Resonant Raman spectroscopies beyond density-functional theory

Abstract

Resonant Raman spectroscopy probes, in a single measurement, how electrons and phonons couple in a material. Density-functional theory (DFT) typically reproduces well phonon frequencies, but resonant Raman intensities hinge on electron-phonon matrix elements and electronic transitions that are far more sensitive to the underlying exchange-correlation approximation. However, electron-phonon coupling has so far been accessible only through linear-response theories developed for a handful of semilocal DFT methods, leaving the sensitivity of resonant Raman intensities to the electronic-structure approximation essentially unexplored. Here, we introduce a general finite-difference framework that can compute resonant Raman tensors for any electronic-structure method capable of delivering forces, eigenvalues, and wavefunctions of pristine and displaced configurations. We apply the formalism to graphene and monolayer MoS$_2$, using hybrid functionals or meta-GGAs, and show that these approaches systematically enhance electron-phonon couplings relative to semilocal DFT, reflecting reduced dielectric overscreening. A decomposition of the Raman tensor shows that accurate intensities require electronic eigenvalues and electron-phonon matrix elements to be treated consistently at the same level of theory. Among the approaches tested, hybrid functionals provide the best overall agreement with experiment. Because the framework needs only quantities every electronic-structure code already produces, it opens the door to systematic, beyond-DFT Raman characterization or benchmarking against experiments, especially for 2D materials.