C-PCM

For all PCM-UAHF calculations, the number of initial tesserae/atomic sphere has been set to 60 by default. For comparative purposes, C-PCM calculations of the... 

FIGURE 2.1 Geometries of the reactants (11-16) and transition structures (S1-S6) at B3LYP level of theory in gas phase, using 6-3 lG(d), 6-311+ G(d,p) (bold characters), 6-311+ G(d,p), S(2df) (underlined), aug-cc-pVTZ (italic) basis sets, and in aqueous solution at B3LYP-C-PCM/6-311 + G(d,p) level of theory (bold characters in parenthesis). Bond length data have been taken from Ref. [13]. 

SCHEME 2.3 Gibbs energy profiles for the benzylation of NH3 (a), H20 (b), and H2S (c) by o-QM in the gas phase (continuous line), water-catalyzed (S4-S6) and uncatalyzed (S1-S3), and in aqueous solution (dotted line, Slaq-S6aq) optimizing both reagents and TSs in aqueous solution [B3LYP-C-PCM/6-311 +G(d,p)]. Data are taken from Ref. [13]. 

Bulk effects of the aqueous solvent have been evaluated by C-PCM solvation model. The specific effect of the solvation on the alkylation pathways has also been... 

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). 

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. 

Summarizing, the reliable electrostatics of gradient-corrected DFT methods provides a good basis for CSMs. Nevertheless, advanced CSMs such as C-PCM or COSMO have achieved an accuracy that is mainly limited by the electrostatic accuracy of DFT, but the next better quantum chemical levels are presently much too expensive for most practical applications. Therefore, we will have to live with the acceptable DFT accuracy for the next years, and no big improvements of the CSMs beyond the present accuracy should be expected, until more accurate quantum levels as CC become practically useful. 

Fig. 9. Torsional potentials for HS-SH molecule calculated in 6-31G basis set (a) ab initio SCF results, lab initio SCF (b) CMMM estimates (c = 6) up to quadrupole-quadrupole term, + CMM (Q-Q) (c) PCM results (c = 6, s = 9, R = 0.1 au), PCM (R = 0.1 au) (Reproduced from [90] copyright-Springer-Verlag)...

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. 

Most of the quantum chemical calculations of the nuclear shielding constants have involved two classes of solvation models, which belong to the second group of models (n), namely, the continuum group (i) the apparent surface charge technique (ASC) in formulation C-PCM and IEF-PCM, and (ii) models based on a multipolar expansion of the reaction filed (MPE). The PCM formalism with its representation of the solvent field through an ASC approach is more flexible as far as the cavity shape is concerned, which permits solvent effects to be taken into account in a more accurate manner. 

M. Cossi, N. Rega, G. Scalmani and V. Barone, Energies, structures, and electronic properties of molecules in solution with the C-PCM solvation model, J. Comput. Chem., 24 (2003) 669. 

Rzepa reported the compnted ECD spectmm and optical activity of 34 and some related compounds. These compnted spectra were obtained using TD-DFT/B3LYP/6-31G(d) method with the C-PCM treatment of the dichloromethane solvent. The compnted ECD spectmm matches nicely with the experimental one, except that the signs at 570 and 620nm are opposite. Rzepa suggests that either the compound is really of P,P configuration or the authors of experimental work have erroneonsly switched their assignments. 

Stronger interaction with the bulk continuum. An ion-dipole structure was located with the C-PCM method, but its energy is more than that of separated reactants. Since all of frequencies for this ion-dipole complex are real, a TS must exits, connecting separated reactants to this complex. The authors did not search for this TS. Nonetheless, these results are in general good agreement with the QM/MC study in terms of the shape of the solution-phase Sj,f2 PES. 

Within the studies of the effect of p-substitution on the gas-phase S 2 reaction described in the previous section was an examination of the solution-phase effect. Listed in Table 6.8 are the experimental values of the relative activation barriers of two simple substitution reactions with increasing p-substitution. The solution-phase barriers for the chloride exchange reactions were computed by adding the C-PCM/B3LYP/6-31G(d) solvation energies to the CBS-QB3 gas-phase energies or using the SM8/M06-2x/6-31-l-G(d,p) method. These computed relative activation barriers are also listed in Table 6.8. The trend of... 

FIGURE 62.1 Plot of PCM latent heat of fusion (kJ/kg) versus melting point (°C). PCM are classified by... 

An extra property very used to characterize the MPCM and PCS is the thermal conductivity. It is calculated in different manners, as Youssef et al. ° reported in a review. One mode to calculate it is by Maxwell s ° relation e q)ressed in Equation 62.5, where mpcm is represented as the thermal omduclivity of the miaocapsule, comis the thermal conductivity of the content, and c pcm is the volume liacliMi of the MPCM ... 

Figure 11.3 Electrostatic solvation energy for classical histidine as a function of dielectric constant. The C-PCM approach is free of the matrix D and achieves the correct conductor limit as e -> oo. Reprinted from Ref [44] copyright 2011 Elsevier.

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... 

The normal derivative of the ansatz in Eq. (11.27) lacks the second term in Eq. (11.28) hence, C-PCM/GCOSMO engenders errors of order as compared to an exact treatment of classical electrostatics. Such errors are negligible in water [44], as seen in Fig. 11.3. 

---