Solvent effects theory

Tapia, O. Solvent effect theories quantum and classical formalisms and their applications in chemistry and biochemistry, J.Math. Chem., 10 (1992), 139-181... 

Angyan, J. Common theoretical framework for quantum chemical solvent effect theories,... 

Not only classic (C.K. Ingold, 1953) but also recent solvent effect theories (Parker, 1969) claim that the influence of the solvent on the rate of reaction is a consequence of specific solvation of initial, transition and final states and of any intermediate. If the lifetime of the transition state is too short ( 10-12 — 10-13 sec), however, the reorientation of the solvent will lag behind (Bell, 1965 Jones, 1969b). Consequently, the solvation of the transition state will resemble that of the initial state. 

Developments in experimental and computational science have shed light on phenomena in bioenvironments and condensed phases that pose significant challenges for theoretical models of solvation [27]. Tapia [22] raises the important distinction between solvation theory and solvent effects theory. Solvation theory is concerned with direct evaluation of solvation free energies this is extensively covered by recent reviews [16,17]. Solvent-effect theory concerns changes induced by the medium onto electronic structure and molecular properties of the solute. Solvent-effect theory is concerned with molecular properties of the solvated molecule relative to the properties in vacuo as such it focuses on chemical features suitable for studying systems at the microscopic level [23]. Extensive reviews of different computational methods are given in a book by Warshel [24]. 

Various solvent effect theories concerning HFS constants in ESR spectra using various reaction held approaches have been developed by Reddoch et al. [385] and Abe et al. [392]. According to Reddoch et al., none of the continuum reaction held models is entirely satisfactory. Therefore, a dipole-dipole model using a held due only to a dipole moment of one solvent molecule instead of various reaction fields was proposed, and applied to di-t-butyl aminyloxide [385]. However, Abe et al. found that the HFS constants are proportional to the reaction held of Block and Walker [393] when protic solvents are excluded [392]. This relationship has been successfully applied to di-t-butyl and diaryl aminyloxides, to the 4-(methoxycarbonyl)-l-methylpyridinyl radical cf. Fig. 6-10), and to the 4-acetyl-1-methylpyridinyl radical (see below) [392]. For another theoretical approach to the calculation of gr-values and HFS constants for di-t-butyl aminyloxide, see reference [501]. 

Abrahem worked out details of the solvent effect theory on changing equilibrium. This theory also accounts for the quadruple interactions with media dipoles. It demonstrates that the accuracy of this theory equations is not better than that obtained from an ordinary... 

ABSTRACT. The geometries of inclusion complexes of a-cyclodextrin(a-CD) with guests, benzoic acid, p-hydroxy benzoic acid, and p-nitrophenol in aqueous solution have been determined by comparing the complexation induced C-13 shifts of guest molecules with quantum chemical predictions. In the calculations, the non-polar environmental effect produced by the a-CD cavity on the C-13 shifts of included guest molecule has been formulated by the so-called solvent effect theory. The geometries of the complexes predicted theoretically were consistent with those... 

The connection with standard solvent effects theories must be made after a statistical mechanical averaging over the solvent configurations has been made. Temperature enters here in a natural manner. 

The level of electronic structure theory used by Mikkelsen et al. [37] is given by the multiconfigurational (MC) selfconsistent field (SCF) where the wavefunction is fully optimized with respect to all variational parameters these include both orbital and configurations. The main deficiency of standard SCF ab initio procedures, namely, lack of correlation effects, is overcome in this MCSCF approach. The level of solvent-effects theory is the standard spherical cavity immersed in a continuum dielectric an early formalism proposed by Rinaldi and Rivail was used (see Ref. [6] for an extensive analysis). 

In a previous report [7], we have successfully applied the quantum chemical method to the determination of the geometry of a-CD inclusion-complexes with substituted benzenes such as p-nitrophenol, p-hydroxy-benzoic acid, and benzoic acid. This method was based on the so-called solvent-effect theory and it was assumed that the a-CD cavity has the environmental effect of lower dielectric constant( l) on a included part of the guest and the other part of guest is exposed to the aqueous phase of higher dielectric constant( 2) shown in Fig,IB. 

Abstract It is well known that solvents can modify the frequency and intensity of the solute spectral bands, the thermodynamics and kinetics of chemical reactions, the strength of molecular interactions or the fate of solute excited states. The theoretical study of solvent effects is quite complicated since the presence of the solvent introduces additional difficulties with respect to the smdy of analogous problems in gas phase. The mean field approximation (MFA) is used for many of the most employed solvent effect theories as it permits to reduce the computational cost associated to the smdy of processes in solution. In this chapter we revise the performance of ASEP/MD, a quanmm mechanics/molecular mechanics method developed in our laboratory that makes use of this approximation. It permits to combine state of the art calculations of the solute electron distribution with a detailed, microscopic, description of the solvent. As examples of application of the method we smdy solvent effects on the absorption spectra of some molecules involved in photoisomerization processes of biological systems. 

