def EN2(molecule, **kwargs): #
"General wrapper for the simple CI method"
nalpha, nbeta = molecule.get_alphabeta()
bfs = getbasis(molecule)
S, h, Ints = getints(bfs, molecule)
energy, (orbea, orbeb), (orbsa, orbsb) = uhf(molecule,
integrals=(S, h, Ints),
bfs=bfs,
**kwargs)
EHF = energy
print "The Hatree-Fock energy is ", EHF
#compute the transformed molecular orbital integrals
aamoints, nbf = TransformInts(Ints, orbsa, orbsa, nalpha)
bbmoints, nbf = TransformInts(Ints, orbsb, orbsb, nbeta)
abmoints, nbf = TransformInts(Ints, orbsa, orbsb, nalpha)
#Initialize the fractional occupations:
Yalpha = zeros((nbf), 'd')
Ybeta = zeros((nbf), 'd')
#set up the occupied and virtual orbitals
aoccs = range(nalpha)
boccs = range(nbeta)
avirt = range(nalpha, nbf) #numbers of alpha virtual orbitals
bvirt = range(nbeta, nbf) #numbers of beta virtual orbitals
######## Computation of the primary energy correction #########
#Set initial correction terms to zero
Ec1 = 0.
sum = 0.
z = 1.
#compute correction term for two alpha electrons
for a in aoccs:
for b in xrange(a):
for r in avirt:
for s in xrange(nalpha, r):
arbs = aamoints[ijkl2intindex(a, r, b, s)]
asbr = aamoints[ijkl2intindex(a, s, b, r)]
rraa = aamoints[ijkl2intindex(r,r,a,a)] - \
aamoints[ijkl2intindex(r,a,a,r)]
rrbb = aamoints[ijkl2intindex(r,r,b,b)] - \
aamoints[ijkl2intindex(r,b,b,r)]
ssaa = aamoints[ijkl2intindex(s,s,a,a)] - \
aamoints[ijkl2intindex(s,a,a,s)]
ssbb = aamoints[ijkl2intindex(s,s,b,b)] - \
aamoints[ijkl2intindex(s,b,b,s)]
rrss = aamoints[ijkl2intindex(r,r,s,s)] - \
aamoints[ijkl2intindex(r,s,s,r)]
aabb = aamoints[ijkl2intindex(a,a,b,b)] - \
aamoints[ijkl2intindex(a,b,b,a)]
eigendif = (orbea[r] + orbea[s] - orbea[a] - orbea[b])
delcorr = (-rraa - rrbb - ssaa - ssbb + rrss + aabb)
delta = eigendif + delcorr * z
Eio = (arbs - asbr)
x = -Eio / delta
if abs(x) > 1:
print "Warning a large x value has been ",\
"discovered with x = ",x
x = choose(x < 1, (1, x))
x = choose(x > -1, (-1, x))
sum += x * x
Yalpha[a] -= x * x
Yalpha[b] -= x * x
Yalpha[r] += x * x
Yalpha[s] += x * x
Ec1 += x * Eio
#compute correction term for two beta electrons
for a in boccs:
for b in xrange(a):
for r in bvirt:
for s in xrange(nbeta, r):
arbs = bbmoints[ijkl2intindex(a, r, b, s)]
asbr = bbmoints[ijkl2intindex(a, s, b, r)]
rraa = bbmoints[ijkl2intindex(r,r,a,a)] - \
bbmoints[ijkl2intindex(r,a,a,r)]
rrbb = bbmoints[ijkl2intindex(r,r,b,b)] - \
bbmoints[ijkl2intindex(r,b,b,r)]
ssaa = bbmoints[ijkl2intindex(s,s,a,a)] - \
bbmoints[ijkl2intindex(s,a,a,s)]
ssbb = bbmoints[ijkl2intindex(s,s,b,b)] - \
bbmoints[ijkl2intindex(s,b,b,s)]
rrss = bbmoints[ijkl2intindex(r,r,s,s)] - \
bbmoints[ijkl2intindex(r,s,s,r)]
aabb = bbmoints[ijkl2intindex(a,a,b,b)] - \
bbmoints[ijkl2intindex(a,b,b,a)]
