2015/07/08 by Piotr Gniewek, Gniewek, Piotr, Bogumił Jeziorski +1
Chemistry · Physics and Astronomy · #Advanced Chemical Physics Studies #Atomic and Molecular Physics #Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Molecular Spectroscopy and Structure #physics.chem-ph
paper · pdf · doi:10.48550/arxiv.1507.02121
11 pages, 3 figures, submitted to J. Chem. Phys
arxiv created 2015/07/08 · openalex publication_date 2015/07/08 · arxiv updated 2015/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The exchange splitting J of the interaction energy of the hydrogen atom with a proton is calculated using the conventional surface-integral formula J_\textrmsurf[φ], the volume-integral formula of the symmetry-adapted perturbation theory J_\textrmSAPT[φ], and a variational volume-integral formula J_\textrmvar[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 j0 in the large-R asymptotic series J(R) = 2 e-R-1 R ( j0 + j1 R-1 + j2 R-2 +⋯ ) converge, with the rate corresponding to the convergence radii equal to 4, 2, and 1 when the J_\textrmvar[φ], J_\textrmsurf[φ], and J_\textrmSAPT[φ] formulas are used, respectively. Additionally, we observe that also the higher jk coefficients are predicted correctly when the multipole expansion is used in the J_\textrmvar[φ] and J_\textrmsurf[φ] formulas. The SAPT formula J_\textrmSAPT[φ] predicts correctly only the first two coefficients, j0 and j1, gives a wrong value of j2, and diverges for higher jn. 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.