Born-Oppenheimer potential for H2
Abstract
The Born-Oppenheimer potential for the 1g+ state of H2 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 -1.174\,475\,931\,400\,216\,7(3). Results for the exchange energy verify the formula of Herring and Flicker [Phys. Rev. 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.