eigendif = (orbeb[r] + orbeb[s] - orbeb[a] - orbeb[b])
delcorr = (-rraa - rrbb - ssaa - ssbb + rrss + aabb)
delta = eigendif + delcorr * z
Eio = (arbs - asbr)
x = -Eio / delta
if abs(x) > 1: print "Warning a large x value has ",\
"been discovered with x = ",x
x = choose(x < 1, (1, x))
x = choose(x > -1, (-1, x))
sum += x * x
Ybeta[a] -= x * x
Ybeta[b] -= x * x
Ybeta[r] += x * x
Ybeta[s] += x * x
Ec1 += x * Eio
#compute correction term for one alpha and one beta electron
for a in aoccs:
for b in boccs:
for r in avirt:
for s in bvirt:
arbs = abmoints[ijkl2intindex(a, r, b, s)]
rraa = aamoints[ijkl2intindex(r,r,a,a)] - \
aamoints[ijkl2intindex(r,a,a,r)]
rrbb = abmoints[ijkl2intindex(r, r, b, b)]
aass = abmoints[ijkl2intindex(a, a, s, s)]
ssbb = bbmoints[ijkl2intindex(s,s,b,b)] - \
bbmoints[ijkl2intindex(s,b,b,s)]
rrss = abmoints[ijkl2intindex(r, r, s, s)]
aabb = abmoints[ijkl2intindex(a, a, b, b)]
eigendif = (orbea[r] + orbeb[s] - orbea[a] - orbeb[b])
delcorr = (-rraa - rrbb - aass - ssbb + rrss + aabb)
delta = eigendif + delcorr * z
Eio = arbs
x = -Eio / delta
if abs(x) > 1: print "Warning a large x value has ",\
"been discovered with x = ",x
x = choose(x < 1, (1, x))
x = choose(x > -1, (-1, x))
sum += x * x
Yalpha[a] -= x * x
Ybeta[b] -= x * x
Yalpha[r] += x * x
Ybeta[s] += x * x
Ec1 += x * Eio
#compute the fractional occupations of the occupied orbitals
for a in aoccs:
Yalpha[a] = 1 + Yalpha[a]
for b in boccs:
Ybeta[b] = 1 + Ybeta[b]
#for a in xrange(nbf):
#print "For alpha = ",a,"the fractional occupation is ",Yalpha[a]
#print "For beta = ",a,"the fractional occupation is ",Ybeta[a]
#print the energy and its corrections
E = energy + Ec1
print "The total sum of excitations is ", sum
print "The primary correlation correction is ", Ec1
print "The total energy is ", E
return E
def EN2(molecule,**opts):#
"General wrapper for the simple CI method"
nalpha,nbeta = molecule.get_alphabeta()
bfs = getbasis(molecule)
S,h,Ints = getints(bfs,molecule)
energy,(orbea,orbeb),(orbsa,orbsb) = uhf(molecule,integrals=(S,h,Ints),
bfs=bfs,**opts)
EHF = energy
print "The Hatree-Fock energy is ",EHF
#compute the transformed molecular orbital integrals
aamoints, nbf = TransformInts(Ints,orbsa,orbsa, nalpha)
bbmoints, nbf = TransformInts(Ints,orbsb,orbsb, nbeta)
abmoints, nbf = TransformInts(Ints,orbsa,orbsb, nalpha)
#Initialize the fractional occupations:
Yalpha = zeros((nbf),'d')
Ybeta = zeros((nbf),'d')
#set up the occupied and virtual orbitals
aoccs = range(nalpha)
boccs = range(nbeta)
avirt = range(nalpha,nbf) #numbers of alpha virtual orbitals
bvirt = range(nbeta,nbf) #numbers of beta virtual orbitals
######## Computation of the primary energy correction #########
#Set initial correction terms to zero
Ec1 = 0.
sum = 0.
z = 1.
