In addition, the Kohn-Sham approach to the interacting electrons problem is to rewrite the Hohenberg-Kohn expression for the energy functional corresponding to the ground state as follows:

(79) |

where is the kinetic energy of the non-interacting electron system. is the energy due to the external potential (external potential means that it is due to the atomic nuclei), and it has the following form:

(80) |

is the Hartree energy, which can be expressed as a functional of the electron density of the system as follows:

(81) |

and finally, is the so called exchange correlation energy term which includes "all remaining" contributions.

We have to note that in practice the correct term is unknown, for this reason the determination of such functional requires some approximation, and it is this approximation which determines the accuracy of the method.

Rocio Yanes