EXPLICITLY CONNECTED EXPANSION FOR THE AVERAGE VALUE OF AN OBSERVABLE IN 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 PSI, related to the Fermi vacuum PHI by the exponential Ansatz PSI = e(T)PHI, is expressed as a finite commutator series containing the cluster 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 order-by-order many-body perturbation theory (MBPT) expansion for the expectation values and density matrices. We also show how the commutator expansion derived by us can be used as a basis for size-extensive infinite-order summation techniques. An operator technique of eliminating the nonlocal, ''off-energy shell'' denominators from MBPT expressions is proposed and applied to obtain compact commutator formulas for the expectation values of one- and two-electron operators through the fourth and third order, respectively, and for the correlation energy through the fifth order of perturbation theory. (C) 1993 John Wiley & Sons, Inc.