Chemical continuum models

Another aspect that has been theoretically studied109,124,129 is experimental evidence that Diels-Alder reactions are quite sensitive to solvent effects in aqueous media. Several models have been developed to account for the solvent in quantum chemical calculations. They may be divided into two large classes discrete models, where solvent molecules are explicitly considered and continuum models, where the solvent is represented by its macroscopic magnitudes. Within the first group noteworthy is the Monte Carlo study... 

Since a valid reaction model is a prerequisite for a continuum model, the first step in any case is to construct a successful reaction model for the problem of interest. The reaction model provides the modeler with an understanding of the nature of the chemical process in the system. Armed with this information, he is prepared to undertake more complex calculations. Chapters 20 and 21 of this book treat in detail the construction of reactive transport models. 

Lichtner, P. C., 1985, Continuum model for simultaneous chemical reactions and mass transport in hydrothermal systems. Geochimica et Cosmochimica Acta 49, 779-800. 

Continuum models have a long and honorable tradition in solvation modeling they ultimately have their roots in the classical formulas of Mossotti (1850), Clausius (1879), Lorentz (1880), and Lorenz (1881), based on the polarization fields in condensed media [32, 57], Chemical thermodynamics is based on free energies [58], and the modem theory of free energies in solution is traceable to Bom s derivation (1920) of the electrostatic free energy of insertion of a monatomic ion in a continuum dielectric [59], and Kirkwood and Onsager s... 

The present chapter thus provides an overview of the current status of continuum models of solvation. We review available continuum models and computational techniques implementing such models for both electrostatic and non-electrostatic components of the free energy of solvation. We then consider a number of case studies, with particular focus on the prediction of heterocyclic tautomeric equilibria. In the discussion of the latter we center attention on the subtleties of actual chemical systems and some of the dangers of applying continuum models uncritically. We hope the reader will emerge with a balanced appreciation of the power and limitations of these methods. 

From a computational view point, chemical reactions in solution present a yet not solved challenge. On one hand, some of the solvent effects can be approximated as if the solute molecule would be in a continuum with a given dielectric characterization of the liquid, and this view point has been pioneered by Bom [1], later by Kirkwood [2] and Onsager [3] and even later by many computational quantum chemists [4-9], On the other hand, the continuum model fails totally when one is interested in the specific... 

In addition to these external electric or magnetic field as a perturbation parameter, solvents can be another option. Solvents having different dielectric constants would mimic different field strengths. In the recent past, several solvent models have been used to understand the reactivity of chemical species [55,56]. The well-acclaimed review article on solvent effects can be exploited in this regard [57]. Different solvent models such as conductor-like screening model (COSMO), polarizable continuum model (PCM), effective fragment potential (EFP) model with mostly water as a solvent have been used in the above studies. 

It is established that a detailed understanding of chemical or biochemical systems is impossible without an accurate description of their solvent effects. Hence, tremendous effort has been made in the past to develop solvation models. In this chapter, a brief introduction to continuum solvation models and their applications are presented. Continuum models reasonably predict solvent effect on... 

Coarse-grained polymer models neglect the chemical detail of a specific polymer chain and include only excluded volume and topology (chain connectivity) as the properties determining universal behavior of polymers. They can be formulated for the continuum (off-lattice) as well as for a lattice. For all coarse-grained models, the repeat unit or monomer unit represents a section of a chemically realistic chain. MD techniques are employed to study dynamics with off-lattice models, whereas MC techniques are used for the lattice models and for efficient equilibration of the continuum models.36 2 A tutorial on coarse-grained modeling can be found in this book series.43... 

Subsequently, DFT methods (B3LYP functional ) were employed to compute (1) natural charges from which changes in charges are mapped out for comparison with the NMR-based conclusions, (2) GIAO-NMR to predict the chemical shifts for comparison with the experimental results, and (3) nuclear-independent chemical shift (NICS) in order to evaluate relative aromaticity in different rings. Finally, solvent effects were estimated by the polarized continuum model (PCM). In selected cases, parallel DNA-binding studies (with MCF-7 human mammary... 

For the description of a solution of alanine in water two models were compared and combined with one another (79), namely the continuum model approach and the cluster ansatz approach (148,149). In the cluster approach snapshots along a trajectory are harvested and subsequent quantum chemical analysis is carried out. In order to learn more about the structure and the effects of the solvent shell, the molecular dipole moments were computed. To harvest a trajectory and for comparison AIMD (here CPMD) simulations were carried out (79). The calculations contained one alanine molecule dissolved in 60 water molecules. The average dipole moments for alanine and water were derived by means of maximally localized Wannier functions (MLWF) (67-72). For the water molecules different solvent shells were selected according to the three radial pair distributions between water and the functional groups. An overview about the findings is given in Tables II and III. 

From a chemical perspective, dielectric- and conductor-like continuum models give sufficiently similar electrostatic results that the differences in their underlying assumptions appear to have no impact. Conductor-like models seem to be slightly more computationally robust in some instances, which may make tliem a better choice if instability is manifest in an SCRF calculation. Some concerns were raised initially that the post facto correction for dielectric behavior might render the models appropriate only for media having reasonably high dielectric constants, but a systematic study by Dolney et al. (2000) indicated non-polar solvents to be equally amenable to treatment by a COSMO model. 

At the heart of chemistry are atoms and molecules - they are the basis set in which chemical events are expressed. While the continuum models described in Chapter 11 can be very efficient and powerful in situations where the molecular nature of a surrounding condensed phase is superfluous to the question at hand, they are unsuitable when knowledge of the explicit behavior of the surroundings is deemed to be as important as its effect on some system embedded therein. 

In Section 11.4.6, the limitations of continuum models in their ability to treat non-equilibrium solvation, at least in their simplest incarnations, were noted and discussed. In principle, exphcit solvent models might be expected to be more appropriate for the study of chemical processes characterized by non-equilibrium solvation. In practice, however, the situation is not much better for the explicit models than for the implicit. 

All of the QM/MM models discussed this far, much like continuum models, envision partitioning a chemical system into (at least) two distinct regions, where the boundary between these regions is everywhere characterized by a very low level of electron density. That is, no atoms on one side of the boundary are bonded to atoms on the other side. As a result, the //qm/mm term in the Hamiltonian of Eq. (13.1) is restricted to non-bonded interactions. 

Basic Methods for Describing Chemical Kinetics in Condensed Media Continuum Models... 

In this paper, a continuum model for chemical osmosis in clay membranes is presented and its novel features, as compared to previous formulations are shown. A simplified version of the model, that allows for analytical solutions, is presented, and an application of this method is shown. 

A large variety of continuum models have been proposed and many are available in popular quantum chemical modeling packages. They differ in the sophistication of the procedure used to determine the shape of the cavity. In the simplest case, this is just a sphere, but most models nowadays use more tailored cavities (as in Figure 10.3), generated, for example, from the combination of a set of spheres placed around individual solute atoms. In most cases, the models include a relaxation of the electronic structure in response to the electric held created by the solvent around it, and in most cases this is then treated fully self-consistently. This effect can be quite important in some cases, as a polar solute may become considerably more polar due to interactions with a polar solvent. Different models are also parameterized in different ways. 

As the title indicates, this chapter focuses on methodological problems relating to the description of phenomena of chemical interest occurring in solution, using methods in which a part of the whole material system is described by continuum models. 

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