Real-Space Quantification of Exciton Localization in Crystals Using Wannier Function Decomposition

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.