PCM method

There are many technical details involved in SCRF calculations, many of which the user can control. Readers of this book are advised to use the default values as much as possible unless they have carefully examined the original literature and tested their modifications. PCM methods are generally more accurate than the Onsager and COSMO methods. 

The original PCM method uses a cavity made of spherical regions around each atom. The isodensity PCM model (IPCM) uses a cavity that is defined by an isosurface of the electron density. This is defined iteratively by running SCF calculations with the cavity until a convergence is reached. The self-consistent isodensity PCM model (SCI-PCM) is similar to IPCM in theory, but different in implementation. SCI-PCM calculations embed the cavity calculation in the SCF procedure to account for coupling between the two parts of the calculation. 

The most common approach to solvation studies using an implicit solvent is to add a self-consistent reaction field (SCRF) term to an ab initio (or semi-empirical) calculation. One of the problems with SCRF methods is the number of different possible approaches. Orozco and Luque28 and Colominas et al27 found that 6-31G ab initio calculations with the polarizable continuum model (PCM) method of Miertius, Scrocco, and Tomasi (referred to in these papers as the MST method)45 gave results in reasonable agreement with the MD-FEP results, but the AM1-AMSOL method differed by a number of kJ/mol, and sometimes gave qualitatively wrong results. 

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... 

Model computational studies aimed at understanding structure-reactivity relationships and substituent effects on carbocation stability for aza-PAHs derivatives were performed by density functional theory (DFT). Comparisons were made with the biological activity data when available. Protonation of the epoxides and diol epoxides, and subsequent epoxide ring opening reactions were analyzed for several families of compounds. Bay-region carbocations were formed via the O-protonated epoxides in barrierless processes. Relative carbocation stabilities were determined in the gas phase and in water as solvent (by the PCM method). 

Table 10.8. n-Electron densities of the HOMO in some pyrimidines at the relevant carbons as calculated by the DFT B3LYP/6-31G(d)//SCRF=PCM method in water (Naumov and von Sonntag, unpublished results). Values of the percentage of OH-attack (in parentheses) are ... 

The first step of the COSMO implementation was the development of a cavity-construction scheme. Since I did not know about the PCM method at that time, which might be considered now as an inexcusable ignorance for a scientist working in that area, I developed an independent code for the cavity construction. Nevertheless, I started from the same idea,... 

In the linear-response-PCM method, the electronic coupling is given by a sum of two terms ... 

The free energies of activation for the Sn2 reactions between acetate ion and ethyl chloride, bromide, and iodide in DMSO and in water have been calculated at the MP4/CEP-31+G(d)/MP2 level of theory.87 The solvent was accounted for using the PCM method. There was good agreement (<2.6 kcalmol-1) between the calculated and experimental values for the reactions in DMSO and water and the relative reactivities of the halides were predicted correctly in both solvents. However, the rate increases found experimentally when the solvent was changed from water to DMSO were underestimated by up to 4.5 kcalmol-1. 

Apart from the ASC-PCM method developed by the Pisa group, there are several other methods based on the polarizable continuum model the MPE (multipole expansion method) by the Nancy group [19,20] and by Mikkelsen and co-workers [21,22], the GBA (generalized Bom approximation) by the Minneapolis group - Cramer and Truhlar [23-26] and others. 

There are currently three different approaches for carrying out ASC-PCM calculations [1,3]. In the original method, called dielectric D-PCM [18], the magnitude of the point charges is determined on the basis of the dielectric constant of the solvent. The second approach is C-PCM by Cossi and Barone [24], in which the surrounding medium is modelled as a conductor instead of a dielectric. The third, IEF-PCM method (Integral Equation Formalism) by Cances et al the most recently developed [16], uses a molecular-shaped cavity to define the boundary between solute and dielectric solvent. We have to mention also the COSMO method (COnductorlike Screening MOdel), a modification of the C-PCM method by Klamt and coworkers [26-28], In the latter part of the review we will restrict our discussion to the methods that actually are used to model solute-solvent interactions in NMR spectroscopy. 

Apart from the ASC-PCM method developed by the Pisa group, there are several other PCM-based methods the MPE (multipole expansion method) of the Nancy group... 

Ab initio calculations of solvent effects on ECD spectra are less abundant than those on OR. An ab initio study of the solvent effects on the ECD spectra were carried out by Pecul et al. [76] using the IEF-PCM method [44,45,47] at the DFT/B3LYP level using LAOs. The rotatory strengths were shown to be strongly influenced by a change of solvent, and for certain transitions in molecules such as methyloxirane, even... 

Our group has coupled the MST (PCM) method to Metropolis Monte Carlo sampling algorithms (MC-MST [78]). Within this approach cavitation and van der Waals terms are computed as in normal MST, while a semiclassical approach [79, 80] is used to compute the electrostatic component of solvation (see Equation (4.37)). Solute-solute energy terms are computed using a classical force field and Metropolis is then applied to the effective energy shown in Equation (4.38). 

In this contribution we will first outline the formalism of the ONIOM method. Although ONIOM has not yet been applied extensively to problems in the solvated phase, we will show how ONIOM has the potential to become a very valuable tool in both the explicit and implicit modeling of solvent effects. For the implicit modeling of solvent, we developed the ONIOM-PCM method, which combines ONIOM with the Polarizable Continuum Method (PCM). We will conclude with a case study on the vertical electronic transition to the it state in formamide, modeled with several explicit solvent molecules. 

As in the case of a microsolvation calculation itself, in a mixed explicit-implicit description the (explicit) solvent molecules and the solute often play different roles and require different levels of theory. Ideally one would use a hybrid method for the solute-solvent cluster, which is then embedded in a continuum. This is illustrated in Figure 4.9 for a chloride anion, methylchloride, and one explicit water molecule. With this in mind, we developed the ONIOM-PCM method [41],... 

T. Vreven, B. Mennucci, C. O. da Silva, K. Morokuma and J. Tomasi, The ONIOM-PCM method Combining the hybrid molecular orbital method and the polarizable continuum model for solvation. Application to the geometry and properties of a merocyanine in solution, J. Chem. Phys., 115 (2001) 62-72. 

Even with the use of the PCM method, which allows us to overcome some of the limitations of DFT calculations, our study is necessarily qualitative. Flowever, the preliminary PCM calculations give further support to our previous conclusions on the effect of... 

The last fundamental aspect characterizing PCM methods, i.e. their quantum mechanical formulation, is presented by Cammi for molecular systems in their ground electronic states and by Mennucci for electronically excited states. In both contributions, particular attention is devoted to the specific aspect characterizing PCM (and similar) approaches, namely the necessity to introduce an effective nonlinear Hamiltonian which describes the solute under the effect of the interactions with its environment and determines how these interactions affect the solute electronic wavefunction and properties. 

PCM method has been extended to compute both the electronic coupling Vs and the screening factor s. 

Acknowledgments Many people, both from our group in Pisa and other groups, have collaborated to the development of the PCM method for excited states M. Caricato, S. Comi, C. Curutchet, L. Frediani, C. Pomelli, G. Scalmani and G.D. Scholes. They are here collectively acknowledged. 

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