Conductor-like PCM

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. 

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. 

The conductor-like screening model (COSMO) is a continuum method designed to be fast and robust. This method uses a simpler, more approximate equation for the electrostatic interaction between the solvent and solute. Line the SMx methods, it is based on a solvent accessible surface. Because of this, COSMO calculations require less CPU time than PCM calculations and are less likely to fail to converge. COSMO can be used with a variety of semiempirical, ah initio, and DFT methods. There is also some loss of accuracy as a result of this approximation. 

The Polarizable Continuum Model (PCM) employs a van der Waals surface type cavity, a detailed description of the electrostatic potential, and parameterizes the cavity/ dispersion contributions based on the surface area. The COnductor-like Screening... 

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. 

Conductor-like screening model (COSMO) is one of variants of PCM method [29]. In this method, the cavity is considered to be embedded in a conductor with an infinite dielectric constant [29]. An extension to this method, called COSMO-RS... 

Since its original description at the semiempirical level, COSMO has also been generalized to the ab initio and density functional levels of theory as well (Klamt et al. 1998). In addition, conductor-like modifications of the PCM formalism have also been described, and to distinguish between the conductor-like version and the original (dielectric) version, the acronyms C-PCM and D-PCM have been adopted for the two, respectively (Barone and Cossi 1998). 

As outlined in Section IV, in the conductor-like version of PCM we have a simple expression of the energy functional, Equation (1.15). It can be discretized as ... 

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). 

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. 

The conductor-like screening model (COSMO) approach replaces the dielectric medium with a conducting medium (basically a medium that effectively has an infinite dielectric constant). Interlocking spheres are used to generate the cavity. The conductor-like screening has been implemented as a PCM version, called CPCM.128,129... 

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]. 

PCM are explicated in Table 11.1. Also listed in this table are the forms of K and R for the so-called conductor-like model, C-PCM [25]. This model is considerably simpler in that the matrix D is absent. C-PCM is identical to the generalized conductor-iike screening modei (GCOSMO) [78], and almost identical to the original COSMO [37]. (G]COSMO was introduced prior to SS(V)PE/1EF-PCM, based on ad hoc arguments and designed to achieve the correct oo limit. We... 

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. 

A method that is very similar to PCM is the conductor-like screening model (COSMO) developed by Klamt and eoworker and used later by Truong and coworkers, and by Barone and Cossi. This model assumes that the surrounding medium is well modeled as a conductor (thus simplifying the eleetrostatics computations) and corrections are made a posteriori for dielectric behavior. 

Several groups have also made relevant contribution to the evolution of the original PCM. A related model based on conductor-like screening (COSMO) has been developed recently by Klamt and Schuiirmann [13]. Likewise, another approach to the PCM has been proposed in which the cavity surface is determined in terms of an electronic isodensity surface [14]. Olivares del Valle and coworkers [15] have focused their attention on aspects such as the inclusion of correlation effects in the PCM, or on the role of nonadditive effects in solute-solvent interactions. Pascual-Ahuir et al. [16] have paid most attention to the problem of the definition of the cavity surface. The work done in Barcelona has focussed mainly on the parametrization of the PCM to treating aqueous and nonaqueous solvents, as well as the application of the PCM to the study of biochemical systems [17, 18]. Finally, we and others have made new methodological developments to allow the implementation of the PCM in molecular dynamics or in Monte Carlo calculations [19]. 

Finally, to simplify the electrostatic algorithm some methods start with a dielectric permittivity e = oo corresponding to a conductor like solvent and then correct the result either by the ratio 2(e-l)/(2e-i-l)of the Onsager factor of the actual dielectric permittivity of the solvent to the limiting value when e = oo, or by the ratio of the Born factors ( -l)/e. Itis noteworthy that the difference may not be negligible for low dielectric constants. This approximation has first been introduced in the COSMO model (Klamt and Schuurmann 1993). A version of the PCM model, known as C-PCM (Barone and Cossi 1998) uses the same approximation to evaluate the electrostatic solvation term. 

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). 

COSMO = conductor-like screening model PCM = polarizable continuum method QM/MM = quantum mecha-nics/molecular mechanics. 

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