Noam Agmon

The Grotthuss mechanism

Abstract Suggested mechanisms for proton mobility are confronted with experimental findings and quantum mechanical calculations, indicating that no model is consistent with the existing data. It is suggested that the molecular mechanism behind prototropic mobility involves a periodic series of isomerizations between H 9 O 4 + and H 5 O 2 + , the first trigerred by hyrdogen-bond cleavage of a second-shell water molecule and the second by the reverse, hydrogen-bond formation process.

CO binding to heme proteins: A model for barrier height distributions and slow conformational changes

A model for the dependence of the potential energy barrier on a ‘‘protein coordinate’’ is constructed. It is based on a two dimensional potential energy surface having as variables the CO–iron distance and a conceptual protein coordinate. The distribution of barrier heights observed in kinetics follows from an initial Boltzmann distribution for the protein coordinate. The experimental nonexponential rebinding kinetics at low temperatures or large viscosities (when the protein coordinates can be assumed ‘‘frozen’’) can be fit with a simply parametrized energy surface. Using the same energy surfaces and the theory of bounded diffusion perpendicular to the reaction coordinate, we generate (in qualitative agreement with experiment) the survival probability curves for larger diffusivity, when the constraint on the protein coordinate is relaxed. On the basis of our results, the outcomes of new experiments which examine the concepts underlying the theory can be predicted.

Geminate recombination in excited‐state proton‐transfer reactions: Numerical solution of the Debye–Smoluchowski equation with backreaction and comparison with experimental results

The well‐known phenomenon of proton dissociation from excited‐state hydroxy‐arenes is analyzed by the Debye–Smoluchowski equation which is solved numerically with boundary conditions which account for the reversibility of the reaction. The numerical solution is then compared with the measured dissociation profiles which were obtained by picosecond time‐resolved fluorescence spectroscopy. The intrinsic rate constants thus determined are used to predict steady‐state rates, yields, and pK values, in agreement with experiment.

An Algorithm for Finding the Distribution of Maximal Entropy

Abstract An algorithm for determining the distribution of maximal entropy subject to constraints is presented. The method provides an alternative to the conventional procedure which requires the numerical solution of a set of implicit nonlinear equations for the Lagrange multipliers. Here they are determined by seeking a minimum of a concave function, a procedure which readily lends itself to computational work. The program also incorporates two preliminary stages. The first verifies that the constraints are linearly independent and the second checks that a feasible solution exists.

A bond-order analysis of the mechanism for hydrated proton mobility in liquid water.

Bond-order analysis is introduced to facilitate the study of cooperative many-molecule effects on proton mobility in liquid water, as simulated using the multistate empirical valence-bond methodology. We calculate the temperature dependence for proton mobility and the total effective bond orders in the first two solvation shells surrounding the H(5)O(2) (+) proton-transferring complex. We find that proton-hopping between adjacent water molecules proceeds via this intermediate, but couples to hydrogen-bond dynamics in larger water clusters than previously anticipated. A two-color classification of these hydrogen bonds leads to an extended mechanism for proton mobility.

Geminate recombination in proton‐transfer reactions. II. Comparison of diffusional and kinetic schemes

The diffusional and kinetic approaches are compared for geminate dissociation–recombination reactions. When steady‐state rate coefficients to and from a distance defined as a ‘‘complex cage’’ are evaluated from the diffusion equation, one obtains encouraging agreement between the transient analytic solution of the rate equations and the exact numerical solution for diffusion with backreaction over a finite time regime. However, the rate equations cannot accurately describe the decay of the dissociating molecule for very long times, since as we prove below, the asymptotic decay according to the diffusional scheme is t−3/2, while for the rate equations it is exponential. New experiments, over an extended time regime confirm these conclusions.

Energy, entropy and the reaction coordinate: thermodynamic-like relations in chemical kinetics☆

Abstract A simple thermodynamic-like interpretation of the relation between the kinetic and the thermodynamic parameters of chemical reactions (“linear free energy relations”) is discussed and applied. The central concept is the introduction of mixing (or configurational) entropy to account for the activation barrier of chemical reactions.

Mechanism of hydroxide mobility

Abstract A suggested mechanism for hydroxide mobility in water identifies the rate limiting step as a cleavage of a second shell hydrogen bond which converts a H 7 O 4 − ion (triply coordinated hydroxide) to (HOHOH) − (deprotonated water dimer). Proton transfer is enabled by an additional O–O bond contraction, not required in H 5 O 2 + . This explains why the activation energy for hydroxide mobility is larger than that of proton mobility by about 0.5 kcal/mol. The transfer cycle is terminated by hydrogen-bond formation to the other oxygen center. Available experimental data, and most of the computational results, can be rationalized in the framework of the above model.

Spherical symmetric diffusion problem

We introduce a general and versatile MS Windows application for solving the spherically symmetric diffusion problem, involving up to two coupled spherically symmetric Smoluchowski equations. The application is based on a modular, configurable, user‐friendly graphical interface, in which input parameters are introduced through a graphical representation of the system of partial differential equations and output attributes can be obtained graphically during propagation.

Diffusion with back reaction

The diffusion equation for a constant and a linear potential is solved with boundary conditions which account for back‐reaction (desorption). The solution is given in terms of Green’s function, from which expressions for the survival probability are derived. Inclusion of back reaction generally results in an ultimate survival probability of unity.