),'d')
for i in xrange(len(self.points)):
gamma[i] = self.points[i].get_gamma()
return gamma
def MP2(aoints,orbs,orbe,nclosed,nvirt):
#moints = TransformInts(aoints,orbs)
moints = TransformIntsMP2(aoints,orbs,nclosed)
occs = range(nclosed)
unoccs = range(nclosed,nclosed+nvirt)
nocc = len(occs)
Epairs = zeros((nocc,nocc),'d')
Emp2 = 0
for a in occs:
for b in occs:
for r in unoccs:
for s in unoccs:
arbs = moints[ijkl2intindex(a,r,b,s)]
asbr = moints[ijkl2intindex(a,s,b,r)]
Epairs[a,b] += arbs*(2*arbs-asbr)/\
(orbe[a]+orbe[b]-orbe[r]-orbe[s])
if VERBOSE:
print "MP2 pair energies"
for a in range(nocc):
for b in range(a):
print a,b,Epairs[a,b]+Epairs[b,a]
print a,a,Epairs[a,a]
return sum(sum(Epairs))
def get_F1_open(atoms,Da,Db):
"One-center corrections to the core fock matrix"
nbf = get_nbf(atoms)
nat = len(atoms)
F1 = zeros((nbf,nbf),'d')
ibf = 0 # bf number of the first bfn on iat
for iat in xrange(nat):
atomi = atoms[iat]
for i in xrange(atomi.nbf):
gii = get_g(atomi.basis[i],atomi.basis[i])
qib = Db[ibf+i,ibf+i]
#electron only interacts with the other electron in orb,
# not with itself
F1[ibf+i,ibf+i] = qib*gii
for j in xrange(atomi.nbf): # ij on same atom
if j != i:
qja = Da[ibf+j,ibf+j]
qjb = Db[ibf+j,ibf+j]
qj = qja+qjb
gij = get_g(atomi.basis[i],atomi.basis[j])
pija = Da[ibf+i,ibf+j]
pijb = Db[ibf+i,ibf+j]
pij = pija + pijb
hij = get_h(atomi.basis[i],atomi.basis[j])
# the following 0.5 is something of a kludge to match
# the mopac results.
F1[ibf+i,ibf+i] += qj*gij - qja*hij
F1[ibf+i,ibf+j] += 2*pij*hij - pija*(hij+gij)
ibf += atomi.nbf
return F1
def get_F1_open(atoms,Da,Db):
"One-center corrections to the core fock matrix"
nbf = get_nbf(atoms)
nat = len(atoms)
F1 = zeros((nbf,nbf),'d')
ibf = 0 # bf number of the first bfn on iat
for iat in range(nat):
atomi = atoms[iat]
for i in range(atomi.nbf):
gii = get_g(atomi.basis[i],atomi.basis[i])
qib = Db[ibf+i,ibf+i]
#electron only interacts with the other electron in orb,
# not with itself
F1[ibf+i,ibf+i] = qib*gii
for j in range(atomi.nbf): # ij on same atom
if j != i:
qja = Da[ibf+j,ibf+j]
qjb = Db[ibf+j,ibf+j]
qj = qja+qjb
gij = get_g(atomi.basis[i],atomi.basis[j])
pija = Da[ibf+i,ibf+j]
pijb = Db[ibf+i,ibf+j]
pij = pija + pijb
hij = get_h(atomi.basis[i],atomi.basis[j])
