Proton vibrational levels

Proton transfer is coupled to the dynamics of two nuclear mode sets with widely different timescales, viz. the proton modes themselves and the environmental protein conformational and external solvent modes. The proton is trapped at the donor fragment at the equilibrium environmental conformational/solvent configuration in the reactants state, but fluctuations in these nuclear coordinates induce a state of resonance between the proton vibrational levels in the reactants and products states. Environmental gating modes with their special status in proton transfer are parts of this process. 

The distinction between the two regimes, whether the ground proton vibrational level is below or above the barrier in the proton coordinate, is critically determined by another important coordinate, the acid-base H-bond A-B separation... 

The Cl-O distance is 2.91 A. The ground and first excited proton vibrational levels are indicated. 

The energy factor Eal also appears in the reaction barrier in Eq. (10.33), as an energetic contribution to that barrier due to thermal activation of the H-bond mode. The isotopic dependence E i tn-i in the barrier plays a key role in isotope and temperature effects, but before recounting these effects, we describe the inclusion of excited proton vibrational levels [1,5]. 

Figure 10.15 Proton potentials for the solvent coordinate TS for four proton vibrational transitions (n -Hp) (a) 0-1, (b) 0-0 and 1-1, and (c) 1-0. The lines indicate diabatic proton vibrational levels.

In this formalism the mobility is determined partly by the value of AW (which occurs as AW ) and partly by the scattering of ion-state waves by lattice vibrations in the form of phonons. Because the ion-state band is so narrow and the difference between proton vibrational levels is so large compared with typical phonon energies, it is not possible for (k) to be scattered to a new state (k ) by emission or absorption of a single phonon. Instead, so that energy and momentum can be conserved, scattering must occur by the simultaneous emission and absorption of a pair of phonons of nearly equal energy. The analysis is therefore rather complicated but, if we assume that orientational defects are present in sufficient concentration that polarization effects do not block ion paths, the... 

Due to strong interaction of the reactants with the medium, the influence of the latter may not be reduced only to the widening of the vibrational levels of the proton in the molecules AH and BH. The theory takes into account the Franck-Condon factor determined by the reorganization of the medium during the course of the reaction. 

Thus, for a transition between any two vibrational levels of the proton, the fluctuation of the molecular surrounding provides the activation. For each such transition, the motion along the proton coordinate is of quantum (sub-barrier) character. Possible intramolecular activation of the H—O chemical bond is taken into account in the theory by means of the summation of the probabilities of transitions between all the excited vibrational states of the proton with a weighting function corresponding to the thermal distribution.3,36 Incorporation in the theory of the contribution of the excited states enabled us in particular to improve the agreement between the theory and experiment with respect to the independence of the symmetry factor of the potential in a wide region of 8[Pg.135]

The energy Ea is a quantum term associated with the proton reaction coordinate coupling to the Q vibration, Ea = h1 /2m. and Co is the tunneling matrix element for the transfer from the 0th vibrational level in the reactant state to the 0th vibrational level in the product state. The term AQe is the shift in the oscillator equilibrium position and F L(Eq, Ea, Laguerre polynomial. For a thorough discussion of Eq. (8), see [13],... 

Expectation Values of the Deuteron-Proton Distance, rd-p, the Deuteron-Electron Distance, rd-e, and the Proton-Electron Distance, r e, and Their Squares for the Vibrational Levels of HD" in the Rotational Ground State"... 

Thus, the spectroscopic results eliminate the model with symmetric hydrogen bonds, but they do not tell us much about the tunnelling of the protons. Actually, this should cause a splitting of the vibrational levels, but a rough estimation [14] of the splitting of the levels for a linear (which is probably not the case) O H 9 O system with an assumed 0—O distance of 2 7 A, yields a value of 15 cm- 1, This is too small a splitting to be observable with such broad bands, having moreover the contour complicated by the overlap with other bands. 

Totally deuterated aromatic hydrocarbons yield measured phosphorescence lifetimes greater than their protonated analogs.182 This behavior is ascribed to the closer spacing of vibrational levels in deuterated compounds with a consequent decrease in probability for nonradiative T -> S0 transitions. Quantum mechanical tunnelling may also contribute to the rate of the radiationless process with the normal compounds. 

The aim of the theoretical studies on the protonated DMAN-s was modeling of the potential energy curves for the proton motion and calculating the vibrational levels for the NHN+ bridge. The object of analysis was 2,7-disubstituted DMAN-s. The substituents at positions 2 and 7, as shown, affect the bridge length and spectral characteristics. So far the 2,7-dibromo-, 2,7-dimethoxy and 2,7-di(trimethylsilyl) derivatives have been studied [17, 19, 20]. 

Figures 6-5 to 6-7 show typical pump-probe spectra of protonated clusters, (NH3)2H+ and (NH3)5H+, through different vibrational levels of the A state, that is, v = 2, 1, 0, respectively. All of these spectra have some features in common, namely, they display a large increase in intensity at t = 0 (maximum temporal overlap between the pump and probe pulses), and thereafter a subsequent rapid intensity drop. However, the various spectra do display some noticeable differences with regard to the shape of the falloff region following the initial substantial peak. Except possibly for v = 0, when the vibrational energy of the A states increases, the long-time intensity level of all cluster ions increases. More important, the difference between (NH3)2H+ and (NH3)5H+ becomes evident at higher vibration levels, that is, v = 1 and v = 2.

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