Alternatives to multireference methods for the molecular electronic structure problem

Abstract

AbstractThe development of robust many‐body methods for the molecular electronic structure problem with respect to multireference functions has attracted much attention over the past two decades. In recent years, multireference methods based on the Brillouin–Wigner expansion have been shown to overcome the intruder state problems which have plagued similar approaches based on the Rayleigh–Schrödinger series. However, there are some problems in molecular electronic structure theory, which may be handled by means of multireference methods, but can be treated by methods that avoid the use of multireference functions. We consider two examples of alternatives to multireference methods for the molecular electronic structure problem. The study of excited states having the same symmetry as the ground state or some lower lying excited state often involves the use of a multireference function. We describe an alternative procedure based on the generalized Rayleigh–Ritz variation principle. Gidopoulos, Glushkov, and Wilson have termed this the optimized trace method. The generalized Rayleigh–Ritz principle for the relativistic formulation of the molecular electronic structure problem is briefly also considered. Molecular dissociative processes are frequently described by quantum chemical methods based on multireference functions. Single‐reference Hartree–Fock methods usually provide a qualitatively incorrect description of such processes even in the simplest of molecules, H2. However, approximate single configuration wave functions constructed from nonorthogonal orbitals can often afford a useful approximation to bond‐breaking processes. Each occupied nonorthogonal orbital is then an eigenfunction of a different Fock‐like operator. Each of these Fock‐like operators supports a spectrum of M single particle states, where M is the size of the basis set, and only the lowest of these is occupied. We briefly consider the relativistic formulation of the molecular electronic structure problem based on approximations involving products of nonorthogonal functions within the Furry bound state interaction picture of quantum electrodynamics. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004