Linear Free Energy Relations LFER

These techniques are known as linear free energy relations, LFER. Imagine that one has determined the rate constants, or the Gibbs free energies of activation, for a series of reactions. The reactions are all the same, save for (for example) a different substituent on each reactant. The substituent is not a direct participant in the reaction. In an LFER, the values of log k or AG are correlated with some characteristic of the substituent as manifested in another reaction series. If the correlation is successful, then the two series of reactions have a common denominator. This technique has proved to be a powerful one for systematizing reactivity. We shall see a number of such correlations. 

Perhaps it is best to start with an example. Consider the rate constants for the series represented by the equation 

The rate constants for reactions with different substituents R correlate with the pA a s for the corresponding acids, RCO2H.1 The plot of log r versus pKa is linear, as shown in Fig. 10-1. One can represent this algebraically in either of two forms  

This plot shows the correlation of the logarithms of the rate constants for reaction (10-1) with the pAf s of the carboxylic acids having the same substituents. Data are from Ref. 1. 

The free energies of activation for the one reaction series are directly proportional to the standard free energy changes for another. This form is emphasized by Eq. (10-3), and is what gives rise to the designation of this approach as an LFER. 

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Recently, Riviere and Brooks (2007) published a method to improve the prediction of dermal absorption of compounds dosed in complex chemical mixtures. The method predicts dermal absorption or penetration of topically applied compounds by developing quantitative structure-property relationship (QSPR) models based on linear free energy relations (LFERs). The QSPR equations are used to describe individual compound penetration based on the molecular descriptors for the compound, and these are modified by a mixture factor (MF), which accounts for the physical-chemical properties of the vehicle and mixture components. Principal components analysis is used to calculate the MF based on percentage composition of the vehicle and mixture components and physical-chemical properties. 

Surface complexation is a typical multi-component reaction, similar to cation exchange. The database for surface complexation includes complexation constants for major elements in groundwater such as and S04 , but not for and HCOs". In the first instance, constants for these ions can be estimated with linear free energy relations (LFER s) in which the properties of similar chemical systems are compared and interpolated (Dzombak and Morel, 1990). Thus, the surface complexation constant for is expected to lie in between the ones for and for Zn, in line with the known differences of the association constants of these heavy metals with OH in water. For the weak sites, the LFER gives ... 

Linear Free Energy Related (LFER) Approaches 187... 

LINEAR FREE ENERGY RELATED (LFER) APPROACHES... 

RP-LC, multivariate analysis methods such as principle component analysis (PCA) and nonlinear mapping (NML), or comparative molecular field analysis (CoMFA) approaches and linear free energy-related (LFER) equations have been used to derive structure-retention relationships in chiral chromatography [16-18]. 

This relation has been used to predict and interpret both self-exchange and crossreaction rates (or even "12), depending on which of the quantities have been measured experimentally. Alternatively, one could study a series of closely related electron-transfer reactions (to maintain a nearly constant X12) as a function of AG 2 a plot of In ki2 vs. In A 12 is predicted to be linear, with slope 0.5 and intercept 0.5 In ( 11 22)- The Marcus prediction (for the normal free-energy region) amounts to a linear free-energy relation (LFER) for outer-sphere electron transfer. 

One can thus use tt values (Table 2.16) to estimate for a compound when an experimental value is not available providing is known for a related compound that differs from the unknown by one or at the most two substituents. For example, if log for anisole (methoxybenzene) is known to be 2.11, one would predict that logiifow for 3-chloroanisole would be 2.11 - - 0.77 = 2.88. This procedure illustrates the concept of linear free energy relations (LFERs) that depends on the fact that the different components of an organic molecule interact both with one another and their environment in a consistent manner and the behavior of the molecule can be defined as the sum of its components. 

Linear free energy relations (see LFER) Lineweaver-Burk treatment, 91 Long-chain approximation, 183... 

The Hammett equation is the best-known example of a linear free-energy relationship (LFER), that is, an equation which implies a linear relationship between free energies of reaction or activation for two related processes48. It describes the influence of polar meta-or para-substituents on reactivity for side-chain reactions of benzene derivatives. 

The above Hansch equations are also generally referred to as linear free energy relationships (LFER) as they are derived from the free energy concept of the drug-receptor complex. They also assume that biological activity is linearly related to the electronic and lipophilic contributions of the various substituents on the parent molecule. 

Table 3.6 Examples of Simple One-Parameter Linear Free Energy Relationships (LFERs) for Relating Partition Constants and/or Partition Coefficients in Different Two-Phase Systems (Including the Pure Compound as Phase)...

Linear free energy relationship (LFER) — For various series of similar chemical reactions it has been empirically found that linear relationships hold between the series of free energies (-> Gibbs energy) of activation AG and the series of the standard free energies of reactions AGf, i.e., between the series of log fc (k -rate constants) and log K (Kt - equilibrium constants) (z labels the compounds of a series). Such relations correlate the - kinetics and -> thermodynamics of these reactions, and thus they are of fundamental importance. The LFER s can be formulated with the so-called Leffler-Grunwald operator dR ... 

In this chapter we provide a historical perspective of the development of the field of computational toxicology. Beginning from the similarity-based grouping of elements into the periodic table, the chapter presents a chronology of developments from the simple observations of qualitative relations between structure and toxicity through LFER (linear free energy related) and QSAR (quantitative structure activity relationship) models, to the current... 

The most promising approach is to further extend this rationale using linear free-energy relationships (LFER) to relate permeability to the physical prop-... 

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