# the following 0.5 is something of a kludge to match
# the mopac results.
F1[ibf+i,ibf+i] += qj*gij - qja*hij
F1[ibf+i,ibf+j] += 2*pij*hij - pija*(hij+gij)
ibf += atomi.nbf
return F1
def get_F2_open(atoms,Da,Db):
"Two-center corrections to the core fock matrix"
nbf = get_nbf(atoms)
nat = len(atoms)
F2 = zeros((nbf,nbf),'d')
ibf = 0 # bf number of the first bfn on iat
for iat in xrange(nat):
atomi = atoms[iat]
jbf = 0
for jat in xrange(nat):
atomj = atoms[jat]
if iat != jat:
gammaij = get_gamma(atomi,atomj)
for i in xrange(atomi.nbf):
for j in xrange(atomj.nbf):
pija = Da[ibf+i,jbf+j]
pijb = Db[ibf+i,jbf+j]
pij = pija+pijb
qja = Da[jbf+j,jbf+j]
qjb = Db[jbf+j,jbf+j]
qj = qja+qjb
qia = Da[ibf+i,ibf+i]
qib = Db[ibf+i,ibf+i]
qi = qia+qib
F2[ibf+i,jbf+j] -= 0.25*pij*gammaij
F2[jbf+j,ibf+i] = F2[ibf+i,jbf+j]
# The following 0.5 is a kludge
F2[ibf+i,ibf+i] += 0.5*qj*gammaij
F2[jbf+j,jbf+j] += 0.5*qi*gammaij
jbf += atomj.nbf
ibf += atomi.nbf
return F2
def grad(self):
pts = self._points
npts = len(pts)
gr = zeros((npts, 3), 'd')
for i in xrange(npts):
gr[i, :] = pts[i].grad()
return gr
def grad_bf_prod(self,a,b):
"Form grad(chia,chib)."
gab = zeros((self.ng,3),'d')
for i in xrange(3):
gab[:,i] = self.bfgrid[:,a]*self.bfgrads[:,b,i] \
+ self.bfgrid[:,b]*self.bfgrads[:,a,i]
return gab
def bfs(self,i):
"Return a vector of the product of two basis functions "
" over the entire grid"
bfs = zeros(len(self.points),'d')
for j in xrange(len(self.points)):
bfs[j] = self.points[j].bfs[i]
return bfs
def bfs(self, i):
"Return a vector of the product of two basis functions "
" over the entire grid"
bfs = zeros(len(self.points), 'd')
for j in xrange(len(self.points)):
bfs[j] = self.points[j].bfs[i]
return bfs
def get_gamma(self):
"Return the density gradient gamma for each point in the grid"
if not self.do_grad_dens: return None
gamma = zeros(len(self.points), 'd')
for i in xrange(len(self.points)):
gamma[i] = self.points[i].get_gamma()
return gamma
def overlap_1(self,other):
"Overlap matrix element with another CGBF"
Sij = zeros(3,'d')
for ipbf in self.prims:
for jpbf in other.prims:
Sij = Sij + ipbf.coef*jpbf.coef*ipbf.overlap_1(jpbf)
return self.norm*other.norm*Sij
def fulleval(self,E):
# This routine doesn't work very well.
g = zeros((self.norb,self.norb),'d')
orbs = range(self.norb)
occs = range(self.nocc)
virts = range(self.nocc,self.norb)
term = 0.
for i in orbs:
for j in orbs:
for a in occs:
for r in virts:
for s in virts:
iras = self.moints[ijkl2intindex(i,r,a,s)]
jras = self.moints[ijkl2intindex(j,r,a,s)]
jsar = self.moints[ijkl2intindex(j,s,a,r)]
term += iras*(2*jras-jsar)/(
E+self.e0[a]-self.e0[r]-self.e0[s])
for a in occs:
for b in occs:
for r in virts:
iabr = self.moints[ijkl2intindex(i,a,b,r)]
jabr = self.moints[ijkl2intindex(j,a,b,r)]
jbar = self.moints[ijkl2intindex(j,b,a,r)]
term += iabr*(2*jabr-jbar)/(
E+self.e0[r]-self.e0[a]-self.e0[b])
g[i,j] = -term
for i in orbs:
g[i,i] += E - self.e0[i]
return det(g)
def fulleval(self, E):
# This routine doesn't work very well.
g = zeros((self.norb, self.norb), 'd')
orbs = range(self.norb)
occs = range(self.nocc)
virts = range(self.nocc, self.norb)
term = 0.
