Solvent effects solvation energies

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. 

Continuum solvation models are nowadays widespread computational techniques to study solvent effects on energy/geometry/reactivity and properties of very different molecular systems (from small molecules to very large biochemical systems such as proteins and enzymes). 

On analyzing the computational results, two important factors are essentially considered as the solvent effect the energy change associated with the solute reorganization (Ereorg) and the solvation free energy (A/j,) upon solvation. 

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... 

In a few cases, where solvent effects are primarily due to the coordination of solute molecules with the solute, the lowest-energy solvent configuration is sufficient to predict the solvation effects. In general, this is a poor way to model solvation effects. 

There is no one best method for describing solvent effects. The choice of method is dependent on the size of the molecule, type of solvent effects being examined, and required accuracy of results. Many of the continuum solvation methods predict solvation energy more accurately for neutral molecules than for ions. The following is a list of preferred methods, with those resulting in the highest accuracy and the least amount of computational effort appearing first ... 

The continuum model, in which solvent is regarded as a continuum dielectric, has been used to study solvent effects for a long time [2,3]. Because the electrostatic interaction in a polar system dominates over other forces such as van der Waals interactions, solvation energies can be approximated by a reaction field due to polarization of the dielectric continuum as solvent. Other contributions such as dispersion interactions, which must be explicitly considered for nonpolar solvent systems, have usually been treated with empirical quantity such as macroscopic surface tension of solvent. 

Solvent effects on chemical equilibria and reactions have been an important issue in physical organic chemistry. Several empirical relationships have been proposed to characterize systematically the various types of properties in protic and aprotic solvents. One of the simplest models is the continuum reaction field characterized by the dielectric constant, e, of the solvent, which is still widely used. Taft and coworkers [30] presented more sophisticated solvent parameters that can take solute-solvent hydrogen bonding and polarity into account. Although this parameter has been successfully applied to rationalize experimentally observed solvent effects, it seems still far from satisfactory to interpret solvent effects on the basis of microscopic infomation of the solute-solvent interaction and solvation free energy. 

It should always be home in mind that solvent effects can modify the energy of both tile reactants and the transition slate. It is the difference in the two solvation effects that is the basis for changes in activation energies and reaction rates. Ihus, although it is conimon to express solvent effects solely in terms of reactant solvation or transition-slate solvation,... 

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. ... 

It should be emphasized again that both the SN1 and the 5 2 reaction show solvent effects but that they do so for different reasons. SN2 reactions are disfavored in protic solvents because the ground-state energy oi the nucleophile is lowered by solvation. S l reactions are favored in protic solvents because the transition-state energy leading to carbocation intermediate is lowered by solvation. 

Although the LD model is clearly a rough approximation, it seems to capture the main physics of polar solvents. This model overcomes the key problems associated with the macroscopic model of eq. (2.18), eliminating the dependence of the results on an ill-defined cavity radius and the need to use a dielectric constant which is not defined properly at a short distance from the solute. The LD model provides an effective estimate of solvation energies of the ionic states and allows one to explore the energetics of chemical reactions in polar solvents. 

Transition states (Continued) in hydrogen abstraction, 25 in phosphodiester hydrolysis, 190 reactant-like vs product-like, 96 solvation energy of, 211, 213,214 solvent effects on, 46 stabilization of charge distribution, 91, 225-227... 

In Eq. (6) Ecav represents the energy necessary to create a cavity in the solvent continuum. Eel and Eydw depict the electrostatic and van-der-Waals interactions between solute and the solvent after the solute is brought into the cavity, respectively. The van-der-Waals interactions divide themselves into dispersion and repulsion interactions (Ed sp, Erep). Specific interactions between solute and solvent such as H-bridges and association can only be considered by additional assumptions because the solvent is characterized as a structureless and polarizable medium by macroscopic constants such as dielectric constant, surface tension and volume extension coefficient. The use of macroscopic physical constants in microscopic processes in progress is an approximation. Additional approximations are inherent to the continuum models since the choice of shape and size of the cavity is arbitrary. Entropic effects are considered neither in the continuum models nor in the supermolecule approximation. Despite these numerous approximations, continuum models were developed which produce suitabel estimations of solvation energies and effects (see Refs. 10-30 in 68)). 

Based on a series of studies of the effect of organic solvent on the reaction of Ca-ATPase with Pj and ATP synthesis, De Meis et al. proposed that a different solvent structure in the phosphate microenvironment in Ej and E2 forms the basis for existence of high- and low-energy forms of the aspartyl phosphate [93]. Acyl phosphates have relatively low free energy of hydrolysis when the activity of water is reduced, due to the change of solvation energy. The covalently bound phosphate may also reside in a hydrophobic environment in E2P of Na,K-ATPase since increased partition of Pj into the site is observed in presence of organic solvent [6] in the same manner as in Ca-ATPase. 

Since around 1950, in studies of solvent effects for organic reactions, empirical solvent parameters have been used these parameters represent the capabilities of solvents for the solute-solvent interactions (especially Lewis acid-base interactions). Though the solute-solvent interactions should depend on the solute as well as on the solvent, the empirical solvent parameters are considered to be irrelevant to solutes in other words, the use of only these parameters enables us to evaluate the solvation energies. Strictly... 

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