Protons vibrational

As noted in Section 34.2, the proton coordinate (such as that of a quantum particle) should be eliminated from the free-energy surfaces used for calculation of the activation free energy. The characteristics of the proton are reflected in the energies at the points of minimum of these free-energy surfaces, which involve the energies of the initial, E°, and final, E°f, ground proton vibrational states, respectively. This is denoted by the superscript 0 in the free-energy surfaces Uf (P) and U° (P). 

The best, and longest known, case is that of the bifluoride anion in NaHF2 and KHF2. In each the FHF ion lies across a centre of symmetry, and careful neutron-diffraction study finds the proton at the centre. However, neutron diffraction also shows, or appears to show, that the proton vibrates with a particularly large amplitude along the F H F bond. So there is a possibility that this may be partly due to disorder — qualitatively like that in ice (see also section 12), but now with the alternative proton sites not more than 0.1 A from the centre. The neutron-diffraction measurements can be equally well explained by two models the proton vibrates... 

K. M. McDonald, W. R. Thorson, and J. H. Choi,/. Chem. Phys., 99,4611 (1993). Classical and Quantum Proton Vibration in a Nonharmonic Strongly Coupled System. 

Denterinm magnetic resonance spectroscopy has fonnd wider applications since the advent of highly sensitive Fonrier transform spectrometers. Denterinm is preferred choice in molecnlar and in H NMR spectroscopy in order to provide additional information abont proton vibrations and resonances spectra measnred before and after denteration help to locate the exchanging hydrogen atoms. 

Two papers have attempted to compare the observed infrared lines of the base pairs in the region of the hydrogen-bond absorption with the calculated data. Rein and Svetina have calculated the proton vibrational states and relative transition probabilities for two guanine-cytosine hydrogen bonds. Their preliminary results seemed to be consistent with the absorption peak at 3489 cm (0.436 eV) reported by Pitha et for the hydrogen bond N-H stretching mode of... 

An electronically adiabatic proton transfer reaction may be either vibrationally adiabatic or vibrationally non-adiabatic. Vibrationally adiabatic refers to the situation in which the proton responds instantaneously to the solvent, while vibrationally non-adiabatic refers to the opposite limit. The adiabatic proton vibrational wave functions are calculated if the Schrodinger equation is solved for fixed values of Zp. 

The description of PCET reactions is particularly challenging due to the quantum mechanical behavior of the ET electrons, the PT electrons, and the transferring protons. The adiabatic mixed electronic/proton vibrational states are calculated when the following Schrbdinger equation is solved for fixed solvent coordinates... 

The adiabatic mixed electronic/proton vibrational surfaces can be calculate by the diagonalization of the matrix H along a two-dimensional grid of solvent coordinates... 

If all four of the new basis states are included, the adiabatic mixed electronic/proton vibrational states are exactly the same as those obtained with the original four VB states. Moreover, the diabatic mixed electronic/proton vibrational states for the new basis states are exactly the same as the adiabatic states obtained with the settings Ho)ia,2a = ( o)ia,26 = ( o)i6,2a = ( )i6,26 = (as described at the end of the previous section). 

The proton vibrational states can be calculated for each of the two electronic states by solution of the Schrodinger equation... 

The previous work of Cukier and coworkers [7, 12] differs from the formulation described in this chapter in a number of fundamental ways. In contrast to the multistate continuum theory described in this chapter, Cukier and coworkers did not calculate mixed electronic/proton vibrational free energy surfaces as functions of two solvent coordinates. Instead, they calculated solvated proton potentials obtained by the assumption that the inertial polarization of the solvent responds instantaneously to the proton position. (This is the limit opposite to the standard adiabatic limit of the fast proton vibrational motion responding instantaneously to... 

The two-dimensional electron transfer diabatic free energy surfaces in Figure 7 have been analyzed with the Golden Rule rate expression given in Eq. 46. This analysis suggests that FT and EPT are possible for both systems, but FT is the dominant path due to significant overlap between the proton vibrational wave... 

The distance between the proton donor and acceptor also affects the rates and mechanisms of PCET reactions. As this distance decreases, the barrier along the proton coordinate rp decreases and eventually disappears. As illustrated in Figures 3-5, the height of this barrier determines the number of localized proton vibrational states. In particular, if the barrier along the proton coordinate is very low or nonexistent, the proton vibrational wave functions are mixtures of a and b, so the distinction between ET and EPT is unclear. For systems in which the potential is a double well along the proton coordinate, however, the rate of EPT decreases as the barrier along the proton coordinate increases due to the decrease of the overlap of the proton vibrational wave functions for the a and b states. 

Since the dielectric continuum representation of the solvent has significant limitations, the molecular dynamics simulation of PCET with explicit solvent molecules is also an important direction. One approach is to utilize a multistate VB model with explicit solvent interactions [34-36] and to incorporate transitions among the adiabatic mixed electronic/proton vibrational states with the Molecular Dynamics with Quantum Transitions (MDQT) surface hopping method [39, 40]. The MDQT method has already been applied to a one-dimensional model PCET system [39]. The advantage of this approach for PCET reactions is that it is valid in the adiabatic and non-adiatic limits as well as in the intermediate regime. Furthermore, this approach is applicable to PCET in proteins as well as in solution. 

Figure 6 Proton vibrational density of states for water contained in 52% hydrated Vycor at 298 K (solid circles). For comparison the corresponding quantity for bulk water (empty circles) is also given [69].

Figure 8 Proton vibrational density of statesfor water at surface of H2O hydrated d-CPC protein 0 = 27.5°, for three temperatures, 333, 223, 150 K, and two levels of hydration, h = 0.50 (crosses) and h = 0.25 (solid circles) [49].

Vibrational spectroscopy measures atomic oscillations practically on the scale as the scale of proton dynamics, 10-15 to 10 12 s. Fillaux et al. [110] note that optical spectroscopies, infrared and Raman, have disadvantages for the study of proton transfer that preclude a complete characterization of the potential. (However, the infrared and Raman techniques are useful to observe temperature effects inelastic neutron spectra are best observed at low temperature.) As mentioned in Ref. 110, the main difficulties arise from the nonspecific sensitivity for proton vibrations and the lack of a rigorous theoretical framework for the interpretation of the observed intensities. 

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