Many-body similarity transformations generated by normal ordered exponential excitation operators

Abstract

Normal ordered exponential operators have been used extensively in open-shell formulations of coupled cluster theory. The inverse of such an operator is known to exist, but a closed form explicit expression for the inverse is not available. We will address the evaluation of many-body similarity transformations generated by normal ordered exponential transformation operators without explicit use of the inverse. The similarity transform can be obtained as the solution of a linear system of equations that can be solved trivially using backward substitution. In addition a closed form diagrammatic expression for the similarity transformed operator is presented. Using the many-body similarity transformation strategy a simple and more general formulation of Fock space coupled cluster theory is presented which is akin in spirit to the formulation by Stolarczyk and Monkhorst [Phys. Rev. A 32, 725, 743 (1985); 37, 1908, 1926 (1988)], but which on the other hand is completely equivalent to the conventional wave operator formulation of Fock space coupled cluster theory (under suitable conditions). Other possible applications of the many-body similarity transformation will be briefly discussed.