A coupled‐cluster method for quasidegenerate states

Abstract

A size-extensive, multireference coupled-cluster method for studies of quasidegenerate states based on the Jeziorski-Monkhorst [16] ansatz for the cluster operator (a = SeqP,, where the sum is extended over the configurations spanning the model space), is presented and applied in pilot calculations. The method is referred to as multireference coupled electron-pair method (MR CEPM), because it is assumed that the individual cluster operators can be approximated by their two-body parts, i.e., T, == T,(2). The linear version of this method (MR L-CEPM) is also discussed. Both methods are applied to two simple model systems: (1) a minimum basis set model involving eight hydrogen atoms in various spacial arrangements for which the degree of quasidegeneracy can be continuously varied; (2) The usefulness of the cluster ansatz for representing the wave function in the many-fermion theory became apparent from the work of Hubbard [ 11 almost 30 years ago. Since then much work has been invested into the development of size-extensive [2,3] methods of approximately solving the Schrodinger equation which are based on this ansatz. Let us just mention the pioneering work of Coester and Kumme1 [4] in the nuclear many-body problem, followed by that of hick [5] in the many-electron theory of atomic and molecular systems. Extensive reviews of both methodological and computational developments of these methods, known as coupled-cluster (cc) methods, are currently available [6-91. Due to the developments just mentioned, various versions of the cc approach have become broadly used standard ab initio methods for electron correlation studies in many-electron closed-shell states. Unfortunately, the generalization of cc methods to the non-closed-shell case, i.e., to quasidegenerate and open-shell states, turned out to be a very difficult problem. Despite the progress achieved during the present decade, for quasidegenerate states the cc methods are still rather far from becoming a reliable standard tool of contemporary quantum chemistry. Since the cluster ansatz may be considered as a very compact representation of a perturbation expansion, the problems encountered

To Multireference or not to Multireference: That is the Question?

“…The MR-LCCM method was influenced by some comments of Paldus [75]. The second, its approximate quadratic extension, has much in common with MR-ACPF (multi-reference averaged coupled-pair) method [76], but uses a different way of counting pairs due to Meissner [77]. Both are examples of approximate state-specific MRCC, as our objective is a single state as in the other examples discussed in this section.…”

A Critical Assessment of Coupled Cluster Method in Quantum Chemistry

“…The fact that the highest valence rank component appears linearly in a given U/< permits a decoupling and thus a successive calculation of higher and higher valence rank components [256]. However, when S is truncated at the pair cluster level, a consideration of at least selective three-body amplitudes of the spectator type is called for [95,228].…”

“…As far as we know, there is no general-purpose implementation of the VU CC method, although numerous applications [ 142, and pilot studies [95,228,260] have been carried out. A two-reference spin-orbital version designed to handle excited states of closed-shell systems is also available [89,230].…”

Reciprocal adjustment of approximate coupled cluster and configuration interaction approaches

“…We can conjecture that all three approaches should yield rather accurate correlation energies, even in quasidegenerate situations, assuming that the MR CISD is large enough to incorporate important nondynamic correlation effects. In the next section we compare the performance of these approximations using several illustrative examples, particularly the simple H 4 [35,36] and H 8 [37] models enabling us to explore the situations with varying degree of quasidegeneracy.…”