Shannon entropy as a new measure of aromaticity, Shannon aromaticity

Abstract

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.

Quantifying aromaticity with electron delocalisation measures

“…113,114 On his side, Noorizadeh and Shakerzadeh used the Shannon entropy of the electron density calculated at the bond critical point to define an aromaticity index. 115 Electron delocalisation has been tightly connected to aromaticity from the very beginning. The old concept of bond order -that later evolved to electron sharing index, Eq.…”

The electron density of delocalized bonds (EDDB) applied for quantifying aromaticity

“…ATI has the same theoretical foundations as the well-known para-delocalization index (PDI) by Poater et al 5,62 but it involves a Hilbert-space partitioning within the basis of atomic orbitals instead of Bader's atomsin-molecule (AIM) 65 or the fuzzy-atomic space (FAS). 61 Shannon aromaticity (SA), 63 which measures the KullbackLeibler distance of the bonding electron density distribution in aromatic ring from uniformity; SA is a non-referential index. Fluctuation index of aromaticity (FLU), 5,64 which has a similar interpretation as the SA index but depends upon parameters determined for an idealized aromatic system.…”

Lithium Including Mixed Sodium Inside Graphene Oxide (GO) as Anodic Electrodes for ion Batteries

“…This entropy is defined as exclusive spaces through minimizing informationentropy 62 by Parr et al, 63,64 .The formula of Shannon's information 64 entropies for normalized and continuous probabilities function is S=-∫ P(x)InP(x)d x (15). S(r)= (16).…”