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Relation between frequency and H bond length in heavy water: Towards the understanding of the unusual properties of H bond dynamics in nanoporous media

This content has been downloaded from IOPscience. Please scroll down to see the full text. 2009 J. Phys.: Conf. Ser. 177 012012 (http://iopscience.iop.org/1742-6596/177/1/012012) View the table of contents for this issue, or go to the journal homepage for more

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Water Interfaces in Physics, Chemistry and Biology: a Multi-Disciplinary Approach IOP Publishing Journal of Physics: Conference Series 177 (2009) 012012 doi:10.1088/1742-6596/177/1/012012

Relation between frequency and H bond length in heavy water: Towards the understanding of the unusual properties of H bond dynamics in nanoporous media Stanislas Pommeret1,Raluca Musat, Jean Philippe Renault, Jean-Claude Leicknam2 and Savo Bratos2 1 * CEA/Saclay, DSM/DRECAM/SCM URA 331 CNRS, Laboratoire de Radiolyse, F-91191 Gif-sur-Yvette, France 2 Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie-Paris6, UMR 7600 (CNRS), Paris, France.

The published work on H bond dynamics mainly refers to diluted solutions HDO/D2O rather than to normal water.1 The reasons for this choice are both theoretical and experimental. Mechanical isolation of the OH vibrator eliminating the resonant energy transfer makes it a better probe of the local H bond network, while the dilution in heavy water reduces the infrared absorption, which permits the use of thicker experimental cells. The isotopic substitution does not alter crucially the nature of the problem. The water dynamics is still the subject of intense theoretical2 and experimental3 studies. The length r of an OH…O group is statistically distributed over a large interval comprised between 2.7 and 3.2 A with a mean value r0 = 2.86 A. Liquid water may thus be viewed as a mixture of hydrogen bonds of different length. Two important characteristics of hydrogen bonding must be mentioned. (i) The OH stretching vibrations are strongly affected by this interaction. The shorter the length r of the hydrogen bond, the strongest the H bond link and the lower is its frequency ω: the covalent OH bond energy is lent to the OH..O bond and reinforces the latter. A number of useful relationships between ω and r were published to express this correlation. The one adopted in our previous work is the relationship due to Mikenda4. (ii) Not only the OH vibrations, but also the HDO rotations are influenced noticeably by hydrogen bonding. This is due to steric forces that hinder the HDO rotations. As they are stronger in short than in long hydrogen bonds, rotations are slower in the first case than in the second. This effect was only recently discovered, but its existence is hardly to be contested.5 In the present contribution, we want to revisit the relationship between the frequency of the OH vibrator and the distance OH..O. Water molecule has three normal modes ω1, ω2, ω3, and the OH stretching frequency of HDO corresponds to ω3. The quantities examined in what follows are and 1

T. Elsaesser, H.J. Bakker, Ultrafast Hydrogen Bonding Dynamics and Proton Transfer Processes in the Condensed Phase, Kluwer, Dordrecht, 2002. 2 M. Diraison, Y. Guissani, J-Cl. Leicknam, and S. Bratos, Femtosecond solvation dynamics of water: solvent response to vibrational excitation of the solute, Chem. Phys. Lett. 258, 348-351 (1996). C. P. Lawrence and J. L. Skinner, Vibrational spectroscopy of HDO in liquid D2O. III. Spectral diffusion, and hydrogen bonding and rotational dynamics, J. Chem.Phys. 118, 264-272 (2003). S. A. Corcelli, C. P. Lawrence, J. B. Asbury, T. Steinel, M. D. Fayer, and J. L. Skinner, Spectral diffusion in a fluctuating charge model of water, J. Chem. Phys. 121, 8897-8900 (2004). 3 J. Stenger, D. Madsen, P. Hamm, E. T. J. Nibbeling and T. Elsaesser, Ultrafast vibrational dephasing of liquid water, Phys.Rev. Lett. 87, 027401 1-4 (2001). C. J. Fecko, J. D. Eaves, J. J. Loparo, A. Tokmakoff and P. L. Geissler, Ultrafast hydrogen bond dynamics in the infrared spectroscopy of water, Science 302, 1698-1702 (2003). S.Yeremenko, M. S. Pshenichnikov and D. A. Wiersma, Hydrogen-bond dynamics in water explored by heterodyne-detected photon echo, Chem.Phys.Lett. 369, 107-113 (2003). 4 W. Mikenda, Stretching frequency versus bond distance correlation of O---D(H) Y (Y = N, O, S, Se, Cl, Br, I) hydrogen bonds in solid hydrates, J. Mol. Struct., 147, 1-15 (1986). 5 S. Woutersen, U. Emmerichs, H.J. Bakker, Femtosecond mid-IR pump-probe spectroscopy of liquid water: Evidence for a two-component structure, Science 278, 658-660 (1997). G. Gallot, S. Bratos, S. Pommeret, N. Lascoux, J.-C. Leicknam, M. Kozinski, W. Amir, and G.M. Gale, Coupling Between Molecular Rotations and OH..O Motions in Liquid Water: Theory and Experiment, J. Chem. Phys., 117, 11301 (2002).

