Page 54 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

A Coupled MCSCF-Perturbation Treatment for Electronic Spectra

O. PARISEL and Y. ELLINGER
Laboratoire de Radioastronomie Millimétrique, E.N.S. et Observatoire de Paris,
24 rue Lhomond, F. 75231 Paris Cedex 05, France

1. Introduction

1.1. PURE VARIATION OR PERTURBATION APPROACHES
Despite continuous efforts over many decades, the determination of accurate wavefunctions
and energies for polyatomic systems remains a challenging problem. Although carefully-
designed implementations of various codes and computational developments allow now for
calculations that were unrealistic even a few years ago, the evaluation of correlation
energies and highly-correlated wavefunctions, that are necessary to properly describe
excited states or potential energy surfaces, remains still in most cases a tremendous task
which can hardly be performed routinely and rigorously for large systems.
If we except the Density Functional Theory and Coupled Clusters treatments (see, for
example, reference [1] and references therein), the Configuration Interaction (CI) and the
Many-Body-Perturbation-Theory (MBPT) [2] approaches are the most widely-used
methods to deal with the correlation problem in computational chemistry. The MBPT
approach based on an HF-SCF (Hartree-Fock Self-Consistent Field) single reference
taking RHF (Restricted Hartree-Fock) [3] or UHF (Unrestricted Hartree-Fock) orbitals [4-
6] has been particularly developed, at various order of perturbation n, leading to the
widespread MPn or UMPn treatments when a Möller-Plesset (MP) partition of the
electronic Hamiltonian is considered [7]. The implementation of such methods in various
codes and the large distribution of some of them as black boxes make the MPn theories a
common way for the non-specialist to tentatively include, with more or less relevancy,
correlation effects in the calculations.

It is however too often forgotten that the usual single-reference MBPT is relevant only for
structures that are already well-described by a single determinant: even a second-order
perturbation treatment on a closed-shell molecule using RHF orbitals and the SCF
determinant as zeroth-order function for the perturbation will be relevant only if this
function dominates the exact wavefunction of the system [8]. It follows that using standard
MPn approaches for the determination of potential energy surfaces which invoke distorded
geometries and breakings of chemical bonds or in the description of molecules involving
transition metals should be considered with an extreme critical mind. This point is even
more crucial for excited states where appropriate perturbative excitonic treatments are
necessary as shown in the pioneering works by Berthier or Pauzat [9-13]. Moreover, there
39
Y. Ellinger and M. Defranceschi (eds.), Strategies and Applications in Quantum Chemistry, 39–53.
© 1996 Kluwer Academic Publishers. Printed in the Netherlands.