def scfopen(atoms, F0, nalpha, nbeta, **opts):
"SCF procedure for open-shell molecules"
verbose = opts.get("verbose", False)
D = get_guess_D(atoms)
Da = 0.5 * D
Db = 0.5 * D
Eold = 0
for i in xrange(10):
F1a = get_F1_open(atoms, Da, Db)
F1b = get_F1_open(atoms, Db, Da)
F2a = get_F2_open(atoms, Da, Db)
F2b = get_F2_open(atoms, Db, Da)
Fa = F0 + F1a + F2a
Fb = F0 + F1b + F2b
Eel = 0.5 * trace2(Da, F0 + Fa) + 0.5 * trace2(Db, F0 + Fb)
if verbose:
print i, Eel
if abs(Eel - Eold) < 0.001:
break
Eold = Eel
orbea, orbsa = eigh(Fa)
orbeb, orbsb = eigh(Fb)
Da = mkdens(orbsa, 0, nalpha)
Db = mkdens(orbsb, 0, nbeta)
return Eel
def geigh(H,A,**kwargs):
"""\
Generalized eigenproblem using a symmetric matrix H.
Options:
have_xfrm False Need to form canonical transformation from S (default)
True A is the canonical transformation matrix
orthog 'Sym' Use Symmetric Orthogonalization (default)
'Can' Use Canonical Orthogonalization
'Chol' Use a Cholesky decomposition
'Cut' Use a symmetric orthogonalization with a cutoff
"""
have_xfrm = kwargs.get('have_xfrm')
orthog = kwargs.get('orthog',settings.OrthogMethod)
if not have_xfrm:
if orthog == 'Can':
X = CanOrth(A)
elif orthog == 'Chol':
X = CholOrth(A)
elif orthog == 'Cut':
X = SymOrthCutoff(A)
else:
X = SymOrth(A)
kwargs['have_xfrm'] = True
return geigh(H,X,**kwargs)
val,vec = eigh(simx(H,A))
vec = matrixmultiply(A,vec)
return val,vec
def scfclosed(atoms, F0, nclosed, **opts):
"SCF procedure for closed-shell molecules"
verbose = opts.get("verbose", False)
do_avg = opts.get("avg", False)
maxiter = opts.get("maxiter", 50)
D = get_guess_D(atoms)
Eold = 0
if do_avg:
avg = SimpleAverager(do_avg)
for i in xrange(maxiter):
if do_avg:
D = avg.getD(D)
F1 = get_F1(atoms, D)
F2 = get_F2(atoms, D)
F = F0 + F1 + F2
Eel = 0.5 * trace2(D, F0 + F)
if verbose:
print i + 1, Eel, get_Hf(atoms, Eel)
# if verbose: print i+1,Eel
if abs(Eel - Eold) < 0.001:
if verbose:
print "Exiting because converged", i + 1, Eel, Eold
break
Eold = Eel
orbe, orbs = eigh(F)
D = 2 * mkdens(orbs, 0, nclosed)
return Eel
def geigh(H, A, **kwargs):
"""\
Generalized eigenproblem using a symmetric matrix H.
Options:
have_xfrm False Need to form canonical transformation from S (default)
True A is the canonical transformation matrix
orthog 'Sym' Use Symmetric Orthogonalization (default)
'Can' Use Canonical Orthogonalization
'Chol' Use a Cholesky decomposition
'Cut' Use a symmetric orthogonalization with a cutoff
"""
have_xfrm = kwargs.get('have_xfrm')
orthog = kwargs.get('orthog', settings.OrthogMethod)
if not have_xfrm:
if orthog == 'Can':
X = CanOrth(A)
elif orthog == 'Chol':
X = CholOrth(A)
elif orthog == 'Cut':
X = SymOrthCutoff(A)
else:
X = SymOrth(A)
kwargs['have_xfrm'] = True
return geigh(H, X, **kwargs)
val, vec = eigh(simx(H, A))
vec = matrixmultiply(A, vec)
return val, vec
def CanOrth(S):
"""Canonical orthogonalization of matrix S. This is given by
U(1/sqrt(lambda)), where lambda,U are the eigenvalues/vectors."""
val,vec = eigh(S)
n = vec.shape[0]
for i in xrange(n):
vec[:,i] = vec[:,i] / sqrt(val[i])
return vec
def CanOrth(S):
"""Canonical orthogonalization of matrix S. This is given by
U(1/sqrt(lambda)), where lambda,U are the eigenvalues/vectors."""
val, vec = eigh(S)
n = vec.shape[0]
for i in xrange(n):
vec[:, i] = vec[:, i] / sqrt(val[i])
return vec
def SymOrth(S):
"""Symmetric orthogonalization of the real symmetric matrix S.
