IEF-PCM

Another method from the same PCM family of solvation methods, namely the IEF-PCM [24] (see also the contribution by Cances), has recently been used to develop an ab initio VB solvation method [25], According to this approach, in order to incorporate solvent effect into the VB scheme, the state wavefunction is expressed in the usual terms as a linear combination of VB structures, but now these VB structures are optimized and interact with one another in the presence of a polarizing field of the solvent. The Schrodinger equation for the VB structures is then solved directly by a self-consistent procedure. 

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. 

A similar system to that discussed in ref. [44] (tetrazine, tetrazole and pyrrole) has been studied by Manalo et al. [47] by means of the CSGT/ASC method at the B3LYP/6-311++G(2d,2p) level. The cavity was defined by using the Pauling radius for each solute atom. In this paper the effects of geometric relaxation (indirect effects) are found to be small, and the direct influence of the intensity of the solvent reaction field on the shielding constants dominates. However, the indirect effect has been found to be important for N, A-dimethylacetamidine in IEF-PCM calculations [48],... 

Let us now review the group of papers discussing the relative weights of the different components in Buckingham equation (Equation (2.23)). Reaction field methods describe only long-range electrostatic interaction, the crE term (or, as in IEF-PCM, some of the (rw term [29]). In order to go beyond the continuum model some solvent molecules... 

The obvious drawback of Mikkelsen s MPE model is the spherical shape of the cavity, making the calculations for extended systems such as peptide models or for oblong molecules such as acetylene rather awkward. This is improved in the IEF-PCM model, which is currently most often used to calculate solvent effects on the spin-spin coupling constants. 

Other examples of the application of calculations of spin-spin coupling constants by means of the PCM/DFT model for chemical problems using the IEF-PCM approach are studies of the spin-spin coupling constants in the keto and enol forms of monosubstituted 2-OH-pyridines [83], of the anomeric effect on the 27HH and 37HH coupling constants in 2-methylthiirane and 2-methyloxirane [83], and of the conformation of pyridine aldehyde derivaties [84], In these studies, PCM has been used to obtain a more realistic... 

Less optimistic conclusions about the performance of the DFT/PCM scheme were drawn in a study of solvent effect on the optical rotation of (.S )- -mclhy I benzyl amine [67]. The authors compared the optical rotation of this amine measured in 39 different solvents (whenever possible extrapolated to infinite dilusion) with the results obtained by means of IEF-PCM with the B3LYP functional and the aug-cc-pVDZ basis set. They observed substantial discrepancies for many of the hydrogen-bond forming solvents (which is not... 

The PCM/DFT model failed to predict the intrinsic rotation (i.e. the specific rotation extrapolated to infinite dilution) of (R)-3-methylcyclopentanone dissolved in carbon tetrachloride, methanol and acetonitrile [68], This molecule has been investigated because it exists in both an equatorial and an axial form, allowing researchers to investigate the interplay of solvent and conformational effects. The conformer populations used in the Boltzmann averaging were derived from IR absorption and VCD spectra. The deviation of the calculated optical rotation from experiment was found actually to be larger when IEF-PCM was used to account for direct solvent effects (and geometry relaxation) on the optical rotation than when the gas-phase values were used. 

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... 

The advantage of the IEF-PCM formulation in this respect is that the surface between the two dielectrics is hidden within the Green s function and only the explicit description of the molecular cavity is needed as for bulk IEF-PCM. Although the IEF-PCM implementation was able to overcome several numerical problems as a result of the explicit description of the dielectric interface, the BEM discretization technique for those tesserae in close proximity of the sharp interface could still potentially lead to unphysical divergences. 

We can let this integrated density o-ONIOM interact with the continuum description of the solvent in the same way as in a conventional IEF-PCM calculation. In other words, we carry out a regular IEF-PCM calculation, but replace the QM density with the ONIOM density. We call this ONIOM-PCM/A, and represent it as ... 

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]. 

However, this identity is not preserved upon discretization, and different implementations of SS(V)PE/IEF-PCM are therefore possible, not all of which perform equally well in practice [44]. This is discussed below. 

Figure 11.2 Comparison of total energies (on a logarithmic scale) for aqueous amino acids, where the solute is described using the amber99 force field and the solvent is a dielectric continuum. The continuum electrostatics problem is solved either by finite-difference solution of Poisson s equation using the APBS software [5], or else using two different forms of lEF-PCM (X = DAS orX = SAD as described in Section 11.2.2.1). What is plotted is the difference ief-pcm — E apbs between these two solutions. The APBS and lEF-PCM solute cavities are identical. APBS calculations used a 193 x 193 x 193 grid with a grid resolution of 0.1 A, whereas lEF-PCM calculations used 590 Lebedev points per atomic sphere with Gaussian blurring.

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