def get_vhf(mol, dm, *args, **kwargs):
"""This function needs to be defined here as it depends on eri2c and eri3c,
which are computed above. This is a bit a la 'por la pata del blumer' but
currently I don't have a better solution because the density lives only
in the namespace inside the function.
"""
naux = eri2c.shape[0]
nao = mol.nao_nr()
rho = np.einsum('ijp,ij->p', eri3c, dm)
rho = np.linalg.solve(eri2c, rho)
jmat = np.einsum('p,ijp->ij', rho, eri3c)
kpj = np.einsum('ijp,jk->ikp', eri3c, dm)
pik = np.linalg.solve(eri2c, kpj.reshape(-1, naux).T)
kmat = np.einsum('pik,kjp->ij', pik.reshape(naux, nao, nao), eri3c)
# Printing the .den file
print >> den_file, len(mol.atom)
print >> den_file, 'Molecule', sys.argv[1]
#
iini = 0
for i in mol.atom:
bas_len = sum(normalization.df_basis_dict[auxmol.basis][i.split()[0]])
print >> den_file, i.strip('\n'), ' ',
print >> den_file, " ".join("%16.12f" % x
for x in rho[iini:iini + bas_len])
#print >>den_file, " ".join("%16.12f" % x for x in rho[iini:iini+bas_len[i.split()[0]]])
iini += bas_len
rho_normalized = rho * normalization.normalize_df(auxmol)[0]
# Compute the Hellmann Feynman Forces from the DF expansion.
print '\nHellmann-Feynman Forces from DF:-----------------------'
print ' x y z'
for atom_id in range(mol.natm):
print atom_id, mol.atom_symbol(atom_id),
for axis in [0, 1, 2]:
norm_aux = fdf.OneGaussian_from_Overlap(auxmol) #*np.sqrt(np.pi*4)
hf = fdf.HellmannFeynman_df(auxmol, atom_id,
axis) #*np.sqrt(np.pi*4)
Coul = grad.grad_nuc(mol)[atom_id][axis]
print '%16.9f' % (hf.dot(rho_normalized) + Coul),
print ''
print '-------------------------------------------------------'
print '\nNorm = %12.6f' % (norm_aux.dot(rho_normalized))
#print '\nRHO =', rho_normalized
# Save the density in numpy arrat .npy file
#rhosave=open('rho.np','w'); np.save(rhosave,rho); rhosave.close()
return jmat - kmat * .5
def _get_hellmann_feynman_mo(mol,density_matrix):
"""Hellmann-Feynman Forces from the MO."""
_hf_forces_mo=np.ones([mol.natm,3])
for i in range(mol.natm):
F_en_0=mo_integrals.hellmann_feynman_mo(mol,i)/2.
F_nn=grad.grad_nuc(mol)
F_en=np.einsum('ij,kji->k',density_matrix,F_en_0)*2. # 2*\Sum P_ij*Phi_i*Phi_j
_hf_forces_mo[i]=F_en+F_nn[i]
return -_hf_forces_mo
def _get_hellmann_feynman_df(rho_normalized,mol,auxmol):
"""Compute the Hellmann Feynman Forces from the DF expansion.
"""
_hf_forces_df = np.ones([mol.natm,3])
for atom_id in range(mol.natm):
hf=df_integrals.hellmann_feynman_df(auxmol,atom_id)
coul=grad.grad_nuc(mol)[atom_id]#[axis]
_hf_forces_df[atom_id]=np.dot(rho_normalized,hf)+coul
return -_hf_forces_df
)
mf = scf.RHF(mol)
mf.conv_tol = 1e-14
ehf = mf.scf()
mycc = ccsd.CCSD(mf)
mycc.conv_tol = 1e-10
mycc.conv_tol_normt = 1e-10
ecc, t1, t2 = mycc.kernel()
eris = mycc.ao2mo()
e3ref = ccsd_t.kernel(mycc, eris, t1, t2)
print ehf+ecc+e3ref
eris = mycc.ao2mo(mf.mo_coeff)
conv, l1, l2 = ccsd_t_lambda.kernel(mycc, eris, t1, t2)
g1 = kernel(mycc, t1, t2, l1, l2, eris=eris, mf_grad=grad.RHF(mf))
print(g1 + grad.grad_nuc(mol))
#O 0.0000000000 0.0000000000 -0.0112045345
#H 0.0000000000 0.0234464201 0.0056022672
#H 0.0000000000 -0.0234464201 0.0056022672
mol = gto.M(
verbose = 0,
atom = '''
H -1.90779510 0.92319522 0.08700656
H -1.08388168 -1.61405643 -0.07315086
H 2.02822318 -0.61402169 0.09396693
H 0.96345360 1.30488291 -0.10782263
''',
unit='bohr',
basis = '631g')
print('-----------------------------------')
mol = gto.M(verbose=0,
atom=[["O", (0., 0., 0.)], [1, (0., -0.757, 0.587)],
[1, (0., 0.757, 0.587)]],
basis='631g')
mf = scf.RHF(mol)
ehf = mf.scf()
mycc = ccsd.CCSD(mf)
mycc.conv_tol = 1e-10
mycc.conv_tol_normt = 1e-10
ecc, t1, t2 = mycc.kernel()
l1, l2 = mycc.solve_lambda()
g1 = kernel(mycc, t1, t2, l1, l2, mf_grad=grad.RHF(mf))
print('gcc')
print(g1 + grad.grad_nuc(mol))
#[[ 0 0 1.00950925e-02]
# [ 0 2.28063426e-02 -5.04754623e-03]
# [ 0 -2.28063426e-02 -5.04754623e-03]]
lib.parameters.BOHR = 1
r = 1.76 #.748
mol = gto.M(verbose=0, atom='''H 0 0 0; H 0 0 %f''' % r, basis='631g')
mf = scf.RHF(mol)
mf.conv_tol = 1e-14
ehf0 = mf.scf()
ghf = grad.RHF(mf).grad()
mycc = ccsd.CCSD(mf)
mycc.conv_tol = 1e-10
mycc.conv_tol_normt = 1e-10
ecc, t1, t2 = mycc.kernel()
print '\nReference Forces:--------------------------------------'
print ' x y z'
for i in range(mol.natm):
print i, mol.atom_symbol(i),
print '%16.9f %16.9f %16.9f' % (hartree_fock_force[i, 0],
hartree_fock_force[i, 1],
hartree_fock_force[i, 2])
print '-------------------------------------------------------'
P = mf.from_chk()
print '\nHellmann-Feynman Forces from MO:-----------------------'
print ' x y z'
for i in range(mol.natm):
F_en_0 = fdf.HellmannFeynman(mol, i) / 2.
F_nn = grad.grad_nuc(mol)
F_en = np.einsum('ij,kji->k', P, F_en_0) * 2. # 2*\Sum P_ij*Phi_i*Phi_j
Ft = F_en + F_nn[i]
print i, mol.atom_symbol(i),
print '%16.9f %16.9f %16.9f' % (Ft[0], Ft[1], Ft[2])
print '-------------------------------------------------------'
mf.get_veff = get_vhf # This substitutes the function 'get_veff' in mf by the
# implementation of density fitting 'get_vhf' which prints the d_l coefficients.
# This is done here after the SCF was solved.
e_fit = mf.energy_tot() # Run this only to get the density basis coefficients.
# Here the function 'get_vhf' is called and give access to the coefficients
# prints the d_l coefficients.