Modeling Linear Free Energy Relationship

Acree, W.E., Jr. Abraham, M.H. (2006). The analysis of solvation in ionic liquids and organic solvents using the Abraham model linear free energy relationship. /. Chem. Technol Biotechnol., 81,1441-1446. 

Solvents exert their influence on organic reactions through a complicated mixture of all possible types of noncovalent interactions. Chemists have tried to unravel this entanglement and, ideally, want to assess the relative importance of all interactions separately. In a typical approach, a property of a reaction (e.g. its rate or selectivity) is measured in a laige number of different solvents. All these solvents have unique characteristics, quantified by their physical properties (i.e. refractive index, dielectric constant) or empirical parameters (e.g. ET(30)-value, AN). Linear correlations between a reaction property and one or more of these solvent properties (Linear Free Energy Relationships - LFER) reveal which noncovalent interactions are of major importance. The major drawback of this approach lies in the fact that the solvent parameters are often not independent. Alternatively, theoretical models and computer simulations can provide valuable information. Both methods have been applied successfully in studies of the solvent effects on Diels-Alder reactions. 

Brown developed the selectivity relationship before the introduction of aromatic reactivities following the Hammett model. The former, less direct approach to linear free-energy relationships was necessary because of lack of data at the time. 

Another method for studying solvent effects is the extrathermodynamic approach that we described in Chapter 7 for the study of structure-reactivity relationships. For example, we might seek a correlation between og(,kA/l ) for a reaction A carried out in a series of solvents and log(/ R/A R) for a reference or model reaction carried out in the same series of solvents. A linear plot of og(k/iJk ) against log(/ R/ linear free energy relationship (LFER). Such plots have in fact been made. As with structure-reactivity relationships, these solvent-reactivity relationships can be useful to us, but they have limitations. 

The second aspect is more fundamental. It is related to the very nature of chemistry (quantum chemistry is physics). Chemistry deals with fuzzy objects, like solvent or substituent effects, that are of paramount importance in tautomerism. These effects can be modeled using LFER (Linear Free Energy Relationships), like the famous Hammett and Taft equations, with considerable success. Quantum calculations apply to individual molecules and perturbations remain relatively difficult to consider (an exception is general solvation using an Onsager-type approach). However, preliminary attempts have been made to treat families of compounds in a variational way [81AQ(C)105]. 

LD model, see Langevin dipoles model (LD) Linear free-energy relationships, see Free energy relationships, linear Linear response approximation, 92,215 London, see Heitler-London model Lysine, structure of, 110 Lysozyme, (hen egg white), 153-169,154. See also Oligosaccharide hydrolysis active site of, 157-159, 167-169, 181 calibration of EVB surfaces, 162,162-166, 166... 

Wolfe NL, Bums LA, Steen WC. 1980. Use of linear free energy relationships and an evaluate model to assess the fate and transport of phthalate esters in the aquatic environment. Chemosphere 9 393-402. 

Lokajova, J., Tesrfova, E., and Armstrong, D.W., Comparative study of three teicoplanin-based chiral stationary phases using the linear free energy relationship model, J. Chromatogr. A, 1088, 57, 2005. 

The monoprotonation of p-[(/>-dimethylamino)phenyI]-azo-benzenesulphonic acid (methyl orange) also gives a mixture of the azonium ion and the ammonium ion, in which the former predominates according to Reeves (1966). Bolton et al. (1973). however, using linear free energy relationships, conclude that the ammonium form is dominant, and question the general acceptance of the tautomeric model for the protonation of p-aminoazobenzene and its derivatives. 

In the last several years, a set of BBB QSAR models have been developed. One of the top models, developed by Abraham et al. in 2006 [44], reached the predictive limit obtainable from the data set they used. The experimental errors of the logBB measurements were estimated to be 0.3. Their model utilized linear free energy relationship (LFER) as descriptors. For the 328-molecule data set, r2 and RMSE of the MLR model were 0.75 and 0.3 log units, respectively. Interestingly, the RMSE for their test set (n = 164) was even lower (0.25 log units). 

Perlinger, J. A., R. Venkatapathy, and J. F. Harrison, Linear free energy relationships for polyhalogenated alkane transformation by electron-transfer mediators in model aqueous systems , J. Phys. Chem. A., 104,2752-2763 (2000). 

In the remainder of this chapter, newly developed methods such as a molecular modeling approach (Bodor and Huang, 1992 Zhou et al., 1993), a group contribution approach (V Mita et al., 1986 Klopman et al., 1992 Kthne et al., 1995 Myrdal et al., 1995), and a frequently used linear free-energy relationship method (Taft et al., 1985 Lee, 1996) will be discussed. 

There are two major concepts involved in the physico-chemical description of a chemical reaction the energetics, which determines the feasibility of the reaction, and the kinetics which determines its rate. In general these two concepts are independent and the rate of a chemical reaction can be varied according to the mechanism (e.g. catalysis) but within certain assumptions there is a mathematical relationship between the rate constant and the reaction free energy difference. These relationships are either linear (linear free energy relationship, LFE) or quadratic (QFE), the latter being often referred to as the Marcus model — a description which should not hide the important contributions of other workers in this field [1],... 

Platts and Abraham (2000) used their LSER or linear free energy relationship (LFER) descriptors to model plant cuticular matrix-water partitioning (Kmxw) ... 

The guidelines of linear-free energy relationships have also been used to capture not only the hydrocarbon stmcture/function but also catalyst structure/function relationships. Thus Liguras et al. (39) have fashioned a model where the rate constant is a function of the reactant, the reaction family, and the catalyst silicon to aluminum ratio. This fledgling approach considerably reduces the number of kinetic parameters and appears to be quite useful in the modelling of complex kinetics of hydrocarbon feedstocks. 

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