Generalized k-particle brillouin conditions and their use for the construction of correlated electronic wavefunctions

The variational form of the Schrödinger equation is shown to be equivalent to a set of generalized Brillouin conditions in terms of arbitrary antihermitean operators R. For a special choice of these R in second-quantization language, k-particle Brillouin conditions are derived that are a generalization of the “generalized one-particle Brillouin conditions” of Levy and Berthier. The application of these conditions to one-particle and two-particle hamiltonians is discussed. A two-particle generalization of the Fock operator is derived and an iterative variational pair-cluster scheme is derived. It is shown that CEPA and SCEP methods satisfy an approximate rather than an exact set of Brilouin conditions.