Projected BCS Tamm‐Dancoff method for molecular electronic structures

Abstract

AbstractA new Tamm–Dancoff method for the ground and excited states of molecular electronic systems is developed. The method begins with a number‐projected BCS (PBCS) wave function and is generated by excitations of particle pairs from the degenerate geminals in the PBCS wave function. A direct optimization of the PBCS wave function is accomplished with successive Bogoliubov transformations so that one‐pair excitation terms in the Tamm‐Dancoff expansion of the ground state vanish (the generalized Brillouin theorem). The spin‐symmetry adapted first‐ and second‐order Tamm–Dancoff bases and matrix elements are calculated by means of the CI expansion of the PBCS wave function with natural orbitals that diagonalize the BCS geminal matrix. Numerical calculations are presented for the H4 system with D2h and D4h conformations and for methylene. The PBCS wave function is not a very good approximation for the ground state, accounting for only about half of the correlation energy. The second‐order Tamm–Dancoff correction improves the result as much as the double excitation CI. The Tamm–Dancoff terms consisting of two triplet pairs coupled to a singlet, and those relaxing the constraint imposed on the pairwise excitations in the PBCS wave function are important.