Use of Gaussian Wave Functions in Molecular Calculations

Gaussian functions have been used in a simple variational approach to calculate the energy of a number of two-electron systems, namely the hydrogen molecule, the negatively charged hydrogen ion, and the (1s)2 1S, (1s) (2s) 3S, and (1s) (2p) 3P states of helium. The last two were included in order to test two different 2s and a 2p function. The error in the total energies varied from 14% to 33%, showing that these functions can give ``fairly good'' energy values. This, and some other evidence, seems to indicate that in such variational calculations the specific form of the starting wave function may not be too important. Calculations were also carried out on one single electron system in order to further compare the two different 2s functions. Both here and in the case of the triplet helium both functions gave almost identical energies.