def get_gradient(self, b):
energy = self.get_energy(b)
Fmoa = simx(self.Fa, self.orbsa)
Fmob = simx(self.Fb, self.orbsb)
bp = zeros(2 * self.nbf, 'd')
for g in xrange(self.nbf):
# Transform Gij[g] to MOs. This is done over the whole
# space rather than just the parts we need. I can speed
# this up later by only forming the i,a elements required
Gmo = simx(self.Gij[g], self.orbsa)
# Now sum the appropriate terms to get the b gradient
for i in xrange(self.nalpha):
for a in xrange(self.nalpha, self.norb):
bp[g] += Fmoa[i, a] * Gmo[i, a] / (self.orbea[i] -
self.orbea[a])
for g in xrange(self.nbf):
# Transform Gij[g] to MOs. This is done over the whole
# space rather than just the parts we need. I can speed
# this up later by only forming the i,a elements required
Gmo = simx(self.Gij[g], self.orbsb)
# Now sum the appropriate terms to get the b gradient
for i in xrange(self.nbeta):
for a in xrange(self.nbeta, self.norb):
bp[self.nbf +
g] += Fmob[i, a] * Gmo[i, a] / (self.orbeb[i] -
self.orbeb[a])
#logging.debug("EXX Grad: %10.5f" % (sqrt(dot(bp,bp))))
return bp
def propagate_dm(D, F, dt, **kwargs):
_prop_ = 'padme'
method = kwargs.get('method')
if method == 'relax':
# direct diagonalization
if _prop_ == 'direct':
'''
Warning : That doesn't work so well
But I don't know why
'''
lambda_F, U_F = scla.eig(F)
v = np.exp(1j * dt * lambda_F)
df = np.diag(simx(D, U_F, 'N'))
prod = np.diag(v * df * np.conj(v))
Dq = simx(prod, U_F, 'T')
# padde approximation
if _prop_ == 'padme':
U = expm(1j * F * dt)
D = np.dot(U, np.dot(D, np.conj(U.T)))
#print D
else:
print 'Propagation method %s not regognized' % method
sys.exit()
return D
def get_gradient(self,b):
energy = self.get_energy(b)
Fmoa = simx(self.Fa,self.orbsa)
Fmob = simx(self.Fb,self.orbsb)
bp = zeros(2*self.nbf,'d')
for g in range(self.nbf):
# Transform Gij[g] to MOs. This is done over the whole
# space rather than just the parts we need. I can speed
# this up later by only forming the i,a elements required
Gmo = simx(self.Gij[g],self.orbsa)
# Now sum the appropriate terms to get the b gradient
for i in range(self.nalpha):
for a in range(self.nalpha,self.norb):
bp[g] += Fmoa[i,a]*Gmo[i,a]/(self.orbea[i]-self.orbea[a])
for g in range(self.nbf):
# Transform Gij[g] to MOs. This is done over the whole
# space rather than just the parts we need. I can speed
# this up later by only forming the i,a elements required
Gmo = simx(self.Gij[g],self.orbsb)
# Now sum the appropriate terms to get the b gradient
for i in range(self.nbeta):
for a in range(self.nbeta,self.norb):
bp[self.nbf+g] += Fmob[i,a]*Gmo[i,a]/(self.orbeb[i]-self.orbeb[a])
#logging.debug("EXX Grad: %10.5f" % (sqrt(dot(bp,bp))))
return bp
def testOrthog(self):
from PyQuante.LA2 import CanOrth, SymOrth, CholOrth, simx
from PyQuante.NumWrap import eigh
solver = SCF(h2, method="HF")
h, S = solver.h, solver.S
X1 = CanOrth(S)
X2 = SymOrth(S)
X3 = CholOrth(S)
h1 = simx(h, X1)
ha = simx(h, X2)
h3 = simx(h, X3)
e1, v1 = eigh(h1)
e2, v2 = eigh(ha)
e3, v3 = eigh(h3)
self.assertAlmostEqual(e1[0], e2[0], 6)
self.assertAlmostEqual(e1[0], e3[0], 6)
def testOrthog(self):
from PyQuante.LA2 import CanOrth, SymOrth, CholOrth, simx
from PyQuante.NumWrap import eigh
solver = SCF(h2,method="HF")
h,S = solver.h, solver.S
X1 = CanOrth(S)
X2 = SymOrth(S)
X3 = CholOrth(S)
h1 = simx(h,X1)
ha = simx(h,X2)
h3 = simx(h,X3)
e1,v1 = eigh(h1)
e2,v2 = eigh(ha)
e3,v3 = eigh(h3)
self.assertAlmostEqual(e1[0],e2[0],6)
self.assertAlmostEqual(e1[0],e3[0],6)
def geigh(H,A,**opts):
"""\
Generalized eigenproblem using a symmetric matrix H.
