Selected Configuration Interaction in a Basis of Cluster State Tensor Products

Abstract

Selected configuration interaction (SCI) methods are currently enjoying a resurgence due to several recent developments which improve either the overall computational efficiency or the compactness of the resulting SCI vector. These recent advances have made it possible to get full CI (FCI) quality results for much larger orbital active spaces, compared to conventional approaches. However, due to the starting assumption that the FCI vector has only a small number of significant Slater determinants, SCI becomes intractable for systems with strong correlation. This paper introduces a method for developing SCI algorithms in a way which exploits local molecular structure to significantly reduce the number of SCI variables. The proposed method is defined by first grouping the orbitals into clusters over which we can define many particle cluster states. We then directly perform the SCI algorithm in a basis of tensor products of cluster states instead of Slater determinants. While the approach is general for arbitrarily defined cluster states, we find significantly improved performance by defining cluster states through a self-consistent Tucker decomposition of the global (and sparse) SCI vector. To demonstrate the potential of this method, called tensor product selected configuration interaction (TPSCI), we present numerical results for a modified Hubbard model with different inter- and intra-cluster hopping terms. We also study the less obviously clusterable cases of bond breaking in N2 and CO and also singlet-triplet gaps in planar {\pi}-conjugated systems. Numerical results show that TPSCI can be used to reduce the number of variables in the variational space quite significantly as compared to other selected CI approaches.