Proton vibrationally adiabatic

Figure 5-3. Active site and calculated PES properties for the reactions studied, with the transferring hydrogen labelled as Hp (a) hydride transfer in LADH, (b) proton transfer in MADH and (c) hydrogen atom transfer in SLO-1. (i) potential energy, (ii) vibrationally adiabatic potential energy, (iii) RTE at 300K and (iv) total reaction path curvature. Reproduced with permission from reference [81]. Copyright Elsevier 2002...

We observe the coherent excitation of an optically inactive mode proving that the reactive process itself and not only the optical excitation drives the observed vibrational motions. Further we demonstrate that during the ESIPT the proton is adiabatically shifted from one site to the other and tunneling of the proton is not rate determining. The dynamics is entirely controlled by the skeletal modes. Interestingly, this is quite similar to ground state proton transfer of HC1, where the fluctuations of the water environment enable the adiabatic process [8]. 

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 vibrationally adiabatic proton wave functions provide the most useful description for PCET reactions. For typical single proton transfer reactions, the lowest adiabatic vibrational state is a double well along Zp, as shown in Figure 2a. In gen-... 

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 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... 

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. 

There have been a number of calculations recently on the vibrations of H5OJ beyond the harmonic approximation. As noted already, such calculations are essential due to the highly anharmonic nature of these vibrations. Attempts to go beyond the harmonic approximation have been done in reduced dimensionality [27, 56] and also with the additional vibrational adiabatic approximation [56], These calculations selected the three proton degrees of freedom and the OO-stretch as the reduced dimensionality space. While such approaches are better in... 

IV), the apparent activation energies depend solely on the solvent properties, so that the isotope substitution affects only the frequency factors through the proton vibration frequency Vy Therefore, from (83.IV) and (87.IV) for electronically non-adiabatic reactions, we get the equations... 

As for the ion AH itself, the calculation for the entirely nonadiabatic reaction does not require any serious limitations in the choice of the model. The calculation may be performed, taking account of all the intramolecular vibrations. However, for simplicity, we shall consider at first a simple model in which the reaction leads to a change of the characteristics of only the proton vibrational states and thus to be able to treat also partly adiabatic reactions (Figure 1). 

Hydrogen-atom or proton-transfer transfers between heavy atoms often lead to vibrationally adiabatic paths with two maxima. Formally, the resolution of this problem should be made in the fi amework of the canonically unified theory [5], In practice, given the approximate nature of our treatment, it suffices to use TST with AFj equal to the value for the maximum point. For these cases, the tunnelling correction of the particles wifli energies between that of the highest of the two maxima and the minimum between tiiese is calculated for the highest barrier only. 

The vibrationally adiabatic path of ISM and the LS potential are combined to reflect the fact that a hydrogen-bonded complex brings the structure of the reactants closer to that of the transition state, as shown in Mechanism (V.I). A hydrogen bond can be regarded as an incipient proton transfer, and the bond order at the precursor complex is no longer n=0, but the bond order of the B- -H bond in that complex, n. .. g. Similarly, for the products, the bond order is not n = 1 but the bond order of the H A bond in the successor complex, (1- h - a)- Thus, for a proton transfer in condensed media, the reaction coordinate n is only defined in the interval [%...b. (1 %...a)]- The precursor and successor complexes are included in the classical reaction path of ISM with a simple transformation of the reaction coordinate [3]... 

When a standard solvent is rq>laced by deuterated one, for example, H2O by D2O, we have the isotope effect by solvent with a complex character. The kinetic isotope effect is characteristic of proton transfer reactions. It depends on the following factors type of the dissociated bond, change in enthalpy, and character of the elementary step of proton transfer (adiabatic or tunneling). For the adiabatic character of the reaction, the isotope effect is maximum for the thamally neutral reaction. The main contribution to the isotope effect is made by the difference in zero energies AE of stretching vibrations of the A—and A—D bonds. The kyjko values are presented below, the effect is due to ASq only for different types of A—bonds (T= 298 K). 

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