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

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.