The data that support the findings of ``Coupled-cluster approach to vibronic effects in resonant inelastic x-ray scattering of quantum materials: Application to a $5d^1$ rhenium oxide'' by T. Matsuzaki et al. All the files are ASCII text files. I. EOM-CCSD calculations (a) Ba2MgReO6 Electronic/10Dq.out : Output file of the calculations of the energy levels (Q = 0). Electronic/SOC.out : Output file of the calculations of the SOC matrices. Vibronic/Eg/EgQ.out : Output files for the calculations of the vibronic coupling constants for the Eg u mode (Q = -16, -14, -12, -10, -8, -6, -4, -2, 2, 4, 6, 8, 10, 12, 14, 16). Vibronic/T2g/T2gQ.out : Output files for the calculations of the vibronic coupling constants for the T2g xy mode (Q = -16, -14, -12, -10, -8, -6, -4, -2, 2, 4, 6, 8, 10, 12, 14, 16). (b) Ba2MgReO6_withoutPC Electronic/Mulliken.out : Output file of the calculations of the Mulliken charges. Electronic/10Dq_SOC.out : Output file of the calculations of the energy levels (Q = 0) and the SOC matrices. Vibronic/Eg/EgQ.out : Output files for the calculations of the vibronic coupling constants for the Eg u mode (Q = -16, -14, -12, -10, -8, -6, -4, -2, 2, 4, 6, 8, 10, 12, 14, 16). Vibronic/T2g/T2gQ.out : Output files for the calculations of the vibronic coupling constants for the T2g xy mode (Q = -16, -14, -12, -10, -8, -6, -4, -2, 2, 4, 6, 8, 10, 12, 14, 16). (c) Ba2MgWO6 Electronic/Energy.out : Output file of the calculations of the energy levels (Q = 0). Vibronic/Eg/EgQ.out : Output files for the calculations of the vibronic coupling constants for the Eg u mode (Q = -16, -14, -12, -10, -8, -6, -4, -2, 2, 4, 6, 8, 10, 12, 14, 16). Vibronic/T2g/T2gQ.out : Output files for the calculations of the vibronic coupling constants for the T2g xy mode (Q = -16, -14, -12, -10, -8, -6, -4, -2, 2, 4, 6, 8, 10, 12, 14, 16). (d) Ba2MgWO6_withoutPC Electronic/Mulliken.out : Output file of the calculations of the Mulliken charges and the energy levels (Q = 0). Vibronic/Eg/EgQ.out : Output files for the calculations of the vibronic coupling constants for the Eg u mode (Q = -16, -14, -12, -10, -8, -6, -4, -2, 2, 4, 6, 8, 10, 12, 14, 16). Vibronic/T2g/T2gQ.out : Output files for the calculations of the vibronic coupling constants for the T2g xy mode (Q = -16, -14, -12, -10, -8, -6, -4, -2, 2, 4, 6, 8, 10, 12, 14, 16). II. RIXS spectra Each file contains two columns. The first column shows energy (eV), and the second column shows intensities/spectra. (a) Electronic Intensity.txt : Intensities of electronic energy levels. Spectrum.txt : Intensities of electronic energy levels convoluted with Gaussian functions. (b) Vibronic_Eg Intensity.txt : Intensities of vibronic energy levels (Eg). Spectrum.txt : Intensities of vibronic energy levels (Eg) convoluted with Gaussian functions. (c) Vibronic_Eg_T2g Intensity.txt : Intensities of vibronic energy levels (Eg and T2g). Spectrum.txt : Intensities of vibronic energy levels (Eg and T2g) convoluted with Gaussian functions.