Shannon entropy as a new measure of aromaticity, Shannon aromaticity

Based on the local Shannon entropy concept in information theory, a new measure of aromaticity is introduced. This index, which describes the probability of electronic charge distribution between atoms in a given ring, is called Shannon aromaticity (SA). Using B3LYP method and different basis sets (6-31G**, 6-31+G** and 6-311++G**), the SA values of some five-membered heterocycles, C(4)H(4)X, are calculated. Significant linear correlations are observed between the evaluated SAs and some other criteria of aromaticity such as ASE, Lambda and NICS indices. According to the obtained relationships, the range of 0.003 < SA < 0.005 is chosen as the boundary of aromaticity/antiaromaticity. Using B3LYP/6-31+G** level of theory, the Shannon aromaticities for a series of mono-substituted benzene derivatives are calculated and analyzed. It is found that the least standard deviation between the aromaticities and the best linear correlation with the Hammett substituent constants are observed for the new index in comparison with the other indices. Also the values of the new index are evaluated for some substituted penta- and heptafulvenes, which successfully predict the order of aromaticity in these compounds. Applying this index to some non-benzonoids, linear and angular polyacenes also give satisfactory results and prove to be quite suitable for determining the local aromaticity of different rings in polyaromatic hydrocarbons.