Gaussian Charge-Based Electrostatic Embedding Scheme for Solid-State Excited-State Modeling

Electrostatic embedding schemes represent an affordable and accurate alternative to more costly approaches to model the excited-state properties of crystalline materials. They are commonly based on point-charge (PC) formalisms, which may lead to numerical instabilities and unphysical electron density (de)localization. In this work, we introduce and validate a Gaussian charge-based (GC) electrostatic embedding scheme for solid-state excited-state calculations based on analytical Ewald lattice summations. The implementation is first validated by systematically comparing electrostatic potentials obtained using PC and GC formalisms at the atomic sites of a broad and representative data set of 530 crystalline structures, covering all space-group types and crystallographic settings. Excellent agreement between PC and GC electrostatic potentials is obtained when the Gaussian width parameter is appropriately chosen. In particular, from the overlap of two GC distributions, we propose a criterion based on the minimal interatomic distance to define an upper bound of the Gaussian width parameter, which still maintains reasonable agreement with the PC-based Ewald potentials for embedded excited-state calculations. The GC embedding scheme is then applied to the modeling of excited-state properties of crystalline imidazole using embedded monomer and hydrogen-bonded dimer models in vacuum, dielectric media, and crystalline environments. The results demonstrate that, although both PC and GC embeddings yield excitation energies in very good agreement with GW-BSE and optimally tuned range-separated hybrid calculations, GC avoids the excessive electron density contraction observed with PC. Overall, the proposed GC-based electrostatic embedding scheme therefore offers a robust and physically sound alternative to PC models for excited-state calculations in solids and constitutes a promising framework for both future methodological developments and practical applications in embedded excited-state calculations.