Some Linear Free Energy Relationships

The basicity of simple 4,5-dihydropyrazoles (A -pyrazolines) has been discussed on the basis of protonation at N-1 in the case of 1-unsubstituted, 1-methyl, and 1-phenyl derivatives <2000JP0372>. The pA values of 15 4,5-dihydropyrazoles substituted at N-1 by /i-nitrophenyl, 2,4-dinitrophenyl, and 2,4,6-trinitrophenyl groups were determined. After examining some linear free energy relationships, to discuss these values further, DFT calculations, including temperature effects, were carried out on the parent compounds (no C-substituents) for the 1-unsubstituted, 1-methyl, 1-phenyl, l-/)-nitrophenyl, and 1-(2,4,6-trinitrophenyl) series. These calculations predicted an inversion of N-1 and N-2 basicities between 1-phenyl- and l-(/>-nitrophenyl)-4,5-dihydropyrazoles. Since there were no experimental data for the protonation of 4,5-dihydropyrazoles in the gas phase, chemical ionization mass spectrometry was used to try to determine the structure of protonated 1-methyl- and l,3-dimethyl-5-phenyl-4,5-dihydropyrazoles. The substituent effects and protonation sites of 1-phenyl-3-methyl-5-A-benzylideneaminopyrazoles were studied by NMR and ab initio (6-31G ) MO calculations <1996J(P2)2383>. 

Table 3 Some linear free energy relationships for rates...

Many researchers have applied similar approaches to develop or apply linear free energy relationships, when the substituent is directly attached to the double bond, with some success. Two of the more notable examples can be found in the Patterns of Reactivity Scheme (Section 7.3.4) and the works of Giese and coworkers.16 19... 

Quite recently, the same research group compared the electrophilicity of 6-nitro-tetrazolo[l,5- ]pyridine and 6,8-dini-trotetrazolo[l,5- ]pyridine 11 with a series of electron-deficient aromatic and heteroaromatic compounds <2005JOC6242>. As reference nucleophiles, fV-methylpyrrole, indole, fV-methylindole, and some morpholino enamines were used. The reactivity of the electrophiles studied followed the linear-free energy relationship defined by Mayr et al. <2003ACR66>. 

The structure-reactivity relationship is a concept familiar to every organic chemist. As commonly used it refers to a linear free energy relationship, such as the Bronsted or Hammett equations, or some more general measure of the effect of changing substituent on the rate or equilibrium of a reaction. A substituent constant is conveniently defined as the effect of the substituent on the free-energy change for a control reaction. So the so-called structure-reactivity relationship is in fact usually a reactivity-reactivity relationship. 

To some extent these effects seem unavoidable and great caution has to be exercised when fine tuning the influence of small structural changes on pKs determined by acidity functions. On the other hand, these effects may well be small in many cases. Evidence supporting this contention originates in the existence of some excellent linear free energy relationships between gas phase and solution acidities and basicities (83MI2). 

Some understanding of the effect of structure on the rate of catalytic hydrogenation has been sought through comparisons with structural effects in other types of reactions. The attempt to find linear free energy relationships... 

This chapter is dedicated to the memory of Robert Wheaton Taft (1922-1996). The contributor enjoyed friendship with Bob Taft for some thirty years. The present chapter, like the corresponding chapters in earlier volumes1-7, contains much discussion of Taft s work in linear free-energy relationships. Since the 1950s he had always been at the forefront of progress in this field. 

For some further discussion on the applicability of linear free energy relationships to second order nonlinear optics, see Ulman, A. J. Phvs. Chem. 1988, 92, 2385-2390. 

Because of the bulk of comparable material available, it has been possible to use half-wave potentials for some types of linear free energy relationships that have not been used in connection with rate and equilibrium constants. For example, it has been shown (7, 777) that the effects of substituents on quinone rings on their reactivity towards oxidation-reduction reactions, can be approximately expressed by Hammett substituent constants a. The susceptibility of the reactivity of a cyclic system to substitution in various positions can be expressed quantitatively (7). The numbers on formulae XIII—XV give the reaction constants Qn, r for the given position (values in brackets only very approximate) ... 

If the type of the molecular frame A and the nature of the polaro-graphically active group R are known, it is possible to distinguish by means of a linear free energy relationship, the kind of the substituent X in the molecule R — A — X. From the measured value of the shift of the half-wave potential and by means of the tabulated values of the substituent constants, the substituent involved can be distinguished or some few substituents that are likely to be responsible for the observed shift of the half-wave potential can be sorted out. This type of application has been demonstrated (160) in the identification of the nature of the substituent and the determination of its position on a pteridine ring. 

The existence of an enthalpy-entropy relationship has some important mechanistic implications. As the subject has been reviewed (Leffler, 1955) it will suffice here to make only a few brief comments. One important consequence of the compensation law is that linear free-energy relationships appear to apply to reactions with variable entropy only when the entropy is a linear function of the enthalpy (Jaffe, 1953 Taft, 1956c). 

Systematic studies of the effects of structure on the biological activities of organic compounds and the analysis of the results are comprised in the term Quantitative Structure-Activity Relationships (QSAR). Many of the treatments employed in the correlation analysis of data in this field closely resemble those used for linear free-energy relationships, e.g. the Hammett equation and extensions thereof, and so the study of the biological properties of organic compounds is often regarded as a part of physical organic chemistry. In recent years, some historical study of work in... 

The rates at which several substituted benzenes quench triplet benzophenone have been measured 17 8). No single linear free energy relationship can be derived. For alkoxybenzenes, alkylbenzenes, benzene itself, and benzotrifluoride as quenchers, one finds a linear plot of log vs. IP with a slope similar to that found for the plot of all substituted benzenes and triplet a-trifluoroacetophenone. A given aromatic such as benzene quenches the fluorinated ketone triplet, which has an E - -E(A /A) value of only 16 kcal, some 50 times faster than it quenches triplet acetophenone or benzophenone 132>. This rate difference reflects only 20% of the full 12 kcal difference in thermodynamic redox potentials. However, the halobenzenes and benzonitrile quench triplet benzophenone faster than does benzene 178>. It seems likely that with these electron poor benzene derivatives, some alternate chemical reaction becomes dominant. Although a reverse CT process has been suggested, with the triplet ketone as donor, it is perhaps more likely that some sort of radical addition occurs with conjugating substituents on... 

This chapter provides a tutorial focused on the uses of quantum mechanical descriptors in linear free energy relationships (LFERs). Often, LFERs derived with empirically based (i.e., experimental) descriptors are superior in quality to those derived with quantum mechanical descriptors. However, theoretically based LFERs have some advantages including ease of calculation. The QM... 

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