Ab initio calculations with a nonspherical Gaussian basis set: Excited states of the hydrogen molecule

A basis set of generalized nonspherical Gaussian functions (GGTOs) is prese nted and discussed. As a first example we report on Born-Oppenheimer energi es of the hydrogen molecule. Although accurate results have been obtained, we conclude that H-2 is too ''simple'' to allow for a substantial gain by u sing nonspherical functions. We rather expect that these functions may be p articularly useful in calculations on large systems. A single basis set of GGTOs was used to simultaneously calculate the potential energy curves of s everal states within each subspace of (1.3)Sigma(g,u) symmetry. We hereby c onsidered the entire region of internuclear distances 0.8 less than or equa l to R less than or equal to 1000 a.u. In particular the results for the fo urth up to sixth electronic states show a high accuracy compared to calcula tions which invoke explicitely correlated functions, e.g., the relative acc uracy is at least of the order of magnitude of 10(-5) a.u. Energies for the 4 (1)Sigma(u)(+) and 4-6 (3)Sigma(u)(+) were improved and accurate data fo r the 6 (3)Sigma(g)(+), 5 (1)Sigma(u)(+) and 6 (1)Sigma(u)(+) state are, to the best of the authors' knowledge, presented for the first time. Energy d ata for the seventh up to the ninth electronic state within each subspace w ere obtained with an estimated error of the order of magnitude of 10(-4) a. u. The 7 (1)Sigma(g)(+) and the 6 (1)Sigma(u)(+) state were found to exhibi t a very broad deep outer well at large internuclear distances. (C) 1998 Am erican Institute of Physics. [S0021-9606(98)30146-4].