def __init__(self, mol, mints):
rhf = RHF(mol, mints)
self.E0 = rhf.computeEnergy()
self.docc = rhf.docc
self.nbf = len(rhf.S)
self.e = rhf.e
self.G = rhf.G
self.C = rhf.C
def rhf_energy(self):
"""
Optimize RHF orbitals; return RHF energy, two-electron integrals,
and coefficient matrix
"""
rhf = RHF(self.mol, self.mints)
return(rhf.E,rhf.g,rhf.C,rhf.orb_e)
class MP2:
def __init__(self,mol,mints):
self.docc = get_docc(mol)
self.nbf = get_nbf(mints)
self.conv = get_conv()
self.maxiter = get_maxiter()
self.rhf = RHF(mol,mints)
self.E_scf = self.rhf.get_energy()
self.e = self.rhf.e
self.G = self.rhf.G
self.C = self.rhf.C
def get_energy(self):
#rename class variables
docc, nbf, conv, maxiter = self.docc, self.nbf, self.conv, self.maxiter
E_scf, e = self.E_scf, self.e
# Gmo = self.transform_integrals_noddy()
# Gmo = self.transform_integrals_einsum()
Gmo = self.transform_integrals_einsum_2()
Ecorr = 0.0
for i in range(docc):
for j in range(docc):
for a in range(docc,nbf):
for b in range(docc,nbf):
Ecorr += (2*Gmo[i,j,a,b]-Gmo[i,j,b,a])*Gmo[i,j,a,b]/(e[i]+e[j]-e[a]-e[b])
return E_scf + Ecorr
def transform_integrals_einsum(self):
G,C = self.G, self.C
return np.einsum("Pqrs,Pp->pqrs",
np.einsum("PQrs,Qq->Pqrs",
np.einsum("PQRs,Rr->PQrs",
np.einsum("PQRS,Ss->PQRs", G, C), C) ,C) ,C)
def transform_integrals_einsum_2(self):
G,C = self.G, self.C
return np.einsum("PQRS,Pp,Qq,Rr,Ss->pqrs",G,C,C,C,C)
def transform_integrals_noddy(self):
nbf = self.nbf
C,G = self.C, self.G
Gmo = np.zeros(self.G.shape)
for p in range(nbf):
for q in range(nbf):
for r in range(nbf):
for s in range(nbf):
for i in range(nbf):
for j in range(nbf):
for k in range(nbf):
for l in range(nbf):
Gmo[p,q,r,s] += C[i,p]*C[j,q]*C[k,r]*C[l,s]*G[i,j,k,l]
return Gmo
def __init__(self,mol,mints):
self.docc = get_docc(mol)
self.nbf = get_nbf(mints)
self.conv = get_conv()
self.maxiter = get_maxiter()
self.rhf = RHF(mol,mints)
self.E_scf = self.rhf.get_energy()
self.e = self.rhf.e
self.G = self.rhf.G
self.C = self.rhf.C
return np.einsum('pqrs, pP, qQ, rR, sS-> PQRS', G, C, C, C, C)
def get_energy(self): # MP2 energy correction
e, E0, ndocc, ntot = self.e, self.E0, self.ndocc, self.ntot
g_mo = self.transform_integrals(
rhf.C, rhf.G) # calls transform_integrals function
E = 0.0
for i in range(
ndocc): # i and j over occupied orbitals, a and b over virtual
for j in range(ndocc):
for a in range(ndocc, ntot):
for b in range(ndocc, ntot):
E += (g_mo[i, a, j, b] *
(2 * g_mo[i, a, j, b] - g_mo[i, b, j, a])) / (
e[i] + e[j] - e[a] - e[b]
) # MP2 energy expression
print('The second order energy correction is {:20.14f}'.format(E))
print('The total RMP2 energy is {:20.14f}'.format(E0 + E))
return E
# testing
if __name__ == '__main__':
rhf = RHF('../../3/bz3wp/Options.ini')
rhf.get_energy()
rmp2 = RMP2(rhf)
rmp2.get_energy()
for i in range(nocc):
for j in range(nocc):
for a in range(nocc, ntot):
for b in range(nocc, ntot):
Ec += gmo[i, a, j, b]*(2*gmo[i, a, j, b] - gmo[i, b, j, a])/\
(e[i] + e[j] - e[a] - e[b])
self.Ec = Ec
self.E_mp2 = Ec + self.E_scf
print('@MP2 correlation energy: {:15.10f}\n'.format(self.Ec))
print('@Total MP2 energy: {:15.10f}\n'.format(self.E_mp2))
return self.E_mp2
if __name__ == "__main__":
import sys
sys.path.insert(0, '../../3/jevandezande')
from rhf import RHF
rhf = RHF('../../3/jevandezande/Options.ini')
rhf.energy()
rmp2 = RMP2(rhf)
e = rmp2.energy()
dfrmp2 = RMP2(rhf, 'cc-pVDZ-RI')
df_e = dfrmp2.energy()
print("Energy Error: {:7.5e}".format(df_e - e))
print("norm(UMP2.gmo - DFUMP2.gmo): {:7.5E}".format(np.linalg.norm(rmp2.gmo - dfrmp2.gmo)))
for j in range(nocc):
for a in range(nocc, ntot):
for b in range(nocc, ntot):
Ec += gmo[i, a, j, b]*(2*gmo[i, a, j, b] - gmo[i, b, j, a])/\
(e[i] + e[j] - e[a] - e[b])
self.Ec = Ec
self.E_mp2 = Ec + self.E_scf
print('@MP2 correlation energy: {:15.10f}\n'.format(self.Ec))
print('@Total MP2 energy: {:15.10f}\n'.format(self.E_mp2))
return self.E_mp2
if __name__ == "__main__":
import sys
sys.path.insert(0, '../../3/jevandezande')
from rhf import RHF
rhf = RHF('../../3/jevandezande/Options.ini')
rhf.energy()
rmp2 = RMP2(rhf)
e = rmp2.energy()
dfrmp2 = RMP2(rhf, 'cc-pVDZ-RI')
df_e = dfrmp2.energy()
print("Energy Error: {:7.5e}".format(df_e - e))
print("norm(UMP2.gmo - DFUMP2.gmo): {:7.5E}".format(
np.linalg.norm(rmp2.gmo - dfrmp2.gmo)))