The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on thermally activated barrier crossing, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry. Theoretical as well as numerical approaches are discussed for single- and many-dimensional metastable systems (including fields) in gases and condensed phases. The role of many-dimensional transition-state theory is contrasted with Kramers' reaction-rate theory for moderate-to-strong friction; the authors emphasize the physical situation and the close connection between unimolecular rate theory and Kramers' work for weakly damped systems. The rate theory accounting for memory friction is presented, together with a unifying theoretical approach which covers the whole regime of weak-to-moderate-to-strong friction on the same basis (turnover theory). The peculiarities of noise-activated escape in a variety of physically different metastable potential configurations is elucidated in terms of the mean-first-passage-time technique. Moreover, the role and the complexity of escape in driven systems exhibiting possibly multiple, metastable stationary nonequilibrium states is identified. At lower temperatures, quantum tunneling effects start to dominate the rate mechanism. The early quantum approaches as well as the latest quantum versions of Kramers' theory are discussed, thereby providing a description of dissipative escape events at all temperatures. In addition, an attempt is made to discuss prominent experimental work as it relates to Kramers' reaction-rate theory and to indicate the most important areas for future research in theory and experiment.

Reaction-rate theory: fifty years after Kramers

Since to form a hole the size of a molecule in a liquid requires almost the same increase in free energy as to vaporize a molecule, the concentration of vapor above the liquid is a measure of such ``molecular'' holes in the liquid. This provides an explanation of the law of rectilinear diameters of Cailletet and Mathias. The theory of reaction rates yields an equation for absolute viscosity applicable to cases involving activation energies where the usual theory of energy transfer does not apply. This equation reduces to a number of the successful empirical equations under the appropriate limiting conditions. The increase of viscosity with shearing stress is explained. The same theory yields an equation for the diffusion coefficient which when combined with the viscosity and applied to the results of Orr and Butler for the diffusion of heavy into light water gives a satisfactory and suggestive interpretation. The usual theories for diffusion coefficients and absolute electrical conductance should be replaced by those developed here when ion and solvent molecule are of about the same size.

Viscosity, Plasticity, and Diffusion as Examples of Absolute Reaction Rates

Implicit Solvation Models: Equilibria, Structure, Spectra, and Dynamics.

Starting from known properties of non-specific salt effects on the surface tension at an air–water interface, we propose the first general, detailed qualitative molecular mechanism for the origins of ion-specific (Hofmeister) effects on the surface potential difference at an air–water interface; this mechanism suggests a simple model for the behaviour of water at all interfaces (including water–solute interfaces), regardless of whether the non-aqueous component is neutral or charged, polar or non-polar Specifically, water near an isolated interface is conceptually divided into three layers, each layer being 1 water-molecule thick We propose that the solute determines the behaviour of the adjacent first interfacial water layer ( I 1 ); that the bulk solution determines the behaviour of the third interfacial water layer ( I 3 ), and that both I 1 and I 3 compete for hydrogen-bonding interactions with the intervening water layer ( I 2 ), which can be thought of as a transition layer The model requires that a polar kosmotrope (polar water-structure maker) interact with I 1 more strongly than would bulk water in its place; that a chaotrope (water-structure breaker) interact with I 1 somewhat less strongly than would bulk water in its place; and that a non-polar kosmotrope (non-polar water-structure maker) interact with I 1 much less strongly than would bulk water in its place We introduce two simple new postulates to describe the behaviour of I 1 water molecules in aqueous solution The first, the ‘relative competition’ postulate, states that an I 1 water molecule, in maximizing its free energy (—δG), will favour those of its highly directional polar (hydrogen-bonding) interactions with its immediate neighbours for which the maximum pairwise enthalpy of interaction (—δ H ) is greatest; that is, it will favour the strongest interactions We describe such behaviour as ‘compliant’, since an I 1 water molecule will continually adjust its position to maximize these strong interactions Its behaviour towards its remaining immediate neighbours, with whom it interacts relatively weakly (but still favourably), we describe as ‘recalcitrant’, since it will be unable to adjust its position to maximize simultaneously these interactions The second, the ‘charge transfer’ postulate, states that the strong polar kosmotrope–water interaction has at least a small amount of covalent character, resulting in significant transfer of charge from polar kosmotropes to water–especially of negative charge from Lewis bases (both neutral and anionic); and that the water-structuring effect of polar kosmotropes is caused not only by the tight binding (partial immobilization) of the immediately adjacent ( I 1 ) water molecules, but also by an attempt to distribute among several water molecules the charge transferred from the solute When extensive, cumulative charge transfer to solvent occurs, as with macromolecular polyphosphates, the solvation layer (the layer of solvent whose behaviour is determined by the solute) can become up to 5- or 6-water-molecules thick We then use the ‘relative competition’ postulate, which lends itself to simple diagramming, in conjunction with the ‘charge transfer’ postulate to provide a new, startlingly simple and direct qualitative explanation for the heat of dilution of neutral polar solutes and the temperature dependence of relative viscosity of neutral polar solutes in aqueous solution This explanation also requires the new and intriguing general conclusion that as the temperature of aqueous solutions is lowered towards o °C, solutes tend to acquire a non-uniform distribution in the solution, becoming increasingly likely to cluster 2 water molecules away from other solutes and surfaces (the driving force for this process being the conversion of transition layer water to bulk water) The implications of these conclusions for understanding the mechanism of action of general (gaseous) anaesthetics and other important interfacial phenomena are then addressed