#compute correction term for two alpha electrons
for a in aoccs:
for b in xrange(a):
for r in avirt:
for s in xrange(nalpha,r):
arbs = aamoints[ijkl2intindex(a,r,b,s)]
asbr = aamoints[ijkl2intindex(a,s,b,r)]
rraa = aamoints[ijkl2intindex(r,r,a,a)] - \
aamoints[ijkl2intindex(r,a,a,r)]
rrbb = aamoints[ijkl2intindex(r,r,b,b)] - \
aamoints[ijkl2intindex(r,b,b,r)]
ssaa = aamoints[ijkl2intindex(s,s,a,a)] - \
aamoints[ijkl2intindex(s,a,a,s)]
ssbb = aamoints[ijkl2intindex(s,s,b,b)] - \
aamoints[ijkl2intindex(s,b,b,s)]
rrss = aamoints[ijkl2intindex(r,r,s,s)] - \
aamoints[ijkl2intindex(r,s,s,r)]
aabb = aamoints[ijkl2intindex(a,a,b,b)] - \
aamoints[ijkl2intindex(a,b,b,a)]
eigendif = (orbea[r] + orbea[s] - orbea[a] - orbea[b])
delcorr = (-rraa - rrbb - ssaa - ssbb + rrss + aabb)
delta = eigendif + delcorr*z
Eio = (arbs - asbr)
x = -Eio/delta
if abs(x) > 1:
print "Warning a large x value has been ",\
"discovered with x = ",x
x = choose(x < 1, (1,x))
x = choose(x > -1, (-1,x))
sum += x*x
Yalpha[a] -= x*x
Yalpha[b] -= x*x
Yalpha[r] += x*x
Yalpha[s] += x*x
Ec1 += x*Eio
#compute correction term for two beta electrons
for a in boccs:
for b in xrange(a):
for r in bvirt:
for s in xrange(nbeta,r):
arbs = bbmoints[ijkl2intindex(a,r,b,s)]
asbr = bbmoints[ijkl2intindex(a,s,b,r)]
rraa = bbmoints[ijkl2intindex(r,r,a,a)] - \
bbmoints[ijkl2intindex(r,a,a,r)]
rrbb = bbmoints[ijkl2intindex(r,r,b,b)] - \
bbmoints[ijkl2intindex(r,b,b,r)]
ssaa = bbmoints[ijkl2intindex(s,s,a,a)] - \
bbmoints[ijkl2intindex(s,a,a,s)]
ssbb = bbmoints[ijkl2intindex(s,s,b,b)] - \
bbmoints[ijkl2intindex(s,b,b,s)]
rrss = bbmoints[ijkl2intindex(r,r,s,s)] - \
bbmoints[ijkl2intindex(r,s,s,r)]
aabb = bbmoints[ijkl2intindex(a,a,b,b)] - \
bbmoints[ijkl2intindex(a,b,b,a)]
eigendif = (orbeb[r] + orbeb[s] - orbeb[a] - orbeb[b])
delcorr = (-rraa - rrbb - ssaa - ssbb + rrss + aabb)
delta = eigendif + delcorr*z
Eio = (arbs - asbr)
x = -Eio/delta
if abs(x) > 1: print "Warning a large x value has ",\
"been discovered with x = ",x
x = choose(x < 1, (1,x))
x = choose(x > -1, (-1,x))
sum += x*x
Ybeta[a] -= x*x
Ybeta[b] -= x*x
Ybeta[r] += x*x
Ybeta[s] += x*x
Ec1 += x*Eio
#compute correction term for one alpha and one beta electron
for a in aoccs:
for b in boccs:
for r in avirt:
for s in bvirt:
arbs = abmoints[ijkl2intindex(a,r,b,s)]
rraa = aamoints[ijkl2intindex(r,r,a,a)] - \
aamoints[ijkl2intindex(r,a,a,r)]
rrbb = abmoints[ijkl2intindex(r,r,b,b)]
aass = abmoints[ijkl2intindex(a,a,s,s)]
ssbb = bbmoints[ijkl2intindex(s,s,b,b)] - \
bbmoints[ijkl2intindex(s,b,b,s)]
rrss = abmoints[ijkl2intindex(r,r,s,s)]
aabb = abmoints[ijkl2intindex(a,a,b,b)]
eigendif = (orbea[r] + orbeb[s] - orbea[a] - orbeb[b])
delcorr = (-rraa - rrbb - aass - ssbb + rrss + aabb)
delta = eigendif + delcorr*z
Eio = arbs
x = -Eio/delta
if abs(x) > 1: print "Warning a large x value has ",\
"been discovered with x = ",x
x = choose(x < 1, (1,x))
x = choose(x > -1, (-1,x))
sum += x*x
Yalpha[a] -= x*x
Ybeta[b] -= x*x
Yalpha[r] += x*x
Ybeta[s] += x*x
Ec1 += x*Eio
#compute the fractional occupations of the occupied orbitals
for a in aoccs:
Yalpha[a] = 1 + Yalpha[a]
for b in boccs:
Ybeta[b] = 1 + Ybeta[b]
#for a in xrange(nbf):
#print "For alpha = ",a,"the fractional occupation is ",Yalpha[a]
#print "For beta = ",a,"the fractional occupation is ",Ybeta[a]
#print the energy and its corrections
E = energy + Ec1
print "The total sum of excitations is ",sum
print "The primary correlation correction is ",Ec1
print "The total energy is ", E
return E
def main():
atomlist = Molecule('NO',atomlist = [(7,(0,0,0)),(8,(2.12955,0,0))],
multiplicity=2)
en,orbe,orbs = uhf(atomlist)
return en
def main():
atomlist = Molecule('NO',
atomlist=[(7, (0, 0, 0)), (8, (2.12955, 0, 0))],
multiplicity=2)
en, orbe, orbs = uhf(atomlist)
return en
