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 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 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 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 two_electron_solve(atomic_number, maximum_order, spin):
Z = atomic_number
H, S = pekeris(Z, maximum_order, spin)
E, V = geigh(H, S)
epsilon = E[0]
E2 = [-Ei**2 for Ei in E]
#print "Energy (h) for order %d: %15.12f %15.12f" % (len(E),E2[0],epsilon)
return E2[0]
def two_electron_solve(atomic_number,maximum_order,spin):
Z = atomic_number
H,S = pekeris(Z,maximum_order,spin)
E,V = geigh(H,S)
epsilon = E[0]
E2 = [-Ei**2 for Ei in E]
#print "Energy (h) for order %d: %15.12f %15.12f" % (len(E),E2[0],epsilon)
return E2[0]
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 __init__(self,H,c=None,tol=1e-5,maxiters=100):
self.H = H
self.Eold = 0
if c is None:
orbe,self.c = geigh(H.i1.T+H.i1.V,H.i1.S)
else:
self.c = c
self.maxiters = maxiters
self.tol = tol
self.converged = False
self.iterations = 0
return
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 eigenv(self, Fa, Fb):
orbea, orbsa = geigh(Fa, self.i1.S)
orbeb, orbsb = geigh(Fb, self.i1.S)
return (orbea, orbsa), (orbeb, orbsb)
def eigenv(self, F):
""" Eigenvalues and Eigenvectors"""
orbe, orbs = geigh(F, self.i1.S)
return orbe, orbs
def gvb(geo,
npair=0,
basisname='sto3g',
maxiter=25,
verbose=False,
return_orbs=False,
input_orbs=None):
"""\
This is a trivial test for the gvb module, because other
pyquante modules are simpler if you're doing closed shell rhf,
and should give the same results.
# -0.46658184546856041 from uhf/sto3g
>>> gvb(h) # doctest: +ELLIPSIS
-0.4665818...
# -1.117099582955609 from rhf/sto3g
>>> gvb(h2) # doctest: +ELLIPSIS
-1.117099...
>>> gvb(lih,maxiter=5) # doctest: +ELLIPSIS
-7.86073...
>>> gvb(li,maxiter=5) # doctest: +ELLIPSIS
-7.31552...
>>> gvb(h2,npair=1) # doctest: +ELLIPSIS
-1.13730...
"""
# Get the basis set and the integrals
bfs = basisset(geo, basisname)
i1 = onee_integrals(bfs, geo)
i2 = twoe_integrals(bfs)
h = i1.T + i1.V
# Get a guess for the orbitals
if input_orbs is not None:
U = input_orbs
else:
E, U = geigh(h, i1.S)
# Set the parameters based on the molecule
nopen = geo.nopen()
ncore = geo.nclosed() - npair
nocc = ncore + nopen + 2 * npair
norb = len(bfs)
virt = range(nocc, norb)
orbs_per_shell = get_orbs_per_shell(ncore, nopen, npair)
nsh = len(orbs_per_shell)
shell = orbital_to_shell_mapping(ncore, nopen, npair)
Enuke = geo.nuclear_repulsion()
f, a, b = fab(ncore, nopen, npair)
if verbose:
np.set_printoptions(precision=4)
print("**** PyQuante GVB ****")
print(geo)
print("Nuclear repulsion energy: %.3f" % Enuke)
print("Basis set: %s" % basisname)
print(" ncore/open/pair: %d,%d,%d" % (ncore, nopen, npair))
print(" occ/bf/orb: %d,%d,%d" % (nocc, len(bfs), norb))
for i in range(nsh):
print("Shell %d" % i)
print(" occupation = %.2f" % f[i])
print(" orbitals in shell %s" % orbs_per_shell[i])
print(" couplings to other shells %s" % zip(a[i, :], b[i, :]))
print("Starting guess at orbitals:\n%s" % U)
print("Shell array: %s" % shell)
print("****")
Eold = 0
for it in range(maxiter):
# Make all of the density matrices:
Ds = [dmat_gen(U, orbs) for orbs in orbs_per_shell]
# Compute the required Hamiltonian matrices:
Js = [i2.get_j(D) for D in Ds]
Ks = [i2.get_k(D) for D in Ds]
# Perform the ROTION step and compute the energy
Eel, Eone, Uocc = ROTION(U[:, :nocc],
h,
Js,
Ks,
f,
a,
b,
nocc,
shell,
verbose=verbose)
if nsh > 1:
U[:, :nocc] = Uocc
# Perform the OCBSE step
U = OCBSE(U, h, Js, Ks, f, a, b, orbs_per_shell, virt)
#E = Enuke+Eone+Etwo
E = Enuke + Eel
Etwo = Eel - 2 * Eone
# Update CI coefs
coeffs = update_gvb_ci_coeffs(Uocc, h, Js, Ks, f, a, b, ncore, nopen,
npair, orbs_per_shell, verbose)
f, a, b = fab(ncore, nopen, npair, coeffs)
if verbose:
print("---- %d : %10.4f %10.4f %10.4f %10.4f" %
((it + 1), E, Enuke, Eone, Etwo))
if np.isclose(E, Eold):
if verbose:
print("Energy converged")
break
Eold = E
else:
print("Maximum iterations (%d) reached without convergence" %
(maxiter))
if return_orbs:
return E, U
return E
def gvb(geo,npair=0,basisname='sto3g',maxiter=25,verbose=False,
return_orbs=False, input_orbs=None):
"""\
This is a trivial test for the gvb module, because other
pyquante modules are simpler if you're doing closed shell rhf,
and should give the same results.
