A Brief Review of Nonrelativistic Density Functional Theory

A Brief Review of Nonrelativistic Density Functional Theory 

Modern DFT is founded on the Hohenberg-Kohn theorems and the Kohn-Sham equations. These are presented in detail in textbooks as well as in the review literature on the subject (Parr and Yang 1989, Koch and Holthausen 2001, Eschrig 1996, Gross and Kurth 1994, Salahub et al. 1994). However, to set the stage for a discussion of the relativistic case, a brief summary of the nonrelativistic foundations serves as a convenient starting point. 

We write the time-independent Hamiltonian for the fV-electron system as 

To prove this theorem we must now show a one-to-one correspondence between i (r) and p r), and we do this using the wave function as an intermediary. Assuming a nondegenerate ground state with energy Eo, the Schrddinger equation 

we conclude that two different densities must correspond to two different potentials, and a nondegenerate ground state can correspond to one and only one potential. 

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