Density Localization of Atomic and Molecular Orbitals. I

A new intrinsic method for the localization of atomic and molecular orbitals is presented, which will be called (charge) density localization method. This new procedure follows an earlier suggestion of Edmiston and Ruedenberg. It is based on the minimization of the sum of the charge density overlap integrals of the orbitals: ${\Sigma }_{\mathrm{i<j}}{\displaystyle \int }\mathrm{|〈}\mathrm{r}{\mathrm{|i〉|}}^2\mathrm{|〈}\mathrm{r}{\mathrm{|j〉|}}^2{d}^3\mathrm{r}\mathrm{,\; |〈}\mathrm{r}{\mathrm{|i〉|}}^2$ being the charge density of orbitals $\mathrm{|i〉.}$ Because of the physical relation between the exchange interaction of wave packets representing fermions and their mutual overlap it is expected that this method is related to the energy localization procedure of Edmiston and Ruedenberg. The density localization method is applied to the atoms Be and Ne, where the four outer shell localized orbitals point to the corners of a tetrahedron. The results are compared with those of other localization procedures. Good agreement is obtained. It is shown in the present and in forthcoming publications that the same physical situation can be described by different but physically equivalent pictures.