Proton transfer dynamics defined

The proton transfer processes described above induce interesting effects on the geometry of these metal complexes upon protonation (see also Section II). If it is assumed that the equatorial cyano ligands form a reference plane and are stationary for any of these distorted octahedral cyano oxo complexes, the protonation/deprotonation process as illustrated in Scheme 3 is responsible for the oxygen exchange at the oxo sites. This process effectively induces a dynamic oscillation of the metal center along the O-M-O axis at a rate defined by kmv, illustrated in Fig. 15. This rate of inversion is determined by the rate at which the proton is transferred via the bulk water from the one... 

An interesting question then arises as to why the dynamics of proton transfer for the benzophenone-i V, /V-dimethylaniline contact radical IP falls within the nonadiabatic regime while that for the napthol photoacids-carboxylic base pairs in water falls in the adiabatic regime given that both systems are intermolecular. For the benzophenone-A, A-dimethylaniline contact radical IP, the presumed structure of the complex is that of a 7t-stacked system that constrains the distance between the two heavy atoms involved in the proton transfer, C and O, to a distance of 3.3A (Scheme 2.10) [20]. Conversely, for the napthol photoacids-carboxylic base pairs no such constraints are imposed so that there can be close approach of the two heavy atoms. The distance associated with the crossover between nonadiabatic and adiabatic proton transfer has yet to be clearly defined and will be system specific. However, from model calculations, distances in excess of 2.5 A appear to lead to the realm of nonadiabatic proton transfer. Thus, a factor determining whether a bimolecular proton-transfer process falls within the adiabatic or nonadiabatic regimes lies in the rate expression Eq. (6) where 4>(R), the distribution function for molecular species with distance, and k(R), the rate constant as a function of distance, determine the mode of transfer. 

Both experiments and theory join in the studies of hydrogen transfer reactions. In general, the approach is of two categories. The first involves the study of prototypical but well-defined molecular systems, either under isolated (microscopic) conditions or in complexes or clusters (mesoscopic) vdth the solvent, in the gas phase or molecular beams. Such studies over the past three decades have provided unprecedented resolution of the elementary processes involved in isolated molecules and en route to the condensed phase. Examples include the discovery of a magic solvent number for acid-base reactions, the elucidation of motions involved in double proton transfer, and the dynamics of acid dissociation in finite-sized clusters. For these systems, theory is nearly quantitative, especially as more accurate electronic structure and molecular dynamics computations become available. 

Proton transfer between donor and acceptor located on a surface of a protein, or a membrane, is a true representation of many reactions taking place in biochemical catalysis, and is the essence of proton-driven coupled reactions. The ability to measure and analyze the dynamics of proton flux between two defined sites allows one to probe a specific area of a macromolecule surface. 

The manner in which protons diffuse is a reflection of the physical properties of the environment, the geometry of the diffusion space, and the chemical composition of the surface that defines the reaction space. The biomembrane, with heterogeneous surface composition and dielectric discontinuity normal to the surface, markedly alters the dynamics of proton transfer reactions that proceed close to its surface. Time-resolved measurements of fast, diffusion-controlled reactions of protons with chromophores and fluorophores allow us to gauge the physical, chemical, and geometric characteristics of thin water layers enclosed between phospholipid membranes. Combination of the experimental methodology and the mathematical formalism for analysis renders this procedure an accurate tool for evaluating the properties of the special environment of the water-membrane interface, where the proton-coupled energy transformation takes place. 

Among such 16 SET paths, we here pick up a single one that seems to serve as a typical example of a series of dynamics of dimerization and double proton transfer as in Fig. 7.19. To track the position of protons, H5 and HIO in Fig. 7.17, the relative coordinate, Xi and X2 are defined and... 

In this method, one considers that the interactions of the proton transfer chain with the rest of the protein and the solvent generate friction and random forces. These processes are characterized by phenomenological parameters evaluated by generating molecular dynamics trajectories, which are also used to build the PMF. The PMF and the phenomenological parameters are then introduced into the Langevin equation to simulate the time evolution of the protonation state of the chain." A transit time can be defined and compared with the experimental data. ... 

Electron Nuclear Dynamics (48) departs from a variational form where the state vector is both explicitly and implicitly time-dependent. A coherent state formulation for electron and nuclear motion is given and the relevant parameters are determined as functions of time from the Euler equations that define the stationary point of the functional. Yngve and his group have currently implemented the method for a determinantal electronic wave function and products of wave packets for the nuclei in the limit of zero width, a "classical" limit. Results are coming forth protons on methane (49), diatoms in laser fields (50), protons on water (51), and charge transfer (52) between oxygen and protons. 

At equilibrium, Eq. (1) is in its dynamic condition, i.e., the rate of forward reaction equals the rate of the reverse reaction. If Eq. (1) departs from equilibrium, i.e., one of the directions of the reaction is faster than the other, then the net fiow of protons and electrons, or current, develops. The anode is defined as the electrode at which the de-electronation reaction occurs and the cathode as the electrode at which the electronation reaction occurs. The rate of the electron transfer reaction can be written in terms of current, which is defined by the movement of electrical charges carried by electrons in an electronic conductor and by ions in an ionic conductor. The more the system is away from equilibrium, the higher the current. As the... 

---