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Author Gniewek, Piotr ♦ Jeziorski, Bogumił
Source United States Department of Energy Office of Scientific and Technical Information
Content type Text
Language English
Subject Keyword INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY ♦ APPROXIMATIONS ♦ ATOMS ♦ CONVERGENCE ♦ ELECTRONS ♦ HYDROGEN ♦ INTEGRALS ♦ INTERACTIONS ♦ PERTURBATION THEORY ♦ SYMMETRY ♦ WAVE FUNCTIONS
Abstract 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 quantum chemistry, it provides an alternative for the determination of the exchange splitting and the exchange contribution of the interaction potential in general.
ISSN 00219606
Educational Use Research
Learning Resource Type Article
Publisher Date 2015-10-21
Publisher Place United States
Journal Journal of Chemical Physics
Volume Number 143
Issue Number 15


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