Single-Center Expansions for One-Electron Systems. H2+

Abstract

The expansion of the H₂⁺ wave function in terms of the set of associated Laguerre functions of order (2l+2) based on a single point in space, the molecular midpoint, is studied by the usual variational approach. In particular, the convergence of the expansion is studied as a function of the number and type of basis functions used, the respective scaling parameters, and the internuclear distance. A peculiar behavior with respect to the scaling parameter, in which, for example, for certain optimum choices of the scale parameter for one group of basis functions no improvement is observed upon the addition of one more such function, is proved to occur generally for these functions with one‐electron Hamiltonians. This behavior emphasizes the necessity for treating such scale factors as mathematical parameters rather than as constants to be chosen by physical intuition. This single‐center expansion is concluded to be only slowly convergent and therefore, the authors feel, likely to have relatively limited use for quantitatively accurate calculations on more complex problems. Such expansions may, however, be useful for certain classes of excited states.