Fig. 5: Spectral signatures of proton transfer.

a–d Decomposition of an excess-proton trajectory d(t) (black solid line in a) into transfer-waiting d_TW (blue solid line in b), transfer-path d_TP (red solid line in c) and normal-mode contributions d_NM (green solid line in d). The time course of the R_OO-dependent most likely proton positions at d^*[R_OO(t)] are shown as thin gray solid lines in (a and b). e IR spectrum of the excess-proton motion projected onto d, shown as a black solid line, and IR spectra of the contributions shown in a–c in the respective color (the green broken line denotes negative values). The power spectrum of the R_OO coordinate is shown as a gray broken line in the lower panel. The inverse of the characteristic time scales τ_TW, \({\tau }_{{R}_{{{{{{{{\rm{OO}}}}}}}}}}\), \(2{\tau }_{{{{{{{{\rm{TP}}}}}}}}}^{c}\) and \(2{\tau }_{{{{{{{{\rm{TP}}}}}}}}}^{i}\) are shown as thin vertical solid gray lines. f Distributions of the transfer-waiting first-passage times of excess protons, see main text for details.