for i in orbs:
for j in orbs:
for a in occs:
for r in virts:
for s in virts:
iras = self.moints[ijkl2intindex(i, r, a, s)]
jras = self.moints[ijkl2intindex(j, r, a, s)]
jsar = self.moints[ijkl2intindex(j, s, a, r)]
term += iras * (2 * jras - jsar) / (
E + self.e0[a] - self.e0[r] - self.e0[s])
for a in occs:
for b in occs:
for r in virts:
iabr = self.moints[ijkl2intindex(i, a, b, r)]
jabr = self.moints[ijkl2intindex(j, a, b, r)]
jbar = self.moints[ijkl2intindex(j, b, a, r)]
term += iabr * (2 * jabr - jbar) / (
E + self.e0[r] - self.e0[a] - self.e0[b])
g[i, j] = -term
for i in orbs:
g[i, i] += E - self.e0[i]
return det(g)
def kinetic_1(self,other):
"KE matrix element with another CGBF"
Tij = zeros(3,'d')
for ipbf in self.prims:
for jpbf in other.prims:
Tij = Tij + ipbf.coef*jpbf.coef*ipbf.kinetic_1(jpbf)
return self.norm*other.norm*Tij
def grad(self):
pts = self._points
npts = len(pts)
gr = zeros((npts,3),'d')
for i in range(npts):
gr[i,:] = pts[i].grad()
return gr
def B(dens, gamma):
"""
Becke 1988 Exchange Functional. From 'Density-functional exchange
energy approximation with correct asymptotic behavior.' AD Becke,
PRA 38, 3098 (1988).
"""
npts = len(dens)
assert len(gamma) == npts
ex = zeros(npts, 'd')
vx = zeros(npts, 'd')
for i in range(npts):
rho = 0.5 * float(dens[i]) # Density of the alpha spin
gam = 0.25 * gamma[i]
exa, vxa = xb(rho, gam)
ex[i] = 2 * exa
vx[i] = vxa
return ex, vx
def der_overlap_matrix(a,bset):
"""
Evaluates the derivative of the overlap integrals
with respect to atomic coordinate
"""
#initialize dS/dR matrices
nbf = len(bset)
dS_dXa = zeros((nbf,nbf),'d')
dS_dYa = zeros((nbf,nbf),'d')
dS_dZa = zeros((nbf,nbf),'d')
for i in xrange(nbf): #rows
for j in xrange(nbf): #columns
dS_dXa[i][j],dS_dYa[i][j],dS_dZa[i][j] = der_overlap_element(a,bset[i],bset[j])
#if a==1: print "dS_dXa"; pad_out(dS_dXa); print "dS_dYa"; pad_out(dS_dYa); print "dS_dZa"; pad_out(dS_dZa);
return dS_dXa,dS_dYa,dS_dZa
def bdg(b,d,g):
"""Basis x Density x Gradient matrix multiply."""
n,m = b.shape
_bdg = zeros((n,3),'d')
db = dot(b,d)
for j in xrange(3):
_bdg[:,j] = abdot(db,g[:,:,j])
return _bdg
def bdg(b,d,g):
"""Basis x Density x Gradient matrix multiply."""
n,m = b.shape
_bdg = zeros((n,3),'d')
db = dot(b,d)
for j in xrange(3):
_bdg[:,j] = abdot(db,g[:,:,j])
return _bdg
def fetch_kints(Ints, i, j, nbf):
temp = zeros(nbf * nbf, 'd')
kl = 0
for k in xrange(nbf):
for l in xrange(nbf):
temp[kl] = Ints[intindex(i, k, j, l)]
kl += 1
return temp
def fetch_kints(Ints,i,j,nbf):
temp = zeros(nbf*nbf,'d')
kl = 0
for k in xrange(nbf):
for l in xrange(nbf):
temp[kl] = Ints[intindex(i,k,j,l)]
kl += 1
return temp
def der_overlap_matrix(a, bset):
"""
Evaluates the derivative of the overlap integrals
with respect to atomic coordinate
"""
#initialize dS/dR matrices
nbf = len(bset)
dS_dXa = zeros((nbf, nbf), 'd')
dS_dYa = zeros((nbf, nbf), 'd')
dS_dZa = zeros((nbf, nbf), 'd')
for i in xrange(nbf): #rows
for j in xrange(nbf): #columns
dS_dXa[i][j], dS_dYa[i][j], dS_dZa[i][j] = der_overlap_element(
a, bset[i], bset[j])
#if a==1: print "dS_dXa"; pad_out(dS_dXa); print "dS_dYa"; pad_out(dS_dYa); print "dS_dZa"; pad_out(dS_dZa);
return dS_dXa, dS_dYa, dS_dZa