Chemical potential equalization principle: Direct approach from density functional theory

In the framework of the density functional theory (DFT) we develop an approximation in which the energy of a molecule is expressed as a functional of perturbations of the atomic electron densities. The result depends on atomic densities, atomic chemical potentials, and hardness kernels that can be found from the solutions of the appropriate atomic DFT problem. A generalized formulation of the chemical potential (electronegativity) equalization principle is suggested. We show how the energy functional can be transformed into a function of the net charges on atoms and discuss the relationship between our approach and the earlier introduced chemical potential (electronegativity) equalization schemes. We present examples where by approximating density perturbations with the squares of Slater orbitals, we obtain values for the net charges that are in reasonable agreement with experiment. This approach can be used for predictions of the transferred charges in the molecules of any size, and its accuracy can be continuously improved by the use of more accurate approximations to the density perturbations.