The PCM Model

Ire boundary element method of Kashin is similar in spirit to the polarisable continuum model, lut the surface of the cavity is taken to be the molecular surface of the solute [Kashin and lamboodiri 1987 Kashin 1990]. This cavity surface is divided into small boimdary elements, he solute is modelled as a set of atoms with point polarisabilities. The electric field induces 1 dipole proportional to its polarisability. The electric field at an atom has contributions from lipoles on other atoms in the molecule, from polarisation charges on the boundary, and where appropriate) from the charges of electrolytes in the solution. The charge density is issumed to be constant within each boundary element but is not reduced to a single )oint as in the PCM model. A set of linear equations can be set up to describe the electrostatic nteractions within the system. The solutions to these equations give the boundary element harge distribution and the induced dipoles, from which thermodynamic quantities can be letermined. 

The, S n2 reaction between lithium isothiocyanate ion pair and methyl fluoride has been calculated at the MP2(full)/6-31H-G //HF/6-311- -G level of theory in the gas phase and in acetone using the PCM model.108 Both the gas phase and acetone reactions occur with inversion, rather than retention, of configuration. However, the transition states and products are different in the gas phase and in solution methyl thiocyanate is formed in the gas phase by transition state (72) whereas methyl isothiocyanate is formed much more slowly in acetone via the looser transition state (73). 

We have now achieved a situation in which dielectric continuum solvation models in general, and especially COSMO, are quite well established for SCF ground-state calculations of organic molecules. Many of the methods, tools, and properties available for gas-phase calculation can also be performed in a dielectric continuum solvation model. The PCM model including C-PCM provides the greatest breadth of implemented functionality. 

Luque and Orozco [62] have developed a parameterization of the PCM model for semi-empirical methods, but that has not been... 

Charges can be obtained at different level of moments such as monopole (s = 1), dipole (s = 3) and quadrupole (s = 9). Torsion energy barriers for the HS-SH molecule calculated by several methods can be seen in Fig. 9 [90]. For the PCM model of this molecule the number of expansion centers is six (c = 6) beside the atomic centers, one center per S-H bond is further included. It can be seen that the PCM result is very close to the CMMM one and the PCM charges can be used for calculating intramolecular electrostatic interactions as well. 

As a matter of illustration, let us write in detail the numerical algorithm for computing ER(p,p ) with the PCM model (1.30) and (1.31) and the Galerkin approximation with P0 planar boundary elements ... 

For a molecule in solution described by the PCM model, the nuclear shielding constant and the indirect spin-spin coupling constants are determined as second derivatives of the free energy functional G of the solute-solvent system [34] ... 

The functional to be minimized is constructed as below in the new implementation of the PCM model [29], including the repulsion and dispersion terms Grep and Gdis while in the former PCM scheme the functional included the polarization term Gpol only. 

Here we further examine the suitability of QM-SCRF methods in two chemical reactions the base-catalysed hydrolysis of methyl acetate in water, and the steric retardation of Sn2 reactions of chloride with ethyl and neopentyl chlorides in water. In the two cases the influence of the solvent is examined by using the MST version of the PCM model (see ref. [85] for a detailed description). 

J. R. Pliego, Jr. and J. M. Riveros, Parametrization of the PCM model for calculating solvation free energy of anions in dimethyl sulfoxide solutions, Chem. Phys. Lett., 355 (2002) 543-546. 

From a mathematical point of view the PCM models can be unified according to the approach they use to solve the linear partial differential equations determining the electrostatic interactions between solute and solvent. This analysis is presented by Cances who reviews both the mathematical and the numerical aspects of such an integral equation approach when applied to PCM models. 

To apply the PCM model to the description of excited electronic states and processes of molecules in solution, several extensions have to be introduced into the basic model, in particular the accounting of dynamical effects and a proper QM evaluation of the excited electronic state. These extensions will be described in the following subsections. 

In gas phase, the most stable conformation always corresponds to a heterochiral one in a chair disposition and the worse one to a homochiral one in a boat disposition. The largest difference between these two extremes is 17 kJ moP1. An estimation of the solvation effect has been carried using the PCM model and water as solvent. The AGsol range between —17 kJ mol-1 for the dimer of X/Y=CF3 to —19 for X/Y=F/H. What is more important is the effect on the relative energy of the different configurations. Thus, in three of the cases studied... 

The first derivative of the density matrix with respect to the magnetic induction (dPfiv/dBi) is obtained by solving the coupled-perturbed Hartree-Fock (or Kohn-Sham) equations to which the first derivative of the effective Fock (or Kohn-Sham) operator with respect to the magnetic induction contributes. Due to the use of GIAOs, specific corrections arising from the effective operator Hcnv describing the environment effects will appear. We refer to Ref. [28] for the PCM model and to Ref. [29] for the DPM within either a HF or DFT description of the solute molecule. 

We are grateful to Prof. J. Tomasi for providing us with his original code of the PCM model, which was modified by us to carry out the MST calculations. This work has been supported by the Ministerio de Ciencia y Tecnologia (CTQ2005-08797-C02-01/BQU) the Centre de Supercomputacid de Catalunya and the Barcelona Supercomputing Center. 

Fig. 10 Comparison of the VA and VCD spectra of ML in water calculated using the PCM model at the three levels of theory (top three traces) with the corresponding experimental spectra in water...

When solvent effects are introduced according to the PCM model, the definition of the matrices A and B involves additional PCM-type potentials according to [24]... 

Statistical analysis showed that, although the separate QSAR models and PCM gave similar predictive ability, interpretation of the PCM model was more reliable. After variable selection, each of the four QSAR models retained different sets of descriptors, which made it difficult to find determinants for the receptor-subtype selectivity of the compounds. In contrast, interpretation of the PCM model was straightforward, and the selectivity of the compounds could be explained on the basis of a relatively small number of cross terms [15]. 

Their early SM model was relatively crude. It had some good aspects in terms of accounting for polarization in the wavefunction, Cramer says. A key feature that nobody else had done was to include terms to account for the other components of solvation. Our model was semiempirical since we fit to experimental data, but that s what people wanted to know—they wanted the free energy of solvation. The PCM models of Tomasi and Rivail were underutilized because it was hard to make contact with particular experimental observables, but we offered that opportunity. Thus began what has been a very fruitful collaboration between Cramer and Truhlar. 

---