"""
X = SymOrthCutoff(A)
val,vec = eigh(simx(H,X))
vec = matrixmultiply(X,vec)
return val,vec
def geigh(H, A, **opts):
"""\
Generalized eigenproblem using a symmetric matrix H.
"""
X = SymOrthCutoff(A)
val, vec = eigh(simx(H, X))
vec = matrixmultiply(X, vec)
return val, vec
def get_gradient(self,b):
energy = self.get_energy(b)
Fmo = simx(self.F,self.orbs)
bp = zeros(self.nbf,'d')
for g in xrange(self.nbf):
# Transform Gij[g] to MOs. This is done over the whole
# space rather than just the parts we need. I can speed
# this up later by only forming the i,a elements required
Gmo = simx(self.Gij[g],self.orbs)
# Now sum the appropriate terms to get the b gradient
for i in xrange(self.nclosed):
for a in xrange(self.nclosed,self.norb):
bp[g] = bp[g] + Fmo[i,a]*Gmo[i,a]/(self.orbe[i]-self.orbe[a])
#logging.debug("EXX Grad: %10.5f" % (sqrt(dot(bp,bp))))
return bp
def iterate(self):
for self.iter in xrange(self.maxit):
if self.converged(): break
self.update()
self.print_iter_info()
self.print_iter_end_info()
if self.do_orth:
self.D = simx(self.D, self.X, 'T')
return
def iterate(self):
for self.iter in xrange(self.maxit):
if self.converged(): break
self.update()
self.print_iter_info()
self.print_iter_end_info()
if self.do_orth:
self.D = simx(self.D,self.X,'T')
return
def compute_F(P, Hcore, X, Ints, mu=0):
# get the matrix of 2J-K for a given fixed P
# P is here given in the non- orthonormal basis
G = get2JmK(Ints, P)
# pass the G matrix in the orthonormal basis
Gp = simx(G, X, 'T')
# form the Fock matrix in the orthonomral basis
F = Hcore + _ee_inter_ * Gp + mu
return F
def solve(self, H, **kwargs):
from PyQuante.LA2 import mkdens_spinavg, simx, geigh
from PyQuante.NumWrap import matrixmultiply, eigh
if self.first_iteration:
self.first_iteration = False
self.orbe, self.orbs = geigh(H, self.S)
else:
Ht = simx(H, self.orbs)
if self.pass_nroots:
self.orbe, orbs = self.solver(Ht, self.nroots)
else:
self.orbe, orbs = self.solver(Ht)
self.orbs = matrixmultiply(self.orbs, orbs)
self.D = mkdens_spinavg(self.orbs, self.nclosed, self.nopen)
self.entropy = 0
return self.D, self.entropy
def solve(self,H,**opts):
from PyQuante.LA2 import mkdens_spinavg,simx,geigh
from PyQuante.NumWrap import matrixmultiply,eigh
if self.first_iteration:
self.first_iteration = False
self.orbe,self.orbs = geigh(H,self.S)
else:
Ht = simx(H,self.orbs)
if self.pass_nroots:
self.orbe,orbs = self.solver(Ht,self.nroots)
else:
self.orbe,orbs = self.solver(Ht)
self.orbs = matrixmultiply(self.orbs,orbs)
self.D = mkdens_spinavg(self.orbs,self.nclosed,self.nopen)
self.entropy = 0
return self.D,self.entropy
def __init__(self, F, Ne, S=None, **opts):
self.tol = opts.get('tol', 1e-7)
self.maxit = opts.get('maxit', 100)
self.do_orth = S is not None
self.N = F.shape[0]
self.I = identity(self.N, 'd')
self.Ne = Ne
if self.do_orth:
self.X = SymOrth(S)
self.F = simx(F, self.X)
self.emin, self.emax = gershgorin_minmax(self.F)
self.initialize()
self.print_init_info()
return
def __init__(self, F, Ne, S=None, **kwargs):
self.tol = kwargs.get('tol', settings.DMPTolerance)
self.maxit = kwargs.get('maxit', settings.DMPIterations)
self.do_orth = S is not None
self.N = F.shape[0]
self.I = identity(self.N, 'd')
self.Ne = Ne
if self.do_orth:
