Page 307 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

290 P. LAZZERETTI ET AL.

6. Fourth-order CHF energy

The CHF formulae (75)-(77) for the response tensors are established by expanding
the Hartree-Fock energy [8],

in powers of the electric field in the same way as (1). In the presence of multiple
perturbations, the first-order perturbed core Hamiltonian can be written

where the parameters a, b, c, etc., are related to the intensity of each perturbation.
The expansion for the energy of a molecule becomes

Comparing this general expression with the analogous expansion (1), one finds (no
sum over repeated Latin indices)

It should be noted that, in this notation, the order of the superscripts is irrelevant;
is the entire perturbed energy term linear in ab ... z and there is no
additional term with permuted ab ... z indices.
The following terms appear in the expression of the 4-th order energy