Spectral density, hydrogen bonds relaxation

The linear response theory [50,51] provides us with an adequate framework in order to study the dynamics of the hydrogen bond because it allows us to account for relaxational mechanisms. If one assumes that the time-dependent electrical field is weak, such that its interaction with the stretching vibration X-H Y may be treated perturbatively to first order, linearly with respect to the electrical field, then the IR spectral density may be obtained by the Fourier transform of the autocorrelation function G(t) of the dipole moment operator of the X-H bond ... 

In the presence of both order-disorder and displacive, as in the KDP family, the two dynamic concepts have somehow to be merged. It could well be that the damping constant Zs becomes somewhat critical too (at least in the over-damped regime of the soft mode), because of the bihnear coupling of r/ and p. It would, however, lead too far to discuss this here in more detail. The corresponding theory of NMR spin-lattice relaxation for the phase transitions in the KDP family has been worked out by Blinc et al. [19]. Calculation of the spectral density is here based on a collective coordinate representation of the hydrogen bond fluctuations connected with a soft lattice mode. Excellent and comprehensive reviews of the theoretical concepts, as well as of the experimental verifications can be found in [20,21]. 

Our findings for rs and th may be compared with results of computer simulations for water. Values between 1 and 2 ps are stated for the average lifetime of a hydrogen bond by different authors (121-123), in satisfactory agreement with our experimental values. It is also interesting to compare with the frequency shift correlation function of the vibrational modes of water obtained from MD computations (124). Recently a slower component of this function with an exponential time constant of 0.8 ps was predicted for HDO in D20 at 300 K and a density of 1.1 g/cm3 (pressure %2 kbar). The existence of the slow component is a necessary prerequisite for the observation of spectral holes and the spectral relaxation time rs reported here. The faster component of the frequency shift correlation function with rc = 50 fs (124) represents rapid fluctuations that contribute to the spectral bandwidths of the spectral species and of the spectral holes. 

As the hot band transitions should exist in both of the v, band of hydrogen-bonded and physisorbed acetonitrile, we must get the accurate v, band without the effect by the hot band transitions. We have to determine the analytical functions for fundamental transitions of v/a and vJp and for hot band transitions upon the least-squares procedure. We assumed that the reorientational-vibrational relaxation processes of physisorbed acetonitrile could be described as a diffusion process like bulk liquid molecule, whose spectral density has a Lorentzian form. Accordingly it is supposed that the v,p band is reproduced as a sum of three Lorentzian curves of the v, p, v," p, and bands. In the previous study [9], it was assumed that the Vj a band has a Gaussian band shape and the hot band transitions could be ignored. In the present study we assumed that the v,a band over the range of PIP, =... 

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...

---