Formulation and implementation of direct algorithm for the symmetry-adapted cluster and symmetry-adapted cluster–configuration interaction method

Abstract

We present a new computational algorithm, called direct algorithm, for the symmetry-adapted cluster (SAC) and SAC-configuration interaction (SAC-CI) methodology for the ground, excited, ionized, and electron-attached states. The perturbation-selection technique and the molecular orbital index based direct sigma-vector algorithm were combined efficiently with the use of the sparse nature of the matrices involved. The formal computational cost was reduced to O(N(2)xM) for a system with N-active orbitals and M-selected excitation operators. The new direct SAC-CI program has been applied to several small molecules and free-base porphin and has been shown to be more efficient than the conventional nondirect SAC-CI program for almost all cases. Particularly, the acceleration was significant for large dimensional computations. The direct SAC-CI algorithm has achieved an improvement in both accuracy and efficiency. It would open a new possibility in the SAC/SAC-CI methodology for studying various kinds of ground, excited, and ionized states of molecules.