KohnShamconstructies

KohnShamconstructies, often referred to as Kohn-Sham calculations or Kohn-Sham DFT, is a theoretical method used in quantum chemistry and condensed matter physics to approximate the electronic structure of many-electron systems. It is a cornerstone of density functional theory (DFT). The core idea behind Kohn-Sham DFT is to transform the problem of solving the complex many-electron Schrödinger equation into a problem of solving a set of simpler, fictitious single-electron equations, known as Kohn-Sham equations.

These Kohn-Sham equations are constructed such that the exact ground-state density of the real interacting system is reproduced by the density of a fictitious system of non-interacting electrons. This fictitious system has the same ground-state density as the real system, but its energy is expressed in terms of single-particle orbitals. The key to the method lies in the definition of the kinetic energy and potential terms within these equations. The kinetic energy is approximated using a non-interacting kinetic energy functional, while the exchange-correlation potential accounts for the complex many-body effects, including electron-electron interactions and the difference between the true kinetic energy and the non-interacting kinetic energy.

The accuracy of Kohn-Sham constructies is highly dependent on the quality of the approximation used for the exchange-correlation functional. Various functionals have been developed over the years, ranging from simple local density approximations (LDA) to more sophisticated generalized gradient approximations (GGA) and hybrid functionals, each offering different balances of accuracy and computational cost. Despite the approximations, Kohn-Sham DFT has proven to be a remarkably versatile and computationally efficient tool for studying a wide range of properties of molecules, solids, and other materials.