self.X = SymOrth(S)
self.F = simx(F, self.X)
self.emin, self.emax = gershgorin_minmax(self.F)
self.initialize()
self.print_init_info()
return
def __init__(self,F,Ne,S=None,**kwargs):
self.tol = kwargs.get('tol',settings.DMPTolerance)
self.maxit = kwargs.get('maxit',settings.DMPIterations)
self.do_orth = S is not None
self.N = F.shape[0]
self.I = identity(self.N,'d')
self.Ne = Ne
if self.do_orth:
self.X = SymOrth(S)
self.F = simx(F,self.X)
self.emin, self.emax = gershgorin_minmax(self.F)
self.initialize()
self.print_init_info()
return
def __init__(self,F,Ne,S=None,**opts):
self.tol = opts.get('tol',1e-7)
self.maxit = opts.get('maxit',100)
self.do_orth = S is not None
self.N = F.shape[0]
self.I = identity(self.N,'d')
self.Ne = Ne
if self.do_orth:
self.X = SymOrth(S)
self.F = simx(F,self.X)
self.emin, self.emax = gershgorin_minmax(self.F)
self.initialize()
self.print_init_info()
return
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 range(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 range(n):
if val[i] > scut:
shalf[i,i] /= sqrt(val[i])
else:
shalf[i,i] = 0.
X = simx(shalf,vec,'T')
return X
def ao2mo(M, C):
return simx(M, C)
def pyq1_rohf(atomtuples=[(2, (0, 0, 0))], basis='6-31G**', maxit=10, mult=3):
from PyQuante import Ints, settings, Molecule
from PyQuante.hartree_fock import get_energy
from PyQuante.MG2 import MG2 as MolecularGrid
from PyQuante.LA2 import mkdens, geigh, trace2, simx
from PyQuante.Ints import getJ, getK
print("PyQ1 ROHF run")
atoms = Molecule('Pyq1', atomlist=atomtuples, multiplicity=mult)
bfs = Ints.getbasis(atoms, basis=basis)
S, h, I2e = Ints.getints(bfs, atoms)
nbf = norbs = len(bfs)
nel = atoms.get_nel()
nalpha, nbeta = atoms.get_alphabeta()
enuke = atoms.get_enuke()
orbe, orbs = geigh(h, S)
eold = 0
for i in range(maxit):
Da = mkdens(orbs, 0, nalpha)
Db = mkdens(orbs, 0, nbeta)
Ja = getJ(I2e, Da)
Jb = getJ(I2e, Db)
Ka = getK(I2e, Da)
Kb = getK(I2e, Db)
Fa = h + Ja + Jb - Ka
Fb = h + Ja + Jb - Kb
energya = get_energy(h, Fa, Da)
energyb = get_energy(h, Fb, Db)
eone = (trace2(Da, h) + trace2(Db, h)) / 2
etwo = (trace2(Da, Fa) + trace2(Db, Fb)) / 2
energy = (energya + energyb) / 2 + enuke
print(i, energy, eone, etwo, enuke)
if abs(energy - eold) < 1e-5: break
eold = energy
Fa = simx(Fa, orbs)
Fb = simx(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]
orbe, mo_orbs = np.linalg.eigh(F)
orbs = np.dot(orbs, mo_orbs)
return energy, orbe, orbs
def main(argv):
parser = argparse.ArgumentParser(
description='Hartree Fock Calculation from scratch')
# molecule information
parser.add_argument('mol', help='xyz file of the molecule', type=str)
parser.add_argument('-basis',
default='sto-3g',
help='basis set to be used in the calculation',
type=str)
parser.add_argument('-charge',
default=0,
help='Charge of the system',
type=float)
parser.add_argument('-units',
default='angs',
help='Units in the xyz file',
type=str)
# HF calculations
parser.add_argument('-MaxIter',
default=100,
help='Maximum number of SCF iterations',
type=int)
parser.add_argument('-eps_SCF',
default=1E-4,
help='Criterion for SCF termination',
type=float)
# field information
parser.add_argument('-ffreq',
default=0.1,
help='Frequency of the field',
type=float)
