Cluster perturbation theory. VI. Ground-state energy series using the Lagrangian

Abstract

We have extended cluster perturbation (CP) theory to comprehend the Lagrangian framework of coupled cluster (CC) theory and derived the CP Lagrangian energy series ( L CP) where the 2 n + 1/2 n + 2 rules for the cluster amplitudes and multipliers are used to get the energy corrections. We have also developed the variational CP [Formula: see text] series, where the total cluster amplitudes and multipliers are determined through the same orders as in the L CP series, but the energy is obtained by inserting the total cluster amplitudes and multipliers in the Lagrangian. The energies of the [Formula: see text] series have errors that are bilinear in the errors of the total cluster amplitudes and multipliers. Test calculations have been performed for S(D) and SD(T) orbital excitation spaces. With the exception of molecular systems that have a low lying doubly excited state compared to the electronic ground state configuration, we find that the fourth order models [Formula: see text]( D−4), [Formula: see text]( T−4), and L CPSD( T−4) give energies of CC target state quality. For the [Formula: see text]( D−4) model, CC target state quality is obtained as the [Formula: see text]( D−4) calculation determines more than 99.7% of the coupled cluster singles and doubles (CCSD) correlation energy as the numerical deviations of the [Formula: see text]( D−4) energy from the CCSD energy were more than an order of magnitude smaller than the triples correlation contribution. For the [Formula: see text]( T−4) and L CPSD( T−4) models, CC target state quality was obtained, given that the [Formula: see text]( T−4) and L CPSD( T−4) calculations recover more than 99% of the coupled cluster singles doubles and triples (CCSDT) correlation contribution and as the numerical deviations of the [Formula: see text]( T−4) and L CPSD( T−4) energies from the CCSDT energy were nearly and order of magnitude smaller than the quadruples correlation contribution. We, thus, suggest that the fourth order models may replace the full target CC models with no or very limited loss of accuracy.