Fragment-Based Configuration Interaction: Towards a Unifying Description of Biexcitonic Processes in Molecular Aggregates

TL;DR

This work delivers a unified, first-principles framework for biexcitons in molecular aggregates by introducing fragment-based configuration interaction (CI) methods that span both one-particle ($LE$, $CT$) and two-particle ($LELE$, $CTCT$, $TT$, $CTX$) manifolds. It presents two complementary realizations: SymbolicCI, which builds analytic, fragment-local CI Hamiltonians in a scalable, spin-adapted basis, and NOCI-F, which achieves benchmark-quality couplings using nonorthogonal, fully relaxed fragment states via GNOME. Benchmarking on ethylene and anthracene models shows that both methods reproduce dominant couplings and trends across packing geometries, with CT-involving interactions challenging SymbolicCI due to basis limitations. A key finding is the prominence of CTX states as electronic gateways bridging the one- and two-particle manifolds, enabling CT-mediated formation, diffusion, and potential relaxation pathways that compete with conventional annihilation; geometric packing critically modulates these pathways. Collectively, the fragment-based CI framework establishes a principled bridge between electronic structure and quantum dynamics for predictive multiexcitonic photophysics and offers design principles to tune biexcitonic connectivity through molecular organization.

Abstract

Biexcitonic states govern singlet fission, triplet-triplet and exciton-exciton annihilation, yet a unified understanding of how these processes compete within a shared electronic manifold remains elusive. We outline a conceptual framework based on fragment-based configuration-interaction that systematically constructs diabatic Hamiltonians spanning the full one-particle (LE, CT) and two-particle (LELE, CTCT, TT, CTX with X = LE, CT, or T) manifolds from monomer-local building blocks, preserving physical interpretability throughout. SymbolicCI provides analytic Hamiltonian matrix elements for efficient large-scale calculations; NOCI-F delivers benchmark-quality couplings. The resulting diabatic Hamiltonians can be coupled to quantum dynamics simulations. Applications to ethylene aggregates and the anthracene crystal reveal CTX configurations as electronic gateways bridging excitonic manifolds, with CT-mediated relaxation pathways competing with conventional annihilation. In H-type aggregates, LECT admixture stabilizes a "bi-excimer" analogous to one-particle excimers. By providing first-principles access to biexciton formation, separation, and transport, we hope to stimulate further exchange between electronic structure and quantum dynamics communities toward a predictive understanding of multiexcitonic photophysics.

Figures (7)

• Figure 1: Scheme illustrating the energetic ordering of the one-particle exciton and the biexciton manifold, indicating the photophysical processes that proceed via intermanifold pathways.
• Figure 2: Overview illustrating the key features of the SymbolicCI and the NOCI-F methodology.
• Figure 3: a) Cutout of the ethylene 15-mer aggregates. Aggregate 1, H-type (red): z-translation 3.50. Aggregate 2, Null-Type (blue): x-translation 1.98, z-translation 3.50. Aggregate 3, Zero-Frenkel (violet): x-translation 2.23, z-translation 3.50. Aggregate 4, J-type (green): x-translation 3.20, z-translation 3.50. b) Cutout of the anthracene 15-mer aggregates. Aggregate 1, H-type (red): z-translation 3.75. Aggregate 2, Null-Type (blue): y-translation 2.30, z-translation 3.75. Aggregate 3, Zero-Frenkel (violet): y-translation 3.00, z-translation 3.75. Aggregate 4, J-type (green): y-translation 4.50, z-translation 3.75. c) Side view of the anthracene crystal cutoff containing 15 monomers, as taken from the experimental crystal structure marciniak_crystal_2002.
• Figure 4: Comparison of the SymbolicCI Hamiltonian (left) with the NOCI-F Hamiltonian (right) of the Aggregate 4, J-type (green): x-translation 3.20, z-translation 3.50. Diabatic energies (on the diagonal) are set to zero.
• Figure 5: Adiabatic energies obtained from diagonalization of the diabatic SymbolicCI Hamiltonian along the scan coordinate. The scan systematically probes the transition from a perfectly stacked H-aggregate to a slipped J-aggregate by displacing the monomers in the x-direction (along the C--C bond) from 0.03.5 in steps of 0.1, while maintaining a constant interplanar distance of 3.5. a) A total of 3146 excited states are represented, with each state color-coded according to its leading diabatic character. The ground state is set to 0. b) The composition of to lowest biexcitonic state along the scan coordinate.