COSMO continuum solvent model

To better understand the possible weak links in the decanio-bate ion that might give rise to oxygen exchange, a molecular dynamics calculation was carried out with the PQS quantum chemistry code (www.pqs-chem.com) of the decaniobate ion embedded in the COSMO continuum solvent model (55) (dielectric constant = 80, probe radius = 1.4 A). The time step was set at... 

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 ... 

Calculated using the PCM continuum solvent model with the conductor field model of electrostatic interactions (COSMO). 

Based on the values obtained by Kiitt et al. [448], Trummal and co-workers [449] applied SMD/B3LYP/6-31G and SMD/M05-2X/6-31G calculations with the COSMO-RS continuum solvent model to estimate the acidities in DCE. The results showed very good correlations with the experimental values r = 0.990 for the M05-2X functional and r = 0.984 for the B3LYP functional. 

Figure 7.13 The oxo-transfer energy scale, showing the oxidized state of each oxo-transfer reaction pair. Energies were calculated at the B3LYP/ def2-TZVDP level in a COSMO continuum solvent with a dielectric constant of 4 (enzyme models in magenta) or 80 (substrates in green), relative to the ojo couple. For the enzyme models, MoO(MPT)XY, only the X/Y ligands are indicated. ...

In addition to these external electric or magnetic field as a perturbation parameter, solvents can be another option. Solvents having different dielectric constants would mimic different field strengths. In the recent past, several solvent models have been used to understand the reactivity of chemical species [55,56]. The well-acclaimed review article on solvent effects can be exploited in this regard [57]. Different solvent models such as conductor-like screening model (COSMO), polarizable continuum model (PCM), effective fragment potential (EFP) model with mostly water as a solvent have been used in the above studies. 

Having recognized the theoretical inadequacy of the dielectric theory for polar solvents, I started to reconsider the entire problem of solvation models. Because the good performance of dielectric continuum solvation models for water cannot be a result of pure chance, in some way there must be an internal relationship between these models and the physical reality. Therefore I decided to reconsider the problem from the north pole of the globe, i.e., from the state of molecules swimming in a virtual perfect conductor. I was probably the first to enjoy this really novel perspective, and this led me to a perfectly novel, efficient, and accurate solvation model based upon, but going far beyond, the dielectric continuum solvation models such as COSMO. This COSMO for realistic solvation (COSMO-RS) model will be described in the remainder of this book. 

The COSMO solvent model has been used to simulate the influence of water on the electronic spectrum of A -methylacetamide [81], and the results was compared with the results of molecular dynamics simulations (where the electronic spectrum were calculated as an average over 90 snapshots from MD simulations). Most of the hydration effects were found to come from the first solvation shell hydrogen-bonded water molecules, and the continuum model does not properly account for these effects. The rotatory strengths were not calculated directly in ref. [81]. However, the results were used to model ECD spectra of peptides via the coupled oscillator model, with satisfactory result. 

In order to determine what interactions dominate the optical rotation of methyloxirane in water, Mukhopadhayay et al. [151] have calculated the optical rotation of the solute-solvent system by including an explicit solvent shell in the calculations. Additional calculations were performed on the solvent shell alone, with the methyloxirane removed. Explicit solvent molecules were modeled by molecular dynamics. Implicit solvation was also considered, modeled by the COSMO continuum model. The optical rotation calculations were performed at the BP86/aug-cc-pVDZ level of theory and did not include zero-point vibrational... 

Although many satisfactory VCD studies based on the gas phase simulations have been reported, it may be necessary to account for solvent effects in order to achieve conclusive AC assignments. Currently, there are two approaches to take solvent effects into account. One of them is the implicit solvent model, which treats a solvent as a continuum dielectric environment and does not consider the explicit intermolecular interactions between chiral solute and solvent molecules. The two most used computational methods for the implicit solvent model are the polarizable continuum model (PCM) [93-95] and the conductor-like screening model (COSMO) [96, 97]. In this treatment, geometry optimizations and harmonic frequency calculations are repeated with the inclusion of PCM or COSMO for all the conformers found. Changes in the conformational structures, the relative energies of conformers, and the harmonic frequencies, as well as in the VA and VCD intensities have been reported with the inclusion of the implicit solvent model. The second approach is called the explicit solvent model, which takes the explicit intermolecular interactions into account. The applications of these two approaches, in particular the latter one will be further discussed in Sect. 4.2. 

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-... 

Recognizing that the continuum solvent calculations are the weakest link in pKa calculations, Ho and Coote [3] used the CPCM (with UAKS and UAFH radii), SM6, IPCM, and COSMO-RS models to predict pKa values for a common data set of neutral organic and inorganic acids. They used four different thermodynamic cycles, and in general found that the COSMO-RS, CPCM, and SM6 models worked best depending on the thermodynamic cycle used. We turn to a discussion of thermodynamic cycles in the next section. 

It is worth noting that adding water as the solvent with the PCM continuum solvent model16 and the conductor field model of electrostatic interactions (COSMO)17 or even specific water molecules to the calculations did not alter the chlorine KIEs, nor the conclusion, significantly. Also noteworthy is the observation that neither the method of calculating the transition state bond order nor anharmonicity affected the conclusions. 

Quantum-Mechanical Continuum Solvation Models. Several ab initio continuum solvation models were discussed in Section 15.22. One can calculate AG, , by such SCRF methods as the dipole-in-a-sphere, the multipole expansion, or the PCM methods using semiempirical methods such as AMI or PM3 instead of an ab initio electronic-structure method. Thus the program MOPAC-93 implements the PCM calculation of solvent effects with semiempirical methods and the program AMPAC 6.0 implements the COSMO method. 

In order to model the surrounding enzyme and solvent, a continuum-solvation method is typically used, such as the polarizable continuum model (PCM) or the conductor-like solvent model (COSMO),employing a dielectric constant (e) close to 4, a common value to model the hydrophobic environment of an enzyme active site. For small QM models, the results may be very sensitive to this value, but the results typically become independent of the dielectric constant after the addition of -200 atoms. Often only the polar part of the solvation energy is included in QM-cluster calculations, although the non-polar parts (the cavitation, dispersion and repulsion energies) are needed to obtain valid solvation energies, as will be discussed below. 

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