Convergence to the Solution of the Eigenvalue Problem by Perturbative Methods.
Abstract
The solution of the Schroedinger equation for molecules leads to a very largedimension 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 multireference RayleighSchroedinger perturbation theory is presented in a configuration based scheme, enabling the evaluation of highorder contributions. Problems associated with the convergence of the multireference 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 nonsymmetric (nonHermitian) eigenvalue problem, which occurs in several manybody approaches for excited states, is investigated and approaches are proposed for its solution.
 Publication:

Ph.D. Thesis
 Pub Date:
 1987
 Bibcode:
 1987PhDT........41Z
 Keywords:

 Physics: Molecular; Chemistry: Physical