def solve_ERI(OEI, TEI, DMguess, numPairs):
mol = gto.Mole()
mol.build(verbose=3)
mol.atom.append(('C', (0, 0, 0)))
mol.nelectron = 2 * numPairs
L = OEI.shape[0]
mf = scf.RHF(mol)
mf.get_hcore = lambda *args: OEI
mf.get_ovlp = lambda *args: np.eye(L)
mf._eri = ao2mo.restore(8, TEI, L)
mf.scf(DMguess)
DMloc = np.dot(np.dot(mf.mo_coeff, np.diag(mf.mo_occ)), mf.mo_coeff.T)
if (mf.converged == False):
mf = rhf_newtonraphson.solve(mf, dm_guess=DMloc)
DMloc = np.dot(np.dot(mf.mo_coeff, np.diag(mf.mo_occ)), mf.mo_coeff.T)
return DMloc
def solve( CONST, OEI, FOCK, TEI, Norb, Nel, Nimp, DMguessRHF, chempot_imp=0.0 ):
# Augment the FOCK operator with the chemical potential
FOCKcopy = FOCK.copy()
if (chempot_imp != 0.0):
for orb in range(Nimp):
FOCKcopy[ orb, orb ] -= chempot_imp
# Get the RHF solution
mol = gto.Mole()
mol.build( verbose=0 )
mol.atom.append(('C', (0, 0, 0)))
mol.nelectron = Nel
mol.incore_anyway = True
mf = scf.RHF( mol )
mf.get_hcore = lambda *args: FOCKcopy
mf.get_ovlp = lambda *args: np.eye( Norb )
mf._eri = ao2mo.restore(8, TEI, Norb)
mf.scf( DMguessRHF )
DMloc = np.dot(np.dot( mf.mo_coeff, np.diag( mf.mo_occ )), mf.mo_coeff.T )
if ( mf.converged == False ):
mf = rhf_newtonraphson.solve( mf, dm_guess=DMloc )
DMloc = np.dot(np.dot( mf.mo_coeff, np.diag( mf.mo_occ )), mf.mo_coeff.T )
ERHF = mf.hf_energy
RDM1 = mf.make_rdm1()
JK = mf.get_veff(None, dm=RDM1)
# To calculate the impurity energy, rescale the JK matrix with a factor 0.5 to avoid double counting: 0.5 * ( OEI + FOCK ) = OEI + 0.5 * JK
ImpurityEnergy = CONST \
+ 0.25 * np.einsum('ji,ij->', RDM1[:,:Nimp], FOCK[:Nimp,:] + OEI[:Nimp,:]) \
+ 0.25 * np.einsum('ji,ij->', RDM1[:Nimp,:], FOCK[:,:Nimp] + OEI[:,:Nimp]) \
+ 0.25 * np.einsum('ji,ij->', RDM1[:,:Nimp], JK[:Nimp,:]) \
+ 0.25 * np.einsum('ji,ij->', RDM1[:Nimp,:], JK[:,:Nimp])
return ( ImpurityEnergy, RDM1 )
def RHF(self):
'''
Restricted Hartree-Fock
'''
Nimp = self.Nimp
FOCK = self.FOCK.copy()
if (self.chempot != 0.0):
for orb in range(Nimp):
FOCK[orb, orb] -= self.chempot
mol = gto.Mole()
mol.build(verbose = 0)
mol.atom.append(('C', (0, 0, 0)))
mol.nelectron = self.Nel
mol.incore_anyway = True
mf = scf.RHF(mol)
mf.get_hcore = lambda *args: FOCK
mf.get_ovlp = lambda *args: np.eye(self.Norb)
mf._eri = ao2mo.restore(8, self.TEI, self.Norb)
mf.scf(self.DMguess)
DMloc = np.dot(np.dot(mf.mo_coeff, np.diag(mf.mo_occ)), mf.mo_coeff.T)
if ( mf.converged == False ):
mf = rhf_newtonraphson.solve( mf, dm_guess=DMloc)
DMloc = np.dot(np.dot(mf.mo_coeff, np.diag(mf.mo_occ)), mf.mo_coeff.T)
ERHF = mf.e_tot
