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#! RHF STO-3G dipole moment computation, performed by applying a finite electric field and numerical differentiation.


molecule h2o {
0 1
O
H 1 r
H 1 r 2 a

r=0.98944
a=100.047
}

pert = 0.001
lambdas = [pert, -pert, 2.0*pert, -2.0*pert]

set {
    basis        sto-3g
    e_convergence   10
    scf_type pk
}

energies = []
for l in lambdas:
    set perturb_h true
    set perturb_with dipole
    set perturb_dipole [0, 0, $l]
    energies.append(energy('scf'))

# Now use 3- and 5-point finite difference formulae to compute the dipole
dm_z_3point = (energies[0] - energies[1]) / (2.0*pert)
dm_z_5point = (8.0*energies[0] - 8.0*energies[1] - energies[2] + energies[3]) / (12.0*pert)

set perturb_h false
# Compute the analytic dipoles, for comparison
e,wfn = energy('scf', return_wfn=True)
oeprop(wfn, "MULTIPOLES(1)")
analytic = get_variable("DIPOLE Z")

# Tabulate the results of the energy computation
for val in range(len(lambdas)):
    print_out("Perturbation strength = %7.4f, computed energy = %16.10f\n" % (lambdas[val], energies[val]))

# The a.u. to Debye conversion factor is automatically available in Psithon as psi_dipmom_au2debye
print_out("Total dipoles\n")
print_out("3 Point formula: mu(z) = %10.6f ea0, %10.6f Debye\n" % (dm_z_3point, dm_z_3point*psi_dipmom_au2debye))
print_out("5 Point formula: mu(z) = %10.6f ea0, %10.6f Debye\n" % (dm_z_5point, dm_z_5point*psi_dipmom_au2debye))