Cluster relations for multireference coupled-cluster theories: A model study

Abstract

The validity of various coupled-cluster conditions, that were recently formulated for both the valence-universal open-shell coupled-cluster theory based on Lindgren’s exponential ansatz and the state-universal theory employing the Jeziorski–Monkhorst ansatz, are examined for two model systems consisting of two and four slightly stretched, interacting hydrogen molecules. These cluster conditions ascertain the possibility to represent four-electron terms in the wave operator through appropriate products of two-electron terms and thus justify the truncation of the open-shell cluster operators employed to at most two-electron terms. A single parameter that determines the geometry of the studied model systems makes it possible to continuously vary the extent of quasidegeneracy between the two lowest energy states over a wide range. It is shown that the cluster conditions are relatively well satisfied only in the strongly quasidegenerate region, except for a few very small amplitudes whose effect on the resulting energies should be insignificant. To assess the validity of the often made assumption of negligibility of one-electron amplitudes, the generalized cluster conditions involving these terms were also examined. The role played by these additional terms was shown to be small. Finally, in the valence-universal case, the role of orbital choice was also investigated by performing cluster analysis with both system and core spin orbitals. The effect of using different orbital alternatives was again found to be small.