Time-reversal symmetry in general coupled cluster theory

In this paper, the symmetry property of time reversal, which is a consequence of the fundamental quantum-mechanical microreversibility principle, is analyzed in the context of relativistic open-shell and multireference coupled cluster theory. The fact is discussed that in projective theories, in contrast to variational theories such as configuration interaction models, the implementation of time-reversal symmetry is far less straightforward and even depends on the projective model theory in question. An operator basis of time reversal even n-body operators is introduced which allows for the formulation of a fully time-reversal-adapted and practical general coupled cluster theory, i.e., covering open-shell models and various types of multireference approaches. The resulting model theory is noncommuting but truncating, albeit at a higher order of commutator nesting.