parser.add_argument('-fint',
default=0.05,
help='Intensity of the field',
type=float)
parser.add_argument('-ft0',
default=0.5,
help='center of the field for gsin',
type=float)
parser.add_argument('-fsigma',
default=0.25,
help='sigma of the field for gsin',
type=float)
parser.add_argument('-fform', default='sin', help='field form', type=str)
parser.add_argument('-fdir',
default='x',
help='direction of the field',
type=str)
# Propagation
parser.add_argument('-tmax',
default=200,
help='maximum evolution time',
type=float)
parser.add_argument('-nT',
default=200,
help='number of time step',
type=int)
parser.add_argument('-time_unit',
default='au',
help='unit of tmax',
type=str)
# export
parser.add_argument('-nb_print_mo',
default=10,
help='Number of orbitals to be written',
type=int)
'''
Possible basis
'3-21g' 'sto3g' 'sto-3g' 'sto-6g'
'6-31g' '6-31g**' '6-31g(d,p)' '6-31g**++' '6-31g++**' '6-311g**' '6-311g++(2d,2p)'
'6-311g++(3d,3p)' '6-311g++(3df,3pd)'
'lacvp'
'ccpvdz' 'cc-pvdz' 'ccpvtz' 'cc-pvtz' 'ccpvqz' 'cc-pvqz' 'ccpv5z' 'cc-pv5z' 'ccpv6z' 'cc-pv6z'
'augccpvdz' 'aug-cc-pvdz' 'augccpvtz' 'aug-cc-pvtz' 'augccpvqz'
'aug-cc-pvqz' 'augccpv5z' 'aug-cc-pv5z' 'augccpv6z' 'aug-cc-pv6z'
'dzvp':'dzvp',
'''
# done
args = parser.parse_args()
print '\n\n=================================================='
print '== PyQuante - Time-dependent hartree-fock =='
print '==================================================\n'
#-------------------------------------------------------------------------------------------
#
# PREPARE SIMULATIONS
#
#-------------------------------------------------------------------------------------------
##########################################################
## Read Molecule
##########################################################
# read the xyz file of the molecule
print '\t Read molecule position'
f = open(args.mol, 'r')
data = f.readlines()
f.close
# get the molecule name
name_mol = re.split(r'\.|/', args.mol)[-2]
# create the molecule object
xyz = []
for i in range(2, len(data)):
d = data[i].split()
xyz.append((d[0], (float(d[1]), float(d[2]), float(d[3]))))
natom = len(xyz)
mol = Molecule(name=name_mol, units=args.units)
mol.add_atuples(xyz)
mol.set_charge(args.charge)
nelec = mol.get_nel()
if np.abs(args.charge) == 1:
mol.set_multiplicity(2)
if args.charge > 1:
print 'charge superior to one are not implemented'
# get the basis function
bfs = getbasis(mol, args.basis)
nbfs = len(bfs)
nclosed, nopen = mol.get_closedopen()
nocc = nclosed
print '\t\t Molecule %s' % args.mol
print '\t\t Basis %s' % args.basis
print '\t\t %d basis functions' % (nbfs)
if _print_basis_:
for i in range(nbfs):
print bfs[i]
# compute all the integrals
print '\n\t Compute the integrals and form the matrices'
S, Hcore, Ints = getints(bfs, mol)
print '\t Compute the transition dipole moments'
mu_at = compute_dipole_atoms(bfs, args.fdir)
##########################################################
## Compute the HF GROUND STATE
##########################################################
print '\n\t Compute the ground state HF Ground State\n\t',
print '-' * 50
L, C, Cp, F0, F0p, D, Dp, P, X = rhf(mol,
bfs,
S,
Hcore,
Ints,
MaxIter=args.MaxIter,
eps_SCF=args.eps_SCF)
print '\t Energy of the HF orbitals\n\t',
