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

/pdf/quantum-mechanical-continuum-solvation-models-3edv963g14.pdf

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.

We explore a recently developed theory of solvation dynamics that analyzes the molecular response of the solvent to a sudden change of the charge distribution of a solute particle immersed in it. We derive an approximate nonequilibrium distribution functionf

 ∑
 
(Γ, t) for a “surrogate” Hamiltonian description of the solvation dynamics process. The surrogate Hamiltonian is expressed in terms of renormalized solute-solvent interactions, a feature that allows us to introduce a simple reduction scheme in the many-body dynamics problem without losing essential solute-solvent static correlations that rule the equilibrium solvation. Withf

 ∑
 
(Γ, t) in hand we calculate the solvation time correlation function in two ways. The first one, previously reported, is basically a “dielectric formulation” in which the local polarization charge density of the solvent is the primary dynamical variable that couples to the field of the solute. In the new development reported here, the “site number density formulation,” the primary dynamical variables comprise the set of local solvent site number densities. We find that the dielectric formulation is embedded in the solvent site number density formulation as shown, for example, by comparing the respective time correlation functions of the solvation dynamics. An important feature of our approach is that at every stage the coupling between the solute and solvent is formulated in terms of the solute-solvent intermolecular interactions, rather than some sort of cavity construction. Furthermore, both the solute and the solvent molecules are represented by interaction site models. Applications of the dielectric theory are illustrated with calculations of the solvation dynamics of a cation in water and an exploration of the effect of the details of the charge distribution on the solvation dynamics of a benzenelike solute in acetonitrile.

Surrogate Hamiltonian description of solvation dynamics. Site number density and polarization charge density formulations

New spectral data are reported for NO2−, ClO2−, and ClO− in aqueous solution.The theory of the electron transfer spectra of aqueous halide ions is extended to uninegative polyatomic ions by allowing for the greater excitation energy of the polyatomic radicals produced in the act of absorption, as compared with the excitation energy of the atoms produced from halide ions. This additional excitation energy arises from the operation of the Franck‐Condon principle in determining the internuclear distances in the radical. Tri‐iodide ion is the only one of the uninegative ions for which the required data are available and for which these data are not consistent with the assignment of the intense ultraviolet bands to transitions involving transfer of an electron to the solvent.It is found that the low intensity absorption bands of NO2− and ClO2− coincide with the bands predicted by R. S. Mulliken for triatomic oxide molecules (AO2), with the same numbers of valence electrons.

On the Ultraviolet Absorption Spectra of Uninegative Ions

The β coefficients in the equation T1−1—T10−1=Σβscs, which represents the nuclear relaxation rate of 23Na+ in dilute aqueous solutions at 25° as a function of solute molarity, have been determined for a variety of ionic solutes and separated into cationic and anionic contributions. For many species β is simply expressed in terms of viscosity and volume effects. Large additional contributions to β are found for a group of symmetrical, singly charged oxy and fluoro anions of which ClO4=, studied in the previous paper, is typical. The same is true for ions such as SO4= and PO4−3 for which extra interaction (such as association) with Na+ has been deduced from other types of measurements. For some solutes, including sucrose, nonlinear contributions to T1−1 dominate at concentrations as low as 0.2M. In the case of SO4= the observed nonlinearity may be attributed to ion association, in which case a dissociation constant (molar scale) of 0.2, in agreement with the result of Davies may be deduced from the data if ...

Nuclear Magnetic Relaxation in Ionic Solution. II. Relaxation of 23Na in Aqueous Solutions of Various Diamagnetic Salts

Heats of Solution of Some Trifluoroacetates, Tetraphenylborates, Iodides, and Perchlorates in Water and in Propylene Carbonate and the Relative Enthalpies of Solvation of the Alkali Metal Ions in Propylene Carbonate

Harold L. Friedman

Papers

Surrogate Hamiltonian description of solvation dynamics. Site number density and polarization charge density formulations

On the Ultraviolet Absorption Spectra of Uninegative Ions

Nuclear Magnetic Relaxation in Ionic Solution. II. Relaxation of 23Na in Aqueous Solutions of Various Diamagnetic Salts

Heats of Solution of Some Trifluoroacetates, Tetraphenylborates, Iodides, and Perchlorates in Water and in Propylene Carbonate and the Relative Enthalpies of Solvation of the Alkali Metal Ions in Propylene Carbonate

Solvation enthalpies of various ions in water and heavy water