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 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 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 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
# a_ij = 0, b_ij = -c_i c_j If i and j are in the same pair
for i in range(ncoresh+nopen,ncoresh+nopen+npair):
a[i,i+npair] = a[i+npair,i] = 0
b[i,i+npair] = b[i+npair,i] = -coeffs[i]*coeffs[i+npair]
return f,a,b
if __name__ == '__main__':
#import doctest; doctest.testmod()
#gvb(h,maxiter=5,verbose=True) # -0.46658
#gvb(lih,maxiter=5,verbose=True) # -7.86073
#gvb(li,maxiter=5,verbose=True) # -7.3155
#gvb(h2,npair=1,verbose=True) # RHF = -1.1171, GVB ?= -1.1373
#
# h- example for Rajib: Does not currently work with GVB.
# RHF energy is -0.4224, GVB energy is -0.3964
h_m = molecule(atomlist = [(1,0,0,0)],charge=-1,name="H-")
from pyquante2.orbman import orbman
E,orbs = gvb(h_m,maxiter=10,basisname='6-31g',npair=0,verbose=True,
return_orbs=True)
o_hf = orbman(orbs,basisset(h_m,'6-31g'),h_m)
E,orbs = gvb(h_m,maxiter=10,basisname='6-31g',npair=1,verbose=True,
return_orbs=True,input_orbs=orbs)
o_gvb = orbman(orbs,basisset(h_m,'6-31g'),h_m)
for i in [0,1]:
print("Orbital %d after HF" % i)
o_hf[i]
print(" GVB")
o_gvb[i]
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
#gvb(h,maxiter=5,verbose=True) # -0.46658
#gvb(lih,maxiter=5,verbose=True) # -7.86073
#gvb(li,maxiter=5,verbose=True) # -7.3155
#gvb(h2,npair=1,verbose=True) # RHF = -1.1171, GVB ?= -1.1373
#
# h- example for Rajib: Does not currently work with GVB.
# RHF energy is -0.4224, GVB energy is -0.3964
h_m = molecule(atomlist=[(1, 0, 0, 0)], charge=-1, name="H-")
from pyquante2.orbman import orbman
E, orbs = gvb(h_m,
maxiter=10,
basisname='6-31g',
npair=0,
verbose=True,
return_orbs=True)
o_hf = orbman(orbs, basisset(h_m, '6-31g'), h_m)
E, orbs = gvb(h_m,
maxiter=10,
basisname='6-31g',
npair=1,
verbose=True,
return_orbs=True,
input_orbs=orbs)
o_gvb = orbman(orbs, basisset(h_m, '6-31g'), h_m)
for i in [0, 1]:
print("Orbital %d after HF" % i)
o_hf[i]
print(" GVB")
o_gvb[i]
