An iterative perturbation theory with a Hamiltonian modifier

• Published in: Journal of mathematical chemistry 2011-03, Vol.49 (3), p.666-686
• Main Authors: Chaves, J., Barroso, J. M., Besalú, E.
• Format: Article
• Language: English
• Subjects: Chemistry; Chemistry and Materials Science; Exact sciences and technology; General and physical chemistry; Math. Applications in Chemistry; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical linear algebra; Original Paper; Physical Chemistry; Sciences and techniques of general use; Theoretical and Computational Chemistry; Theory of reactions, general kinetics. Catalysis. Nomenclature, chemical documentation, computer chemistry
• ISSN: 0259-9791; 1572-8897
• DOI: 10.1007/s10910-010-9762-7

The aim of this paper is to show that the so-called Autoadjusting Perturbation Theory presented years ago [E. Besalú and R. Carbó-Dorca, J. Math. Chem ., 22 , 85 ( 1997 )] can be modified and expressed in terms of operators, opening the possibility to define diverse variants with better convergence properties. This methodology is called here modified autoadjusting perturbation theory which is superior, at least numerically, to Rayleigh Schrödinger perturbation theory and the superconvergent perturbation theory [W. Scherer, Phys. Rev. Lett ., 74 , 1495 ( 1995 )] applied to the one-dimensional quartic anharmonic oscillator. The new feature of this method is the Hamiltonian modifier which can be chosen in a proper way in order to improve the calculations and to obtain convergent energy series and wavefunction when Rayleigh Schrödinger perturbation theory gives divergent ones. Resummation techniques are used to check whether the correction terms of modified autoadjusting perturbation theory series resums similarly to the Rayleigh Schrödinger perturbation one. The iterative nature of the proposed method allows for a linear time scaling and for memory economization when it is numerically implemented.