c 2009 IOP Publishing Ltd

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. In these functions, ω3(r,t) indicates the value of the frequency ω3 at time t given that the OH...O bond length was r at time 0. Moreover, ∆ω3(r,t) = ω3(r,t) - . In calculating statistical averages, intramolecular vibrations were treated by quantum mechanics and all remaining variables by classical mechanics. The potential employed was the pair-additive extended-simple-point-charge (SPCE) potential of Berendsen et al. 6 The classical calculations were performed as follows. The simulation box contained 255 D2O molecules and one HDO molecule with periodic boundary conditions. The long-range electrostatic interactions were taken into account by calculating the Ewald sum. The equations of motion were integrated with the help of leap frog algorithm. The thermodynamic point considered here corresponds to T=300 K and ρ = 1.09 g/cm3. The statistical quantities were extracted from two independent runs of 5 ns after equilibration; the time step of the simulation was 0.5 fs. The configurations of the system were saved every 5 fs and the frequency of the OH vibrator computed. The O…O distance rOO between the oxygen atom of the HOD molecule and that of a D2O molecule can be defined in different ways. Some authors assimilated it to the O…O distance between the HDO and the closest D2O. We preferred to attribute it to D2O molecule for which the H…O distance is the smallest in the same pair of molecules. Then, using quantum mechanical perturbation theory, one obtained analytical expressions of ω3(r,τ) in terms of the derivatives of the intermolecular potential with respect the internal vibrations.7 Once the instantaneous frequency ω3(t) and distance rOO(t) have been computed for a large number of steps of molecular dynamics, one can examine some properties of H bonds. As noted earlier8, the variables ω3 and rOO are correlated. This correlation is strong enough to exhibit a well defined peak in the (ω3 , rOO) plane. It is then possible to compute the mean distance rOO at a given frequency ω3, and the mean frequency ω3 at a given distance rOO. These two functions are plotted in Figure 1A. It is clear that, even if they are different, the difference between them is small. Comparing them with the Mikenda relation4, one finds a good agreement. Note that the empirical relationship was established for solids. 3.2

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Figure 1: Relationship between the frequency ω3 of the OH vibrator and the distance rOO. (A) Solid line is the Mikenda relation4; the long dash curve gives the mean distance rOO for a given frequency ω3; and the dash dot dot curve gives the mean frequency ω3 at a given distance rOO. (B) Parametric plot of < ω3(r,t)> as a function of for times varying between 0 and 3 ps, and r varying between 2.6 and 3.2 A. The solid line is .

6 H. J. C. Berendsen, J. R. Grigera and T. P. Straatsma, The missing term in effective pair potentials,.J. Phys. Chem., 91, 6269-6271 (1987). 7 M. Diraison, J-Cl. Leicknam, G. Tarjus, and S. Bratos, Computer simulation study of inelastic neutron scattering from liquid water, Phys. Rev. E 50 2689-2695 (1994). 8 R. Ray, K. B. Moller and J. T. Hynes, Hydrogen bond dynamics in water and ultrafast infrared spectroscopy, J. Phys.Chem.A 106, 11993-11996 (2002)

2


Having established a relationship between the frequency and the distance in static conditions, we re-examined it from dynamical point of view. In order to do it, we have computed the mean distance and the mean frequency for different times t: we extracted from the MD runs the configurations for which the H bond distance was equal to r, and followed the mean frequency and the mean distance in time. The parametric plot (Figure 1B) shows a strong correlation between these two quantities, whatever the initial value of r. To go further in the comparison between frequency and distance as a function of time, we have developed a new theory that makes the link between the distance and the frequency, assuming that the initial wavepacket is selected by a femtosecond laser pulse. It is inspired by a recent theory of time resolved X-ray diffraction.9 This theory requires the knowledge of two time dependent functions: that we presented earlier and (2) C = - This function is much alike the standard frequency shift correlation function , but is not identical to it. The frequency shift correlation function is well fitted (Figure 2A) by two exponentials (40 and 625 fs). If t and t’ are large with respect to 625 fs, the system has lost the memory of its initial condition and it is easy to show that C→ C. In Figure 2B, we illustrated the time dependence of C for r = 2.86 A. For long times, this function reaches the value of C = 11780 cm-2, but at short time its value is only 4000 cm-2. This indicates that when pumping at a given frequency, one selects a narrow range of distances of the H bond network. The evolution of the function toward the asymptotic value is characterized, as in the frequency shift correlation function, by a fast and a slow component. r0 = 2.86 A

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Figure 2: Frequency correlation functions: A) Frequency shift correlation function . B) Function .

The present study confirms the link between the frequency of an OH vibrator and the H bond network surrounding it. Even so the relation between the distance rOO and ω3 is statistical in nature; it is sufficiently narrow to affirm that the measurement of the mean frequency ω3 at a given time is related to the distance rOO at a given time as it was stated earlier.10 The present results are currently being expanded to nanoporous media and compared with the recent findings of the CEA team on the unusual properties of the H bond dynamics.

9

S. Bratos, F. Mirloup, R. Vuilleumier and M. Wulff, Time resolved X-ray diffraction: statistical theory and its application to the photophysics of molecular iodide, J. Chem. Phys. 116, 10615-10625 (2002). 10 G.M. Gale, G. Gallot, F. Hache, N. Lascoux, S. Bratos, J.-Cl. Leicknam, Femtosecond dynamics of hydrogen bond in liquid water: a real time study, Phys. Rev. Lett. 82, 1068-1071 (1999). 3