COSMO model

Ab initio Simulating MeCN (the Onsager Model), semiempirical The COSMO Model, MOPAPC 93 keywords NSPA = 60, EPS = 35.9, TS, PRECISE. 

Fig. 2.3 The solvent accessible surface (SAS) area corresponds to that mapped out by the center of a sphere representing the solvent molecule (gray) as it is rolled over the van der Waals surface of the solute (light gray). In the COSMO model, the SAS is then divided into a series of segments of area S and charge density cr, centered at a position R(j. ...

TABLE 5. Calculated [B3LYP/6-311+G(d,p)] activation parameters (kcal mol and eu) for the epoxidation of cyclohexene and isobutene with dimethyldioxirane (DMDO), peroxybenzoic add (PBA), m-chloroperoxybenzoic add (m-CPBA) and peroxyformic acid (PFA). Solvent corrections were performed with the COSMO model. The numbers in bold are experimental values -Numbers in parentheses are at the B3LYP/6-311- -G(3df,2p)//B3LYP/6-311- -G(d,p) level of theory... 

Of course, the response of a conductor to a solute charge distribution is complete , while that of a dielectric medium is not. So, in COSMO models, the more simply evaluated conductor-polarization free energy is scaled by a factor of 2(s — l)/(2e -f-1) after its computation (i.e., by the Onsager factor in the case of the SM5C model, however, the scaling factor is (e — l)/e - see Section 11.3.3). 

From a chemical perspective, dielectric- and conductor-like continuum models give sufficiently similar electrostatic results that the differences in their underlying assumptions appear to have no impact. Conductor-like models seem to be slightly more computationally robust in some instances, which may make tliem a better choice if instability is manifest in an SCRF calculation. Some concerns were raised initially that the post facto correction for dielectric behavior might render the models appropriate only for media having reasonably high dielectric constants, but a systematic study by Dolney et al. (2000) indicated non-polar solvents to be equally amenable to treatment by a COSMO model. 

COSMO models [27-30] were compared with the SM approach [22] by Klamt [43] and by Cramer and Truhlar [44]. A very recent paper by Klamt and coworkers [45] shows that improved calculated pKa values are obtained for the limited domain of strong to moderately weak acids by a cluster-continuum method in which the acid and conjugate base are each associated with one or a few solvent molecules and this cluster is then continuum-calculated with COSMO-RS. The authors point out, however, that for the calculation of pKa a consistent and generally applicable method is still lacking . This paper clarifies the problem raised in [41]. The matter is under study.1... 

Continuum solvent models are normally parameterized with the solvent dielectric constant (but see the COSMO models, Chapter 8). First we note that dielectric constant and dipole moment are not in general well correlated from Chapter 8 ... 

Finally, the COSMO model introduced in ref. [1] can be recovered as follows. First, the IEFPCM Equation (1.37) can be rewritten as... 

The COSMO model is an approximation of Equations (1.38) consisting in solving exactly the first of Equations (1.38) and in replacing the second equation by... 

Still within continuum solvation models, Wang et al. [5] have used an ab initio SCRF Onsager model to compute vibrational frequencies at different levels of the ab initio QM molecular theory, the G-COSMO model has been used by Stefanovich and Truong to calculate vibrational frequencies at the DFT level [6], and the multipole SCRF model, developed by the group of Rivail, has been extended to the calculation of frequency shifts at the HF, MP2 and DFT levels, including nonequilibrium effects [7],... 

Although, the agreement with experiments did not show a significant improvement over the simpler COSMO model we are still confident that the combination of DRF with TDDFT is computationally an attractive solution for calculating chiro-optical properties of molecules in solution when the explicit solvent structure is of interest. 

Few of the many theoretical studies of PNA explicitly address excited state molecular geometries. Among them we cite here the work of Farztdinov et al. [38], who performed semiempirical SAMI calculations on the excited state nuclear dynamics of PNA in gas-phase and in water (using the COSMO model [39]) and a successive study by Moran et al. [32] using an excited state molecular dynamics... 

In an effort to understand the role of nomicotine in catalyzing aqueous aldol reactions, Noodleman and Janda examined the aldol reaction of acetaldehyde and acetone in an organic solvent (THF, tetrahydrofuran) and water. The calculations were performed at B3LYP/6-311-l-G(2d,2p)//B3LYP/6-311(d,p) and were corrected for ZPVE at HF/3-21G and the effects of solvent using the COSMO model at B3LYP/6-311(d,p). 

COSMO-ART Aerosols and Reactive Trace Gases Within the COSMO Model... 

Table 32 Transition wavelengths and dipole strengths for Af-methylacetamide in the gas phase and in an aqueous solution. Both the COSMO model and a supermolecule approach (denoted clusters) have been applied for treating the solvent. In the latter case, averages over 90 configurations have been calculated, resulting in the error bars for those calculations. All results are from ref. 91... 

To end up this Section, we consider now an alternative ASC approach which strongly deviates from the basic set up previously discussed. The quantum system, the solute , has been considered immersed in a continuum solvent distribution characterized, pritna facie, by its dielectric response function. Klamt and Schuiirman (1993) propose to replace the dielectric response function with the response function of a liquid electric conductor (the so-called COSMO model). In doing so, one has other electrostatic problems, with simpler boundary conditions. In fact, for a system of charges (the solute) in a screening conductor (where = oo), the electro-... 

Table 8. The optimized Pt-L distances between Pt and the N, O, or Cl atom (in A) in the COSMO model and a comparison with gas-phase results from Table 4. Structures P06 = P09, P10 = P13. ...

For a comparison with experimental measurements, there are several results available.25 27,39 From Table 7, it follows that a very good agreement with the experimental data was achieved. The differences are within an order of magnitude for the forward reaction and slightly worse for reverse processes. For the second dechlorination step, reactions rl2 and rl4, agreement with the published measurements is also fairly good, but here slightly different reactions are considered. Unfortunately there are no data for the evaluation of kinetic parameters such as AG2 in the thermodynamic part. Nevertheless, the rate constants for the second step are not too far from the experimental data, and substantial improvement of the results obtained with the COSMO model in comparison with the in vacuo calculation was achieved. 

Combining the PCM approach with the gas phase methodology is the most promising way to understand and model the effect of a water solution. The COSMO model was used for the determination of the interaction energies and the activation barriers at the CCSD(T)/6-31++G(d,p) level. 

The capital letter used in eq.(1.12) for the matrix containing the apparent charges indicates that the latter are here derived for a real conductor, for which e = oo if the COSMO model is used to simulate a solvent with dielectric constant e, these apparent charges have to be scaled an effective way to do this is to multiply each charge by the factor (e — l)/e. 

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