Solvent effects Onsager model

Note that systems having a dipole moment of 0 will not exhibit solvent effects for the Onsager SCRF model, and therefore Onsager model (SCRF=Dipole) calculations performed on them will give the same results as for the gas phase. This is an inherent limitation of the Onsager approach. 

As the plot of AE indicates, the energy difference between the two forms decreases in more polar solvents, and becomes nearly zero in acetonitrile. The left plot illustrates the fact that the IPCM model (at the B3LYP/6-31+G(d) level of theory) does a much better job of reproducing the observed solvent effect than the two Onsager SCRF models. In contrast, the Onsager model at the MP2 level treats the solvated systems more accurately than it does the gas phase system, leading to a poorer value for the solvent effect. ... 

Compute the frequency associated with carbonyl stretch in solution with acetonitrUe for the carbonyl systems we looked at in the gas phase in Chapter 4. Run your calculations using RHF/6-31+G(d) with the Onsager SCRF model. Discuss the substituent effect on the predicted solvent effects. 

Both of these substitution pathways in MeCN solution have been simulated using the Onsager model (Tables IV and V). Whereas pathway b is favored in the gas phase, inclusion of solvent effects in the calculations causes pathway a to be energetically favored. Substitution of Cl via pathway a is now 1.6 kcal/mol more favorable. In addition, TS(X)/TS(Pyr) calculations (Scheme 15) for the OMe (40) and OSiMes (41) cations have been performed. TS(X) of both 40 and 41 remain significantly disfavored (+66.9 kcal/mol and +46.6 kcakmol, respectively), thus indicating that pathway b should be preferred in MeCN.Tliese calculations are in complete agreement with experimental observations. 

From a computational view point, chemical reactions in solution present a yet not solved challenge. On one hand, some of the solvent effects can be approximated as if the solute molecule would be in a continuum with a given dielectric characterization of the liquid, and this view point has been pioneered by Bom [1], later by Kirkwood [2] and Onsager [3] and even later by many computational quantum chemists [4-9], On the other hand, the continuum model fails totally when one is interested in the specific... 

As a first approximation, solvent effects can be described by models where the solvent is represented by a dielectric continuum, e.g., the Onsager reaction-field model. 

Since the development of the Onsager model, there have been a number of elaborations on the model [4,5]. For example, the spherical cavity has been replaced by molecularly-shaped cavities. The state of the art within the field of solvent effects described by continuum solvent models is now implemented in, e.g., the Gaussian program package. 

The experimental data reported in the Table for gas phase have been extracted from measurements in dioxane solution by applying the Onsager reaction field model to eliminate the solvent effect [37], By contrast, the cyclohexane experimental dipole moments have been obtained from those reported in Ref. [37] re-including the proper reaction field factors. Once recalled these facts, we note that the observed solvent-induced changes on both ground and excited state dipole moments are quantitatively reproduced by the calculations. 

Local ordering effects have long been recognised experimentally in measurements of dipole moments of polar solutes in non-polar solvents, where the value obtained on the basis of the simple model differs from the value obtained for the pure solute in the gas phase, even when the results are extrapolated to infinite dilution. This so-called solvent effect is due to the Onsager reaction field. If there is no strong local ordering, Onsager s formula (2.52) is valid and the apparent solution moment is related to the isolated molecule or gas moment by... 

Figure 3 Energy profiles for proton transfer in the C1H... H20 complex. The effect of environment is accounted for by the Onsager model with different values of the solvent dielectric constant e...

These approaches date back to the classical papers by Onsager(9) and Kirkwood(lO). A self-consistent reaction field (SCRF) was developed and applied to several solvent effects with reasonable success(8, 11). However, it seems to become clear that these models where the solute and the solvent are represented by separated non-overlapping wave functions are too crude in some cases(12). Studies of solvent effects involving the interaction of the solute with a proton donor solvent (the so-called protic solvents) for instance usually leads to hydrogen bonds and therefore neglecting the overlap of the electron densities between the two subsystem is very difficult to justify. A similar difficulty is obtained for those absorptions where electron is trans-... 

While this result confirmed the feasibility of the general approach, it did not precipitate wider exploration of dielectric medium effects. Recently, however, Wiberg et al. have incorporated the Onsager self-consistent reaction-field model into ab initio MO theory in an implementation which provides analytical gradients and second derivatives. The model considers just the dipole of the solute molecules and a spherical cavity whose radius is chosen for a given solute molecule from the molecular volume estimated at the 0.001 eB electron-density contour (B is the Bohr radius), plus an empirical constant 0.5 A to account for the nearest approach of solvent molecules [164]. Cieplak and Wiberg have used this model to probe solvent effects on the transition states for nucleophilic additions to substituted acetaldehydes [165]. For each... 

The chemical shifts of polar molecules are frequently found to be solvent dependent. Becconsall and Hampson have studied the solvent effects on the shifts of methyl iodide and acetonitrile. The results obtained from dilution studies in various solvents may be explained as arising from a reaction field around the solute molecules. The spherical cavity model due to Onsager was used to describe this effect, and this model was completely consistent with the experimental data when a modified value for the dielectric constant, s, of the particular solvent was used. 

The effect of the solvent is usually modelled either by the use of the Onsager s self consistent reaction field (SCRF) [20] or by the polarizable continuum method (PCM) [21]. With regard to the relative stability of cytosine tautomers in aqueous solution, these methods provided results [14,15] which, in spite of some discrepancies, are in reasonable agreement with experimental data [3]. However, continuum-based methods do not explicitly take into consideration the local solvent-solute interaction which is instead important in the description of the proton transfer mechanism in hydrogen-bonded systems. A reasonable approach to the problem was recently proposed [22,23] in which the molecule of interest and few solvent molecules are treated as a supermolecule acting as solute, while the bulk of the solvent is represented as a polarizable dielectric. 

The charge distribution of the molecule can be represented either as atom-centred partial charges or as a multipole expansion. For a neutral molecule, the lowest order approximation considers only the dipole moment. This may be a quite poor approximation, and fails completely for symmetric molecules that do not have a dipole moment. For obtaining converged results, it is often necessarily to extend the expansion up to order six or more, i.e. including dipole, quadrupole, octupole, etc., moments. Furthermore, only for small and symmetric molecules can the approximation of a spherical or ellipsoidal cavity be considered realistic. The use of the Bom/ Onsager/Kirkwood models should therefore only be considered as a rough estimate of the solvent effects, and quantitative results can rarely be obtained. 

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