Indirect solvent effects

From a computational point of view, the effects of the surrounding medium on the NMR parameters can be divided into direct and indirect solvent effects [5], The direct effects arise from the interaction of the electronic distribution of the solute with the surrounding medium, assuming a fixed molecular geometry, while indirect (secondary) effects are caused by the changes in the solute molecular geometry by the solvent. Experimentally the total effect is observable, while in the computational models they can be separated. 

By taking as a reference the calculation in vacuo, the presence of the solvent introduces several complications. In fact, besides the direct effect of the solvent on the solute electronic distribution (which implies changes in the solute properties, i.e. dipole moment, polarizability and higher order responses), it should be taken into account that indirect solvent effects exist, i.e. the solvent reaction field perturbs the molecular potential energy surface (PES). This implies that the molecular geometry of the solute (the PES minima) and vibrational frequencies (the PES curvature around minima in the harmonic approximation) are affected by the presence of a solvating environment. Also, the dynamics of the solvent molecules around the solute (the so-called nonequilibrium effect ) has to be... 

Also, because such derivatives are to be evaluated at the equilibrium geometry, a key point is the determination of that geometry on the solvated PES, which leads to the so-called indirect solvent effects , which still requires a viable method to calculate free energy gradients (and possibly hessians). The problem of the formulation of free energy derivatives within continuum solvation models is treated elsewhere in this book and for this reason it will not considered here. Instead, it is worth remarking in this context another implication of such a formulation, i.e. that a choice between a complete equilibrium scheme or the account for vibrational and/or electronic nonequilibrium solvent effects [42, 43] should be done (see below). 

To account for indirect solvent effects, solvation models must allow for geometry optimizations and frequency calculations including the solute-solvent interactions. Indeed, many ab initio continuum solvation models and in particular those belonging to the family of the PCM [3] provide analytical first and second derivatives of the free energy with respect to the nuclear coordinates [4,5], In the following we shall present in detail the formalism for the derivatives in the PCM and Conductor-PCM (CPCM) [6] models. 

Solvation free energies can be used to evaluate conformational preferences, energy minima and reaction profiles for any chemical system in solution of course the quality of the results depends also on the level of the theoretical approach (i. e. on the calculation in vacuo), but in many cases one can say that the inclusion of solvent effects does not lower the performances of the overall description. In this framework, it is very useful to evaluate the solvent effects on the solute geometry (this is sometimes called indirect solvent effect), and also on the vibrational frequencies (adding zero point energy corrections to the calculated free energies) as briefly sketched above, PCM is able to compute both geometry and vibrational corrections effectively. Recently PCM has been used for the ab initio prediction of the pKa of a number of carboxylic acids[111] ... 

The hcc s obtained at the B3LYP/EPR-II level are shown in Table 12. The calculated hcc s can be dissected into three terms a contribution due to the electronic and structural configurations assumed by the radicals in the gas phase (first column in Table 12) a contribution due to the solvent-induced polarization on the solute wave function without allowing any relaxation of the gas-phase geometry (direct solvent effect, second coliunn in Table 12), and a last contribution due to the solvent-induced geometry relaxation (indirect solvent effect, third column in Table 12). 

Solvent-induced effects on NMR shielding of 1,2,4,5-tetrazine and two isomeric tetrazoles are calculated using density functional theory combined with the polarizable continuum model and using the continuous set gauge transformation/ Direct and indirect solvent effects on shielding are also calculated. 

Studies on the reactions of small model radicals with monomers provide indirect support but do not prove the bootstrap effect.111 Krstina et ahL i showed that the reactivities of MMA and MAN model radicals towards MMA, S and VAc were independent of solvent. However, small but significant solvent effects on reactivity ratios are reported for MMA/VAc111 and MMA S 7 copolymerizations. For the model systems, where there is no polymer coil to solvate, there should be no bootstrap effect and reactivities are determined by the global monomer ratio [Ma0]/[Mb0].1j1... 

Levy (Chapter 6) has also explored the use of supercomputers to study detailed properties of biological macromolecule that are only Indirectly accessible to experiment, with particular emphasis on solvent effects and on the Interplay between computer simulations and experimental techniques such as NMR, X-ray structures, and vltratlonal spectra. The chapter by Jorgensen (Chapter 12) summarizes recent work on the kinetics of simple reactions In solutions. This kind of calculation provides examples of how simulations can address questions that are hard to address experimentally. For example Jorgensen s simulations predicted the existence of an Intermediate for the reaction of chloride Ion with methyl chloride In DMF which had not been anticipated experimentally, and they Indicate that the weaker solvation of the transition state as compared to reactants for this reaction In aqueous solution Is not due to a decrease In the number of hydrogen bonds, but rather due to a weakening of the hydrogen bonds. 

A major source of error in any indirect method is inaccuracy of the basis rate constants. Errors can result from determinations of rate constants by a sequence of several indirect studies or by an unanticipated solvent effect on the kinetics of a basis reaction. An error can also result in calibration of a radical clock if the requisite assumption that the clock radical will react with a rate constant equal to that of a simple model radical is not correct. Nevertheless, indirect methods in general, and radical clock studies in particular, have been the workhorse of radical kinetic determinations. 

As discussed in Section 1.2.3, it is crucial tbat the effects of solvents are studied at fixed water activity, or else indirect effects due to competition for water between enzyme and solvent will cause strong effects and mask the true solvent effects. In general, when correcting for substrate solvation, hydrophobic solvents seem to give higher rates than other solvents [5]. 

Solvent effects on the positions of the 14N resonances for pyrrole and indole have been studied indirectly, through observation of the variation in NH proton resonance intensity... 

At a more detailed level, we note that the solvent effects on the optical rotation have the same origins as solvent effects on the energy itself, as described in detail in other contributions to this book. Most other studies of solvent effects on natural optical activity have focused on the electrostatic contributions. These contributions can be partitioned into direct effects arising from the influence of the dielectric environment on the electronic density of the solute, and into indirect effects arising from the relaxation of the nuclear structure in the solvent. For conformationally flexible molecules, we may also consider a third possible solvent effect due to the changes in the conformational equilibria when going from the gas phase to solution. 

This final expression for the coupling allows us, from the combination of the Harcourt and the PCM-LR approaches, to coherently account for direct through-space (Coulombic and Dexter) and indirect through-bond (charge-transfer) interactions, both of them including solvent effects. 

Calculations of the vibrational contributions to the static polarizability and hyperpolarizability have also been attempted. As far as the EFISH experiment is concerned, which depends on the square of an optical frequency field, it is assumed that there will be no direct contribution to (—2static contribution is comparable with the static electronic contribution to /1(0 0,0). An indirect vibrational effect through the linear polarizability of the solvent molecules is more important. Calculations of the vibrational effects in pNA cannot be carried out reliably even for the static case since the second term in the perturbation theory is much larger then the first and there is no evidence of convergence. 

Disproportionation equilibria have been studied for various systems. Cauquis and co-workers investigated by electrochemical means the matrix of equilibria corresponding to Scheme 2 for 3,7-dimethoxypheno-thiazine and its derivatives, and applied the measurement of the response of the equilibria to different conditions of basicity to the definition of a scale of basicity in acetonitrile. The disproportionation kinetics of the iron-thionine system were measured several years ago solvent effects on the disproportionation rate constant have been examined, and, lately, an indirect measurement of the synproportionation rate constant of thionine and leucothionine has been made. ... 

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