Microscopic solvent effect theories imply an extensive sampling of the configurational space of the solute-solvent system. Furthermore, most of processes of chemical interest involve large charge redistribution and its study requires the use of high-level quantum-mechanical methods with the consequent increase in the computational cost. The mean field approximation provides a way of reducing the number of quantum calculations and, consequently, it permits to reduce the computational cost associated with the inclusion of solvent effects. In this chapter the theoretical basis of this approximation have been analyzed. We have paid special attention to the ASEP/MD method that implements this approximation in QM/MM methods. 

There is naturally a wealth of publications on aspects of solvation and a comprehensive review would need a whole book. Hence, it is not practical to wade through all the developments in solvent effect theory, especially as other articles in this encyclopedia also deal with some aspects of solvation (see Related Articles at the end of this article). Instead, the focus will be on the methods used for the evaluation of the thermodynamics of cavity formation (TCF), which is a large part of solvation thermodynamics, and in particular on the application of the most successful statistical mechanical theory for this purpose, namely, the scaled particle theory (SPT) for hard sphere fluids (see Scaled Particle Theory). This article gives a brief introduction to the thermodynamic aspects of the solvation process, defines energy terms associated with solvation steps and presents a short review of statistical mechanical and empirical... 

PEP theory has also been applied to modelling the free energy profiles of reactions in solution. An important example is the solvent effect on the SN2 reaction... 

Constanciel R and R Contreras 1984. Self-Consistent Field Theory of Solvent Effects Representation by Continuum Models - Introduction of Desolvation Contribution. Theoretica Chimica Acta 65 1-11. 

Several alternative attempts have been made to quantify Lewis-acid Lewis-base interaction. In view of the HSAB theory, the applicability of a scale which describes Lewis acidity with only one parameter will be unavoidably restricted to a narrow range of struchirally related Lewis bases. The use of more than one parameter results in relationships with a more general validity ". However, a quantitative prediction of the gas-phase stabilities of Lewis-acid Lewis-base complexes is still difficult. Hence the interpretation, not to mention the prediction, of solvent effects on Lewis-add Lewis-base interactions remains largely speculative. 

The integral equation method is free of the disadvantages of the continuum model and simulation techniques mentioned in the foregoing, and it gives a microscopic picture of the solvent effect within a reasonable computational time. Since details of the RISM-SCF/ MCSCF method are discussed in the following section we here briefly sketch the reference interaction site model (RISM) theory. 

Other measures of nucleophilicity have been proposed. Brauman et al. studied Sn2 reactions in the gas phase and applied Marcus theory to obtain the intrinsic barriers of identity reactions. These quantities were interpreted as intrinsic nucleo-philicities. Streitwieser has shown that the reactivity of anionic nucleophiles toward methyl iodide in dimethylformamide (DMF) is correlated with the overall heat of reaction in the gas phase he concludes that bond strength and electron affinity are the important factors controlling nucleophilicity. The dominant role of the solvent in controlling nucleophilicity was shown by Parker, who found solvent effects on nucleophilic reactivity of many orders of magnitude. For example, most anions are more nucleophilic in DMF than in methanol by factors as large as 10, because they are less effectively shielded by solvation in the aprotic solvent. Liotta et al. have measured rates of substitution by anionic nucleophiles in acetonitrile solution containing a crown ether, which forms an inclusion complex with the cation (K ) of the nucleophile. These rates correlate with gas phase rates of the same nucleophiles, which, in this crown ether-acetonitrile system, are considered to be naked anions. The solvation of anionic nucleophiles is treated in Section 8.3. 

The observed solvent effect can be expressed quantitatively with the aid of the Leffler-Grunwald operator 5m introduced in Chapter 7. For rate constant k measured in medium M we have, from transition state theory, k = (kT//i)exp ( —AGm// T) and similarly for rate constant ko measured in a reference solvent. Combining these two expressions gives... 

To go from experimental observations of solvent effects to an understanding of them requires a conceptual basis that, in one approach, is provided by physical models such as theories of molecular structure or of the liquid state. As a very simple example consider the electrostatic potential energy of a system consisting of two ions of charges Za and Zb in a medium of dielectric constant e. 

Ultimately physical theories should be expressed in quantitative terms for testing and use, but because of the eomplexity of liquid systems this can only be accomplished by making severe approximations. For example, it is often neeessary to treat the solvent as a continuous homogeneous medium eharaeterized by bulk properties such as dielectric constant and density, whereas we know that the solvent is a molecular assemblage with short-range structure. This is the basis of the current inability of physical theories to account satisfactorily for the full scope of solvent effects on rates, although they certainly can provide valuable insights and they undoubtedly capture some of the essential features and even cause-effect relationships in solution kinetics. Section 8.3 discusses physical theories in more detail. 

After an introductory chapter, phenomenological kinetics is treated in Chapters 2, 3, and 4. The theory of chemical kinetics, in the form most applicable to solution studies, is described in Chapter 5 and is used in subsequent chapters. The treatments of mechanistic interpretations of the transition state theory, structure-reactivity relationships, and solvent effects are more extensive than is usual in an introductory textbook. The book could serve as the basis of a one-semester course, and I hope that it also may be found useful for self-instruction. 

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. ... 

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