Conductor-polarized continuum model

Over the last years, the basic concepts embedded within the SCRF formalism have undergone some significant improvements, and there are several commonly used variants on this idea. To exemplify the different methods and how their results differ, one recent work from this group [52] considered the sensitivity of results to the particular variant chosen. Due to its dependence upon only the dipole moment of the solute, the older approach is referred to herein as the dipole variant. The dipole method is also crude in the sense that the solute is placed in a spherical cavity within the solute medium, not a very realistic shape in most cases. The polarizable continuum method (PCM) [53,54,55] embeds the solute in a cavity that more accurately mimics the shape of the molecule, created by a series of overlapping spheres. The reaction field is represented by an apparent surface charge approach. The standard PCM approach utilizes an integral equation formulation (IEF) [56,57], A variant of this method is the conductor-polarized continuum model (CPCM) [58] wherein the apparent charges distributed on the cavity surface are such that the total electrostatic potential cancels on the surface. The self-consistent isodensity PCM procedure [59] determines the cavity self-consistently from an isodensity surface. The UAHF (United Atom model for Hartree-Fock/6-31 G ) definition [60] was used for the construction of the solute cavity. 

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. 

In addition to SMx and the cluster-continuum model, other continuum models have also been used to study reactions in liquids, including the polarized continuum model [133-135] (PCM), the conductor-like screening model (COSMO [136] and COSMO-RS [137,138]), the generalized COSMO [139] (GCOSMO) model, conductorlike PCM [140] (CPCM), and isodensity PCM [141] (IPCM). 

Generalized Bom (GB) approach. The most common implicit models used for small molecules are the Conductor-Like Screening Model (COSMO) [77,78], the DPCM [79], the Conductor-Like Modification to the Polarized Continuum Model (CPCM) [80,81], the Integral Equation Formalism Implementation of PCM (IEF-PCM) [82] PB models, and the GB SMx models of Cramer and Truhlar [23,83-86]. The newest Minnesota solvation models are the SMD universal Solvation Model based on solute electron density [26] and the SMLVE method, which combines the surface and volume polarization for electrostatic interactions model (SVPE) [87-89] with semiempirical terms that account for local electrostatics [90]. Further details on these methods can be found in Chapter 11 of Reference [23]. 

The cluster-continuum moder iUuslrated in scheme 1 was used to simulate the most common electrolytes of LIBs. The supra-molecular cluster applied to the inner ring (scheme 1) incorporates the mutual effect between salt and solvent molecules by including the first solvation shell of the salt. Due to the minor effect that the salt anion XT has on the reductive behavior of solvent molecules coordinated with Li, XT and the surrounding solvent molecules are not discussed in the current chapter. The bulk solvent effect in the second ring of scheme 1 is treated by polarized continuum models, such as PCM, conductor-like PCM (CPCM), isodensity PCM (IPCM), and self-consistent isodensity PCM (SCl-PCM), which were developed on the basis of the Onsager reaction field theory and are recognized to provide reliable results for systems without specific interactions such as hydrogen bond. 

In 1999, Quast found dipolar and polarizable solvents such as lV,iV -dimethylprop-ylene urea (DMPU) strongly affect and even may reverse the relative stabilities of the localized and delocalized structures of 4,8-diphenylsemibullvalene-2,6-dicarboni-trile. The author calculated electrical dipole and quadrupole moments and molecular polarizabilities using the B3LYP/6-31G method and computed solvation energies with the conductor-like polarized continuum model (CPCM). The results indicate that the solvent effects are due to the greater polarity and polarizability of the delocalized structures relative to the localized structures (Fig. 4.10) [10]. 

For solvation of small molecules, the polarizable continuum model (PCM) and its variants have been widely used for calculation of solvation energy. The conductor-like PCM (CPCM) model gives a concise formulation of solvent effect, in which the solvent s response to the solute polarization is represented by the presence of induced surface charges distributed on the solute-solvent interface. In this formulation, no volume polarization (extension of solute s electron distribution into the solvent region) is allowed. The induced surface charge counterbalances the electrostatic potential on the interface generated by the solute molecule. 

In order to model the surrounding enzyme and solvent, a continuum-solvation method is typically used, such as the polarizable continuum model (PCM) or the conductor-like solvent model (COSMO),employing a dielectric constant (e) close to 4, a common value to model the hydrophobic environment of an enzyme active site. For small QM models, the results may be very sensitive to this value, but the results typically become independent of the dielectric constant after the addition of -200 atoms. Often only the polar part of the solvation energy is included in QM-cluster calculations, although the non-polar parts (the cavitation, dispersion and repulsion energies) are needed to obtain valid solvation energies, as will be discussed below. 

Solvent effects may be treated using several models self-consistent reaction field (SCRF) (Karelson et aL 1986, 1993 Kirkwood 1934 Tapia and Goscinski 1975), polarizable continuum model (PCM) (Cammi and Tomasi 1995 Miertui et al. 1981 Tomasi and Persico 1994 Tomasi et al. 2005), surface and simulation of volume polarization for electrostatics (SS(V)PE) (Chipman 1997, 2000, 2002), and conductor-like screening model (COSMO) (Baldridge and Klamt 1997 Klamt 1995 Klamt and Schiiurmann 1993). 

Additionally, for flexible molecules, the presence of multiple conformations may require the consideration of solvent effects, mainly if experimental data in polar solvents are to be reproduced. The relative energies of conformers and their chiroptical properties can be largely affected by solvent effects, and thus, in some cases, the inclusion of either the polarizable continuum model (PCM) or the conductor-like screening model (COSMO) since geometry optimization steps may be beneficial." ... 

Having recognized the theoretical inadequacy of the dielectric theory for polar solvents, I started to reconsider the entire problem of solvation models. Because the good performance of dielectric continuum solvation models for water cannot be a result of pure chance, in some way there must be an internal relationship between these models and the physical reality. Therefore I decided to reconsider the problem from the north pole of the globe, i.e., from the state of molecules swimming in a virtual perfect conductor. I was probably the first to enjoy this really novel perspective, and this led me to a perfectly novel, efficient, and accurate solvation model based upon, but going far beyond, the dielectric continuum solvation models such as COSMO. This COSMO for realistic solvation (COSMO-RS) model will be described in the remainder of this book. 

Another type of mobility is that of electrons in the solid phase this is partly described by the continuum electrostatic approach for dielectrics and conductors, but for metals (the most important conductors) it is better to resort to the jellium model. A QM treatment of jellium models permits us to describe electric polarization waves (polarons, solitons) and their mutual interplay with the liquid across the surface. 

The lEF-PCM method creates the solute cavity via a set of overlapping spheres [34-36]. The COSMO [37] model differs from the PCM model in that a scaled conductor boundary condition is used instead of the much more complicated dielectric boundary condition for the calculation of the polarization charges of a molecule in a continuum like with lEF-PCM. In the case of lEF-PCM, frequency calculations at the same level of theory were performed to ensure that all structures are minima on the potential energy surface. 

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