Equilibria, solvent effects

For analysing equilibrium solvent effects on reaction rates it is connnon to use the thennodynamic fomuilation of TST and to relate observed solvent-mduced changes in the rate coefficient to variations in Gibbs free-energy differences between solvated reactant and transition states with respect to some reference state. Starting from the simple one-dimensional expression for the TST rate coefficient of a unimolecular reaction a— r... 

Adamo, C., and F. Lelj. 1994. Equilibrium solvent effects in the framework of density functional theory. Application to the study of the thermodynamics of some organic and inorganic tautomereic equilibria. Chem. Phys. Lett. 223, 54. 

R degrees of freedom. (Sometimes the collective solvent coordinate is assumed to be the reaction coordinate itself [70] rather than, as here, finding a reaction coordinate in the space obtained by augmenting the solute coordinates by the collective solvent coordinate.) As in ESP theory, in NES theory the equilibrium solvent effects are included by replacing V(R) by W(R) in nontunneling parts of the calculation and by t/(R) in tunneling algorithms. 

There are, in principle, two ways in which solvents can affect the reaction rates of homogeneous chemical reactions through static, or equilibrium, solvent effects and through dynamic, or frictional, solvent effects [463, 465, 466]. 

Because of the large dielectric constant of water, electron transfer reactions in this liquid are strongly coupled to solvent polarization modes. The equilibrium solvent effects are well accounted for within the celebrated Marcus theory of electron transfer reactions [19]. The dynamic effects of electron transfer reactions have been the subject of many interesting discussions in the scientific literature and revealed some nice aspects of chemical kinetics in general, as articulated below. Study of the dynamics of electron transfer uses the results obtained in SD. 

QM/EFPl scheme was used for investigating a variety of chemical processes in aqueous environment, including chemical reactions, amino acid neutral/zwitterion equilibrium, solvent effects on properties of a solute such as changes in dipole moment and shifts in vibrational spectrum, and solvatochromic shifts of electronic levels [36, 56, 59-60, 71-79]. Applications of a general QM/EFP scheme were limited so far to studies of electronic excitations and ionization energies in various solvents [56-58]. Extensions of QM/EFP to biological systems have been also developed [80-85]. 

We have so far examined some points of the original PCM procedure. Other elements of interest for the present paper, drawn from the numerous procedures implemented and tested later (Tomasi et al. 2005), will be here considered. These points regard the improvements in the description of the solute s electronic wave function, and the description of excited states, including non-equilibrium solvent effects. 

Ha S, J Gao, B Tidor, J W Brady and M Karplus 1991. Solvent Effect on the Anomeric Equilibrium in d Glucose A Free Eneigy Simulation Analysis. Journal of the American Chemical Sod. ty 113 1553-1557... 

Recently the solvent effect on the [4+2] cycloaddition of singlet oxygen to cyclic dienes has been subjected to a multiparameter analysis. A pre-equilibrium with charge-transfer character is involved, which is affected by the solvent through dipolarity-polarisability (n ) and solvophobic interactions ( Sjf and Another multiparameter analysis has been published by Gajewski, demonstrating the... 

A prototype of such phenomena can be seen in even the simplest carboxylic acid, acetic acid (CH3CHOOH). Acidity is determined by the energy or free energy difference between the dissociated and nondissociated forms, whose energetics usually depend significantly on their conformation, e.g., the syn/anti conformational change of the carboxyl-ate group in the compound substantially affects the acid-base equilibrium. The coupled conformation and solvent effects on acidity is treated in Ref. 20. 

Swain et al. ° analyzed solvent effects on 1080 pieces of rate and equilibrium data, showing that more than 98% of the effects could be correlated by the four-parameter equation... 

For sparingly soluble salts of a strong acid the effect of the addition of an acid will be similar to that of any other indifferent electrolyte but if the sparingly soluble salt MA is the salt of a weak acid HA, then acids will, in general, have a solvent effect upon it. If hydrochloric acid is added to an aqueous suspension of such a salt, the following equilibrium will be established ... 

The pH will depend upon the ionic strength of the solution (which is, of course, related to the activity coefficient — see Section 2.5). Hence, when making a colour comparison for the determination of the pH of a solution, not only must the indicator concentration be the same in the two solutions but the ionic strength must also be equal or approximately equal. The equation incidentally provides an explanation of the so-called salt and solvent effects which are observed with indicators. The colour-change equilibrium at any particular ionic strength (constant activity-coefficient term) can be expressed by a condensed form of equation (4) ... 

Most of these results have been obtained in methanol but some of them can be extrapolated to other solvents, if the following solvent effects are considered. Bromine bridging has been shown to be hardly solvent-dependent.2 Therefore, the selectivities related to this feature of bromination intermediates do not significantly depend on the solvent. When the intermediates are carbocations, the stereoselectivity can vary (ref. 23) widely with the solvent (ref. 24), insofar as the conformational equilibrium of these cations is solvent-dependent. Nevertheless, this equilibration can be locked in a nucleophilic solvent when it nucleophilically assists the formation of the intermediate. Therefore, as exemplified in methylstyrene bromination, a carbocation can react 100 % stereoselectivity. 

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