Density cumulant theory is an electronic structure method to solve the full configuration interaction problem. The central task of approximations to the method is to efficiently parameterize the cumulant of the rank-two reduced density matrix. After reviewing the full configuration interaction problem and reduced density matrix methods, we study the definition of the cumulant in detail and find that it can be defined in a way extremely similar to coupled cluster theory. We then study ansätze for the parameterization. Approximations of the previously proposed ansatz, which we call OUDCT, are found to lead to a poor description of H2 dissociation. It is shown that the exact method encounters numerically unstable near-zero denominators. We then introduce a new ansatz, in which the parameters of the theory shift from unitary coupled cluster amplitudes to “off-diagonal” elements of the cumulant of arbitrary rank. It is shown that this ansatz is rigorously free of the near-zero denominators. Benchmark results indicate that this ansatz is able to describe H2 dissociation well. However, this ansatz also requires the inclusion of triples to improve equilibriumproperties compared to previously known methods.
