def uhf_simple(geo,basisname='sto3g',maxiter=25,verbose=False):
if geo.nopen() == 0: return scf_simple(geo,basisname,maxiter,verbose)
bfs = basisset(geo,basisname)
i1 = onee_integrals(bfs,geo)
i2 = twoe_integrals(bfs)
h = i1.T + i1.V
E,U = geigh(h,i1.S)
Enuke = geo.nuclear_repulsion()
Eold = Energy = 0
ca = cb = U
na,nb = geo.nup(),geo.ndown()
for i in xrange(maxiter):
Energy = Enuke
Da = dmat(ca,na)
Db = dmat(cb,nb)
h = i1.T + i1.V
Energy += trace2(Da+Db,h)/2
Ja,Ka = i2.get_j(Da),i2.get_k(Da)
Jb,Kb = i2.get_j(Db),i2.get_k(Db)
Fa = h + Ja + Jb - Ka
Fb = h + Ja + Jb - Kb
orbea,ca = geigh(Fa,i1.S)
orbeb,cb = geigh(Fb,i1.S)
Energy += trace2(Fa,Da)/2 + trace2(Fb,Db)/2
print ("UHF: %d %10.4f : %10.4f" % ((i+1),Energy,Enuke))
if np.isclose(Energy,Eold):
break
Eold = Energy
else:
print ("Warning: Maxiter %d hit in scf_simple" % maxiter)
return Energy,E,U
def fock_energy(self, Da, Db):
# Fock
h = self.h
J = self.i2.get_j(Da + Db)
Ka, Kb = self.i2.get_k(Da), self.i2.get_k(Db)
Ga = J - Ka
Gb = J - Kb
Fa = h + Ga
Fb = h + Gb
# Energy
Eone = trace2(Da + Db, h)
Etwo = trace2(Ga, Da) / 2 + trace2(Gb, Db) / 2
E = self.Enuc + Eone + Etwo
# Create Effective Fock Matrixs
P = (Da + Db) / 2 # charge density matrix
M = (Da - Db) / 2 # spin density matrix
# obtain Cno - natural orbitals
Fc = (Fa + Fb) / 2.0
c = slice(0, self.ndown)
o = slice(self.ndown, self.nup)
v = slice(self.nup, self.norb)
Fa[c, v] = Fc[c, v]
Fb[v, c] = Fc[v, c]
return Fa, Fb, E
def scf_simple(geo,basisname='sto-3g',maxiter=25,verbose=False):
bfs = basisset(geo,basisname)
i1 = onee_integrals(bfs,geo)
i2 = twoe_integrals(bfs)
if verbose: print ("S=\n%s" % i1.S)
h = i1.T + i1.V
if verbose: print ("h=\n%s" % h)
if verbose: print ("T=\n%s" % i1.T)
if verbose: print ("V=\n%s" % i1.V)
E,U = geigh(h,i1.S)
if verbose: print ("E=\n%s" % E)
if verbose: print ("U=\n%s" % U)
Enuke = geo.nuclear_repulsion()
nocc = geo.nocc()
Eold = Energy = 0
if verbose: print ("2e ints\n%s" % i2)
for i in xrange(maxiter):
D = dmat(U,nocc)
if verbose: print ("D=\n%s" % D)
Eone = trace2(h,D)
G = i2.get_2jk(D)
H = h+G
Etwo = trace2(H,D)
E,U = geigh(H,i1.S)
Energy = Enuke+Eone+Etwo
print ("HF: %d %10.4f : %10.4f %10.4f %10.4f" % ((i+1),Energy,Enuke,Eone,Etwo))
if np.isclose(Energy,Eold):
break
Eold = Energy
else:
print ("Warning: Maxiter %d hit in scf_simple" % maxiter)
return Energy,E,U
def uhf_simple(geo,basisname='sto3g',maxiter=25,verbose=False):
if geo.nopen() == 0: return scf_simple(geo,basisname,maxiter,verbose)
bfs = basisset(geo,basisname)
i1 = onee_integrals(bfs,geo)
i2 = twoe_integrals(bfs)
h = i1.T + i1.V
E,U = geigh(h,i1.S)
Enuke = geo.nuclear_repulsion()
Eold = Energy = 0
ca = cb = U
na,nb = geo.nup(),geo.ndown()
for i in xrange(maxiter):
Energy = Enuke
Da = dmat(ca,na)
Db = dmat(cb,nb)
h = i1.T + i1.V
Energy += trace2(Da+Db,h)/2
Ja,Ka = i2.get_j(Da),i2.get_k(Da)
Jb,Kb = i2.get_j(Db),i2.get_k(Db)
Fa = h + Ja + Jb - Ka
Fb = h + Ja + Jb - Kb
orbea,ca = geigh(Fa,i1.S)
orbeb,cb = geigh(Fb,i1.S)
Energy += trace2(Fa,Da)/2 + trace2(Fb,Db)/2
