Master equations for calculating heterolysis energies in solution

Abstract

A simple "master equation" for predicting the heterolysis energies of bonds to give resonancestabilized ions is tested by reaction of six carbocations with 21 carbanions and four phenoxide anions. The original equation31" is enormously improved in precision and generality by replacing pAR+ values as the measure of cation stability. If calculated delocalization energies are used, data for 33 reactions are correlated by eq 5 with r = 0.9948 (instead of r = 0.8812) so that the standard deviation of AHhet is ± 0.702 kcal/mol. With Mfhet for 9-(methoxycarbonyl)fluorenide anion as the model anion, 66 values are correlated with r = 0.9960, proving the self-consistency of our data as well as the soundness of this approach. Equations such as (5) should provide a simple means for estimating quantitative heterolysis energies in solution for thousands of bonds that give resonance-stabilized ions as products. 9-CNRH 8.30

The relevance of calorimetry to physical organic chemistry

“…(29) Through these correlation equations, the heats of heterolysis of many other compounds could be predicted if the relevant pK terms for the cations and anions were known or could be predicted by linear free-energy relationships.…”

Structural dependence of heterolytic bond dissociation energy of carbon–carbon σ bonds in hydrocarbons

“…Arnett and co-workers proposed, 40 as one of the results of their systematic studies on carbon-carbon bond formation through the reaction of carbocations and carbanions, empirical relationships (master equations) that correlate, with high precision, the heat of heterolysis (DH het ) with the thermodynamic stabilities of cations (pK R ) and anions (pK HA ). From the results of calorimetry for the coordination of resonance-stabilized carbocations and carbanions in sulfolane or acetonitrile over a wide range of ion stability, they demonstrated that equation (1) or (2), depending on the class of the generating carbocation, predicts heats of heterolysis of carbon-carbon s bonds.…”

Synthesis of a Hydrocarbon Salt Having a Fullerene Framework

“…The stable existence of C 60 •- , C 60 (CN) - , or 1 - in the presence of 2 + appears to be due principally to the extremely high thermodynamic stabilities of both cationic and anionic species. However, Arnett's empirical equation, which correlates the heat of coordination of a carbocation and a carbanion with their p K R + and p K HA values, predicts that the coordination of 1 - with 2 + is energetically favorable by 7.5 kcal/mol…”