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 relaxation time of the nuclei of sodium ions has been measured for aqueous solutions of sodium chloride and sodium perchlorate at 25°. The longitudinal and transverse relaxation times are equal and depend on solution composition according to the rate law T1−1=17.55+0.55cNaCl+11.95cNaClO4±0.30, with T1 in seconds and cX in moles of X per liter, for single and mixed electrolyte solutions at concentrations less than 1M. Deviations from the equation are small up to 3M total concentration, and also in D2O if the coefficients are first multiplied by the ratio of solvent viscosities.The limiting value of T1 at low concentration agrees roughly with the calculation of the effect of fluctuating electric‐field gradients due to reorientational Brownian motion of water molecules coordinated to the sodium ion, but there are some very uncertain factors in the calculation. The coefficients of the rate law may be related to the distance of closest approach of the ions in various ways, with the result that this distanc...

Nuclear Magnetic Relaxation in Ionic Solution. I. Relaxation of 23Na in Aqueous Solutions of NaCl and NaClO4

A system of excess functions is developed for electrolyte solutions and other solutions with an essentially unsymmetrical solvent‐solute relation. These new functions vanish for a solution whose practical (molal scale) osmotic coefficient is unity at all compositions, temperatures and pressures. The use of these excess functions offers some advantages over other methods of comparing Mayer's ionic solution theory with experiment, of representing the properties of solutions of single or mixed electrolytes, and of making qualitative interpretations of the molecular basis of thermodynamic properties.Graphs showing the ionic‐strength dependence of the excess free energy, excess enthalpy, excess entropy, and excess volume are given for several aqueous solutions of single electrolytes up to 6 molal. Experimental values of the cluster integral sum, the characteristic function of the Mayer theory, have also been calculated. The concentration dependence of this function is very similar to that of the excess free en...

Thermodynamic Excess Functions for Electrolyte Solutions

For solutions of a mixture of two electrolytes with a common ion, the characteristic free energy function is ΔmGex, the change in excess free energy on forming the solution from solutions of the single electrolytes. This is closely related to ΔmS, where S is the cluster integral sum of the Mayer theory. For systems that conform to Harned's rule the contributions of most of the cluster integrals to ΔmS are negligible. The form of the principle contribution to ΔmS depends on whether the two electrolytes have the same charge type (symmetrical mixtures) or not.The equations for symmetrical mixtures which nearly conform to Harned's rule are developed in detail, first for the general case in which the components of the potential of average force are arbitrary and then for the special case of hard sphere ions, designated as the primitive model for electrolyte solutions. The leading term of ΔmS is determined by the difference in short‐range interaction of pairs of ions of the same charge and does not depend at al...

Mayer's Ionic Solution Theory Applied to Electrolyte Mixtures

A procedure recently developed by Talman for the rapid numerical evaluation of Fourier transforms of slowly decaying functions is applied to the evaluation of convolution integrals appearing in integral equations describing pair correlations in ionic systems. The correlation functions are tabulated at uniformly spaced intervals in a variable ρ=lnr, where r is the interparticle distance. In the regime of weak screening, this procedure permits simultaneous efficient sampling of both the rapidly varying part of the functions near particle contact and the long range slowly decaying portion. The effectiveness of the procedure is demonstrated by evaluating accurate solutions to the hypernetted chain equation for a model of a 2–2 aqueous electrolyte at 25 °C over the range of salt concentrations from 10−7 to 10−2 M. Comparison of these results to those obtained from other approximate integral equations shows that significant differences persist to exceedingly small concentrations.

Accurate solutions to integral equations describing weakly screened ionic systems

The Ornstein–Zernike equation with either the hypernetted chain (HNC) closure or a composite HNC/Percus–Yevick (PY) closure approximation is applied to the primitive model of highly asymmetric electrolytes that mimic ionic micellar solutions. There is substantial agreement of the calculated partial structure factor with the small angle neutral scattering data for a lithium dodecylsulfate solution. New theoretical results are applied to calculate the ionic self‐diffusion coefficients for Smoluchowski models with equilibrium structures obtained from the HNC approximation. Fair agreement with experimental data is found for the small ions whereas the theory predicts too fast diffusion for the colloidal particles.

Harold L. Friedman

Papers

Nuclear Magnetic Relaxation in Ionic Solution. I. Relaxation of 23Na in Aqueous Solutions of NaCl and NaClO4

Thermodynamic Excess Functions for Electrolyte Solutions

Mayer's Ionic Solution Theory Applied to Electrolyte Mixtures

Accurate solutions to integral equations describing weakly screened ionic systems

An integral equation approach to structure and dynamics of ionic colloidal solutions