Frank E. Harris
Department of Physics, University of Utah
Quantum Theory Project, University of Florida
(Submitted to Int. J. Quantum Chem., August 2001).
The use of cumulant expansions for the approximation of reduced density matrices (RDM's) 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 wavefunction. Approximations involved in Mazziotti's recently proposed ``formal solution for reconstruction'' are identified. The behavior of this 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 thereby casts doubt as to the probable effectiveness of Mazziotti's reconstruction scheme.