RDM1 = mf.make_rdm1()
jk = mf.get_veff(None, dm=RDM1)
# To calculate the impurity energy, rescale the JK matrix with a factor 0.5 to avoid double counting: 0.5 * ( OEI + FOCK ) = OEI + 0.5 * JK
ImpurityEnergy = 0.5*np.einsum('ij,ij->', RDM1[:Nimp,:], self.OEI[:Nimp,:] + FOCK[:Nimp,:]) \
+ 0.5*np.einsum('ij,ij->', RDM1[:Nimp,:], jk[:Nimp,:])
return (ImpurityEnergy, ERHF, RDM1)
N -1.323645520078 -1.013034361391 0.000000000000
C -2.609849686479 -1.716498251901 0.000000000000
H -2.689209473523 -2.357766508547 0.889337124082
H -2.689209473523 -2.357766508547 -0.889337124082
H -3.397445032059 -0.956544015308 0.000000000000
H 3.126343795339 -1.409688574359 0.000000000000
H 2.260091440174 -2.714879611857 -0.890143668130
H 2.260091440174 -2.714879611857 0.890143668130
H 2.453380552599 3.037434448146 0.000000000000
H -1.400292735506 3.159575123448 0.000000000000
H -0.135202960256 4.062674697502 0.897532201407
H -0.135202960256 4.062674697502 -0.897532201407
'''
mol.basis = '6-31g'
mol.symmetry = 1
mol.charge = 0
mol.spin = 0 #2*S; multiplicity-1
mol.build()
mf = scf.RHF( mol )
mf.verbose = 4
mf.max_cycle = 1
mf.scf()
DMloc = np.dot(np.dot( mf.mo_coeff, np.diag( mf.mo_occ )), mf.mo_coeff.T )
if ( mf.converged == False ):
mf = rhf_newtonraphson.solve( mf, dm_guess=DMloc )
DMloc = np.dot(np.dot( mf.mo_coeff, np.diag( mf.mo_occ )), mf.mo_coeff.T )
def solve(CONST,
OEI,
FOCK,
TEI,
Norb,
Nel,
Nimp,
DMguessRHF,
energytype='LAMBDA',
chempot_imp=0.0,
printoutput=True):
assert ((energytype == 'LAMBDA') or (energytype == 'LAMBDA_AMP')
or (energytype == 'LAMBDA_ZERO') or (energytype == 'CASCI'))
# Killing output if necessary
if (printoutput == False):
sys.stdout.flush()
old_stdout = sys.stdout.fileno()
new_stdout = os.dup(old_stdout)
devnull = os.open('/dev/null', os.O_WRONLY)
os.dup2(devnull, old_stdout)
os.close(devnull)
# Augment the FOCK operator with the chemical potential
FOCKcopy = FOCK.copy()
if (chempot_imp != 0.0):
for orb in range(Nimp):
FOCKcopy[orb, orb] -= chempot_imp
# Get the RHF solution
mol = gto.Mole()
mol.build(verbose=0)
mol.atom.append(('C', (0, 0, 0)))
mol.nelectron = Nel
mol.incore_anyway = True
mf = scf.RHF(mol)
mf.get_hcore = lambda *args: FOCKcopy
mf.get_ovlp = lambda *args: np.eye(Norb)
mf._eri = ao2mo.restore(8, TEI, Norb)
mf.scf(DMguessRHF)
DMloc = np.dot(np.dot(mf.mo_coeff, np.diag(mf.mo_occ)), mf.mo_coeff.T)
if (mf.converged == False):
mf = rhf_newtonraphson.solve(mf, dm_guess=DMloc)
DMloc = np.dot(np.dot(mf.mo_coeff, np.diag(mf.mo_occ)), mf.mo_coeff.T)
# Check the RHF solution
assert (Nel % 2 == 0)
