Kohn-Sham method
The most majorly-used calculation methodology based on density functional theory (DFT). The Kohn-Sham method was developed to provide a good approximation for the kinetic energy of many-electron systems, which was found to be very difficult when trying to parametrize as a pure (orbital-free) density functional. The kinetic energy, which holds the largest portion of the total energy, is approximated by the kinetic energy of a reference noninteracting system with the same electron density. The rest of the total energy was assigned to the exchange-correlation energy functional, and as a result, the many-body problem was reformulated as a system of single-electron Schroedinger-like equations (Kohn-Sham equations) in an effective potential.