Structure of the exact wave function. II. Iterative configuration interaction method

This is the second progress report on the study of the structure of the exa ct wave function. First, Theorem II of Paper I (H. Nakatsuji, J. Chem. Phys . 113, 2949 (2000)) is generalized: when we divide the Hamiltonian of our s ystem into N-D (number of division) parts, we correspondingly have a set of N-D equations that is equivalent to the Schrodinger equation in the necess ary and sufficient sense. Based on this theorem, the iterative configuratio n interaction (ICI) method is generalized so that it gives the exact wave f unction with the N-D number of variables in each iteration step. We call th is the ICIND method. The ICIGSD (general singles and doubles) method is an important special case in which the GSD number of variables is involved. Th e ICI methods involving only one variable [ICION(one) or S(simplest)ICI] an d only general singles (GS) number of variables (ICIGS) are also interestin g. ICIGS may be related to the basis of the density functional theory. The convergence rate of the ICI calculations would be faster when N-D is larger and when the quality of the initial guess function is better. We then stud y the structure of the ICI method by expanding its variable space. We also consider how to calculate the excited state by the ICIGSD method. One metho d is an ICI method aiming at only one exact excited state. The other is to use the higher solutions of the ICIGSD eigenvalues and vectors to compute a pproximate excited states. The latter method can be improved by extending t he variable space outside of GSD. The underlying concept is similar to that of the symmetry-adapted-cluster configuration-interaction (SAC-CI) theory. A similar method of calculating the excited state is also described based on the ICIND method. (C) 2001 American Institute of Physics.