Use of 1<i>s</i> Gaussian Wavefunctions for Molecular Calculations. I. The Hydrogen Atom and the Hydrogen Molecule Ion

Abstract

The 1s, 2s, 2p, 3s, 3p, 3dz, and 3dxy hydrogen-atom wavefunctions were expanded with linear combinations of 1s Gaussian functions of the form exp(—ar2), centered at different points in space to give the proper orbital symmetry. Energy values of −0.499999, −0.124630, −0.124947, −0.055170, −0.055460, −0.055450, and −0.055527 a.u. were found for 1s, 2s, 2p, 3s, 3p, 3dz, and 3dxy functions, respectively. Trial functions for the 2Σg+ and 2IIu states of the hydrogen molecule ion were constructed from the 1s Gaussian expansion functions of 1s and 2p hydrogen-atom wavefunctions, introducing an effective charge and a polarization parameter which are closely related to the distortion of an atomic orbital in molecule formation. The trial functions, which have two nolinear parameters, give total energy errors of 0.055% and 0.16% at the equilibrium internuclear distance for the 2Σg+ and 2IIu states, respectively, of the hydrogen molecule ion. The extension of this procedure to polyatomic molecules is discussed, and the simplicity of the required integrals and the small number of nonlinear parameters for the procedure are emphasized.