Born-Oppenheimer potential for H2

The Born-Oppenheimer potential for the (1)Sigma(+)(g) state of H-2 is obtained in the range 0.1-20 a.u., using analytic formulas and recursion relations for two-center two-electron integrals with exponential functions. For small distances, the James-Coolidge basis is used, while for large distances, the Heitler-London functions with arbitrary polynomial in electron variables are used. In the whole range of internuclear distance, about 10(-15) precision is achieved; as an example, at the equilibrium distance r = 1.4011 a.u., 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. A 134, 362 ( 1964)] for the large-internuclear-distance asymptotics. The presented analytic approach to Slater integrals opens a window for high-precision calculations in an arbitrary diatomic molecule.