numPairs = Nel / 2
FOCKloc = FOCKcopy + np.einsum(
'ijkl,ij->kl', TEI, DMloc) - 0.5 * np.einsum('ijkl,ik->jl', TEI, DMloc)
eigvals, eigvecs = np.linalg.eigh(FOCKloc)
idx = eigvals.argsort()
eigvals = eigvals[idx]
eigvecs = eigvecs[:, idx]
print "psi4cc::solve : RHF h**o-lumo gap =", eigvals[numPairs] - eigvals[
numPairs - 1]
DMloc2 = 2 * np.dot(eigvecs[:, :numPairs], eigvecs[:, :numPairs].T)
print "Two-norm difference of 1-RDM(RHF) and 1-RDM(FOCK(RHF)) =", np.linalg.norm(
DMloc - DMloc2)
# Get the CC solution from pyscf
ccsolver = ccsd.CCSD(mf)
ccsolver.verbose = 5
ECORR, t1, t2 = ccsolver.ccsd()
ERHF = mf.hf_energy
ECCSD = ERHF + ECORR
# Compute the impurity energy
if (energytype == 'CASCI'):
# The 2-RDM is not required
# Active space energy is computed with the Fock operator of the core (not rescaled)
print "ECCSD =", ECCSD
ccsolver.solve_lambda()
pyscfRDM1 = ccsolver.make_rdm1() # MO space
pyscfRDM1 = 0.5 * (pyscfRDM1 + pyscfRDM1.T) # Symmetrize
pyscfRDM1 = np.dot(mf.mo_coeff,
np.dot(pyscfRDM1,
mf.mo_coeff.T)) # From MO to localized space
ImpurityEnergy = ECCSD
if (chempot_imp != 0.0):
# [FOCK - FOCKcopy]_{ij} = chempot_imp * delta(i,j) * delta(i \in imp)
ImpurityEnergy += np.einsum('ij,ij->', FOCK - FOCKcopy, pyscfRDM1)
else:
# Compute the DMET impurity energy based on the lambda equations
if (energytype == 'LAMBDA'):
ccsolver.solve_lambda()
pyscfRDM1 = ccsolver.make_rdm1() # MO space
pyscfRDM2 = ccsolver.make_rdm2() # MO space
if (energytype == 'LAMBDA_AMP'):
# Overwrite lambda tensors with t-amplitudes
pyscfRDM1 = ccsolver.make_rdm1(t1, t2, t1, t2) # MO space
pyscfRDM2 = ccsolver.make_rdm2(t1, t2, t1, t2) # MO space
if (energytype == 'LAMBDA_ZERO'):
# Overwrite lambda tensors with 0.0
fake_l1 = np.zeros(t1.shape, dtype=float)
fake_l2 = np.zeros(t2.shape, dtype=float)
pyscfRDM1 = ccsolver.make_rdm1(t1, t2, fake_l1,
fake_l2) # MO space
pyscfRDM2 = ccsolver.make_rdm2(t1, t2, fake_l1,
fake_l2) # MO space
pyscfRDM1 = 0.5 * (pyscfRDM1 + pyscfRDM1.T) # Symmetrize
# Print a few to things to double check
'''
print "Do we understand how the 1-RDM is stored?", np.linalg.norm( np.einsum('ii->', pyscfRDM1) - Nel )
print "Do we understand how the 2-RDM is stored?", np.linalg.norm( np.einsum('ijkk->ij', pyscfRDM2) / (Nel - 1.0) - pyscfRDM1 )
'''
# Change the pyscfRDM1/2 from MO space to localized space
pyscfRDM1 = np.dot(mf.mo_coeff, np.dot(pyscfRDM1, mf.mo_coeff.T))
pyscfRDM2 = np.einsum('ai,ijkl->ajkl', mf.mo_coeff, pyscfRDM2)
pyscfRDM2 = np.einsum('bj,ajkl->abkl', mf.mo_coeff, pyscfRDM2)
