Proton tunneling potential energy surface

The effect of the solvent upon the breaking of the symmetry of the potential energy surface for proton transfer has a profound consequence for the reaction dynamics for proton transfer. The tunneling of the proton out of the reactant state... 

This model has obvious shortcomings. For example, the interaction with the solvent in the initial state is straightforward since the proton is in the ionic form, whereas in the final state, the proton is the nonionic adsorbed H atom and its interaction with the solvent should be negligible. No consideration of this fact was made in the potential of the final state Uf m Eq. (43). However, this treatment incorporates the basic feature of the proton transfer reaction interaction with the solvent, tunneling as well as classical transition of the proton, and the effect of the electric field on the potential energy surfaces of the system. 

This variation in the isotope effect, due to variation in the isotope sensitivity of vf, has been called the Westheimer symmetry effect, and it will be one of the central ideas of this paper. However, in connection with proton transfers it has been attacked, for when more realistic potential energy surfaces are used (that is pf > 0), a much greater degree of force constant asymmetry is required to get a much reduced isotope effect9-11. Bell has therefore suggested that much of the observed variation in the isotope effect is due to variation in the tunnel correction, QhIQd-... 

With one exception, these results are based solely on quantum-chemical calculations of the potential energy surface. Theoretical evaluation of the transfer dynamics has been attempted only for the formic acid dimer, for which two general level splittings have been observed and assigned to synchronous double proton tunneling in the ground state and a vibrational excited state, respectively. 

The potential energy surface for the proton motion is not of a simple shape in our model calculation. Hence, the Eckart barrier formula is used for proton tunneling by adjusting the two variables in it [41]. Thus, the barrier for the proton transfer was fitted to the following Eckart formula ... 

IV. Proton Tunneling in Symmetric and Near-Symmetric Potential Energy Surface, 158... 

The ultrafast PT, which occurs typically on time scales of 10 13-10 14 s will not be considered. Such transfers are observed in molecular systems in which the potential energy surface (PES) governing the proton motion is essentially barrierless but has different minima positions in different electronic states, so that the proton finds itself in an off-equilibrium position after electronic excitation and relaxes to the new equilibrium position. The contribution of tunneling may be disregarded and the rate of these processes does not depend very strongly on temperature. These reactions, which are of great current interest, are intensely studied by ultrafast laser spectroscopy and are reviewed elsewhere [16,17],... 

IV. PROTON TUNNELING IN SYMMETRIC AND NEAR-SYMMETRIC POTENTIAL ENERGY SURFACE... 

Figure 3. Zig-zag tunneling path in a two-dimensional electron-proton tunneling space. The wavy line denotes the electron s tunneling when the proton rearranges to the proper configuration to symmetrize the electron potential energy surface. The straight arrows denote the protons motion for the initial i and final f electron states,...

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