The relations between the repulsive interactions and the electron density overlaps are investigated for various closed shell-closed shell pairs, including the systems containing alkali and halide ions. It is found that the repulsive interaction($V_{rep}$) depends on the overlap of the electron density($S_{ ho}$) according to a simple exponential relation, $V_{rep}$ = $As_{ ho};^{alpha}$. Furthermore, for most of the closed shell systems the $alpha$ values are near unity and the A values do not vary much. The same tests are also performed for the open shell-closed shell, and the open shell-open shell pairs. Although the results for these systems also show exponential dependences of the repulsive interactions on the density overlaps, the details of the dependence differ greatly from those for the closed shell systems and also vary widely from one individual system to another.