print '-' * 50
index_homo = nocc - 1
nb_print = int(min(nbfs, args.nb_print_mo) / 2)
for ibfs in range(index_homo - nb_print + 1, index_homo + nb_print + 1):
print '\t\t orb %02d \t occ %1.1f \t\t Energy %1.3f Ha' % (
ibfs, np.abs(2 * P[ibfs, ibfs].real), L[ibfs].real)
# store the field free eigenstates
C0 = np.copy(C)
C0p = np.copy(Cp)
# invert of the X matrix
Xm1 = np.linalg.inv(X)
##########################################################
## Transform the matrices in the OB
##########################################################
# pass the other matrices as well
Hcore_p = simx(Hcore, X, 'T')
mu_at_p = simx(mu_at, X, 'T')
# copy the Fock matrix
Fp = np.copy(F0p)
# transtion matrix at t=0
mup = mu_at_p
# check if everythong is ok
if _check_ortho_:
w, u = np.linalg.eigh(F0p)
if np.sum(np.abs(w - L)) > 1E-3:
print '\t == Warning orthonormalisation issue'
sys.exit()
#-------------------------------------------------------------------------------------------
#
# TEST IF EVERYTHING IS OF SO FAR
#
#-------------------------------------------------------------------------------------------
# verify the basis transformation between
# Atomic Orbitals and Orthonormal orbitals
#
if _test_:
print '\n\t Run Check on the matrices'
#print'\n'
#print'='*40
print '\t\t Verify the basis transformation from diagonal to AO basis ',
x = np.dot(np.diag(L), np.linalg.inv(C))
x = np.dot(C, x)
x = np.dot(S, x)
if np.abs(np.sum(x - F0)) < 1E-3:
print '\t Check'
else:
print '\t NOT OK'
#print'='*40
if _verbose_:
print '\t\t reconstructed Fock matrix'
print x
print '\t\t original Fock matrix'
print F0
#print'\n\t'
#print'='*40
print '\t\t Verify the basis transformation from AO to diagonal basis ',
y = np.dot(F0, C)
y = np.dot(np.linalg.inv(S), y)
y = np.dot(np.linalg.inv(C), y)
if np.abs(np.sum(y - np.diag(L))) < 1E-3:
print '\t Check'
else:
print '\t NOT OK'
#print'='*40
if _verbose_:
print '\t\t reconstructed eigenvalues'
print y
print '\t\t original eigenvalues'
print L
#
# verify the basis transformation between
# Atomic Orbitals and Orthonormal orbitals
#
if _test_:
#print'\n'
#print'='*40
print '\t\t Verify the basis transformation from AO basis to ORTHO basis ',
#print'='*40
if np.abs(np.sum(D - np.dot(X, np.dot(Dp, X.T)))) < 1E-3:
print '\t Check'
else:
print '\t NOT OK'
if _verbose_:
print '\t\t reconstructed density in the AO'
print np.dot(X, np.dot(Dp, X.T))
print '\t\t Original density in the AO'
print D
#
# verify the basis transformation between
# Atomic Orbitals and Orthonormal orbitals
#
if _test_:
#print'\n'
#print'='*40
print '\t\t Verify the basis transformation from AO basis to ORTHO basis ',
#print'='*40
if np.abs(np.sum(Dp - np.dot(Xm1, np.dot(D, Xm1.T)))) < 1E-3:
print '\t Check'
else:
print '\t NOT OK'
if _verbose_:
print '\t\t reconstructed density in the OB'
print np.dot(Xm1, np.dot(D, Xm1.T))
print '\t\t original density in the OB'
print Dp
# test if the Fock matrix and densitu matrix in OB
# share the same eigenbasis
# due to degeneracies in the density matrix only a few
# eigenvectors might be the same
if _verbose_:
print '\t\t verify that the Fock matrix and the density matrix '
print '\t\t in the ORTHOGONAL BASIS have the same eigenvector',
