Librational motion of molecules

Solvation in water was extensively studied and processes on different timescales were described ranging from 30 fs to several ps [8]. Due to our experimental resolution the shortest decay time we measure contains various superimposed contributions from the ultrafast processes presumably the inertial response of water and initial librational motions of molecules in the first solvation layer. 

The Kerr profile includes 2 normal mode and at 218 cm and 314 cm respectively in CCl as well as the r and r responses (McMorrow et al., 1988b). Presumably the perturbation on the vibrational and librational motions of molecules in the stabilized clusters will lead to a shift in these frequencies and amplitudes and thus a change in the Kerr profiles in the presence of ions or e. We hope to observe such shifts given the satisfactory Kerr response in electrolyte solutions and in DMSO and HMPA in the absence of electrons. 

Fast librational motions of the fluorophore within the solvation shell should also be consideredd). The estimated characteristic time for perylene in paraffin is about 1 ps, which is not detectable by time-resolved anisotropy decay measurement. An apparent value of the emission anisotropy is thus measured, which is smaller than in the absence of libration. Such an explanation is consistent with the fact that fluorescein bound to a large molecule (e.g. polyacrylamide or monoglucoronide) exhibits a larger limiting anisotropy than free fluorescein in aqueous glycerolic solutions. However, the absorption and fluorescence spectra are different for free and bound fluorescein the question then arises as to whether r0 could be an intrinsic property of the fluorophore. 

Just as in our abbreviated descriptions of the lattice and cell models, we shall not be concerned with details of the approximations required to evaluate the partition function for the cluster model, nor with ways in which the model might be improved. It is sufficient to remark that with the use of two adjustable parameters (related to the frequency of librational motion of a cluster and to the shifts of the free cluster vibrational frequencies induced by the environment) Scheraga and co-workers can fit the thermodynamic functions of the liquid rather well (see Figs. 21-24). Note that the free energy is fit best, and the heat capacity worst (recall the similar difficulty in the WR results). Of more interest to us, the cluster model predicts there are very few monomeric molecules at any temperature in the normal liquid range, that the mole fraction of hydrogen bonds decreases only slowly with temperature, from 0.47 at 273 K to 0.43 at 373 K, and that the low... 

Fig. 22 Librational motion of 9-hydroxyphenalenone [6] in the crystal. The arrow shows the dipole moment of the molecule.

The low activation energy of the thermal addition polymerization reaction confirms the necessity of a (librational) motion of the molecules in the initiation process. The first addition process differs from all the following addition proccesses by the metastable monomer diradical structure, which — in contrast to the DR , AC , and DC structures with n > 2 — has a limited life-time given by the phosphorescence decay of the monomer triplet state. Therefore, the librational excitation must be performed during the life-time of the monomer reaction centre. In the case of the low temperature photopolymerization reaction the librational excitation has to be prepared optically via the decay of the electronic excitation. This is in contrast to the photopolymerization reaction at high temperatures, where numerous molecular motions are thermally and stationary present in the crystals. Due to this difference two photons (2hv) are required in every dimer initiation process at low temperatures and only one photon (hv -i- kT) is required at high temperatures. The two paths of the photoinitiation reaction are illustrated below by the arrows in Fig. 26. The respective pair states are characterized by M M and M M as discussed below. 

The depolarized LS spectrum on the same sample obtained by the double monochromator are shown in Fig. lb. The insert shows a spectrum obtained by the tandem interferometer. It consists of a very strong peak around the center and the weak shoulders at both sides. The former is called a central mode and comes from the diffusive reorientation process, while the latter is called a low-frequency phonon mode and comes from the librational motion of the molecule around its mean confi ration. 

One sees that the corresponding peaks for hydration water in protein are also shifted upward slightly compared to the bulk water at the same temperature and as it is observed for water confined in Vycor (Figure 6). The up-shift of the librational peak increases either as the temperature is lowered or as the level of hydration is decreased, which reflects the amplified effect of confinement [49]. This indicates that both the translational and librational motions of water molecules near or at the protein surface are slightly more hindered, in agreement with observation from computer simulations. 

The normal mode analysis thus shows that the time scale separation between translational and rotational motions is sensible, so that liquid water meets a necessary condition for the Boltzmann-Jeans-type scenario. We should remark that rotational motions referred to here are not real rotation but just librational or flipping motions of molecules. This is in a contrast to the situation the Boltzmann-Jeans-type scenario assumes. The original Boltzmann-Jeans conjecture was proposed for the interpretation for freezing of high-frequency motions in gases, in which real rotational motions take place. However, since a crucial point of the argument is just the presence of different time scales, a type... 

Since it became clear from various observations that the librational motions of the molecules, even in the ordered a and y phases of nitrogen at low temperature, have too large amplitudes to be described correctly by (quasi-) harmonic models, we have resorted to the alternative lattice dynamics theories that were described in Section IV. Most of these theories have been developed for large-amplitude rotational oscillations, hindered or even free rotations, and remain valid when the molecular orientations become more and more localized. 

In particular they consider a set of simulations for a system of CX4 molecules at three different temperatures ( hot , intermediate and cool ) which bears a close resemblance to our computations made in the presence of a second rank interaction potential. Their hot case corresponds to our low potential coupling cases, whereas their cool simulation is related to our high potential results that is, a decrease in temperature corresponds in our rescaled coordinates to an increase in the potential coupling. One may note that the presence of a negative tail, assigned by Lynden-Bell to librational motion of the observed molecule in an instantaneous cage, causes the momentum correlation functions to behave differently in the cool state with respect to the purely diffusive decay observed for the hot state. This behavior is very similar to our 2BKM-SRLS case for ta, = 5 and V2 = 3 (cf. Fig. 13b). 

In particular. Nelson and co-workers have collected a set of experimental data concerning the reorientational dynamic of CSj both in temperature-dependent [64] and pressure-dependent [65] ISS experiments. In both cases they observed weakly oscillatory responses in the signal either for low temperature regimes or for high pressure regimes. These have been identified as librational motions of the probe molecule in the transient local potential minima inside the instantaneous cages formed by its neighbors. 

We consider here possible alternative structural schemes of librational motion of rigid dipoles. These schemes should, in principle, be in line with possible configurations of molecules in water and ice. For simplicity, we regard the case of one dimensional motion. 

In order to account for some of the differences in thermodynamic properties of H2O and D2O, theoretical studies have been applied. Swain and Bader first calculated the differences in heat content, entropy, and free energy by treating the librational motion of each water molecule as a three-dimensional isotopic harmonic oscillator. Van Hook demonstrated that the vapor pressure of H2O and D2O on liquid water and ice could be understood quantitatively within the framework of the theory of isotope effects in condensed systems. Nemethy and Scheraga showed that in a model based on the flickering cluster concept, the mean number of hydrogen bonds formed by each water molecule is about 5% larger in D2O than in H2O at 25 °C. 

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