Cumulant-based approximations to reduced density matrices

The use of cumulant expansions for the approximation of reduced density matrices (RDMs) is reviewed. It is pointed out that the oft-cited theorems of Nakatsuji and Rosina are insufficient to guarantee either N-representability or that an N-representable RDM has a unique antecedent wave function. Approximations involved in Mazziotti's recently proposed formal solution for reconstruction are identified. The behavior of his scheme, and of an older one in which all cumulants beyond the second are neglected, are illustrated by detailed examination of a model problem. The limited experience provided by this example casts doubt as to the probable effectiveness of Mazziotti's reconstruction scheme. (C) 2002 Wiley Periodicals, Inc. Int.