Brillouin's theorem
Theorem in quantum chemistry / From Wikipedia, the free encyclopedia
In quantum chemistry, Brillouin's theorem, proposed by the French physicist Léon Brillouin in 1934, relates to Hartree–Fock wavefunctions. Hartree–Fock, or the self-consistent field method, is a non-relativistic method of generating approximate wavefunctions for a many-bodied quantum system, based on the assumption that each electron is exposed to an average of the positions of all other electrons, and that the solution is a linear combination of pre-specified basis functions.
![]() | This article may be too technical for most readers to understand. (July 2013) |
The theorem states that given a self-consistent optimized Hartree–Fock wavefunction , the matrix element of the Hamiltonian between the ground state and a single excited determinant (i.e. one where an occupied orbital a is replaced by a virtual orbital r) must be zero.
This theorem is important in constructing a configuration interaction method, among other applications.
Another interpretation of the theorem is that the ground electronic states solved by one-particle methods (such as HF or DFT) already imply configuration interaction of the ground-state configuration with the singly excited ones. That renders their further inclusion into the CI expansion redundant.[1]