Selected Configuration Interaction in a Basis of Cluster State Tensor Products

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 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 diverse set of examples: (1) modified Hubbard model
with different inter- and intracluster hopping terms, (2) less obviously
clusterable cases of bond breaking in N2 and F2, and (3) ground state energies of large planar π-conjugated
systems with active spaces of up to 42 electrons in 42 orbitals. These
numerical results show that TPSCI can be used to significantly reduce
the number of SCI variables in the variational space, thus paving
a path for extending these deterministic and variational SCI approaches
to a wider range of physical systems.