Continuum dielectric approaches

The complications for fhe fheoretical description of proton fransporf in the interfacial region befween polymer and water are caused by the flexibility of fhe side chains, fheir random distributions at polymeric aggregates, and their partial penetration into the bulk of water-filled pores. The importance of an appropriate flexibilify of hydrated side chains has been explored recently in extensive molecular modeling studies. Continuum dielectric approaches and molecular dynamics simulations have been utilized to explore the effects of sfafic inferfacial charge distributions on proton mobility in single-pore environments of Molecular level simulations were employed... 

Demchuk E, Wade RC (1996) Improving the continuum dielectric approach to calculating pKas of ionizable groups in proteins, J Phys Chem, 100 17373-17387... 

E. Demchuk, R. C. Wade, Improving the Continuum Dielectric Approach to Calculating pKas of lonizable Groups in Proteins, J. Phys. Chem. 1996, 100, 17373-17387. 

Truchon, f.-F., Nicholls, A., Roux, B., Ifiimie, R.I., and Bayly, C.I. (2009) Integrated continuum dielectric approaches to treat molecular polarizability and the condensed phase refractive index and implicit solvation. Journal of Chemical Theory and Computation, 5 (7), 1785-1802. 

EVB-based MD simulations as well as continuum dielectric approaches involve empirical correlations between the structure of acid-functionalized interfaces in PEM and proton distributions and mobilities in aqueous domains. The results remain... 

Electro-osmotic drag phenomena are closely related to the distribution and mobility of protons in pores. The molecular contribution can be obtained by direct molecular dynamics simulations of protons and water in single ionomer pores, as reviewed in the sections Proton Transport in Water and Stimulating Proton Transport in a Pore. The hydrodynamic contribution to nd can be studied, at least qualitatively, using continuum dielectric approaches. The solution of the Poisson-Boltzmann equation... 

J.-F. Truchon, A. Nicholls, B. Roux, R. I. Iftimie,and C. I. Bayly,/. Chew. Theory Cowpat, 5(7), 1785-1802 (2009). Integrated Continuum Dielectric Approaches to Treat Mole ar Polarizability and the Condensed Phase Refractive Index and Implicit Solvation. 

For reasons of space and because of their prime importance, we focus here on free energy calculations based on detailed molecular dynamics (MD) or Monte Carlo (MC) simulations. However, several other computational approaches exist to calculate free energies, including continuum dielectric models and integral equation methods [4,14]. 

In this section, a group of related approaches is discussed in which the continuum dielectric description of the microscopic environment is replaced by a more detailed model in which the atomic details of the structure and the dynamics of the microscopic environment are taken into account. These models will be referred to here as coupled DFT/Molecular Mechanics (DFT/MM). For a general overview of coupled ab initio/Molecular Mechanics methods, see the recent reviews by Aquist and Warshel186 and by Gao187. 

Karelson et al. [268] used the AMI D02 method with a spherical cavity of 2.5 A, radius to study tautomeric equilibria in the 3-hydroxyisoxazole system (the keto tautomer 13 is referred to as an isoxazolone). AMI predicts 13 to be 0.06 kcal/mol lower in energy than 14 in the gas phase. However, the AMI dipole moments are 3.32 and 4.21 D for 13 and 14, respectively. Hydroxy tautomer 14 is better solvated within the D02 model, and is predicted to be 2.6 kcal/mol lower in energy than 13 in a continuum dielectric with e = 78.4. Karelson et al. note, however, that the relative increase in dipole moment upon solvation is larger for 13 than for 14 (aqueous AMI dipole moments of 5.05 and 5.39 D, respectively). This indicates that the relative magnitude of gas-phase dipole moments will not always be indicative of which tautomer will be better solvated within a DO solvation approach — the polarizability of the solutes must also be considered. In any case, the D02 model is consistent with the experimental observation [266] of only the hydroxy tautomer in aqueous solution. 

