Spectral calculations liquid water

Among the dynamical properties the ones most frequently studied are the lateral diffusion coefficient for water motion parallel to the interface, re-orientational motion near the interface, and the residence time of water molecules near the interface. Occasionally the single particle dynamics is further analyzed on the basis of the spectral densities of motion. Benjamin studied the dynamics of ion transfer across liquid/liquid interfaces and calculated the parameters of a kinetic model for these processes [10]. Reaction rate constants for electron transfer reactions were also derived for electron transfer reactions [11-19]. More recently, systematic studies were performed concerning water and ion transport through cylindrical pores [20-24] and water mobility in disordered polymers [25,26]. 

We have described our most recent efforts to calculate vibrational line shapes for liquid water and its isotopic variants under ambient conditions, as well as to calculate ultrafast observables capable of shedding light on spectral diffusion dynamics, and we have endeavored to interpret line shapes and spectral diffusion in terms of hydrogen bonding in the liquid. Our approach uses conventional classical effective two-body simulation potentials, coupled with more sophisticated quantum chemistry-based techniques for obtaining transition frequencies, transition dipoles and polarizabilities, and intramolecular and intermolecular couplings. In addition, we have used the recently developed time-averaging approximation to calculate Raman and IR line shapes for H20 (which involves... 

Appendix 1. Calculation of Fourier Amplitudes b -i for Librators Appendix 2. Transformation of Integral for Spectral Function of Precessors Appendix 3. Optical Constants of Liquid Water... 

Let us calculate the broadband spectra of liquid water H20 and D20. The adopted experimental data are presented in Table XII. In accord with the scheme (238), we use Eq. (249) for the complex susceptibility x and use Eqs. (242) and (243) for the modified spectral function R(z). All other expressions used in these calculations are the same as were employed in Section V. 

With local information given by INM analysis in mind, we next see the character of rotational relaxation in liquid water. The most familiar way to see this, not only for numerical simulations [76-78] but for laboratory experiments, is to measure dielectric relaxation, by means of which total or individual dipole moments can be probed [79,80]. Figure 10 gives power spectra of the total dipole moment fluctuation of liquid water, together with the case of water cluster, (H20)io8- The spectral profile for liquid water is nearly fitted to the Lorentzian, which is consistent with a direct calculation of the correlation function of rotational motions. The exponential decaying behavior of dielectric relaxation was actually verified in laboratory experiments [79,80]. On the other hand, the profile for water cluster deviates from the Lorentzian function. As stated in Section III, the dynamics of finite systems may be more difficult to be understood. 

In Figure 9 we depict the frequency dependences of the partial absorption coefficients aq(v) and a (v) pertinent to two harmonic-vibration modes. These frequency dependences are calculated from formulas (A6), (21) [24], (25), (28), and (29). When the above-mentioned coupling is accounted for (solid lines in Fig. 9), the spectral functions are taken from Eq. (Al). On the other hand, when the coupling is neglected (open circles in Fig. 9), then Lq and L are found from Eq. (19). We see from Fig. 9a that for both cases the calculated partial absorption a (v) practically coincide. The same assertion is valid also for the partial absorption ocq(v) depicted in Fig. 8b. Hence, there is no practical need to account for the coupling between the harmonic reorientation and vibration of HB molecules for calculation of spectra in liquid water. However, the effect of such coupling becomes noticeable (being, however, a rather small) in the case of ice, where the absorption lines are much narrower. 

Fig. 1.2 The experimentally determined spectral density of states of liquid water using the optical Kerr effect -linear response) is shown for comparison [3], Water is one of the most structured liquids in which there is large separation in timescales. The frequency range between 300 and 1,000 cm (1) is related to librational motions (note that the spectrum represented here is artificially truncated at 600 cm due to laser bandwidth hmitations), the peak at 170 cm (2) is hindered translational motion of the heavy O atoms, the 60 cm mode (3) is transverse or shear motion, and below 25 cm (4) corresponds to diffusive relaxation and hydrogen bond breaking [8]. The issue of inhomogeneous to homogeneous interpretations of the dynamic structure of liquid water still holds despite this additional structure. The agreement is quite good with the theoretical calculation of the corresponding spectral density of states for water but the calculations are rather insensitive to basis with respect to this observable. Reprinted with permission from [3]. Copyright 1994, American Chemical Society...

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