BrillouinWignerAnsätze

BrillouinWignerAnsätze refer to a class of methods used in quantum chemistry and physics to approximate the ground-state and excited-state wave functions of a quantum system. These ansätze are based on the concept of excitation operators acting on a reference state, typically the Hartree-Fock determinant. The Brillouin-Wigner formulation is distinct from other configuration interaction methods like Møller-Plesset perturbation theory in its treatment of the energy denominator and the inclusion of size-extensive corrections.

The core idea is to express the true many-body wave function as a linear combination of Slater determinants. These determinants are generated by applying creation operators (which add electrons to orbitals) to a reference determinant. The coefficients of this linear combination and the energy of the system are then determined by solving a set of secular equations derived from the time-independent Schrödinger equation. A key feature of Brillouin-Wigner ansätze is their iterative nature.

The "Brillouin-Wigner" name originates from the fact that these methods are closely related to Brillouin-Wigner perturbation theory, which also involves excitation operators. However, ansätze offer a more direct variational or iterative approach to finding the wave function and energy, rather than relying on an expansion in a small parameter. Different levels of approximation exist, such as singles, doubles, triples, etc., corresponding to the maximum number of excitations considered from the reference state. These methods are computationally intensive, with the cost increasing rapidly with the size of the system and the level of excitation included. Despite their complexity, they can provide accurate descriptions of electron correlation.