Born s idea was taken up by Kirkwood and Onsager [24,25], who extended the dielectric continuum solvation approach by taking into account electrostatic multipole moments, Mf, i.e., dipole, quadrupole, octupole, and higher moments. Kirkwood derived the general formula ... 

The remainder of this contribution is organized as follows In the next section, the connection between the experimentally observed dynamic Stokes shift in the fluorescence spectrum and its representation in terms of intermolecular interactions will be given. The use of MD simulation to obtain the SD response will be described and a few results presented. In Section 3.4.3 continuum dielectric theories for the SD response, focusing on the recent developments and comparison with experiments, will be discussed. Section 3.4.4 will be devoted to MD simulation results for e(k, w) of polar liquids. In Section 3.4.5 the relevance of wavevector-dependent dielectric relaxation to SD will be further explored and the factors influencing the range of validity of continuum approaches to SD discussed. 

A final perpective on the dielectric continuum (DC) approach for solvent RF energetics is provided by a comparison of As obtained for ET in a given DBA system, using both DC and molecular-level (ML) treatments. Figure 3.31 presents As calculated for ET in aqueous solution between transition metal redox complexes (D (Ru2+/3+) and A (Co2+/3+)) linked by an organic bridge (a tetraproline helix) [19],... 

Also the second class of methods include very different approaches however, in all of them we can individuate a common aspect, namely the use of a mean-field description for the part of the system encircling the subsystem of real interest. In the application of this class of methods to the study of liquid solutions, the most important mean-field approach is represented by continuum models. In such models, the solute is assumed to be inside a cavity of proper shape and dimension within an infinite continuum dielectric mimicking the solvent. 

By contrast, the description given by a continuum description does not require any knowledge of the solvent configuration around the solute as a structureless continuum dielectric is introduced instead. The response of such a dielectric to the presence of the solute is determined by its macroscopic properties (namely the dielectric constant and the refractive index) and thus it will be implicitly averaged. Contrary to what happens in a QM/MM approach, here a single calculation on a given solute contained within the continuum dielectric will be sufficient to get the correct picture of the solvated system. 

Although many satisfactory VCD studies based on the gas phase simulations have been reported, it may be necessary to account for solvent effects in order to achieve conclusive AC assignments. Currently, there are two approaches to take solvent effects into account. One of them is the implicit solvent model, which treats a solvent as a continuum dielectric environment and does not consider the explicit intermolecular interactions between chiral solute and solvent molecules. The two most used computational methods for the implicit solvent model are the polarizable continuum model (PCM) [93-95] and the conductor-like screening model (COSMO) [96, 97]. In this treatment, geometry optimizations and harmonic frequency calculations are repeated with the inclusion of PCM or COSMO for all the conformers found. Changes in the conformational structures, the relative energies of conformers, and the harmonic frequencies, as well as in the VA and VCD intensities have been reported with the inclusion of the implicit solvent model. The second approach is called the explicit solvent model, which takes the explicit intermolecular interactions into account. The applications of these two approaches, in particular the latter one will be further discussed in Sect. 4.2. 

Several combinations of QM approaches with a continuum dielectric model [175, 325, 360-369] have been focused upon. Continuum solvation models have their origin in the work of Onsager [325] for describing ions in solution these models have shown flexibility and accuracy enough to become a popular tool nowadays. Generally in these methods the solute is placed inside a cavity with appropriate shape, made in a continuous medium characterised by a dielectric constant. The electronic distribution of the solute induces a charge density at the surface of the cavity which creates a field that modifies the energy... 

The answer to these issues is to take some account of the environment which, after all, is required for the system to be stable in the first place. The simplest computational approach is to embed the model system in a continuum dielectric with a dielectric constant chosen to simulate the environment. There has been some debate about what the effective dielectric constant for the interior of a protein should be. Based on a combination of experimental measurements and theoretical simulations [17, 42, 43] the interi-... 

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