print ("UHF: %d %10.4f : %10.4f" % ((i+1),Energy,Enuke))
if np.isclose(Energy,Eold):
break
Eold = Energy
else:
print ("Warning: Maxiter %d hit in scf_simple" % maxiter)
return Energy,E,U
def rhf_simple(geo,basisname='sto3g',maxiter=25,verbose=False):
bfs = basisset(geo,basisname)
i1 = onee_integrals(bfs,geo)
i2 = twoe_integrals(bfs)
if verbose: print ("S=\n%s" % i1.S)
h = i1.T + i1.V
if verbose: print ("h=\n%s" % h)
if verbose: print ("T=\n%s" % i1.T)
if verbose: print ("V=\n%s" % i1.V)
E,U = geigh(h,i1.S)
if verbose: print ("E=\n%s" % E)
if verbose: print ("U=\n%s" % U)
Enuke = geo.nuclear_repulsion()
nocc = geo.nocc()
Eold = Energy = 0
if verbose: print ("2e ints\n%s" % i2)
for i in xrange(maxiter):
D = dmat(U,nocc)
if verbose: print ("D=\n%s" % D)
Eone = trace2(h,D)
G = i2.get_2jk(D)
H = h+G
Etwo = trace2(H,D)
E,U = geigh(H,i1.S)
Energy = Enuke+Eone+Etwo
print ("HF: %d %10.4f : %10.4f %10.4f %10.4f" % ((i+1),Energy,Enuke,Eone,Etwo))
if np.isclose(Energy,Eold):
break
Eold = Energy
else:
print ("Warning: Maxiter %d hit in scf_simple" % maxiter)
return Energy,E,U
def update(self,D):
self.energy = self.geo.nuclear_repulsion()
H = self.i1.T + self.i1.V
self.energy += trace2(H,D)
JK = self.i2.get_2jk(D)
H = H + JK
self.energy += trace2(H,D)
E,c = geigh(H,self.i1.S)
self.orbe = E
self.orbs = c
return c
def update(self,D):
self.energy = self.geo.nuclear_repulsion()
H = self.i1.T + self.i1.V
self.energy += trace2(H,D)
JK = self.i2.get_2jk(D)
H = H + JK
self.energy += trace2(H,D)
E,c = geigh(H,self.i1.S)
self.orbe = E
self.orbs = c
return c
def update(self, Da, Db, orbs):
from pyquante2.utils import ao2mo
nalpha = self.geo.nup()
nbeta = self.geo.ndown()
norbs = len(orbs) # Da.shape[0]
E0 = self.geo.nuclear_repulsion()
h = self.i1.T + self.i1.V
E1 = 0.5 * trace2(Da + Db, h)
Ja, Ka = self.i2.get_j(Da), self.i2.get_k(Da)
Jb, Kb = self.i2.get_j(Db), self.i2.get_k(Db)
Fa = h + Ja + Jb - Ka
Fb = h + Ja + Jb - Kb
E2 = 0.5 * (trace2(Fa, Da) + trace2(Fb, Db))
self.energy = E0 + E1 + E2
# print (self.energy,E1,E2,E0)
Fa = ao2mo(Fa, orbs)
Fb = ao2mo(Fb, orbs)
# Building the approximate Fock matrices in the MO basis
F = 0.5 * (Fa + Fb)
K = Fb - Fa
# The Fock matrix now looks like
# F-K | F + K/2 | F
# ---------------------------------
# F + K/2 | F | F - K/2
# ---------------------------------
# F | F - K/2 | F + K
# Make explicit slice objects to simplify this
do = slice(0, nbeta)
so = slice(nbeta, nalpha)
uo = slice(nalpha, norbs)
F[do, do] -= K[do, do]
F[uo, uo] += K[uo, uo]
F[do, so] += 0.5 * K[do, so]
F[so, do] += 0.5 * K[so, do]
F[so, uo] -= 0.5 * K[so, uo]
F[uo, so] -= 0.5 * K[uo, so]
E, cmo = np.linalg.eigh(F)
c = np.dot(orbs, cmo)
self.orbe = E
self.orbs = c
return c
def update(self,Da,Db,orbs):
from pyquante2.utils import ao2mo
nalpha = self.geo.nup()
nbeta = self.geo.ndown()
norbs = len(orbs) # Da.shape[0]
E0 = self.geo.nuclear_repulsion()
h = self.i1.T + self.i1.V
E1 = 0.5*trace2(Da+Db,h)
Ja,Ka = self.i2.get_j(Da),self.i2.get_k(Da)
Jb,Kb = self.i2.get_j(Db),self.i2.get_k(Db)
