Hydrogen bonding dampings

The intramolecular hydrogen-bonded molecules are generally planar because the hydrogen bond damps the strain present in the chelate ring. In their open form this strain is no longer balanced and in some cases the... 

Example In this exam pit. the van tier Waals (6-12 i and hydrogen bond (1 0-12) poteiilials are qiiiekly damped. 

Eomple In this example, the van der Waals (6-12) and hydrogen bond (10-12) potentials are quickly damped. 

Here, t/(f) is the reduced time evolution operator of the driven damped quantum harmonic oscillator. Recall that representation II was used in preceding treatments, taking into account the indirect damping of the hydrogen bond. After rearrangements, the autocorrelation function (45) takes the form [8]... 

It has been shown that the autocorrelation function (46) is the limit situation in the absence of damping of the autocorrelation function of the hydrogen bond within the indirect damping [8]. It must be emphasized that this autocorrelation function does not require for computation any particular caution because of its analytic character. Thus, it may be considered as a numerical reference for the computation involving representation I or III. 

We must stress that the use of a single damping parameter y supposes that the relaxations of the fast and bending modes have the same magnitude. A more general treatment of damping has been proposed [22,23,71,72] however, this treatment (discussed in Section IV.D) requires the use of the adiabatic approximation, so that its application is limited to very weak hydrogen bonds. 

Figure 12. Hydrogen bond involving a Fermi resonance damping parameters switching the intensities. The lineshapes were computed within the adiabatic and exchange approximations. Intensities balancing between two sub-bands are observed when modifying the damping parameters (a) with y0 =0.1, and y5 = 0.8 (b) with ya = ys = 0.8 (c) with yB — 0.8 and ys — 0.1. Common parameters oto = 1, A = 150cm, 2g)5 = 2850cm-1, and T = 30 K.

Figure 13. Hydrogen bond involving a Fermi resonance relative influence of the damping parameters. Spectral densities 7sf(co) computed from Eq. (81). Common parameters a0 = 1, A = 160cm-1, co0 = 3000cm-1, co00 = 150cm-1, 2t05 = 2790cm-1, and T = 300K.

It is not possible for the indirect damping mechanism, as considered semiclassically by Robertson and Yarwood [84] and later quantum mechanically by Boulil et al. [90], to be the unique damping mechanism occurring in a hydrogen bond, because the quantum mechanism leads, at the opposite of the less rigorous semiclassical treatment, to a drastic collapse of the lineshapes. 

Although most of the reported gas-phase experiments do not investigate the temporal evolution of alcohol clusters explicitly, the frequency-domain spectral information can nevertheless be translated into the time domain, making use of some elementary and robust relationships between spectral and dynamical features [289]. According to this, the 10-fs period of the hydrogen-bonded O—H oscillator is modulated and damped by a series of other phenomena. Energy flow into doorway states is certainly slower than for aliphatic C—H bonds [290] but on a time scale of a few picoseconds, energy will nevertheless have... 

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]. 

We found that rc of the O H- - -Cl- hydrogen-bond length increases from 14 2 ps at 25 °C, to 24 5 ps at 65 °C, to 30 6 ps at 85 °C. This increase of rc can be explained within the framework of the Brownian oscillator model. The time constant rc is related to the frequency cchb of the hydrogen-bond stretch vibration via rc = t/o hr [11], with 7 the damping of the hydrogen-bond stretch vibration. An increase in temperature leads to a decrease of wI1B, and thus to an increase of rc. 

According to literature on time scales of about 1 ps overdamped, collective translational modes of the bulk liquid occur as well as heavily damped restricted translational modes of the liquid with hydrogen bond bending and breaking character [9,10]. We interpret our longer decay time (-750 fs) to trace the dynamics of these processes. The significant reduction of... 

Fig. 9. The molecular structure of the salicylaldehyde thiosemicarbazone complex 239 clearly shows displacement of the NMe2 group of the damp ligand, which is monodentate and C-bonded. The N-H proton shows an intramolecular hydrogen bond to the chlorine atom.

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