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

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 $-(2/e)R{e}^{-R}$, but approximate it with very different convergence rates. In the case of the SAPT formula, the convergence is geometric with the error falling as $3^{-K}$, where $K$ is the order of the applied polarization expansion. The error of the surface-integral formula decreases exponentially as $a^K/(K+1)!$, where $a=\ln 2-\frac{1}{2}$. The variational formula performs best, its error decays as $K^{1/2}[a^K/(K+1)!{]}^2$. 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.

arXiv comment5 pages, 1 figure

References in corpus (3)

• Energetics and control of ultracold isotope-exchange reactions between heteronuclear dimers in external fields
• Asymptotics of the exchange splitting energy for a diatomic molecular ion from a volume integral formula of symmetry-adapted perturbation theory
• Convergence properties of the multipole expansion of the exchange contribution to the interaction energy

Cited by in corpus (2)

• First-order symmetry-adapted perturbation theory for multiplet splittings
• Long-range asymptotics of exchange energy in the hydrogen molecule