pyscfRDM2 = np.einsum('ck,abkl->abcl', mf.mo_coeff, pyscfRDM2)
pyscfRDM2 = np.einsum('dl,abcl->abcd', mf.mo_coeff, pyscfRDM2)
ECCSDbis = CONST + np.einsum(
'ij,ij->', FOCKcopy,
pyscfRDM1) + 0.5 * np.einsum('ijkl,ijkl->', TEI, pyscfRDM2)
print "ECCSD1 =", ECCSD
print "ECCSD2 =", ECCSDbis
# To calculate the impurity energy, rescale the JK matrix with a factor 0.5 to avoid double counting: 0.5 * ( OEI + FOCK ) = OEI + 0.5 * JK
ImpurityEnergy = CONST \
+ 0.25 * np.einsum('ij,ij->', pyscfRDM1[:Nimp,:], FOCK[:Nimp,:] + OEI[:Nimp,:]) \
+ 0.25 * np.einsum('ij,ij->', pyscfRDM1[:,:Nimp], FOCK[:,:Nimp] + OEI[:,:Nimp]) \
+ 0.125 * np.einsum('ijkl,ijkl->', pyscfRDM2[:Nimp,:,:,:], TEI[:Nimp,:,:,:]) \
+ 0.125 * np.einsum('ijkl,ijkl->', pyscfRDM2[:,:Nimp,:,:], TEI[:,:Nimp,:,:]) \
+ 0.125 * np.einsum('ijkl,ijkl->', pyscfRDM2[:,:,:Nimp,:], TEI[:,:,:Nimp,:]) \
+ 0.125 * np.einsum('ijkl,ijkl->', pyscfRDM2[:,:,:,:Nimp], TEI[:,:,:,:Nimp])
# Reviving output if necessary
if (printoutput == False):
sys.stdout.flush()
os.dup2(new_stdout, old_stdout)
os.close(new_stdout)
return (ImpurityEnergy, pyscfRDM1)
C 1.177413455163 -1.426586745678 -3.035930309273
C 2.308221759410 -0.727692905561 -2.604000392388
C 0.000000000000 -0.698863692631 -3.485659405234
C -0.000000000000 0.698863692631 -3.485659405234
C 2.604000385623 -2.308221792277 -0.727692910676
C 3.035930522186 -1.177413550960 -1.426586813835
C 2.604000385623 -2.308221792277 0.727692910676
C 3.035930522186 -1.177413550960 1.426586813835
C 3.485659767723 0.000000000000 -0.698863749657
C 3.485659767723 0.000000000000 0.698863749657
C 2.308221759410 0.727692905561 -2.604000392388
C 1.177413455163 1.426586745678 -3.035930309273
'''
mol.basis = 'sto-3g'
mol.symmetry = 0
mol.charge = 0
mol.spin = 0 #2*S; multiplicity-1
mol.build()
# Perform RHF calculation
mf = scf.RHF(mol)
mf.verbose = 4
mf.scf()
Energy1 = mf.e_tot
# Redo with Newton-Raphson --> start from 'minao' guess
mf = rhf_newtonraphson.solve(mf, safe_guess=True)
Energy2 = mf.e_tot
assert (abs(Energy1 - Energy2) < 1e-9)
def CAS(self, CAS, CAS_MO, Orbital_optimization = False, solver = 'FCI'):
'''
CASSCF with FCI or DMRG solver from BLOCK or CheMPS2
'''
Norb = self.Norb
Nimp = self.Nimp
FOCK = self.FOCK.copy()
if (self.chempot != 0.0):
for orb in range(Nimp):
FOCK[orb, orb] -= self.chempot
mol = gto.Mole()
mol.build(verbose = 0)
mol.atom.append(('C', (0, 0, 0)))
mol.nelectron = self.Nel
mol.incore_anyway = True
mf = scf.RHF( mol )
mf.get_hcore = lambda *args: FOCK
mf.get_ovlp = lambda *args: np.eye(Norb)
mf._eri = ao2mo.restore(8, self.TEI, Norb)
