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In a recent paper [JCTC, 2020, 16, 6098], we introduced a new approach foraccurately approximating full CI ground states in large electronicactive-spaces, called Tensor Product Selected CI (TPSCI). In TPSCI, a largeorbital active space is first partitioned into disjoint sets (clusters) forwhich the exact, local many-body eigenstates are obtained. Tensor products ofthese 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 compactselected CI expansion. While we demonstrated that this approach can improveaccuracy for a variety of systems, there is even greater potential forapplications to excited states, particularly those which have some excitedstate character. In this paper, we report on the accuracy of TPSCI for excitedstates, including a far more efficient implementation in the Julia programminglanguage. In traditional SCI methods that use a Slater determinant basis,accurate excitation energies are obtained only after a linear extrapolation andat a large computational cost. We find that TPSCI with perturbative correctionsprovides accurate excitation energies for several excited states of variouspolycyclic aromatic hydrocarbons (PAH) with respect to the extrapolated result(i.e. near exact result). Further, we use TPSCI to report highly accurateestimates of the lowest 31 eigenstates for a tetracene tetramer system with anactive space of 40 electrons in 40 orbitals, giving direct access to theinitial bright states and the resulting 18 doubly excited (biexcitonic) states.

Generalization of the tensor product selected CI method for molecular excited states