Excited-State Dynamics: I

The degree of spatial localization of excitons in crystals is key for understanding absorption spectroscopy, exciton dynamics, and more. Here, we introduce a scheme to quantify exciton localization within the ab-initio Bethe-Salpeter equation formalism that decomposes the Bloch exciton wave function into a product of single-particle electron and hole Wannier functions. This real-space approach enables precise site- and orbital-resolved quantification of Frenkel and charge-transfer excitons. We then demonstrate this method for singlet and triplet excitons in acene crystals, highlighting the pressure, spin-state, and center-of-mass momentum dependence of exciton localization, and comparing where possible to results obtained with exciton Wannier functions. We outline extensions of this framework, including efficient Wannier-Fourier k-grid interpolation of exciton coefficients and the evaluation of expectation values involving position operators, highlighting its potential as a general tool for both analyzing and computing excitonic properties.