Ultrafast Vibrational and Structural Dynamics of the Proton in Liquid Water

The dynamical behavior of excess protons in liquid water is investigated using femtosecond vibrational pump-probe spectroscopy. By resonantly exciting the $\mathrm{O}\mathrm{\text{−}}{\mathrm{H}}^{+}$-stretching mode of the ${\mathrm{H}}_9{\mathrm{O}}_4^{+}$ (Eigen) hydration structure of the proton and probing the subsequent absorption change over a broad frequency range, the dynamics of the proton is observed in real time. The lifetime of the protonic stretching mode is found to be approximately 120 fs, shorter than for any other vibration in liquid water. We also observe the interconversion between the ${\mathrm{H}}_9{\mathrm{O}}_4^{+}$ (Eigen) and ${\mathrm{H}}_5{\mathrm{O}}_2^{+}$ (Zundel) hydration structures of the proton. This interconversion, which constitutes an essential step of proton transport in water, is found to occur on an extremely fast ($<100\mathrm{fs}$) time scale.

Figure 1

Infrared spectrum of a $5M$ solution of $\mathrm{HCl}:\mathrm{DCl}$ in $\mathrm{HDO}:{\mathrm{D}}_2\mathrm{O}$, with a $\mathrm{H}:\mathrm{D}$ ratio of $1:20$. The bars indicate the frequency regions of the O-H-stretching modes of the Eigen(I) and Zundel/Eigen(II) structures.

Figure 2

Absorption change as function of delay after resonant excitation (at $2935{\mathrm{cm}}^{-1}$) of the $\mathrm{O}\mathrm{\text{−}}{\mathrm{H}}^{+}$-stretching mode of the Eigen(I) structure. The absorption change is shown for two probing frequencies, one resonant with the Eigen(I) structure, and one resonant with the Zundel and Eigen(II) structures. The curves superimposed on the experimental points are least-squares fits of bi-exponential decays convoluted with the cross correlation of pump and probe. The time constants are 120 fs and 0.7 ps for the dotted curve, and 130 fs and 0.8 ps for the solid curve.

Figure 3

Absorption change as function of frequency, 200 fs after resonant excitation (at $2935{\mathrm{cm}}^{-1}$) of the $\mathrm{O}\mathrm{\text{−}}{\mathrm{H}}^{+}$-stretching mode of the Eigen structure. The spectrum was constructed from spectrally overlapping data sets obtained from samples with $\mathrm{H}:\mathrm{D}$ ratios of $1:5$ and $1:20$. Scaling factors were determined by matching the data in the regions of overlap.

Figure 4

Absorption changes at a delay of 200 fs after excitation of the $\mathrm{O}\mathrm{\text{−}}{\mathrm{H}}^{+}$-stretching mode of the Eigen(I) structure, and after excitation of the O-H-stretching mode of HDO. The data have been scaled for better comparison.