An intermediate level of approximation for computing the dual descriptor

At present, there are two levels of approximation to compute the dual descriptor (DD). The first uses the total electronic density of the original system along with the electronic densities of the system with one more electron and one less electron, but this procedure is time consuming and normal termination of computation of total electronic densities is not guaranteed. The second level of approximation uses only the electronic densities of frontier molecular orbitals, HOMO and LUMO, to avoid the former approximation; however, the orbital relaxation implicitly included in the first level of approximation is absent in the second, thus risking an incorrect interpretation of local reactivity. Between the lowest occupied molecular orbital (LOMO) and the highest unoccupied molecular orbital (HUMO), a framework to provide an expression of the DD in terms of the electronic densities of all molecular orbitals (except HUMO and LOMO) has been proposed to be implemented by programmers as a computational code. This methodology implies another level of approximation located between the conventional approximation methods mentioned above. In this study, working equations have been oriented toward molecular closed- and open-shell systems. In addition, the mathematical expression for a closed-shell system was applied to acetylene in order to assess the capability of this approach to generate the DD.