Density functional theory

The Schrödinger wave equation, H EΨ Ψ= , is definitely a work of genius based on the very origin of physics. Unfortunately, the equation is useful in practice only for the simplest systems due to the underlying difficulties of the many-body quantum effect. People often say that first-principles methods require only a single set of input data, the atom number, and nothing else for the calculation. This is true in principle, but the reality is not as simple as the statement sounds. The reason is that the wave equation is a partial differential equation that depends on the 3n coordinates of n electrons. Even if we knew how to do such a calculation, a computer that can handle such a massive task is not available, and this will be true no matter how fast computers may be in the future.