Structure of the exact wave function. IV. Excited states from exponential ansatz and comparative calculations by the iterative configuration interaction and extended coupled cluster theories

摘要

In a previous paper of this series [Paper III: Nakatsuji, J. Chys. 105, 2465 (2001)], the author showed a high poteniiality of the extended coupled cluster (ECC) method to calculate the exact wave function of the groupnd state. In this paper, we propose ECC-configuration interaction (CI) method, which is an accurate useful method to calculate the excited states from te ECC wave function of the ground state. In contrast to the ECC method, the standard ECC-CI method is approximate, but we can make it exact by generalizing its excitation operator (ECC-CI general). The ECC-CI method is applicable not only to the excited states having the same spin-space synmetry as the ground state, but also to those having different spin-space symmetries and to the ionized and electron-attached states. The theoretical framework of the ECC-CI method is similar to that of the symmetry-adapted-cluster (SAC)-CI method proposed in 1978 by the present author. Next in this paper, we examine the performance of the methods proposed in this series of papers for a simple one-dimensional harmonic oscillator. The iterative configuratio interaction (ICI) and ECC methods are examined for the gound state and the ICI-CI methods for the excited states. The ICI method converges well to the exac ground state and the excited states are calculated nicely by the ICI-CI method in both the standard and general active spaces. In contrast to the simplest (S)ECC examined in Paper III, the ECC2 method shows quite a rapid convergence o the exact ground state, which enables us to calculate the true exact wave function in the ECC form. The ECC-CI methods in both the standard and general active spaces also work well to calculate the excited states. Thus, we conclude that the ICI and ECC approaches have a potentiality to provide useful method to calculate accurate wave function of the ground and excited states. A merit of ECC is that it provides the exact wave function in a simple explicit form.