Kohn-Sham Equations

The Kohn-Sham equations are a fundamental part of density functional theory used in quantum chemistry to model how electrons behave in atoms and molecules. Instead of tracking each electron individually, these equations describe a system of non-interacting electrons moving in an effective potential that accounts for their interactions. This approach simplifies complex many-electron problems, allowing accurate calculations of electronic structure and properties with manageable computational effort. Essentially, they help us understand the distribution and energy of electrons in matter by solving equations for non-interacting particles under an effective field generated by all electrons combined.