Electronic Structure Calculations Via Density Functional Theory

1 Electronic Structure Calculations Via Density Functional Theory 

The basic building blocks of the materials world are electrons and nuclei interacting via electrostatic Coulomb interactions. Thus, the starting point of a theoretical treatment of the chemical and physical properties of materials is the Hamiltonian 

Other potentials representing (external) fields (e.g., electric or magnetic) that act on the electronic degrees of freedom may be included in the external potential. Note that for a single-body (that is, one electron) problem only the external potential (and the kinetic energy operator) act on the one-electron wave function. 

For a given nuclear configuration [i.e., given external potential (1.16)], the solution of (1.13) is the many-body wave function from which observables can be calculated, including the particle density (which will play a key role in what follows) 

The above scheme which constitutes the usual quantum-mechanical approach may be summarized schematically as follows 

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