Development of density cumulant functional theory

Ab initio quantum chemistry has been dominated by the wavefunction-based approaches to electron correlation. Alternatively, methods that seek approximate solutions in terms of the reduced density matrices (RDMs) have been developed. RDM methods circumvent the computation of the many-electron wavefunction, but have been shown to incorrectly describe the separability into non-interacting molecular fragments and scaling of the energy with the number of electrons. Recently, a new approach to electron correlation called density cumulant functional theory (DCFT) was proposed that eliminates these shortcomings. Herein, we present new developments of DCFT extending the applicability of the theory. We begin by deriving and implementing the analytic energy gradients for the original DCFT method. We then formulate a new DCFT method with the improved description of the one-particle density matrix. Finally, a new orbital-optimized DCFT formulation is proposed and implemented. We offer a perturbative analysis of the new methods and benchmark their performance for a variety of chemical systems.