Studies in density functional theory

The first chapter begins with reviews of density-functional theory and Green's function method. The connections between these two theories are emphasized. Then we present an approximate model of kinetic energy functional and a possible form of the universal functional is given through an equality obeyed by true ground state densities.; Chapter two is aimed at developing a general formulation of the response function in density-functional theory. We first give our definition of response functions in the context of functional derivative. The parameter-differentiation technique employed greatly reduces the efforts for computations. The advantage of this method is its numerical simplicity. It is also the aim of this chapter to elucidate the connections between exchange-correlation potential and the response functions. We show that the computations of response functions in the Kohn-Sham formulation will be exact if the so-called uniqueness assumption we present here is true. Various integral formulas for nonlinear response functions are derived here for the first time.; In the third chapter we demonstrate that the exchange-correlation functional given in the form of Pade approximation to gradient expansion approximation, yields excellent results when applied to atoms. The coefficients for the Pade approximation are derived by numerical fits to the exchange and exchange-correlation energies of the atoms He through Ar. The fitted non-local gradient corrections are used in the minimization of the Kohn-Sham functional to solve for the exchange and exchange-correlation total energies. The resulting standard deviations in the calculated total energies are 0.0043 for exchange only and 0.0014 for exchange-correlation.; The conjoint relation of kinetic and exchange energy functionals is proposed in the fourth chapter. Supportive evidence is given numerically and theoretically. Test cases are the second-row atoms and a group of small molecules with Becke equivalent form, and twelve closed-shell atoms with Pade form.; In the last chapter, the redefined HSAB principle is stated as: Among the potential partners of a given chemical potential, hard likes hard and soft likes soft. A proof is given of this principle. The proof assumes that each of two interacting species prefers a state of minimum grand potential, and this new idea is discussed.