Chapter 1 An Introduction to the State of the Art in Quantum Chemistry

Abstract

This chapter presents the state-of-the-art in quantum chemistry. The fundamental building blocks in quantum chemistry are nuclei and electrons. The small electronic mass necessitates the use of quantum mechanics for describing the electron distribution, but the nuclear masses are sufficiently heavy, and hence their motion to a good approximation can be described by classical mechanics. The large difference in mass is the basis for the Born–Oppenheimer approximation, where the coupling between the nuclear and electronic motions is neglected. The variational principle states that an approximate wave function will always have energy higher than the exact wave function and the best wave function can, thus, be determined by minimizing the energy. In an independent particle picture, each electron is described by an orbital and the whole wave function is a product of such orbitals. For large systems, the dominating integrals are those describing the Coulomb interaction among electrons, leading to an overall scaling. In fast-multipole methods, the Coulomb contribution is not calculated by two-electron integrals, but is replaced with the interaction between two electron densities.