Fa = h + Ja + Jb - Ka
Fb = h + Ja + Jb - Kb
E2 = 0.5*(trace2(Fa,Da)+trace2(Fb,Db))
self.energy = E0+E1+E2
#print (self.energy,E1,E2,E0)
Fa = ao2mo(Fa,orbs)
Fb = ao2mo(Fb,orbs)
# Building the approximate Fock matrices in the MO basis
F = 0.5*(Fa+Fb)
K = Fb-Fa
# The Fock matrix now looks like
# F-K | F + K/2 | F
# ---------------------------------
# F + K/2 | F | F - K/2
# ---------------------------------
# F | F - K/2 | F + K
# Make explicit slice objects to simplify this
do = slice(0,nbeta)
so = slice(nbeta,nalpha)
uo = slice(nalpha,norbs)
F[do,do] -= K[do,do]
F[uo,uo] += K[uo,uo]
F[do,so] += 0.5*K[do,so]
F[so,do] += 0.5*K[so,do]
F[so,uo] -= 0.5*K[so,uo]
F[uo,so] -= 0.5*K[uo,so]
E,cmo = np.linalg.eigh(F)
c = np.dot(orbs,cmo)
self.orbe = E
self.orbs = c
return c
def update(self,Da,Db):
self.energy = self.geo.nuclear_repulsion()
h = self.i1.T + self.i1.V
self.energy += trace2(Da+Db,h)/2
Ja,Ka = self.i2.get_j(Da),self.i2.get_k(Da)
Jb,Kb = self.i2.get_j(Db),self.i2.get_k(Db)
Fa = h + Ja + Jb - Ka
Fb = h + Ja + Jb - Kb
orbea,ca = geigh(Fa,self.i1.S)
orbeb,cb = geigh(Fb,self.i1.S)
self.energy += trace2(Fa,Da)/2 + trace2(Fb,Db)/2
self.orbea = orbea
self.orbsa = ca
self.orbeb = orbeb
self.orbsb = cb
return ca,cb
def update(self,Da,Db):
self.energy = self.geo.nuclear_repulsion()
h = self.i1.T + self.i1.V
self.energy += trace2(Da+Db,h)/2
Ja,Ka = self.i2.get_j(Da),self.i2.get_k(Da)
Jb,Kb = self.i2.get_j(Db),self.i2.get_k(Db)
Fa = h + Ja + Jb - Ka
Fb = h + Ja + Jb - Kb
orbea,ca = geigh(Fa,self.i1.S)
orbeb,cb = geigh(Fb,self.i1.S)
self.energy += trace2(Fa,Da)/2 + trace2(Fb,Db)/2
self.orbea = orbea
self.orbsa = ca
self.orbeb = orbeb
self.orbsb = cb
return ca,cb
def update(self,D):
from pyquante2.dft.dft import get_xc
E0 = self.geo.nuclear_repulsion()
self.energy = E0
H = self.i1.T + self.i1.V
E1 = 2*trace2(H,D)
self.energy += E1
J = self.i2.get_j(D)
Ej = 2*trace2(J,D)
# The 0.5 before the D comes from making the alpha density from the total density
Exc,Vxc = get_xc(self.grid,0.5*D,xcname=self.xcname)
H = H + 2*J + Vxc
self.energy += Ej+Exc
if self.verbose: print(self.energy,E1,Ej,Exc,E0)
E,c = geigh(H,self.i1.S)
self.orbe = E
self.orbs = c
return c
def update(self,D):
from pyquante2.dft.dft import get_xc
E0 = self.geo.nuclear_repulsion()
self.energy = E0
H = self.i1.T + self.i1.V
E1 = 2*trace2(H,D)
self.energy += E1
J = self.i2.get_j(D)
Ej = 2*trace2(J,D)
# The 0.5 before the D comes from making the alpha density from the total density
Exc,Vxc = get_xc(self.grid,0.5*D,xcname=self.xcname)
H = H + 2*J + Vxc
self.energy += Ej+Exc
if self.verbose: print(self.energy,E1,Ej,Exc,E0)
E,c = geigh(H,self.i1.S)
self.orbe = E
self.orbs = c
return c
def energy(self, Da, Db, Fa, Fb):
""" Energy"""
Ea = trace2(self.h + Fa, Da)
Eb = trace2(self.h + Fb, Db)
return self.Enuc + (Ea + Eb) / 2
def energy(self, D, F):
""" Energy"""
Exc = 0.0 # TODO: not implemented
return self.Enuc + trace2(self.h + F, D) + Exc
def energy(self, D, F):
""" Energy"""
return self.Enuc + trace2(self.h + F, D)
