Inhomogeneous electron gas

Shobhana Narasimhan’s article ‘A Tryst With Density’ in this issue of Resonance describes a remarkable theorem proved by Hohenberg and Kohn in 1964, and its aftermath. These authors considered a system of electrons in an external potential. This is an excellent idealised model of an atom, molecule or solid because the nuclei are so much heavier than the electrons and can be treated as an external potential. The difficulty lies in accounting for the interaction between the electrons – what one electron is doing depends on what all the others are doing. It therefore came as a shock when the ground state energy of this very general and nontrivial system was shown by Hohenberg and Kohn to be the result of minimising an expression which only contained a function of three variables. This function was just the number of electrons per unit volume as a function of position, something which chemists and crystallographers had long dealt with as a very meaningful and measurable quantity. The theorem showed that such an expression exists, but did not provide the form, which could contain nonlinear terms, derivatives, and integrals of the electron density. While approximate theories of this kind had been proposed before, it was unexpected that the idea of using the electron density could be made exact. What a marvellous turn of events that an existence theorem, proved by contradiction in a modestly written paper would revolutionise the modeling of materials half a century later and win a Nobel Prize in Chemistry for one of the authors