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Stochastic Liouville equations for hydrogen-bonding fluctuations and their signatures in two-dimensional vibrational spectroscopy of water
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Image of FIG. 1.
FIG. 1.

Energy-level diagram for the OH stretch in HOD. The model has five vibrational parameters (two transition frequencies and three transition dipole moments) relevant for the infrared spectra.

Image of FIG. 2.
FIG. 2.

Static distribution of the OH stretch transition frequencies (, , and ) and anharmonicity ().

Image of FIG. 3.
FIG. 3.

Autocorrelation functions of the transition frequencies (, , and ) and the anharmonicity .

Image of FIG. 4.
FIG. 4.

Scatter plot showing the correlation between the anharmonicity and the fundamental frequency .

Image of FIG. 5.
FIG. 5.

Upper panel: The vertical lines marked with stars show the center position of the four states of the FSJ model. The height of each line marks the probability of the state. The Gaussian lines on top illustrate the slowly changing frequency distribution added on top of each state (solid: I, dotted: II, dashed: III, and dash-dotted: IV). Middle panel: The solid line is the distribution of the collective electrostatic coordinate. The dashed line on top is the Gaussian distribution corresponding to the combination of the Gaussian distributions of the coordinates and . The distributions of these coordinates are the dotted and dash-dotted lines, respectively. Lower panel: solid line: The correlation function of the collective electrostatic coordinate; dashed line: the biexponential fit. The dotted line is the FSJ frequency correlation function.

Image of FIG. 6.
FIG. 6.

Distribution of the fundamental and overtone frequencies for the four hydrogen-bond species. I: solid, II: dotted, III: dash-dotted, IV: dash-dot-dotted, and total: dashed line. The integrated intensity of each curve gives the abundance of each species.

Image of FIG. 7.
FIG. 7.

Kinetic scheme for the four hydrogen-bonding configurations. Reactions A and C hydrogen bonds on oxygen, while B and D hydrogen bonds on hydrogen.

Image of FIG. 8.
FIG. 8.

Lifetime histograms for the four hydrogen-bond configurations. is the probability that the the configuration survives a specified time. Solid line: configuration I, small dashed line: II, large dashed line: III, and dash-dotted: IV. The dashed lines are fitted exponential decays.

Image of FIG. 9.
FIG. 9.

The three Liouville space pathways contributing to the photon-echo signal. represents stimulated emission, represents ground-state bleach, and shows excited-state absorption.

Image of FIG. 10.
FIG. 10.

Linear absorption calculated using the SLE. Dashed: CEC(i), dotted: FSJ, and solid: experiment (Ref. 19). The experimental spectrum is displaced to the blue for a better comparison of the line shapes.

Image of FIG. 11.
FIG. 11.

(Color) Comparison of the photon-echo spectra calculated using the two SLE models. The full black line illustrates the diagonal, the dashed line is displaced above the diagonal. The red and blue lines show where the antidiagonal slices for Fig. 12 are taken on the red and blue sides, respectively.

Image of FIG. 12.
FIG. 12.

Antidiagonal slices of the photon-echo spectra of Fig. 11 intersecting the diagonal. The slices are made at 3350 and .

Image of FIG. 13.
FIG. 13.

(Color) Effect of the anharmonicity fluctuations. (a) CEC(ii) spectrum with fluctuating anharmonicity. (b) CEC(ii) spectrum with fixed anharmonicity. The vertical arrows indicate the anharmonic shift at . (c) The anharmonic shift vs . Black: fluctuating anharmonicity; red: fixed anharmonicity.

Image of FIG. 14.
FIG. 14.

(Color) Photon-echo spectra for different delay times calculated using CEC(ii) and CEC(iii).

Image of FIG. 15.
FIG. 15.

Three-pulse photon-echo peak shift spectrum. Solid line: experiment (Ref. 19); dotted: CEC(ii); dot-dashed: CEC(iii); and dashed: simulated data reported in Ref. 28.


Generic image for table
Table I.

Statistical data for the fluctuating frequencies for the considered transitions.

Generic image for table
Table II.

Number of hydrogen bonds to each atom (H, D, and O), average frequency , frequency spread , and abundance for the hydrogen-bonding configurations.

Generic image for table
Table III.

Frequencies ( and ), frequency distributions ( and ), anharmonicity dependence on the hydrogen-bond configuration, lifetime , and abundance .

Generic image for table
Table IV.

Reaction dynamics for hydrogen-bond breaking and forming.

Generic image for table
Table V.

Antidiagonal linewidths for cuts through the diagonal peak in photon-echo spectrum on the red and blue sides (red and blue lines in Fig. 11). The asymmetry parameter is defined in Eq. (12).


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Stochastic Liouville equations for hydrogen-bonding fluctuations and their signatures in two-dimensional vibrational spectroscopy of water