Density cumulant functional theory: the DC-12 method, an improved description of the one-particle density matrix

Density cumulant functional theory (DCFT) is a theory that, in principle, can compute energies and properties exactly without a wavefunction. To accomplish this, the energy is expressed as an exact, known functional of the one-particle density matrix and two-particle density cumulant. The correlation contribution to the one-particle density matrix is obtained from the cumulant, to eliminate redundancy in the equations. The previous formulation of DCFT introduced this relationship in an approximate way, to obtain tractable equations. In this research, it is demonstrated that the correlation contribution to the one-particle density matrix can be extracted exactly from the cumulant, with minimal computational overhead and no increase in the asymptotic cost of the theory. We present numerical results, showing the improvements resulting from this reformulation (DC-12), and offer a perturbative analysis of the new equations to compare them to their predecessors.