n-Electron problem and its formulation in terms of k-particle density cumulants



Approaches to the solution of the n-electron problem in terms of the reduced k-particle density matrices γk or their cumulants λk are critically reviewed. The advantages of a cumulant-based theory are outlined, especially its extensivity, which implies a connected-diagram theorem. A perturbative analysis of the hierarchy of k-particle approximations, based on the irreducible contracted Schrödinger equations (ICSEk) (which are conditions for the stationarity of the energy), reveals that the three-particle approximation is necessary to obtain the energy correct to the MP2 (second-order Møller–Plesset) level. This disqualifies the naive use of the k-particle hierarchy, in a linearly converging iterative scheme, as ineffective (compared, e.g., to coupled-cluster theory). A promising alternative is, however, a quadratically convergent iterative scheme based on successive unitary transformations in Fock space. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003