Energy Principle of Atomic and Molecular Systems

The fundamental equation to describe condensed matter physics, quantum chemistry, or molecular biology is well known, which is no other than the Schrodinger equation, but it is in general too complicated to solve. The difficulty is often suggested as due to Coulomb interactions, leading to ingenious methods, for example, the density functional theory to model the electron-electron interaction, and the pseudopotential theory to model the electron-ion interaction. However, the electron-ion interaction relies on the one-body electron distribution, and the electron-electron interaction the two-body. It is shown that the electron kinetic energy cannot be reduced to few-body interactions from the many-body without incurring an error, since a particle in the many-body environment encounters more spatial bumpiness due to collisions with neighboring particles to thus jack up its kinetic energy. The correlation and coherence effect, the Slater´s determinant, the virial theorem, effective and pseudo potentials, and their applications to simple atoms and molecules are discussed.