Improvement of Molecular Gaussian Wavefunctions

Gaussian electronic wavefunctions for H, H₂⁺, and H₂ are presented and it is shown how they may be improved by, in each case, adding to the basis set a function of the form $${\mathrm{\chi \hspace{0.17em}=\hspace{0.17em}(\rho \hspace{0.17em}-\hspace{0.17em}r)}}^l\mathrm{for}\mathrm{r\le \rho }$$ $$\text{=\hspace{0.17em}0}\mathrm{for}\mathrm{r>\rho }$$ , centered on each nucleus, where $r$ is the distance from the nucleus and $\rho$ and $l$ are parameters which may be chosen to minimize the electronic energy. Such improvement is shown to be greater than that which would be obtained by adding a further Gaussian function to the basis set.