lf, cf = scla.eigh(F0p)
r = 1E-6 * np.random.rand(nbfs, nbfs)
r += r.T
ld, cd = scla.eigh(Dp + r)
x1 = simx(Dp, cf, 'N')
x2 = simx(F0p, cd, 'N')
s1 = np.sum(np.abs(x1 - np.diag(np.diag(x1))))
s2 = np.sum(np.abs(x2 - np.diag(np.diag(x2))))
if s1 < 1E-6 and s2 < 1E-6:
print '\t\t Check'
else:
print '\t\t NOT OK'
if _verbose_:
print '\t\tDensity matrix in eigenbasis of the Fock matrix'
print np.array_str(x1, suppress_small=True)
print '\t\t\Fock matrix in eigenbasis of the Density matrix'
print np.array_str(x2, suppress_small=True)
print '\n'
print '\t\t',
print '=' * 40
print '\t\teigenvector/eigenvalues of the fock matrix'
print lf
print cf
print ''
print '\t\teigenvector/eigenvalues of the density matrix'
print ld
print cd
print '\t\t',
print '=' * 40
#
# check the initial population of the molecular orbital
#
if _verbose_:
print '\t\t',
print '=' * 40
print '\t\t Initial population of the molecular orbitals'
print '\t\t ',
for i in range(len(P)):
print '%1.3f ' % (P[i, i].real),
print ''
print '\t\t',
print '=' * 40
#
#-------------------------------------------------------------------------------------------
#
# SIMUALTIONS
#
#-------------------------------------------------------------------------------------------
##########################################################
## Define time and outputs
##########################################################
if args.time_unit == 'fs':
tmax_convert = args.tmax * 1E-15 / au2s
elif args.time_unit == 'ps':
tmax_convert = args.tmax * 1E-12 / au2s
elif args.time_unit == 'au':
tmax_convert = args.tmax
# a few shortcut
ffreq = args.ffreq
fint = args.fint
ft0 = args.ft0 * tmax_convert
fsigma = args.fsigma * tmax_convert
fform = args.fform
# readjust the frequency in case it is not specified
if ffreq < 0:
ffreq = L[nocc] - L[nocc - 1]
print '\n\t Field frequency adjusted to %f' % (ffreq)
T = np.linspace(0, tmax_convert, args.nT)
Tplot = np.linspace(0, args.tmax, args.nT)
FIELD = np.zeros(args.nT)
N = np.zeros((nbfs, args.nT))
Q = np.zeros((natom, args.nT))
mu0 = 0
for i in range(natom):
Q[i, :] = mol[i].Z
mu0 += mol[i].Z * mol.atoms[i].r[0]
MU = mu0 * np.ones(args.nT)
dt = T[1] - T[0]
##########################################################
## Loop over time
##########################################################
print '\n'
print '\t Compute the TDHF dynamics'
print '\t Simulation done at %d percent' % (0),
for iT in range(0, args.nT):
################################################################
## TIMER
################################################################
if iT * 10 % int(args.nT) == 0:
sys.stdout.write('\r\t Simulation done at %d percent' %
(iT * 100 / args.nT))
sys.stdout.flush()
################################################################
## Compute the observable
################################################################
# compute the Lowdin atomic charges
for iorb in range(nbfs):
atid = bfs[iorb].atid
Q[atid, iT] -= 2 * Dp[iorb, iorb].real
# compute the population of the orbitals
for iorb in range(nbfs):
N[iorb,
iT] = (np.dot(C0p[:, iorb], np.dot(Dp.real, C0p[:, iorb].T)) /
np.linalg.norm(C0p[:, iorb])**2).real
# compute the instantaneous dipole
MU[iT] -= np.trace(np.dot(mu_at, D)).real
