EXPLICITLY CONNECTED EXPANSION FOR THE AVERAGE VALUE OF AN OBSERVABLEIN THE COUPLED-CLUSTER THEORY

An explicitly connected commutator expansion for the average value of an observable in the coupled-cluster theory is derived. Specifically, it is shown that the expectation value of an operator for the state PS I, related to the Fermi vacuum PHI by the exponential Ansatz PSI = e(T )PHI, is expressed as a finite commutator series containing the cluste r operator T and an auxiliary operator S, defined by a linear equation involving again a finite commutator series in T. The above result is applied to derive the explicitly connected commutator form of the orde r-by-order many-body perturbation theory (MBPT) expansion for the expe ctation values and density matrices. We also show how the commutator e xpansion derived by us can be used as a basis for size-extensive infin ite-order summation techniques. An operator technique of eliminating t he nonlocal, ''off-energy shell'' denominators from MBPT expressions i s proposed and applied to obtain compact commutator formulas for the e xpectation values of one- and two-electron operators through the fourt h and third order, respectively, and for the correlation energy throug h the fifth order of perturbation theory. (C) 1993 John Wiley & Sons, Inc.