Efficient calculation of RPA correlation energy in the Adiabatic Connection Fluctuation-Dissipation Theory

After this short Introduction, we will present in Chapter 1 basic concepts of electronic structure theory with emphasis on Density Func- tional Theory in the plane-wave pseudopotential approach. The failure of LDA and GGAs for van der Waals systems and the need for the development of new approaches will be discussed at the beginning of Chapter 2. We then will recall the formalism by which exchange and correlation energies of an electronic system can be expressed in term of linear response functions through an exact formula. Our efficient implementation for the calculation of correlation energy in the RPA is also described here with some technical details of its implementation in plane-wave pseudopotential method. To validate the implementation and to improve its efficiency, we have chosen bulk silicon system as the test ground to perform a detailed analysis of relevant issues. We will then apply our approach to study the system of Beryllium dimer where LDA or GGA fails qualitatively. Although EXX/RPA+ study of this system has been performed in the past [12], we will show that our calculation is more accurate and the result will demonstrate that in fact special care must be taken in the calculation of both exact-exchange and RPA correla- tion energies. Chapter 3 will be devoted to the discussion of approximate linear response functions using the non-interacting Thomas–Fermi–von Weizs ̈acker kinetic energy func- tional. Applications of the methods described in Chapter 2 and Chapter 3 to study some test cases will be shown in Chapter 4. We will first present the results and comparisons for the asymptotic long-range interactions via van der Waals coefficients of atoms and molecules calculated both from exact and approximate response functions. We will also demonstrate the efficiency of our implementation of ACFD formula for the calculations of correlation energy of atomic systems. The potential of TFvW approximation to capture the essence of long range correlations will be discussed on the basis of the results of correlation energies obtained for atomic and molecular systems.