######################################
## Propagation
######################################
if _predict_ and iT < args.nT - 1:
# predict the density matrix
dp = propagate_dm(Dp, Fp, dt, method='relax')
#predicted dm in AO basis
d = np.dot(X, np.dot(dp, X.T))
# value of the field
fp1 = compute_field(T[iT + 1],
ffreq=ffreq,
fint=fint,
t0=ft0,
s=fsigma,
fform=fform)
mup_p1 = mu_at_p * fp1
# predicted fock matrix
fp = compute_F(d, Hcore_p, X, Ints, mup_p1)
# form the intermediate fock matrix
fm = 0.5 * (Fp + fp)
# propagte the density matrix with that
Dp = propagate_dm(Dp, fm, dt, method='relax')
else:
# propagte the density matrix with that
Dp = propagate_dm(Dp, Fp, dt, method='relax')
######################################
## New Density Matrix in AO
######################################
# DM in AO basis
D = np.dot(X, np.dot(Dp, X.T))
######################################
## New Field
######################################
# value of the field
FIELD[iT] = compute_field(T[iT],
ffreq=ffreq,
fint=fint,
t0=ft0,
s=fsigma,
fform=fform)
mup = mu_at_p * FIELD[iT]
######################################
## New Fock Matrix
######################################
# new Fock matrix
Fp = compute_F(D, Hcore_p, X, Ints, mup)
sys.stdout.write('\r\t Simulation done at 100 percent')
# save all the data
print '\n\t Save data\n'
np.savetxt('time.dat', Tplot)
np.savetxt('orb_pops.dat', N)
np.savetxt('charges.dat', Q)
np.savetxt('dipole.dat', MU)
np.savetxt('field.dat', FIELD)
#-------------------------------------------------------------------------------------------
#
# EXPORT THE RESULTS
#
#-------------------------------------------------------------------------------------------
##########################################################
## PLOT THE DATA WITH MATPLOTLIB
##########################################################
if _plot_:
plot(Tplot, FIELD, N, Q, MU, cutlow=0.05, cuthigh=0.9)
##########################################################
## Export the MO in VMD Format
##########################################################
if _export_mo_:
print '\t Export MO Gaussian Cube format'
index_homo = nocc - 1
nb_print = int(min(nbfs, args.nb_print_mo) / 2)
fmo_names = []
for ibfs in range(index_homo - nb_print + 1,
index_homo + nb_print + 1):
if ibfs <= index_homo:
motyp = 'occ'
else:
motyp = 'virt'
file_name = mol.name + '_mo' + '_' + motyp + '_%01d.cube' % (index)
xyz_min, nb_pts, spacing = mesh_orb(file_name, mol, bfs, C0, ibfs)
fmo_names.append(file_name)
##########################################################
## Export the MO
## in bvox Blender format
##########################################################
if _export_blender_:
print '\t Export MO volumetric data for Blender'
bvox_files_mo = []
for fname in fmo_names:
fn = cube2blender(fname)
bvox_files_mo.append(fn)
##########################################################
## Create the
## Blender script to visualize the orbitals
##########################################################
path_to_files = os.getcwd()
pdb_file = name_mol + '.pdb'
create_pdb(pdb_file, args.mol, args.units)
# create the blender file
blname = name_mol + '_mo_volumetric.py'
create_blender_script_mo(blname, xyz_min, nb_pts, spacing,
