Comparison of contracted Schrodinger and coupled-cluster theories

The theory of the contracted Schrodinger equation (CSE) [D. A. Mazziotti, P hys. Rev. A 57, 4219 (1998)] is connected with traditional methods of elect ronic structure including configuration-interaction (CI) and coupled-cluste r (CC) theory. We derive a transition contracted Schrodinger equation (TCSE ) which depends on the wave function psi as well as another N-particle func tion chi through the two-, three-, and four-particle reduced transition mat rices (RTMs). By reconstructing the 3 and 4 RTMs approximately from the 2-R TM, the indeterminacy of the equation may be removed. The choice of the rec onstruction and the function chi determines whether one obtains the CI, CC, or CSE theory. Through cumulant theory and Grassmann algebra we derive rec onstruction formulas for the 3- and 4-RTMs which generalize both the reduce d density matrix (RDM) cumulant expansions as well as the exponential ansat z for the CC wave function. This produces a fresh approach to CC theory thr ough RTMs. Two theoretical differences between the CC and the CSE theories are established for energetically nondegenerate states: (i) while the CSE h as a single exact solution when the 3-and 4-RDMs are N-representable, the C C equations with N-representable 3- and 4-RTMs have a family of solutions. Thus, N-representability conditions offer a medium for improving the CSE so lution but not the CC solution, and (ii) while the 2-RDM for an electronic Hamiltonian reconstructs to unique N-repnsentable 3- and 4-RDMs, the 2-RTM builds to a family of N-representable 3- and 4-RTMs. Hence, renormalized re constructions beyond the cumulant expansion may be developed for the 2-RDM but not for the 2-RTM without explicit use of the Hamiltonian. In the appli cations we implement our recently developed reconstruction formula for the 3-RDM which extends beyond the cumulant approximation. Calculations compare the 3-RDM and 3-RTM reconstructions for the molecules LiH, BeH2, BH3, and H2O as well as for systems with more general two-particle interactions. The TCSE offers a unified approach to electronic structure. [S1050-2947(99)018 12-0].