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.

A new Monte Carlo simulation procedure is developed which is expected to produce more rapid convergence than the standard Metropolis method. The trial particle moves are chosen in accord with a Brownian dynamics algorithm rather than at random. For two model systems, a string of point masses joined by harmonic springs and a cluster of charged soft spheres, the new procedure is compared to the standard one and shown to manifest a more rapid convergence rate for some important energetic and structural properties.

Brownian dynamics as smart Monte Carlo simulation

The method of molecular dynamics is applied to a solvent‐averaged model of electrolyte solutions, described by a generalized Langevin equation. For Brownian motion without solute–solute interactions, we recover the characteristic features of an infinitely dilute solution. For interacting brownons, the results exhibit a noticeable dependence of the calculated self‐diffusion coefficients on the influence of the Coulomb forces. The model system exhibits ion association when the Coulomb forces are made strong enough.

Brownian dynamics: Its application to ionic solutions

Computations have been made for a system of charged hard spheres with parameters chosen to correspond to an aqueous solution of a 1 − 1 electrolyte in the range from 0.001 to 1M. Correlation functions were computed by the analogues of the HNC and PY integral equations due to Allnatt in which the integral equations are constructed after the Mayer resummation has been performed on the expansion of g(r). Activity and osmotic coefficients are computed both by the compressibility and pressure equations and tested for consistency. Based on this test and others, including a comparison with computations published by Carley, it is concluded that the HNC equation gives very accurate results for this primitive model at least up to 1M. The accurate results show that the effect of the excluded volume of the hard‐sphere cores has been considerably underestimated in earlier treatments of the primitive model.

Integral Equation Methods in the Computation of Equilibrium Properties of Ionic Solutions

The hypernetted‐chain integral equation is used to calculate the ion–ion pair correlation functions and the thermodynamic properties of models for aqueous alkali halides based on an ion–ion pair potential function having four terms: the usual Coulomb term, a core repulsion term of order r−9, a well‐known dielectric repulsion term of order r−4, and a “Gurney” term to represent the effect of the overlap of the structure‐modified regions, “cospheres,” about the ions when the ions come close together. The only parameter in the potential which is adjusted to fit excess free energy data for solutions is the coefficient Aij of the Gurney term for the interaction of ions of species i and j. This is scaled so it represents the molar free energy change of water displaced from the cospheres when they overlap. The corresponding entropy change Sij and volume change Vij are adjusted to fit, respectively, heat of dilution and apparent molal volume data. Some thermodynamic problems in this fitting process, due to the und...

Study of a Refined Model for Aqueous 1‐1 Electrolytes

The heats of solution of the sodium n-alkyl sulfonates from methyl to octyl have been measured at 25°C in water, D2O, and three alcohol-rich mixtures with water, all at solute concentrations low enough so that solute-solute interaction is negligible. Methylene-group contributions to the enthalpies of transfer are readily identified. Collation with the results of earlier studies of enthalpies of transfer leads to the conclusion that methylene-group enthalpies of transfer can be identified as follows: 0.87 kcal-mole−1 for transfers to the gas phase from water and −0.035 kcal-mole−1 for transfers to D2O from H2O, independent of the solute type provided only that methylene-group contributions can be identified in the data. Compared to other solvents, water is about as lipophilic as dimethylsulfoxide or a mixture of 27 moles of water with 73 moles of methanol. However, the range of the interactions between different groups on a given solute molecule seems to be much greater in water than in any of the other solvents studied, making it more difficult to identify group contributions to solvation in water. Another example of the complexity of the solvation of alkyl groups in water is encountered when one compares the solvation enthalpy of hexane in various solvents with some of the above results.

Harold L. Friedman

Papers

Brownian dynamics as smart Monte Carlo simulation

Brownian dynamics: Its application to ionic solutions

Integral Equation Methods in the Computation of Equilibrium Properties of Ionic Solutions

Study of a Refined Model for Aqueous 1‐1 Electrolytes

Enthalpies of alkyl sulfonates in water, heavy water, and water-alcohol mixtures and the interaction of water with methylene groups