Collect. Czech. Chem. Commun. 2004, 69, 105-120

Convergence Enhancement in Perturbation Theory

Peter R. Surján* and Ágnes Szabados

Department of Theoretical Chemistry, Eötvös University, P.O. Box 32, H-1518 Budapest 112, Hungary


The Frobenius norm of operator QW is minimized with respect to level shift parameters applied to the zero-order spectrum, where W is the perturbation while Q is the reduced resolvent of the zero-order Hamiltonian. The stationary condition leads to a simple formula for the level shifts which eliminates degeneracy-induced singularities. Such level shifts may increase the radius of convergence of the perturbation series, and may improve low-order perturbative estimations - as it is found in the cases of a simple matrix eigenvalue problem and the one-dimensional quartic anharmonic oscillator.

Keywords: Perturbation theory; Convergence; Partitioning; Level shifts; Anharmonic oscillator; Hamiltonian; Quantum chemistry.

References: 42 live references.