Electron density distribution functions and the ASED – MO theory

A diatomic charge density distribution function may be partitioned into free atom and delocalization components. Integrating the electrostatic force on one of the nuclei as the atoms join to bond yields a repulsive atom superposition energy Er(R) and an attractive delocalization energy Ed(R) which, when added, equal the Born‐Oppenheimer potential energy, E(R). Bond stretch force constants may be calculated to quite good accuracy from the Poisson equation ▽ E(R) = 4πZbpa(r = R), where Zb is the charge of nucleus b at a distance of R from nucleus a and pa is the charge‐density distribution function of isolated atom a. This equation follows if the delocalization density component is rigid during molecular vibrations and Ed = c/R, where c is a constant. Ed(R) is well approximated by the change in orbital energy, δEMO(R), for the bond‐forming reaction a + b → a ‐ b as obtained from a modified extended Hückel procedure. The resulting E() = Er(R) + δEMO(R) generalizes immediately to polyatomic molecules and solids and can be used for the calculation of structures and other properties and their molecular orbital interpretation. The current understanding of the atom superposition and electron delocalization molecular orbital (ASED‐MO) theory is presented in this article. It is pointed out that a parallel exists with the density functional theory, wherein the Born‐Oppenheimer potential function may be constructed from energy points E(R) that are functionals of the molecular charge density distribution function. Calculations of molecular structures with density functional theory has also become possible only through the introduction of electron orbitals. However, the approaches are otherwise different, for density functional theory works with the total energy of the molecule and the ASED approach works with the molecular binding energy obtained by integrating the electrostatic force on a nucleus, which is zero for the isolated atoms.