Determination of the exchange interaction energy from the polarization expansion of the wave function

Piotr Gniewek and Bogumił Jeziorski
Phys. Rev. A 94, 042708 – Published 26 October 2016

Abstract

The exchange contribution to the energy of the hydrogen atom interacting with a proton is calculated from the polarization expansion of the wave function using the conventional surface-integral formula and two formulas involving volume integrals: the formula of the symmetry-adapted perturbation theory (SAPT) and the variational formula recommended by us. At large internuclear distances R, all three formulas yield the correct expression (2/e)ReR, but they approximate it with very different convergence rates. In the case of the SAPT formula, the convergence is geometric with the error falling as 3K, where K is the order of the applied polarization expansion. The error of the surface-integral formula decreases exponentially as aK/(K+1)!, where a=ln212. The variational formula performs best, its error decays as K1/2[aK/(K+1)!]2. These convergence rates are much faster than those resulting from approximating the wave function through the multipole expansion. This shows the efficiency of the partial resummation of the multipole series effected by the polarization expansion. Our results demonstrate also the benefits of incorporating the variational principle into the perturbation theory of molecular interactions.

  • Figure
  • Received 23 July 2016

DOI:https://doi.org/10.1103/PhysRevA.94.042708

©2016 American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & OpticalGeneral Physics

Authors & Affiliations

Piotr Gniewek* and Bogumił Jeziorski

  • Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland

  • *pgniewek@tiger.chem.uw.edu.pl
  • jeziorsk@chem.uw.edu.pl

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Issue

Vol. 94, Iss. 4 — October 2016

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