pdb_file, bvox_files_mo, path_to_files)
##########################################################
## Export the MO DYNAMICS in VMD Format
##########################################################
if _export_mo_dynamics_:
# step increment
nstep_mo = 4
# resolution i.e. point per angstrom
ppa = 1
# just a test
norm = 1 - np.min(N[0, :])
# loop to create all the desired cube files
fdyn_elec, fdyn_hole = [], []
for iT in range(0, args.nT, nstep_mo):
if iT * 10 % int(args.nT) == 0:
sys.stdout.write(
'\r\t Export Cube File \t\t\t\t %d percent done' %
(iT * 100 / args.nT))
sys.stdout.flush()
felec, fhole, xyz_min, nb_pts, spacing = mesh_exc_dens(
mol, bfs, N, C0, iT, nocc, resolution=ppa)
fdyn_elec.append(felec)
fdyn_hole.append(fhole)
sys.stdout.write('\r\t Export Cube File \t\t\t\t 100 percent done\n')
# create the vmd script to animate the voxel
create_vmd_anim(mol.name, args.nT, nstep_mo)
##########################################################
## Export the DYN
## in bvox Blender format
##########################################################
if _export_blender_:
print '\t Export volumetric data for Blender'
# create the bvox files for electron
bvox_files_dyn_elec = []
for fname in fdyn_elec:
fn = cube2blender(fname)
bvox_files_dyn_elec.append(fn)
# create the bvox files for holes
bvox_files_dyn_hole = []
for fname in fdyn_hole:
fn = cube2blender(fname)
bvox_files_dyn_hole.append(fn)
# create the pdb file
pdb_file = name_mol + '.pdb'
create_pdb(pdb_file, args.mol, args.units)
# path to files
path_to_files = os.getcwd()
# create the blender script
blname = name_mol + '_traj_volumetric.py'
create_blender_script_traj(blname, xyz_min, nb_pts, spacing,
pdb_file, bvox_files_dyn_elec,
bvox_files_dyn_hole, path_to_files)
print '\n\n=================================================='
print '== Calculation done =='
print '==================================================\n'
def pyq1_rohf(atomtuples=[(2,(0,0,0))],basis = '6-31G**',maxit=10,mult=3):
from PyQuante import Ints,settings,Molecule
from PyQuante.hartree_fock import get_energy
from PyQuante.MG2 import MG2 as MolecularGrid
from PyQuante.LA2 import mkdens,geigh,trace2,simx
from PyQuante.Ints import getJ,getK
print ("PyQ1 ROHF run")
atoms = Molecule('Pyq1',atomlist=atomtuples,multiplicity=mult)
bfs = Ints.getbasis(atoms,basis=basis)
S,h,I2e = Ints.getints(bfs,atoms)
nbf = norbs = len(bfs)
nel = atoms.get_nel()
nalpha,nbeta = atoms.get_alphabeta()
enuke = atoms.get_enuke()
orbe,orbs = geigh(h,S)
eold = 0
for i in range(maxit):
Da = mkdens(orbs,0,nalpha)
Db = mkdens(orbs,0,nbeta)
Ja = getJ(I2e,Da)
Jb = getJ(I2e,Db)
Ka = getK(I2e,Da)
Kb = getK(I2e,Db)
Fa = h+Ja+Jb-Ka
Fb = h+Ja+Jb-Kb
energya = get_energy(h,Fa,Da)
energyb = get_energy(h,Fb,Db)
eone = (trace2(Da,h) + trace2(Db,h))/2
etwo = (trace2(Da,Fa) + trace2(Db,Fb))/2
energy = (energya+energyb)/2 + enuke
print (i,energy,eone,etwo,enuke)
if abs(energy-eold) < 1e-5: break
eold = energy
Fa = simx(Fa,orbs)
Fb = simx(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]
orbe,mo_orbs = np.linalg.eigh(F)
orbs = np.dot(orbs,mo_orbs)
return energy,orbe,orbs
def ao2mo(M,C): return simx(M,C) def mo2ao(M,C,S):
def mo2ao(M,C,S):
SC = matrixmultiply(S,C)
return simx(M,SC,'t')