A New Set of Aromaticity Descriptors Based on the Electron Density Employing the Distributed Multipole Analysis (DMA)

Aromatic compounds are energetically stable and have low reactivity, but an aromaticity concept is difficult to establish because it cannot be measured. For this reason, different descriptors have been developed to rationalize and quantify this phenomenon. Given that cyclic electron delocalization is an essential property of aromatic compounds, in this work, we propose six new aromatic descriptors based on Stone's distributed multipole analysis (DMA) to partition the molecular electron density into electric multipoles localized on different sites of a molecule. The new aromatic descriptors are based on different components of the DMA quadrupole electric moment tensor <b><i>Q</i> ₂</b> , the first term of the DMA multipole expansion having contributions from the out-of-plane electron density. The proposed descriptors are straightforward to obtain because the DMA method is implemented on different popular electronic structure packages. For users of Gaussian, the formatted checkpoint file with the calculated molecular electron density is used as input for the GDMA2 program of Stone to compute the necessary <b><i>Q</i> ₂</b> components. A Python script is provided to calculate the proposed descriptors. The computer protocol for determining the <b><i>Q</i> ₂</b> -based descriptors in either way is presented. To assess the performance of the aromaticity descriptors, we used 12 tests of the Girona benchmark developed by the Solà group involving different distortions of benzene, substitutions, complexation, ring size dependence, atom size dependence, heteroatomic species, Clar systems, and fulvenes. The descriptors normalized by the corresponding benzene values presented the most consistent results. The correct aromaticity trends of the six normalized new indices were predicted entirely in 65% of the cases; for 22%, most trends were predicted and only failed utterly in 13%. The failed cases were related to the molecular symmetry, which led to the partial cancellation of the <b><i>Q</i> ₂</b> tensor components, thereby affecting the aromatic descriptors and, in some cases, due to a contamination of sigma electrons. Our proposal joins others to contribute to understanding the important and complex chemical concept of aromaticity.