Exploring alternative approaches to improve the convergence pattern in solving the coupled-cluster equations

Abstract

The perturbational parameter λ formally appearing in the coupled-cluster (CC) and perturbation theory (PT) frameworks is included explicitly in the Hamiltonian and the CC formalism. Using the Møller–Plesset (MP) partitioning, properties of the resulting λ-dependent amplitude functions are discussed. Truncating the cluster expansion at singles and doubles (CCSD), we use these properties and knowledge of the CCSD amplitudes at values to estimate the CCSD amplitudes without solving the relevant equations at (corresponding to the original, physical problem). This extrapolation scheme is explored, with emphasis on convergence improvement of CC iterations. The approximate amplitudes generated by this procedure are used as the starting point for the CCSD iterations, an alternative to the first order MP (MP1) set. Numerical examples are presented which show that the technique combined with the direct inversion in the iterative subspace (DIIS) method is especially helpful in situations where the standard CCSD iterations converge slowly or not at all. We report cases where starting from MP1, the solution process has an unfavourable convergence pattern even with DIIS applied, while the amplitudes generated by our method provide a much better starting point, overcoming the divergence issues of the original sequence.