Exact matrix elements for general two-body central-force interactions, expressed as sums of products

Jonathan Jerke, Jacek Karwowski, Bill Poirier

Research output: Contribution to journalArticlepeer-review

Abstract

In a manner similar to but distinct from concurrent tensor efforts in electronic structure, it is shown that the Laplace transform can serve as a generator for a sum-of-products (SOP) form that allows one to write essentially any function of distance between two particles (i.e. any central force potential) as an exact two-body matrix. In particular, exact expressions for the Coulomb, Yukawa and long-range Ewald two-body operators are evaluated in a band-limited (Sinc function) basis. The resultant exact, full-basis, SOP representations for these interaction potentials–acting in conjunction with an external harmonic confining field–are validated via comparison with energy eigenstate solutions obtained via an independent calculation based on separation of variables. The new two-body matrix representations may have substantial impact in any of the many disciplines in which pair-wise central force interactions are relevant–especially, electronic structure and dynamics.

Original languageEnglish
Pages (from-to)1264-1275
Number of pages12
JournalMolecular Physics
Volume117
Issue number9-12
DOIs
StatePublished - Jun 18 2019

Keywords

  • Coulomb
  • Hookean system
  • Laplace transform
  • Sum of products
  • Yukawa
  • long-range Ewald

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