Born-Oppenheimer potential for H${}_2$

Abstract

The Born-Oppenheimer potential for the ${}^1{\Sigma }_g^{+}$ state of H${}_2$ is obtained in the range of 0.1 -- 20 au, using analytic formulas and recursion relations for two-center two-electron integrals with exponential functions. For small distances James-Coolidge basis is used, while for large distances the Heitler-London functions with arbitrary polynomial in electron variables. In the whole range of internuclear distance about $10^{-15}$ precision is achieved, as an example at the equilibrium distance $r=1.4011$ au the Born-Oppenheimer potential amounts to $-1.1744759314002167(3)$. Results for the exchange energy verify the formula of Herring and Flicker [Phys. Rev. {\bf 134}, A362 (1964)] for the large internuclear distance asymptotics. The presented analytic approach to Slater integrals opens a window for the high precision calculations in an arbitrary diatomic molecule.

14 pages, 5 tables, 1 figure, corrected numerics

References in corpus (3)

• Spin-Dependent Macroscopic Forces from New Particle Exchange
• Relativistic, QED, and nuclear mass effects in the magnetic shielding of ${}^3$He
• Two-center two-electron integrals with exponential functions

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