Aromaticity constants

Table 2. Atom Types and Corresponding Aromaticity Constants Ah for R = H...

Balaban31a has assigned values of —26 and —77 for the aromaticity constants for pyrrole and the pyrrolyl anion, respectively (benzene = 0). 

Table 2 Aromaticity constants (relative electronegativities) of first-row atoms...

In this expression B is a constant and set at 1. Values for the corrected aromaticity constant A = AxAt for heteroaromatics are given in Table V. 

Balaban and Simon159 have argued that an index based on the relative electrophilicity and nucleophilicity of a ring compared with benzene is a useful means of expressing in numerical terms the aromaticity of a ring system. The authors derive an aromaticity constant K from a summation of k values for each ring position, where k is an expression of the tendency of the atom to release or attract -electrons from the delocalized 7r-cloud and is defined by... 

There appear to be rather few data available for the pyrylium cation. Balaban and Simon169 have reported a high value of +97 for the aromaticity constant, a reflection of its electrophilicity. The PMR spectrum, as expected, shows absorptions in the 8.5-9.6 ppm region,296 and qualitative agreement between chemical shifts and r-electron density, as calculated by the HMO method, has been reported.297 Further calculations of charge... 

Berezin162 has calculated the coefficients of influence (Section II,F, 3) for four azines, including pyridine, and points out that the values decrease in the same order as the magnitude of the aromaticity constants increase (although pyridine or pyrazine appears to be anomalous). 

There have been very few studies on the borepin ring system and accordingly discussions of its aromatic character have been sparse. Balaban and Simon169 calculated a K value (aromaticity constant) of +28, which is much lower than for tropylium cation (+100). Further evidence of aromaticity has been based very much on qualitative interpretations of spectral features. 

Hammen equation A correlation between the structure and reactivity in the side chain derivatives of aromatic compounds. Its derivation follows from many comparisons between rate constants for various reactions and the equilibrium constants for other reactions, or other functions of molecules which can be measured (e g. the i.r. carbonyl group stretching frequency). For example the dissociation constants of a series of para substituted (O2N —, MeO —, Cl —, etc.) benzoic acids correlate with the rate constant k for the alkaline hydrolysis of para substituted benzyl chlorides. If log Kq is plotted against log k, the data fall on a straight line. Similar results are obtained for meta substituted derivatives but not for orthosubstituted derivatives. 

Adopting the view that any theory of aromaticity is also a theory of pericyclic reactions [19], we are now in a position to discuss pericyclic reactions in terms of phase change. Two reaction types are distinguished those that preserve the phase of the total electi onic wave-function - these are phase preserving reactions (p-type), and those in which the phase is inverted - these are phase inverting reactions (i-type). The fomier have an aromatic transition state, and the latter an antiaromatic one. The results of [28] may be applied to these systems. In distinction with the cyclic polyenes, the two basis wave functions need not be equivalent. The wave function of the reactants R) and the products P), respectively, can be used. The electronic wave function of the transition state may be represented by a linear combination of the electronic wave functions of the reactant and the product. Of the two possible combinations, the in-phase one [Eq. (11)] is phase preserving (p-type), while the out-of-phase one [Eq. (12)], is i-type (phase inverting), compare Eqs. (6) and (7). Normalization constants are assumed in both equations ... 

Jedrzejas, M. J., Singh, S. Brouillette, W. J. Air, G. M. Luo, M. A. 1995. Strategy for theoretical binding constant, Ki calculation for neuraminidase aromatic inhibitors, designed on the basis of the active site structure of influenza virus neuraminidase. Proteins Struct. Funct. Genet. 23 (1995) 264-277... 

The correction term in Eq. (9) shows that the basic assumption of additivity of the fragmental constants obviously does not hold true here. Correction has to be appHed, e.g., for structural features such as resonance interactions, condensation in aromatics or even hydrogen atoms bound to electronegative groups. Astonishingly, the correction applied for each feature is always a multiple of the constant Cu, which is therefore often called the magic constant . For example, the correction for a resonance interaction is +2 Cj, or per triple bond it is -1 A detailed treatment of the Ef system approach is given by Mannhold and Rekker [5]. 

Purely aromatic ethers e.g., diphenyl ether), which are commonly encountered, are very hmited in number. Most of the aromatic ethers are of the mixed aliphatic - aromatic type. They are not attacked by sodium nor by dilute acids or alkahs. When hquid, the physical proper-ties (b.p., d . and ) are useful constants to assist in their identification. Three important procedures are available for the characterisation of aromatic ethers. 

Cleavage with hydriodic acid. Aromatic ethers undergo fission when heated with constant boihng point hydriodic acid ... 

The mixed aliphatic - aromatic ethers are somewhat more reactive in addition to cleavage by strong hydriodio acid and also by constant b.p. hydrobromio acid in acetic acid solution into phenols and alkyl halides, they may be bromi-nated, nitrated and converted into sulphonamides (Section IV,106,2). 

Determination of the dissociation constants of acids and bases from the change of absorption spectra with pH. The spectrochemical method is particularly valuable for very weak bases, such as aromatic hydrocarbons and carbonyl compounds which require high concentrations of strong mineral acid in order to be converted into the conjugate acid to a measurable extent. 

