Convergence to the Solution of the Eigenvalue Problem by Perturbative Methods.

The solution of the Schroedinger equation for molecules leads to a very large-dimension matrix eigenvalue problem. Convergence to the solution of the eigenvalue problem using perturbative methods is investigated. Partitioning technique and perturbation theory are discussed as the basis for large scale diagonalization procedures. In particular multi-reference Rayleigh-Schroedinger perturbation theory is presented in a configuration based scheme, enabling the evaluation of high-order contributions. Problems associated with the convergence of the multi-reference series, as related to the choice of reference space, are discussed and the role of the Pade' approximants for acceleration of convergence is explored. Application of this method to problems of potential energy surfaces and excitation energy calculations are presented. General purpose diagonalization procedures for application to large sparse matrices are also discussed. The relationship of these procedures to the partitioning technique and perturbation theory as well as some examples are presented. The non-symmetric (non-Hermitian) eigenvalue problem, which occurs in several many-body approaches for excited states, is investigated and approaches are proposed for its solution.