This is given by Ut(1/sqrt(lambda))U, where lambda,U are the
eigenvalues/vectors."""
val,vec = eigh(S)
n = vec.shape[0]
shalf = identity(n,'d')
for i in xrange(n):
shalf[i,i] /= sqrt(val[i])
X = simx(shalf,vec,'T')
return X
def SymOrth(S):
"""Symmetric orthogonalization of the real symmetric matrix S.
This is given by Ut(1/sqrt(lambda))U, where lambda,U are the
eigenvalues/vectors."""
val, vec = eigh(S)
n = vec.shape[0]
shalf = identity(n, 'd')
for i in xrange(n):
shalf[i, i] /= sqrt(val[i])
X = simx(shalf, vec, 'T')
return X
def scfopen(atoms,F0,nalpha,nbeta,**kwargs):
"SCF procedure for open-shell molecules"
verbose = kwargs.get('verbose')
D = get_guess_D(atoms)
Da = 0.5*D
Db = 0.5*D
Eold = 0
for i in xrange(10):
F1a = get_F1_open(atoms,Da,Db)
F1b = get_F1_open(atoms,Db,Da)
F2a = get_F2_open(atoms,Da,Db)
F2b = get_F2_open(atoms,Db,Da)
Fa = F0+F1a+F2a
Fb = F0+F1b+F2b
Eel = 0.5*trace2(Da,F0+Fa)+0.5*trace2(Db,F0+Fb)
if verbose: print i,Eel
if abs(Eel-Eold) < 0.001: break
Eold = Eel
orbea,orbsa = eigh(Fa)
orbeb,orbsb = eigh(Fb)
Da = mkdens(orbsa,0,nalpha)
Db = mkdens(orbsb,0,nbeta)
return Eel
def SymOrthCutoff(S,scut=1e-5):
"""Symmetric orthogonalization of the real symmetric matrix S.
This is given by Ut(1/sqrt(lambda))U, where lambda,U are the
eigenvalues/vectors.
Only eigenvectors with eigenvalues greater that a cutoff are kept.
This approximation is useful in cases where the basis set has
linear dependencies.
"""
val,vec = eigh(S)
n = vec.shape[0]
shalf = identity(n,'d')
for i in xrange(n):
if val[i] > scut:
shalf[i,i] /= sqrt(val[i])
else:
shalf[i,i] = 0.
X = simx(shalf,vec,'T')
return X
def SymOrthCutoff(S, scut=1e-5):
"""Symmetric orthogonalization of the real symmetric matrix S.
This is given by Ut(1/sqrt(lambda))U, where lambda,U are the
eigenvalues/vectors.
Only eigenvectors with eigenvalues greater that a cutoff are kept.
This approximation is useful in cases where the basis set has
linear dependencies.
"""
val, vec = eigh(S)
n = vec.shape[0]
shalf = identity(n, 'd')
for i in xrange(n):
if val[i] > scut:
shalf[i, i] /= sqrt(val[i])
else:
shalf[i, i] = 0.
X = simx(shalf, vec, 'T')
return X
def scfclosed(atoms,F0,nclosed,**kwargs):
"SCF procedure for closed-shell molecules"
verbose = kwargs.get('verbose')
do_avg = kwargs.get('avg',settings.MINDOAveraging)
maxiter = kwargs.get('maxiter',settings.MaxIter)
D = get_guess_D(atoms)
Eold = 0
if do_avg: avg = SimpleAverager(do_avg)
for i in xrange(maxiter):
if do_avg: D = avg.getD(D)
F1 = get_F1(atoms,D)
F2 = get_F2(atoms,D)
F = F0+F1+F2
Eel = 0.5*trace2(D,F0+F)
if verbose: print i+1,Eel,get_Hf(atoms,Eel)
#if verbose: print i+1,Eel
if abs(Eel-Eold) < 0.001:
if verbose:
print "Exiting because converged",i+1,Eel,Eold
break
Eold = Eel
orbe,orbs = eigh(F)
D = 2*mkdens(orbs,0,nclosed)
return Eel
def CIS(Ints, orbs, orbe, nocc, nvirt, ehf):
CIMatrix = CISMatrix(Ints, orbs, ehf, orbe, nocc, nvirt)
Ecis, Vectors = eigh(CIMatrix)
return Ecis
def CIS(Ints,orbs,orbe,nocc,nvirt,ehf):
CIMatrix = CISMatrix(Ints,orbs,ehf,orbe,nocc,nvirt)
Ecis,Vectors = eigh(CIMatrix)
return Ecis