The use of Gaussian (exponential quadratic) wave functions in molecular problems. II. Wave functions for the ground states of the hydrogen atom and of the hydrogen molecule

The results reported in this paper constitute a first examination of the use of Gaussian wave functions with correlation as approximations to electronic wave functions. Functions of the form $\sum^{k=n}_{k=1}$ C$_k$ exp (-Q$_k$), where C$_k$ is a constant and Q$_k$ is a quadratic form corresponding to orbitals with cylindrical symmetry, variable centres and with correlation, are used for the hydrogen molecule. Binding energies of 4.30, 4.42, 4.52 and 4.58 eV are obtained with functions containing, respectively, 26, 35, 53 and 71 independent parameters. The accuracy of the results and the moderate computing times suggest that there is considerable scope for wave functions of this type. For the hydrogen atom, approximations to the 1s-orbital in terms of $\sum^{k=n}_{k=n}$ C$_k$ exp (-a$_k$r$^2$) are given for n = 3, 4, 5, 6 and 8.