Chemical potential equalization in the 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 on the atomic densities. The result depends on atomic densities, atomic chemical potentials, and atomic 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. With the help of this approximation we obtain the values of the net charges for a number of heteronuclear molecules with the average error of only 5.4% compared to the experimental data. Our approach also allows us to treat homonuclear diatomics in the same way as heteronuclear.; We discuss the forms of the atomic hardness kernels that enter our energy expression and apply our approach to the problem of finding the response of molecules to an applied field. This scheme is used for calculations of atomic and molecular dipole polarizabilities. We report the results of calculations of polarization tensor components for several polyatomic planar molecules which are in a good agreement with the experiment.; We also show that the variational principle in the Density Functional Theory can be substituted by a set of variational principles for the spatial domains provided that special natural boundary conditions are satisfied on each boundary. We develop a perturbative approach which allows us to express the energy of a molecule through only the characteristics of free atoms. We show that when different approximations to the energy functional are made in different parts of space, the satisfaction of the natural boundary conditions becomes essential for providing the minimum of the energy. We conclude that important changes to the earlier introduced chemical potentials (electronegativity) equalization models are needed in order to correctly describe charge distributions in large molecules.