Quantum chemistry in Fock space. IV. The treatment of permutational symmetry. Spin-free diagrams with symmetrized vertices

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Abstract
The theory of effective Hamiltonians in Fock space is extended by the use of spin-free basis operators as well as vertices (matrix elements) that are adapted to the permutation group. This reduces the number of the necessary operators considerably, especially for operators of high particle rank. An extension of the generalized Wick theorem of spin-free quantum chemistry to permutation symmetry adapted operators is presented and illustrated graphically. The second order diagrams for the energy and the fully contracted (vacuum) diagrams to third and fourth order are given explicitly. The diagram symmetry group GD that consists of line exchanges at the vertices and permutations of external lines is studied in detail and a recipe for the construction of permutation symmetry adapted diagrams with spin-free symmetrized vertices is derived. The use of permutation symmetry in nonperturbative approaches is discussed and the construction of the matrix elements for the final CI is illustrated. In this formalism there is no need for spin algebra.