Treatment of the H 2 + -ion by means of one-, two- and three-center wave functions

Abstract

The ground state energy of H 2 + is calculated with one- and multi-center wave functions by means of the variational method. By using hydrogen-like one-center wave functions a bound state is found even with Is function if it is centered-near one of the nuclei. Results can be improved by taking the linear combination of two or three of the one-center wave functions of the type 1s, 2s, 2p 2, 3d 2. By varying the position of the center we get the best results when the center is either located in one of the nuclei or in the middle point between the nuclei. A better approximation can be obtained with the two-center linear combination of 1s type wave functions centered on the two nuclei. The results can be essentially improved with the three-center wave function which is a linear combination of 1s wave functions centered on the two nuclei and on the middle point. In this case the energy and the internuclear distance areE = −0.5972e 2/a 0 andR = 2a 0, respectively, corresponding to the exact values − 0.60263e 2/a 0 and 2a 0.