Efficiency of a Multi-Reference Coupled Cluster method

Abstract: The multi-reference Coupled Cluster method first proposed by Meller et al (J. Chem. Phys. 1996) has been implemented and tested. Guess values of the amplitudes of the single and double excitations (the ${\hat T}$ operator) on the top of the references are extracted from the knowledge of the coefficients of the Multi Reference Singles and Doubles Configuration Interaction (MRSDCI) matrix. The multiple parentage problem is solved by scaling these amplitudes on the interaction between the references and the Singles and Doubles. Then one proceeds to a dressing of the MRSDCI matrix under the effect of the Triples and Quadruples, the coefficients of which are estimated from the action of ${\hat T}^2$. This dressing follows the logics of the intermediate effective Hamiltonian formalism. The dressed MRSDCI matrix is diagonalized and the process is iterated to convergence. The method is tested on a series of benchmark systems from Complete Active Spaces (CAS) involving 2 or 4 active electrons up to bond breakings. The comparison with Full Configuration Interaction (FCI) results shows that the errors are of the order of a few milli-hartree, five times smaller than those of the CASSDCI. The method is totally uncontracted, parallelizable, and extremely flexible since it may be applied to selected MR and/or selected SDCI. Some potential generalizations are briefly discussed.