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Title: Exchange splitting of the interaction energy and the multipole expansion of the wave function

The exchange splitting J of the interaction energy of the hydrogen atom with a proton is calculated using the conventional surface-integral formula J{sub surf}[Φ], the volume-integral formula of the symmetry-adapted perturbation theory J{sub SAPT}[Φ], and a variational volume-integral formula J{sub var}[Φ]. The calculations are based on the multipole expansion of the wave function Φ, which is divergent for any internuclear distance R. Nevertheless, the resulting approximations to the leading coefficient j{sub 0} in the large-R asymptotic series J(R) = 2e{sup −R−1}R(j{sub 0} + j{sub 1}R{sup −1} + j{sub 2}R{sup −2} + ⋯) converge with the rate corresponding to the convergence radii equal to 4, 2, and 1 when the J{sub var}[Φ], J{sub surf}[Φ], and J{sub SAPT}[Φ] formulas are used, respectively. Additionally, we observe that also the higher j{sub k} coefficients are predicted correctly when the multipole expansion is used in the J{sub var}[Φ] and J{sub surf}[Φ] formulas. The symmetry adapted perturbation theory formula J{sub SAPT}[Φ] predicts correctly only the first two coefficients, j{sub 0} and j{sub 1}, gives a wrong value of j{sub 2}, and diverges for higher j{sub n}. Since the variational volume-integral formula can be easily generalized to many-electron systems and evaluated with standard basis-set techniques of quantummore » chemistry, it provides an alternative for the determination of the exchange splitting and the exchange contribution of the interaction potential in general.« less
Authors:
;  [1]
  1. Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw (Poland)
Publication Date:
OSTI Identifier:
22493122
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 143; Journal Issue: 15; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; APPROXIMATIONS; ATOMS; CONVERGENCE; ELECTRONS; HYDROGEN; INTEGRALS; INTERACTIONS; PERTURBATION THEORY; SYMMETRY; WAVE FUNCTIONS