Proton Donor-Acceptor Motion

The proton donor-acceptor motion plays an important role in PCET reactions. This motion modulates the proton tunneling distance and therefore the overlap between the reactant and product proton vibrational wavefunctions. Thus, the nonadiabatic coupling between the reactant and product vibronic states for PCET 

In the simplest case, the R mode is characterized by a low frequency and is not dynamically coupled to the fluctuations of the solvent. The system is assumed to maintain an equilibrium distribution along the R coordinate. In this case, ve can exclude the R mode from the dynamical description and consider an equilibrium ensemble of PCET systems with fixed proton donor-acceptor distances. The electrons and transferring proton are assumed to be adiabatic with respect to the R coordinate and solvent coordinates within the reactant and product states. Thus, the reaction is described in terms of nonadiabatic transitions between two sets of intersecting free energy surfaces ( R, and ej, Zp, corresponding to 

The above rate expression does not follow rigorously from the Golden Rule general expression. Nevertheless, it provides a physically reasonable method for estimating the rate constant in cases for which the dynamical coupling of the slow R mode to the solvent fluctuations is negligible. 

In another limit, the R mode is characterized by a high frequency Q and a relatively low reduced mass M. In this case, the motion along the R mode occurs on a much faster timescale than the timescale associated with the dominant solvent fluctuations, so the R mode fluctuations are dynamically uncoupled from the solvent fluctuations. In contrast to the previous case of the slow dynamically uncoupled R mode, however, the quantum character of this motion becomes important, especially at low temperatures where To include these quan- 

This expression formally resembles the expression in Eq. (16.4) except that the quantities are calculated for pairs of mixed electron-proton-R-mode vibronic free energy surfaces. 

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This chapter presents a general theoretical formulation for PCET and summarizes the applications of this theory to a wide range of experimentally relevant systems. Section 16.2 reviews the fundamental physical concepts of PCET reactions and discusses approaches for inclusion of the proton donor-acceptor motion, explicit molecular solvent and protein, and the corresponding dynamical effects. Section 16.3 provides an overview of theoretical studies of PCET reactions in solution and in proteins. General conclusions are given in Section 16.4. 

We have used this theoretical formulation to analyze the dynamical aspects of model PCET reactions in solution with molecular dynamics simulations [56, 57]. For these model systems, the time dependence of the probability flux correlation function is dominated by the solvent damping term, and only the short-time equilibrium fluctuations of the solvent impact the rate. The proton donor-acceptor motion does not impact the dynamical behavior of the reaction but does influence the magnitude of the rate. 

The mode is a bending motion of the entire molecule which reduces primarily the proton donor-acceptor distance and introduces only slight changes in other parameters (see Fig. 11.10). A coherent excitation of very similar vibrational modes was found in all ESIPT molecules we investigated and also in DHAQ [30], BBXHQ [31], and 10-HBQ [32]. In HBT and HBO this mode also modulates the... 

The theoretical results were generated with the multistate continuum theory including the proton donor-acceptor vibrational motion. Reproduced from Ref [47]. 

To reliably describe PT reactions in the gas and condensed phases, the usual parameterization of a force field in terms of harmonic bonded interactions is not sufficient. H-bonded systems are quite anharmonic around the bottom of the well for bond-stretching motions, and angular bending vibrations are equally affected. Furthermore, the hydrogen motion between the donor and acceptor atoms is strongly coupled to the donor-acceptor motion. These aspects need to be taken into account for a reliable model of hydrogen or proton motion between a donor-acceptor pair. 

This interpretation of the microwave spectrum stimulated a flurry of activity to unearth the correct equilibrium geometry. It was suggested, for example, that photoelectron spectroscopy was not inconsistent with a cyclic structure whereas iirfrared photodissociation and matrix infrared measurements suggested the two molecules are not equivalent and supported the microwave equilibrium geometry. Another set of measurements led to the notion that a tunneling motion, similar to that in the HE dimer, which interchanges the roles of proton donor and acceptor, was responsible for the two IR bands observed in the gas phase. State selection in a hexapole electric field indicated that the dimer has a small dipole moment and that it is not a symmetric top structure. ... 

Next, Ch. 11 by Lochbrunner, Schriever and Riedle deals with excited electronic state intramolecular tautomerization proton transfers in nonpolar, rather than polar, solvents. But there is a connection to the previous chapter the ultrafast optical experiments discussed here emphasize evidence that the proton is not the reaction coordinate. The proton transfer is controlled by low vibrational modes of the photo-acids, rather than by the proton motion itself, an interpretation supported by separate vibrational spectroscopic studies and theoretical calculations The key role of modes reducing the donor-acceptor distance for proton transfer is highlighted, and for the featured molecule of this chapter, the proton adiabatically follows the low frequency modes, and no tunneling or barrier for the proton occurs. (See also Ch. 15 by Elsaesser for direct ultrafast vibrational studies on these issues). 

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