Polarizable Continuum Models PCM

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... 

As can be seen from the histogram in Figure l-l(b), the loose conformation is preferred over the tight one, a result only possible with inclusion of solvent effects. Ab-initio calculations of those conformers show that, without the inclusion of solvent effects, the tight conformer is preferred by 7.4 kcal/mol, while the inclusion of solvent effects (with polarizable continuum model, PCM) shifts the preference towards the loose conformer, which becomes more stable than the tight one by 0.1 kcal/mol. 

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. 

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. 

It is relatively straightforward to implement the polarizable continuum model (PCM) via Eq. (39).11 12,105,117 The potential of the reaction field, VCT(r), is due to the ostensible (virtual) charge distribution o(r) on the cavity surface, which in turn is related to the potential Vsoiutc(r) that arises from the nuclei and electrons of the solute molecule, Eq. (2). Since the latter is likely to be further polarized by VCT(r), thus affecting Vs0,utc(r), iteration to self-consistency is needed,105,106 as already has been pointed out. (However Montagnani and Tomasi suggest that this often has little practical consequence.)118... 

Application of CBS extrapolations to the A5-ketosteroid isomerase-catalyzed conversion of A5-androstene-3,17-dione to the A4 isomer (Fig. 4.10) provides a test case for extensions to enzyme kinetics. This task requires integration of CBS extrapolations into multilayer ONIOM calculations [56, 57] of the steroid and the active site combined with a polarizable continuum model (PCM) treatment of bulk dielectric effects [58-60], The goal is to reliably predict absolute rates of enzyme-catalyzed reactions within an order of magnitude, in order to verify or disprove a proposed mechanism. 

Since the Tomassi et a/.86,87 Polarizable Continuum Model, PCM, to describe dielectric solvent effects is implemented within the Gaussian9881 suite of programs, Peralta and Barone s modified version of the Gaussian98 suite of programs can be used to calculate solvent effects on the FC, SD and DSO terms (however for the FC term the perturbative FPT approach should be used if solvent effects are to be calculated). 

DFT was employed to study the mechanism of ammonolysis of phenyl formate in the gas phase, and the effect of various solvents on the title reaction was assessed by the polarizable continuum model (PCM). The calculated results show that the neutral concerted pathway is the most favourable one in the gas phase and in solution.24 The structure and stability of putative zwitterionic complexes in the ammonolysis of phenyl acetate were examined using DFT and ab initio methods by applying the explicit, up to 7H20, and implicit PCM solvation models. The stability of the zwitterionic tetrahedral intermediate required an explicit solvation by at least five water molecules with stabilization energy of approximately 35 kcalmol-1 25... 

In the standard continuum solvation model, exemplified by the Polarizable Continuum Model (PCM) we developed in Pisa [9], the solute-solvent interaction energies are described by four Qx operators, each having a clearly defined physical nature. Each term gives a contribution to the solvation energy which has the nature of a free energy. The free energy of M in solution is thus defined as the sum of these four terms, supplemented by a fifth describing contributions due to thermal motions of the molecular framework ... 

In a previous contribution in this book, Cancfes has presented the formal background of the integral equation methods for continuum models and has shown how the corresponding equations can be solved using numerical methods. In this chapter the specific aspects of the implementation of such numerical algorithms within the framework of the Polarizable Continuum Model (PCM) [1] family of methods will be considered. 

A more sophisticated description of the solvent is achieved using an Apparent Surface Charge (ASC) [1,3] placed on the surface of a cavity containing the solute. This cavity, usually of molecular shape, is dug into a polarizable continuum medium and the proper electrostatic problem is solved on the cavity boundary, taking into account the mutual polarization of the solute and solvent. The Polarizable Continuum Model (PCM) [1,3,7] belongs to this class of ASC implicit solvent models. 

The purpose of this chapter is to present an overview of the computational methods that are utilized to study solvation phenomena in NMR spectroscopy. We limit the review to first-principle (ab initio) calculations, and concentrate on the most widespread solvation model the polarizable continuum model (PCM), which has been largely described in the previous chapter of this book. 

The recent progress of computational quantum chemistry has made it possible to get realistic descriptions of vibrational frequencies for polyatomic molecules in solution. The first attempt in this direction was made by Rivail el al. [1] by exploiting a semiempirical QM molecular model coupled with a continuum description of the medium to compute vibrational frequency shifts for molecular solutes. An extension to ab initio QM methods, including the treatment of electron correlation effects and electrical and mechanical anharmonicities, was then proposed [2 1] in the framework of the Polarizable Continuum Model (PCM). 

B. Mennucci, J. Tomasi, R. Cammi, J. R. Cheeseman, M. J. Frisch, F. J. Devlin, S. Gabriel and P. J. Stephens, Polarizable Continuum Model (PCM) calculations of solvent effects on optical rotations of chiral molecules, J. Phys. Chem. A, 106 (2002) 6102-6113. 

The approach which will be reviewed here has been formulated within the framework of the quantum mechanical polarizable continuum model (PCM) [7], Within this method, the effective properties are introduced to connect the outcome of the quantum mechanical calculations on the solvated molecules to the outcome of the corresponding NLO experiment [8], The correspondence between the QM-PCM approach and the semi-classical approach will also be discussed in order to show similarities and differences between the two approaches. 

The sharp dielectric surface was implemented for the Polarizable Continuum Model (PCM) for the first time by Bonaccorsi et al. [9] and further developed by Hoshi etal. [10] The only requirements for the employment of the PCM is a knowledge of the constitutive parameters of the system geometry of the dielectrics and corresponding dielectric constants. The same model has been subsequently revisited in 2000 [11] supplemented with the modelling of nonelectrostatic interactions (see later). 

In vacuo most peptides are constrained to quasi-planar conformations (, i/i 0°, 180°), while Polarizable Continuum Model (PCM) calculations show that in aqueous solution another stable structure appears for 4> -60°, tft -60° this is noteworthy because such angles are typical of a-helix conformations of polypeptides, which is particularly favoured by the solvent [2], This feature is illustrated in Figure 3.2, where Ramachandran maps (i.e. plots of the energy versus 4> and tft) are reported both in vacuo and in aqueous solution. 

J. Tomasi, R. Cammi and B. Mennucci, Medium effects on the properties of chemical systems An overview of recent formulations in the polarizable continuum model (PCM), Int. J. Quantum Chem., 75 (1999) 783-803. 

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