Analysis of xd and Gad clarifies and quantifies the electronically adiabatic nature of PT when the relevant nuclear coordinate for the combined ET-PT reaction may be the proton displacement and is on the order of 1 For any pure ET reaction (also see the helpful comparison, inside the context of ET, of the 518-34-3 Epigenetic Reader Domain electronic and nonadiabatic couplings in ref 127), x in Figure 24 could be a nuclear reaction coordinate characterized by larger displacements (and therefore larger f values) than the proton coordinate in electron-proton transfer, but the relevant modes commonly have significantly smaller frequencies (e.g., 1011 s-1; see section 9) than proton vibrational frequencies. Consequently, based on eq five.56, the electronic coupling threshold for PTI-428 Technical Information negligible xd(xt) values (i.e., for the onset on the adiabatic regime) can be significantly smaller sized than the 0.05 eV value estimated above. Having said that, the V12 value decreases approximately exponentially with all the ET distance, plus the above evaluation applied to typical biological ET systems leads to the nonadiabatic regime. In general, charge transfer distances, specifics of charge localization and orientation, coupled PT, and relevant nuclear modes will ascertain the electronic diabatic or adiabatic nature of the charge transfer. The above discussion gives insight in to the physics and also the approximations underlying the model system made use of by Georgievskii and Stuchebrukhov195 to describe EPT reactions, however it also supplies a unified framework to describe unique charge transfer reactions (ET, PT, and EPT or the particular case of HAT). The following points that emerge in the above discussion are relevant to describing and understanding PES landscapes related with ET, PT, and EPT reactions: (i) Smaller V12 values create a larger range from the proton- solvent conformations on each and every side with the intersection amongst the diabatic PESs exactly where the nonadiabatic couplings are negligible. This circumstance leads to a prolonged adiabatic evolution in the charge transfer system more than each and every diabatic PES, exactly where V12/12 is negligible (e.g., see eq five.54). Even so, smaller sized V12 values also make stronger nonadiabatic effects close enough towards the transition-state coordinate, exactly where 2V12 becomes substantially larger than the diabatic power difference 12 and eqs 5.50 and five.51 apply. (ii) The minimum energy separation amongst the two adiabatic surfaces increases with V12, as well as the effects in the nonadiabatic couplings lower. This implies that the two BO states develop into very good approximations of your precise Hamiltonian eigenstates. Rather, as shown by eq five.54, the BO electronic states can differ appreciably from the diabatic states even near the PES minima when V12 is sufficiently significant to ensure electronic adiabaticity across the reaction coordinate variety. (iii) This very simple two-state model also predicts increasing adiabatic behavior as V12/ grows, i.e., as the adiabatic splitting increases and the power barrier (/4) decreases. Even when V12 kBT, so that the model leads to adiabatic ET, the diabatic representation may well still be handy to make use of (e.g., to compute energy barriers) provided that the electronic coupling is much less than the reorganization power. 5.three.three. Formulation and Representations of Electron- Proton States. The above evaluation sets circumstances for theReviewadiabaticity on the electronic element of BO wave functions. Now, we distinguish involving the proton coordinate R and a further collective nuclear coordinate Q coupled to PCET and construct mixed elect.