mf.scf(self.DMguess)
DMloc = np.dot(np.dot(mf.mo_coeff, np.diag(mf.mo_occ)), mf.mo_coeff.T)
if ( mf.converged == False ):
mf = rhf_newtonraphson.solve( mf, dm_guess=DMloc)
DMloc = np.dot(np.dot(mf.mo_coeff, np.diag(mf.mo_occ)), mf.mo_coeff.T)
if CAS == None:
CAS_nelec = self.Nel
CAS_norb = Norb
CAS = 'full'
else:
CAS_nelec = CAS[0]
CAS_norb = CAS[1]
print(" Active space: ", CAS)
# Replace FCI solver by DMRG solver in CheMPS2 or BLOCK
if Orbital_optimization == True:
mc = mcscf.CASSCF(mf, CAS_norb, CAS_nelec)
else:
mc = mcscf.CASCI(mf, CAS_norb, CAS_nelec)
if solver == 'CheMPS2':
mc.fcisolver = dmrgscf.CheMPS2(mol)
elif solver == 'Block':
mc.fcisolver = dmrgscf.DMRGCI(mol)
if CAS_MO is not None:
print(" Active space MOs: ", CAS_MO)
mo = mc.sort_mo(CAS_MO)
ECAS = mc.kernel(mo)[0]
else:
ECAS = mc.kernel()[0]
###### Get RDM1 + RDM2 #####
CAS_norb = mc.ncas
core_norb = mc.ncore
CAS_nelec = mc.nelecas
core_MO = mc.mo_coeff[:,:core_norb]
CAS_MO = mc.mo_coeff[:,core_norb:core_norb+CAS_norb]
casdm1 = mc.fcisolver.make_rdm12(mc.ci, CAS_norb, CAS_nelec)[0] #in CAS space
# Transform the casdm1 (in CAS space) to casdm1ortho (orthonormal space).
casdm1ortho = np.einsum('ap,pq->aq', CAS_MO, casdm1)
casdm1ortho = np.einsum('bq,aq->ab', CAS_MO, casdm1ortho)
coredm1 = np.dot(core_MO, core_MO.T) * 2 #in localized space
RDM1 = coredm1 + casdm1ortho
casdm2 = mc.fcisolver.make_rdm12(mc.ci, CAS_norb, CAS_nelec)[1] #in CAS space
# Transform the casdm2 (in CAS space) to casdm2ortho (orthonormal space).
casdm2ortho = np.einsum('ap,pqrs->aqrs', CAS_MO, casdm2)
casdm2ortho = np.einsum('bq,aqrs->abrs', CAS_MO, casdm2ortho)
casdm2ortho = np.einsum('cr,abrs->abcs', CAS_MO, casdm2ortho)
casdm2ortho = np.einsum('ds,abcs->abcd', CAS_MO, casdm2ortho)
coredm2 = np.zeros([Norb, Norb, Norb, Norb]) #in AO
coredm2 += np.einsum('pq,rs-> pqrs',coredm1,coredm1)
coredm2 -= 0.5*np.einsum('ps,rq-> pqrs',coredm1,coredm1)
effdm2 = np.zeros([Norb, Norb, Norb, Norb]) #in AO
effdm2 += 2*np.einsum('pq,rs-> pqrs',casdm1ortho,coredm1)
effdm2 -= np.einsum('ps,rq-> pqrs',casdm1ortho,coredm1)
RDM2 = coredm2 + casdm2ortho + effdm2
ImpurityEnergy = 0.50 * np.einsum('ij,ij->', RDM1[:Nimp,:], FOCK[:Nimp,:] + self.OEI[:Nimp,:]) \
+ 0.125 * np.einsum('ijkl,ijkl->', RDM2[:Nimp,:,:,:], self.TEI[:Nimp,:,:,:]) \
+ 0.125 * np.einsum('ijkl,ijkl->', RDM2[:,:Nimp,:,:], self.TEI[:,:Nimp,:,:]) \
+ 0.125 * np.einsum('ijkl,ijkl->', RDM2[:,:,:Nimp,:], self.TEI[:,:,:Nimp,:]) \
+ 0.125 * np.einsum('ijkl,ijkl->', RDM2[:,:,:,:Nimp], self.TEI[:,:,:,:Nimp])
return (ImpurityEnergy, ECAS, RDM1)