Cumulant approach to the direct calculation of reduced density matrices: A critical analysis

In this paper we address a number of topics regarding the contracted Schrodinger equation (CSE): (i) The cumulant expansion of reduced density matrices (RDMs), and the reduction of the CSE to a connected form. (ii) The comparison of the resulting formalism to coupled cluster theory. (iii) The direct calculation of the two-particle RDM in terms of the cumulants, without explicitly imposing any N-representability conditions. We explore a number of approximations, the most elaborate of which is the 3,5-CSE in which the cumulant expansion is carried out to the three-particle level, and the only approximation made is to equate the four- and five-particle cumulants to zero. Overall the numerical results we present for selected small model systems are found to be disappointing and we provide a critical analysis of the perceived shortcomings of our cumulant approach to the CSE. (C) 2003 American Institute of Physics.