Structure of the exact wave function. III. Exponential ansatz

We continue to study exponential ansatz as a candidate of the structure of the exact wave function. We divide the Hamiltonian into N-D (number of divi sions) parts and extend the concept of the coupled cluster (CC) theory such that the cluster operator is made of the divided Hamiltonian. This is call ed extended coupled cluster (ECC) including N-D variables (ECCND). It is sh own that the S(simplest)ECC, including only one variable (N-D=1), is exact in the sense that it gives an explicit solution of the Schrodinger equation when its single variable is optimized by the variational or H-nijou method . This fact further implies that the ECCND wave function with N(D)greater t han or equal to2 should also have a freedom of the exact wave function. The refore, by applying either the variational equation or the H-nijou equation , ECCND would give the exact wave function. Though these two methods give d ifferent expressions, the difference between them should vanish for the exa ct wave function. This fact solves the noncommuting problem raised in Paper I [H. Nakatsuji, J. Chem. Phys. 113, 2949 (2000)]. Further, ECCND may give more rapidly converging solution than SECC because of its non-linear chara cter, ECCND may give the exact wave function at the sets of variables diffe rent from SECC. Thus, ECCND is exact not only for N-D=1, but also for N(D)g reater than or equal to2. The operator of the ECC, exp(S), is an explicit e xpression of the wave operator that transforms a reference function into th e exact wave function. The coupled cluster including general singles and do ubles (CCGSD) proposed in Paper I is an important special case of the ECCND . We have summarized the method of solution for the SECC and ECCND truncate d at order n. The performance of SECC and ECC2 is examined for a simple exa mple of harmonic oscillator and the convergence to the exact wave function is confirmed for both cases. Quite a rapid convergence of ECC2 encourages a n application of the ECCND to more general realistic cases. (C) 2001 Americ an Institute of Physics.