6.2.2. Definition of Effective Properties 3064 6.3. Response Properties to Magnetic Fields 3066 6.3.1. Nuclear Shielding 3066 6.3.2. Indirect Spin−Spin Coupling 3067 6.3.3. EPR Parameters 3068 6.4. Properties of Chiral Systems 3069 6.4.1. Electronic Circular Dichroism (ECD) 3069 6.4.2. Optical Rotation (OR) 3069 6.4.3. VCD and VROA 3070 7. Continuum and Discrete Models 3071 7.1. Continuum Methods within MD and MC Simulations 3072

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Quantum mechanical continuum solvation models.

https://zenodo.org/record/1258475/files/article.pdf

Electron transfers in chemistry and biology

From the Publisher:
Artificial "neural networks" are now widely used as flexible models for regression classification applications, but questions remain regarding what these models mean, and how they can safely be used when training data is limited. Bayesian Learning for Neural Networks shows that Bayesian methods allow complex neural network models to be used without fear of the "overfitting" that can occur with traditional neural network learning methods. Insight into the nature of these complex Bayesian models is provided by a theoretical investigation of the priors over functions that underlie them. Use of these models in practice is made possible using Markov chain Monte Carlo techniques. Both the theoretical and computational aspects of this work are of wider statistical interest, as they contribute to a better understanding of how Bayesian methods can be applied to complex problems. Presupposing only the basic knowledge of probability and statistics, this book should be of interest to many researchers in statistics, engineering, and artificial intelligence. Software for Unix systems that implements the methods described is freely available over the Internet.

Bayesian learning for neural networks

Hamiltonian dynamics can be used to produce distant proposals for the Metropolis algorithm, thereby avoiding the slow exploration of the state space that results from the diffusive behaviour of simple random-walk proposals. Though originating in physics, Hamiltonian dynamics can be applied to most problems with continuous state spaces by simply introducing fictitious "momentum" variables. A key to its usefulness is that Hamiltonian dynamics preserves volume, and its trajectories can thus be used to define complex mappings without the need to account for a hard-to-compute Jacobian factor - a property that can be exactly maintained even when the dynamics is approximated by discretizing time. In this review, I discuss theoretical and practical aspects of Hamiltonian Monte Carlo, and present some of its variations, including using windows of states for deciding on acceptance or rejection, computing trajectories using fast approximations, tempering during the course of a trajectory to handle isolated modes, and short-cut methods that prevent useless trajectories from taking much computation time.

MCMC using Hamiltonian dynamics

Dynamic strength of molecular adhesion bonds.

The dynamic solvation time correlation function Z(t) is, within linear response, formulated in terms of the intermolecular solute–solvent interactions, without recourse to the intrinsically macroscopic concept of a cavity carved out of a dielectric medium. For interaction site models (ISM) of both the solute and the solvent, the theory relates the fluctuating polarization charge density of the solvent to the fluctuating vertical energy gap that controls Z(t). The theory replaces the factual (or bare) solute charge distribution by a surrogate expressed in terms of the solute–solvent site–site direct correlation functions. Calculations for solute ions in water and in acetonitrile lead to Z(t) and the second moment of the associated spectral density in good agreement with molecular dynamics simulation results in the literature. We also use the theory to calculate Z(t) for model solutes in which the ‘‘sudden’’ change of the charge distribution involves multipoles of higher order. The response is qualitatively...

A molecular theory of solvation dynamics

The rate constant for the Fe2+–Fe3+ electron exchange is formulated as k23= ∫ 0∞g23(r) k23(r) 4πr2 dr, a form which also is used to analyze the data for the nuclear spin relaxation in Al3+ induced by collision with Ni2+. It is assumed that the equilibrium pair correlation function g23(r) is the same function of ionic composition and temperature in the two cases and that in the spin relaxation process the local rate constant k23(r) has the form that may be deduced from the Solomon–Bloembergen equations. In the case of the exchange reaction the theory of k23(r) is developed with respect to the contributions from slow inner shell or outer shell reorganization (activation) dynamics. It is concluded that in the present case these complications are not important and that the controlling dynamics is the crossing from the reactant to the product diabatic Born– Oppenheimer surface. Neither the exchange nor the spin relaxation data can be accounted for if the smallest metal–metal distance in collisions is that given by the closest approach of the envelopes of the M(H2O)6n+ complexes. However, allowing for overlap of the envelopes as one complex pokes into the interstices of the other reduces the distance of closest approach from 6.9 to 4.5 A. Then one can find Gurney type models for the ion–ion forces in solution such that the model calculations are in good agreement with the experimental exchange and relaxation rate constants and their dependence on temperature and ionic strength, as far as the limited data for the last allow.

The theory of the Fe2+–Fe3+ electron exchange in water

By using a Green function Q to characterize the linear response of a dielectric body to electric charges, we obtain a theory for the solvent dielectric contribution to relaxation along the reaction coordinate RC(t) in an electron transfer process. For an electron transfer reaction model, in which the ions are embedded in a dielectric continuum, the theory gives, at t=0, the reorganization free energy derived by Marcus in 1956. For the same model the characteristic time τQ associated with RC(t) is evaluated in terms of the dielectric function eω of the medium. How the rate constant ket for an electron transfer process depends on τQ is illustrated for both high‐barrier and low‐barrier cases by approximating RC(t) as a Smoluchowski process on a potential surface. Applying the theory to a molecular model (charged hard sphere ions in a dipolar hard sphere solvent), treated in the mean spherical approximation for the response at any frequency (Wolynes, 1987), indicates that the effects of the molecular structure of the solvent on τQ are large even if the ion is several times larger than a solvent molecule.

Green function theory of charge transfer processes in solution

Corresponding states ideas are applied to correlate a number of equilibrium properties of ionic fluids. Consideration is given to the thermodynamic excess functions used to characterize dilute ionic fluids, to ion pairing and higher association, and to the characteristic coexistence curve and critical point found in many ionic fluids. The correlation applies to simple ionic fluids such as liquid or gaseous salts, to plasmas, and to ionic solutions as well as to the primitive model to the degree that the properties of all these systems are known. New HNC calculations are reported that were made to elucidate the structural changes in an ionic system as it is compressed along an isotherm corresponding to 2–2 aqueous electrolytes. Finally an evaluation is given of the usefulness of a number of approximation methods for calculating the equilibrium properties of the primitive model, and presumeably other Hamiltonian models, in various regions of the corresponding states diagram. Among these methods is the theory of Bjerrum (1926) which is surprisingly accurate, although some of its limitations are illustrated in the present work.

Harold L. Friedman

Papers

A molecular theory of solvation dynamics

The theory of the Fe2+–Fe3+ electron exchange in water

Green function theory of charge transfer processes in solution

Corresponding states for ionic fluids

The Visible and Ultraviolet Absorption Spectrum of the Tetrachloroferrate(III) Ion in Various Media1