Obviously the Fourier transform of this quantum autocorrelation function still gives the frequency ω, but it should mainly be considered to correspond to the 1 → 2 transition. By comparing this quantum autocorrelation function with the classical autocorrelation function obtained from excited state CMES in Eq. 15, we only see a difference by a pre-factor, suggesting that it may be viable to use excited state CMES-MD to obtain excited state absorption spectra.