NMR signals of the amino acid ligand that are induced by the ring current of the diamine ligand" ". From the temperature dependence of the stability constants of a number of ternary palladium complexes involving dipeptides and aromatic amines, the arene - arene interaction enthalpies and entropies have been determined" ". It turned out that the interaction is generally enthalpy-driven and counteracted by entropy. Yamauchi et al. hold a charge transfer interaction responsible for this effect. 

The operation of the nitronium ion in these media was later proved conclusively. "- The rates of nitration of 2-phenylethanesulphonate anion ([Aromatic] < c. 0-5 mol l i), toluene-(U-sulphonate anion, p-nitrophenol, A(-methyl-2,4-dinitroaniline and A(-methyl-iV,2,4-trinitro-aniline in aqueous solutions of nitric acid depend on the first power of the concentration of the aromatic. The dependence on acidity of the rate of 0-exchange between nitric acid and water was measured, " and formal first-order rate constants for oxygen exchange were defined by dividing the rates of exchange by the concentration of water. Comparison of these constants with the corresponding results for the reactions of the aromatic compounds yielded the scale of relative reactivities sho-wn in table 2.1. 

The activity coefficients in sulphuric acid of a series of aromatic compounds have been determined. The values for three nitro-com-pounds are given in fig. 2.2. The nitration of these three compounds over a wide range of acidity was also studied, and it was shown that if the rates of nitration were corrected for the decrease of the activity coefficients, the corrected rate constant, varied only slightly... 

The value of the second-order rate constant for nitration of benzene-sulphonic acid in anhydrous sulphuric acid varies with the concentration of the aromatic substrate and with that of additives such as nitromethane and sulphuryl chloride. The effect seems to depend on the total concentration of non-electrolyte, moderate values of which (up to about 0-5 mol 1 ) depress the rate constant. More substantial concentrations of non-electrolytes can cause marked rate enhancements in this medium. Added hydrogen sulphate salts or bases such as pyridine... 

The results in table 2.6 show that the rates of reaction of compounds such as phenol and i-napthol are equal to the encounter rate. This observation is noteworthy because it shows that despite their potentially very high reactivity these compounds do not draw into reaction other electrophiles, and the nitronium ion remains solely effective. These particular instances illustrate an important general principle if by increasing the reactivity of the aromatic reactant in a substitution reaction, a plateau in rate constant for the reaction is achieved which can be identified as the rate constant for encounter of the reacting species, and if further structural modifications of the aromatic in the direction of further increasing its potential reactivity ultimately raise the rate constant above this plateau, then the incursion of a new electrophile must be admitted. 

For nitrations in sulphuric and perchloric acids an increase in the reactivity of the aromatic compound being nitrated beyond the level of about 38 times the reactivity of benzene cannot be detected. At this level, and with compounds which might be expected to surpass it, a roughly constant value of the second-order rate constant is found (table 2.6) because aromatic molecules and nitronium ions are reacting upon encounter. The encounter rate is measurable, and recognisable, because the concentration of the effective electrophile is so small. 

A similar circumstance is detectable for nitrations in organic solvents, and has been established for sulpholan, nitromethane, 7-5 % aqueous sulpholan, and 15 % aqueous nitromethane. Nitrations in the two organic solvents are, in some instances, zeroth order in the concentration of the aromatic compound (table 3.2). In these circumstances comparisons with benzene can only be made by the competitive method. In the aqueous organic solvents the reactions are first order in the concentration of the aromatic ( 3.2.3) and comparisons could be made either competitively or by directly measuring the second-order rate constants. Data are given in table 3.6, and compared there with data for nitration in perchloric and sulphuric acids (see table 2.6). Nitration at the encounter rate has been demonstrated in carbon tetrachloride, but less fully explored. ... 

The kinetics of the reactions were complicated, but three broad categories were distinguished in some cases the rate of reaction followed an exponential course corresponding to a first-order form in others the rate of reaction seemed to be constant until it terminated abruptly when the aromatic had been consumed yet others were susceptible to autocatalysis of varying intensities. It was realised that the second category of reactions, which apparently accorded to a zeroth-order rate, arose from the superimposition of the two limiting kinetic forms, for all degrees of transition between these forms could be observed. 

The relative basicities of aromatic hydrocarbons, as represented by the equilibrium constants for their protonation in mixtures of hydrogen fluoride and boron trifluoride, have been measured. The effects of substituents upon these basicities resemble their effects upon the rates of electrophilic substitutions a linear relationship exists between the logarithms of the relative basicities and the logarithms of the relative rate constants for various substitutions, such as chlorination and... 

The solubility of hydrogen chloride in solutions of aromatic hydrocarbons in toluene and in w-heptane at —78-51 °C has been measured, and equilibrium constants for Tr-complex formation evaluated. Substituent effects follow the pattern outlined above (table 6.2). In contrast to (T-complexes, these 7r-complexes are colourless and non-conducting, and do not take part in hydrogen exchange. 

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