Page 56 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

A COUPLED MCSCF-PERTURBATION TREATMENT OF ELECTRONIC SPECTRA 41
In order to systematically remedy the previous drawbacks, we recently proposed to
perform a perturbation treatment, not on a wavefunction built iteratively, but on a
wavefunction that already contains every components needed to properly account for the
the chemistry of the problem under investigation [34]. In that point of view, we mean that
this zeroth-order wavefunction has to be at least qualitatively correct: the quantitative
aspects of the problem are expected to be recovered at the perturbation level that will
include the remaining correlation effects that were not taken into account in the variational
process: any unbalanced error compensations or non-compensations between the
correlation recovered for different states is thus avoided contrary to what might happen
when using any truncated CIs. In this contribution, we will report the strategy developed
along these lines for the determination of accurate electronic spectra and illustrate this
process on the formaldehyde molecule taken as a benchmark.

2. Theoretical background in the perturbation theory
2.1. PERTURBATIONS AND THE SPECTRAL DECOMPOSITION OF THE
HAMILTONIAN
Let suppose is an exact solution to the eigenvalue problem :

where is an hermitian zeroth order hamiltonian. Considering the perturbation to and
induced by the perturbation operator V on , the first order correction can be
developed on a set of basis functions

The Rayleigh-Schrödinger Perturbation Theory (see [2]) leads then to the following system
of linear equations for the determination of

where is the first order correction to the zeroth order energy
Let us now define :

If the following relations are both valid:

then, equation (3) can be simplified, which gives :