  In a recent paper [JCTC, 2020, 16, 6098], we introduced a new approach for
accurately approximating full CI ground states in large electronic
active-spaces, called Tensor Product Selected CI (TPSCI). In TPSCI, a large
orbital active space is first partitioned into disjoint sets (clusters) for
which the exact, local many-body eigenstates are obtained. Tensor products of
these locally correlated many-body states are taken as the basis for the full,
global Hilbert space. By folding correlation into the basis states themselves,
the low-energy eigenstates become increasingly sparse, creating a more compact
selected CI expansion. While we demonstrated that this approach can improve
accuracy for a variety of systems, there is even greater potential for
applications to excited states, particularly those which have some excited
state character. In this paper, we report on the accuracy of TPSCI for excited
states, including a far more efficient implementation in the Julia programming
language. In traditional SCI methods that use a Slater determinant basis,
accurate excitation energies are obtained only after a linear extrapolation and
at a large computational cost. We find that TPSCI with perturbative corrections
provides accurate excitation energies for several excited states of various
polycyclic aromatic hydrocarbons (PAH) with respect to the extrapolated result
(i.e. near exact result). Further, we use TPSCI to report highly accurate
estimates of the lowest 31 eigenstates for a tetracene tetramer system with an
active space of 40 electrons in 40 orbitals, giving direct access to the
initial bright states and the resulting 18 doubly excited (biexcitonic) states.
