Mean reaction field method

The reported results for equilibrium properties were obtained by means of the standard Monte Carlo (MC), molecular dynamics (MD), and Gibbs ensemble (GE) simulation methods [23, 24], For the trial systems of a finite range the simple spherical cutoff was used, whereas in simulations of the full systems either the Ewald summation or the reaction field method were used. For further technical details we refer the reader to the original papers. 

Thermochemistry. Chen et al.168 combined the Kohn-Sham formalism with finite difference calculations of the reaction field potential. The effect of mobile ions into on the reaction field potential Poisson-Boltzman equation. The authors used the DFT(B88/P86)/SCRF method to study solvation energies, dipole moments of solvated molecules, and absolute pKa values for a variety of small organic molecules. The list of molecules studied with this approach was subsequently extended182. A simplified version, where the reaction field was calculated only at the end of the SCF cycle, was applied to study redox potentials of several iron-sulphur clusters181. 

This Chapter has outlined several different approaches to the computational determination of solution properties. Two of these address solute-solvent interactions directly, either treating the effects of individual solvent molecules upon the solute explicitly or by means of a reaction field due to a continuum model of the solvent. The other procedures establish correlations between properties of interest and certain features of the solute and/or solvent molecules. There are empirical elements in all of these methods, even the seemingly more rigorous ones, such as the parameters in the molecular dynamics/Monte Carlo intermolecular potentials, Eqs. (16) and (17), or in the continuum model s Gcavitation and Gvdw, Eqs. (40) and (41), etc. 

The classical-path approximation introduced above is common to most MQC formulations and describes the reaction of the quantum DoF to the dynamics of the classical DoF. The back-reaction of the quantum DoF onto the dynamics of the classical DoF, on the other hand, may be described in different ways. In the mean-field trajectory (MFT) method (which is sometimes also called Ehrenfest model, self-consistent classical-path method, or semiclassical time-dependent self-consistent-field method) considered in this section, the classical force F = pj acting on the nuclear DoF xj is given as an average over the quantum DoF... 

To answer the above question new results have been obtained by the study of very fast protolytic reactions in aqueous solution. These were carried out during the last few years by means of relaxation methods (sound absorption, dispersion of the dissociation field effect, temperature jump method) (for a survey cf. [3]). The neutralization reaction HgO+ -j- OH- - (Ha0)8 is the most characteristic example. It was possible to determine the rate constant of this reaction by measuring the time dependence of the dissociation field effect of very pure water of specific conductivity of 6 7 10-8 (at 25°C). 

This paper deals with one of the mean-field methods of modeling the connectivity build-up that can be applied to polymerization processes. As in the other mean-field methods of modeling, certain physical features such as concentration fluctuations or fluctuation coupled diffusion control of reaction steps, etc., are neglected. 

A similar system to that discussed in ref. [44] (tetrazine, tetrazole and pyrrole) has been studied by Manalo et al. [47] by means of the CSGT/ASC method at the B3LYP/6-311++G(2d,2p) level. The cavity was defined by using the Pauling radius for each solute atom. In this paper the effects of geometric relaxation (indirect effects) are found to be small, and the direct influence of the intensity of the solvent reaction field on the shielding constants dominates. However, the indirect effect has been found to be important for N, A-dimethylacetamidine in IEF-PCM calculations [48],... 

Solvation effects at the transition-state level of electron-transfer reactions is a field that is opening up by means of clusters reactions. Reactions within clusters (see Section 2.7) or at the surface of clusters (see Section 2.8) provide an experimental tool to observe the effect of gradual solvation on electron-transfer reactions. Femtosecond methods appear highly valuable for characterizing the electron transfer in reactions within clusters, since in neutral clusters the electrostatic effects of solvation will show up intensely at the electron-transfer level and for a short period of time, before the products are fully developed. In the gas phase the solvation of electrons is directly sensed by photoelectron spectroscopy, as exemplified in the (nonreactive) case of ultrafast solvation of electrons in water clusters [305]. 

The continuum model has been applied to an experimental study of the solvent effect on the 6-chloro-2-hydroxypyridine/6-chloro-2-pyridone equilibrium in a variety of essentially non-hydrogen-bonding solvents (Beak et al., 1980). In this study, a plot of log A nh/oh) versus (e - 1)/ (2e + 1), the solvent dielectric term, yielded a linear least-squares fit with a slope of 2.5 0.2, an intercept of -1.71, and a correlation coefficient of 0.9944. This result was used to estimate the gas phase free-energy difference of 9.2 kJ mole-1, which compares favorably with the observed value of 8.8 kJ mole-1 for this system. The authors also reported that alcohol solvents are correlated fairly well in this study but that other solvents seem to be divided into two classes, those that are electron-pair donors and those that are electron-pair acceptors in a hydrogen bond. The hydrogen bonding effect is assumed to be independent from the reaction field effect and is included in the continuum model by means of the Kamlet and Taft (1976) empirical parameters. The interested reader is referred to the original paper for a detailed discussion of the method and its application. 

In recent years, there have been many attempts to combine the best of both worlds. Continuum solvent models (reaction field and variations thereof) are very popular now in quantum chemistry but they do not solve all problems, since the environment is treated in a static mean-field approximation. The Car-Parrinello method has found its way into chemistry and it is probably the most rigorous of the methods presently feasible. However, its computational cost allows only the study of systems of a few dozen atoms for periods of a few dozen picoseconds. Semiempirical cluster calculations on chromophores in solvent structures obtained from classical Monte Carlo calculations are discussed in the contribution of Coutinho and Canuto in this volume. In the present article, we describe our attempts with so-called hybrid or quantum-mechanical/molecular-mechanical (QM/MM) methods. These concentrate on the part of the system which is of primary interest (the reactants or the electronically excited solute, say) and treat it by semiempirical quantum chemistry. The rest of the system (solvent, surface, outer part of enzyme) is described by a classical force field. With this, we hope to incorporate the essential influence of the in itself uninteresting environment on the dynamics of the primary system. The approach lacks the rigour of the Car-Parrinello scheme but it allows us to surround a primary system of up to a few dozen atoms by an environment of several ten thousand atoms and run the whole system for several hundred thousand time steps which is equivalent to several hundred picoseconds. 

---