Importance truncation for large-scale configuration interaction approaches

Abstract

We introduce an iterative importance truncation scheme that aims at reducing the dimension of the model space of configuration interaction approaches by an a priori selection of the physically most relevant basis states. Using an importance measure derived from multiconfigurational perturbation theory in combination with an importance threshold, we construct a model space optimized for the description of individual eigenstates of a given Hamiltonian. We discuss in detail various technical aspects and refinements of the importance truncation, such as perturbative corrections for excluded basis states, threshold extrapolation techniques, and different iterative model-space update schemes. We apply the idea of the importance truncation in the context of the no-core shell model (NCSM) for the ab initio description of nuclear ground states. In a series of benchmark calculations for closed- and open-shell nuclei up to $^{16}\mathrm{O}$, we compare the ground-state energies obtained in the importance truncated NCSM to the full NCSM. All calculations show an excellent agreement of importance truncated and full NCSM for all cases where the latter is feasible. The results demonstrate that the importance truncated NCSM, while preserving most of the advantages of the full NCSM, gives access to much larger ${N}_{\mathrm{max}}\ensuremath{\hbar}\ensuremath{\Omega}$ spaces and heavier nuclei. In this way we are able to perform importance truncated NCSM calculations for nuclei such as $^{12}\mathrm{C}$ and $^{16}\mathrm{O}$ up to ${N}_{\mathrm{max}}=22$.