Density functional theory (developed by Hohenberg, Kohn, and Sham [1,2]) gives a relatively simple prescription for the total energy of a system of electrons and nuclei. For the purpose of this course, you may take this discussion as giving our basic postulates of quantum mechanics. (For a more fundamental discussion, you may wish to consider Phys 683.)
There are two basic types of energy which we must consider, potential energy and the kinetic of the electrons. (Remember that we regard the nuclei as stationary.) We begin below in Section 3.1 with the potential energy, which classical electrostatic theory describes quite well. Then, to deal with the kinetic energy, we will have to introduce quantum mechanics in Section 3.2.