We develop a first-principles approach to compute infrared (IR) vibrational absorption and Raman scattering spectra with excitonic effects included. Our method is based on a perturbative expansion of electron-phonon and electron-light couplings in the time-dependent adiabatic GW (TD-aGW) theory. We show that excitonic effects in the IR absorption spectrum can be included by replacing the free electron-hole propagators in the perturbative expression for independent particles with their interacting counterparts, which are readily available from standard GW-Bethe-Salpeter-equation calculations. For the Raman spectrum, our derived expression agrees with the single- and double-resonance terms from a diagrammatic approach. We show significant excitonic enhancement in both the IR and resonance Raman scattering intensity for monolayer ${\mathrm{MoS}}_2$, ${\mathrm{WS}}_2$, and ${\mathrm{WSe}}_2$. Moreover, the exciton-phonon coupling strength and exciton energy landscape can be accessed by analyzing resonance Raman spectrum of these two-dimensional materials.

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• Electron-phonon coupling
• Excitons
• First-principles calculations