Multiconfigurational Perturbation Theory

The most interesting and technologically relevant problems such as chemical reactions, chemisorption, defects in solids etc. require an accurate description of both the equilib­ rium and partially or fully dissociated limits of a chemical system. Useful theoretical methods must address these problems by providing chemically accurate potential sur­ faces at a reasonable computational cost. The general theme of the work presented here is the development of a computationally efficient perturbative scheme of achieving this goal. This work is concerned with both a reasonable and physically appealing zeroth-order description of electronic structure and computationally efficient perturba­ tive methods for improving the accuracy of this zeroth-order description. It is well-established that wave functions of the self-consistent multiconfigurational (MCSCF) type are essential for describing the correct overall shape of a potential sur­ face. The basic physical consideration which goes into the construction of these wave functions is that each electron should be described by a unique spatial orbital ampli­ tude. This form of the wave function is necessary in order to obtain an energetically reasonable description of the spatial separation of electronic alnplitudes involved in most distortions away from equlibrium and in some cases, such as in silicon clusters [1] and surfaces [2], at equilibrium. The familiar and simpler Hartree-Fock wave function composed of doubly occupied spatial orbitals is absolutely incapable of describing such spatial separation of the pairs of electrons occupying each orbital. When the spatial orbital amplitudes of the MCSCF wave functions using one unique orbital per electron are expressed as localized overlapping orbitals, the resulting wave function is of the generalized valence-bond (GVB) [3] type. The GVB wave function can also be constructed to describe any spin coupling among these spatial orbitals. The GVB wave function is therefore amenable to an appealing interpretation in terms of classical chemically bonded or reacting structures. A computationally useful ap­ proximation to the GVB wave function is the so-called GVB-restricted-CI (GVB-RCI) multiconfigurational expansion generated byapproximating each GVB orbital by two orthogonal natural spin-orbitals. The GVB-RCI expansion can be optimized using well