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0033583500005369

The Hofmeister effect and the behaviour of water at interfaces.

Concepts in reaction dynamics

The theory of absolute reaction rates is developed for condensed phases. The equation for the rate of a reaction of any order in any phase where the slow process is the passage over an energy barrier consists of the product of a transmission coefficient κ, a frequency kT/h, an equilibrium constant between an activated complex and the reactants and an activity coefficient factor. Previous theories of reaction rates such as Bronsted's, the collision theory of Mc C. Lewis, etc., are seen to be special cases of the general theory. A variety of examples are considered.

The Absolute Rate of Reactions in Condensed Phases

Answer to a Criticism by Moelwyn‐Hughes of a Paper by Wynne‐Jones and Eyring

[With the development of statistical mechanics and the formulation of potential-energy surfaces the way was prepared for the development of an improved treatment of the absolute rates of reactions. A simple formulation that has been of very great value was made in 1935 by Henry Eyring (cf. also Paper 4). The paper reproduced below is not his first on this subject but is somewhat more comprehensive in the treatment of the activated complex than the earlier paper referred to in the introduction. In particular, the nature of the quasi-equilibrium between reactants and the activated complex is described at some length. Also, the theory is shown to explain the rates of certain reactions which on the basis of collision theory are abnormally fast or abnormally slow.

William Francis Kenrick Wynne-Jones was born in 1903 and was Leverhulme Research Fellow at Princeton University when he collaborated with Henry Eyring in the writing of the paper here reproduced. He was for a time head of the chemistry division of the Royal Aircraft Establishment, Farnborough, and at present is Professor and Head of the School of Chemistry at the University of Newcastle. In 1965 he was created Baron Wynne-Jones of Abergele.]
Abstract
The theory of absolute reaction rates is developed for condensed phases. The equation for the rate of a reaction of any order in any phase where the slow process is the passage over an energy barrier consists of the product of a transmission coefficient κ, a frequency kT/h, an equilibrium constant between an activated complex and the reactants and an activity coefficient factor. Previous theories of reaction rates such as Bronsted's, the collision theory of McC. Lewis, etc., are seen to be special cases of the general theory. A variety of examples are considered.

Paper 5 – the absolute rate of reactions in condensed phases†

/pdf/errata-the-absolute-rate-of-reactions-in-condensed-phases-2y4q2ygtte.pdf

W. F. K. Wynne‐Jones

Papers

The Absolute Rate of Reactions in Condensed Phases

Answer to a Criticism by Moelwyn‐Hughes of a Paper by Wynne‐Jones and Eyring

Paper 5 – the absolute rate of reactions in condensed phases†

Errata: The Absolute Rate of Reactions in Condensed Phases