Nonadiabatic Tunneling Proton Transfer

General Nonadiabatic Proton Transfer Perspective and Rate Constant 

The rate constant for nonadiabatic PT between reactant and product proton ground vibrational states with the H-bond separation Q fixed is [1, 26] 

For extremely low temperatures C0g RT, the Q vibrational mode resides primarily in its ground state, and the PT rate expression is [1] 

Here AQ = Qp eq — Qa.eq is the difference in the P and R equilibrium positions, and Eq = jmgCOgAQ is the associated reorganization energy. is a quantum energy associated with the tunneling probability s variation with the Q vibration 

Even with AQ = 0 (Eg = 0), C is increased from its fixed value C(Qeqj by exp( L/ fflgj there is a finite probability of smaller H-bond separations even at low T due to Qs the zero point motion. The ratio E -JhcoQ identifies E i as a quantum energy scale for the localization of the Q wavefunction [1, 5]. When E ilhcoQ 1, the coupling C is essentially that for fixed Q,=Qeq. As Eai/ticoQ increases, C increases, corresponding to increased quantum accessibility of smaller Q values. 

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Below we will use Eq. (16), which, in certain models in the Born-Oppenheimer approximation, enables us to take into account both the dependence of the proton tunneling between fixed vibrational states on the coordinates of other nuclei and the contribution to the transition probability arising from the excited vibrational states of the proton. Taking into account that the proton is the easiest nucleus and that proton transfer reactions occur often between heavy donor and acceptor molecules we will not consider here the effects of the inertia, nonadiabaticity, and mixing of the normal coordinates. These effects will be considered in Section V in the discussion of the processes of the transfer of heavier atoms. 

In this section, we switch gears slightly to address another contemporary topic, solvation dynamics coupled into the ESPT reaction. One relevant, important issue of current interest is the ESPT coupled excited-state charge transfer (ESCT) reaction. Seminal theoretical approaches applied by Hynes and coworkers revealed the key features, with descriptions of dynamics and electronic structures of non-adiabatic [119, 120] and adiabatic [121-123] proton transfer reactions. The most recent theoretical advancement has incorporated both solvent reorganization and proton tunneling and made the framework similar to electron transfer reaction, [119-126] such that the proton transfer rate kpt can be categorized into two regimes (a) For nonadiabatic limit [120] ... 

The DKL model for nonadiabatic proton transfer at a fixed distance R allows for the tunneling of the proton out of any of the bound vibrations, n, associated with the proton-transfer coordinate, into any of the bound vibrations in the product state, m [10]. 

In 1989, Borgis and Hynes proposed a theory for nonadiabatic proton transfer that includes all the parameters contained with the DKL model. In addition, they addressed the important issue of low-frequency vibrations serving as promoting modes in proton tunneling [11]. For nonadiabatic proton transfer, the distance dependence of the tunneling coupling, C(Q), has the analytical form [13]... 

Whether the process is adiabatic or nonadiabatic (tunneling), the range of proton transfer is restricted to distances no more than 1 A and mechanisms rely exclusively on reactive complex formation. Thus, in contrast to electron transfer, the short range, bond-length nature of proton transfer necessitates considerations of structure. 

The second molecular mechanism encountered in this process of acid/base solvation is diffusion in water of the H3O+ or OH ions formed during the ionization step described previously. It is represented in Figure 6.5 for both H3O+ and O H ions. The mechanism of this proton transfer is not the same as that encountered in ionization. Following Ando and Hynes (19) this proton transfer is also adiabatic. This point is however a matter of discussion, as other authors (21) find that this may be true in supercooled water but at room temperature and above, a nonadiabatic tunnelling is responsible for this proton transfer. In this mechanism, the influence of the surrounding is less marked, and instead of having a potential V(q, Qq)... 

Kiefer, P. and Hynes, J. (2004). Kinetic isotope effects for nonadiabatic proton transfer reactions in a polar environment 1 Interpretation of tunneling kinetic isotopic effects. J. Phys. Chem. A. 108, 11793-11808... 

Nonlinear behavior is also observed in the wide-range (0.1-2.5 GPa) pressure dependence of the ESPT rate of DCN2 in alcohols [44[. At low pressure, the proto-lytic photodissociation rate slightly increases, reaching the maximum value. With further pressure increase this rate decreases below the initial value at atmospheric pressure (Fig. 13.11). To explain the unique nonexponential dependence of ESPT rate constants on pressure, as well as temperature, Huppert et al. have developed an approximate stepwise two coordinate proton-transfer model that bridges the high-temperature nonadiabatic proton tunneling limit with the rate constant... 

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