Resonant Raman spectroscopies beyond density-functional theory

Resonant Raman spectroscopy probes, in a single measurement, how electrons and phonons couple in a material. While density-functional theory (DFT) typically reproduces well phonon frequencies, resonant Raman intensities hinge on electron-phonon matrix elements and electronic transitions that are far more sensitive to the underlying exchange-correlation approximation, yet accessible so far only for a handful of semilocal functionals. Here, we introduce a general finite-difference framework that computes resonant Raman tensors for any electronic-structure method able to deliver forces, eigenvalues, and wavefunctions. Applying it to graphene and monolayer MoS₂ with hybrid functionals and meta-GGAs, we show that these methods systematically enhance electron-phonon couplings relative to semilocal DFT, reflecting reduced dielectric overscreening. Accurate intensities require eigenvalues and electron-phonon matrix elements to be treated consistently at the same level of theory; among the approaches tested, hybrid functionals agree best with experiment, opening the door to systematic beyond-DFT Raman characterization of 2D materials.