# -0.46658184546856041 from uhf/sto3g
>>> gvb(h) # doctest: +ELLIPSIS
-0.4665818...
# -1.117099582955609 from rhf/sto3g
>>> gvb(h2) # doctest: +ELLIPSIS
-1.117099...
>>> gvb(lih,maxiter=5) # doctest: +ELLIPSIS
-7.86073...
>>> gvb(li,maxiter=5) # doctest: +ELLIPSIS
-7.31552...
>>> gvb(h2,npair=1) # doctest: +ELLIPSIS
-1.13730...
"""
# Get the basis set and the integrals
bfs = basisset(geo,basisname)
i1 = onee_integrals(bfs,geo)
i2 = twoe_integrals(bfs)
h = i1.T + i1.V
# Get a guess for the orbitals
if input_orbs is not None:
U = input_orbs
else:
E,U = geigh(h,i1.S)
# Set the parameters based on the molecule
nopen = geo.nopen()
ncore = geo.nclosed() - npair
nocc = ncore + nopen + 2*npair
norb = len(bfs)
virt = range(nocc,norb)
orbs_per_shell = get_orbs_per_shell(ncore,nopen,npair)
nsh = len(orbs_per_shell)
shell = orbital_to_shell_mapping(ncore,nopen,npair)
Enuke = geo.nuclear_repulsion()
f,a,b = fab(ncore,nopen,npair)
if verbose:
np.set_printoptions(precision=4)
print("**** PyQuante GVB ****")
print(geo)
print("Nuclear repulsion energy: %.3f" % Enuke)
print("Basis set: %s" % basisname)
print(" ncore/open/pair: %d,%d,%d" % (ncore,nopen,npair))
print(" occ/bf/orb: %d,%d,%d" % (nocc,len(bfs),norb))
for i in range(nsh):
print("Shell %d" % i)
print(" occupation = %.2f" % f[i])
print(" orbitals in shell %s" % orbs_per_shell[i])
print(" couplings to other shells %s" % zip(a[i,:],b[i,:]))
print("Starting guess at orbitals:\n%s"%U)
print("Shell array: %s" % shell)
print("****")
Eold = 0
for it in range(maxiter):
# Make all of the density matrices:
Ds = [dmat_gen(U,orbs) for orbs in orbs_per_shell]
# Compute the required Hamiltonian matrices:
Js = [i2.get_j(D) for D in Ds]
Ks = [i2.get_k(D) for D in Ds]
# Perform the ROTION step and compute the energy
Eel,Eone,Uocc = ROTION(U[:,:nocc],h,Js,Ks,f,a,b,nocc,shell,
verbose=verbose)
if nsh > 1:
U[:,:nocc] = Uocc
# Perform the OCBSE step
U = OCBSE(U,h,Js,Ks,f,a,b,orbs_per_shell,virt)
#E = Enuke+Eone+Etwo
E = Enuke+Eel
Etwo = Eel-2*Eone
# Update CI coefs
coeffs = update_gvb_ci_coeffs(Uocc,h,Js,Ks,f,a,b,ncore,nopen,npair,
orbs_per_shell,verbose)
f,a,b = fab(ncore,nopen,npair,coeffs)
if verbose:
print ("---- %d : %10.4f %10.4f %10.4f %10.4f" % ((it+1),E,Enuke,Eone,Etwo))
if np.isclose(E,Eold):
if verbose:
print("Energy converged")
break
Eold = E
else:
print("Maximum iterations (%d) reached without convergence" % (maxiter))
if return_orbs:
return E,U
return E
