On Convergence Acceleration of Multipolar and Orthogonal Expansions

Herbert H. H.Homeier
Email: herbert.homeier@na-net.ornl.gov
Institut für Physikalische und Theoretische Chemie
Universität Regensburg
D-93040 Regensburg, Germany

Abstract:

Multipolar expansions arise in many branches of the computational sciences. They are an example of orthogonal expansions. We present methods for the convergence acceleration of such expansions. As an example, the computation of the electrostatic potential and its multipolar expansion is treated for the case of a two-center charge density of exponential-type orbitals. This potential may also be considered as a special molecular integral, namely as a three-center nuclear attraction integral. It is shown that in this example, the extrapolation to the limit of the corresponding expansions via suitable nonlinear sequence transformations leads to a pronounced convergence acceleration.

Category: Methods Development

Keywords: Multipoles, electrostatic potential, spherical harmonics, molecular integrals, extrapolation

• 1 Introduction
• 2 Multipole Expansion of the Electrostatic Potential
• 3 Three-center Nuclear Attraction Integrals
• 4 Extrapolation Methods for Orthogonal Expansions
• 5 A Simple Example
• 6 Numerical Tests
  • 6.1 Multipole Expansion
  • 6.2 Exact Expansion in spherical harmonics
• 7 Tables
• 8 Figures
• Bibliographic Information with Hyperlinks