D2BIA-flexible, not (explicitly) arbitrary and reference/structurally invariant-a very effective and improved version...

Although there are a multitude of aromaticity indexes, only a few have a widespread usage. All famous aromaticity indexes are limited: HOMA and FLU are reference-dependent; ELF is π-bond-dependent; PDI is structurally dependent and NICS is ring size dependent. These limitations stimulate the continuous search for better (i.e., having no dependency), more flexible (i.e., applied to any aromatic system) and more effective (i.e., with excellent correlations with other indexes) aromaticity indexes. The D3BIA was our first topological aromaticity index. It is flexible, reference-independent and effective for planar and caged aromatic molecules. However, one of its terms, the degree of degeneracy (δ), is arbitrary and difficult to carry out for new users. Thus, in this work, we show that D2BIA-an improved version of D3BIA-is a good candidate to be used widely, since it retains the strong points of D3BIA while avoiding its weak point. In particular cases where all studied systems have δ = 1 (e.g., for acenes), then D2BIA equals D3BIA. For our recent study with acenes, D3BIA (and, as a consequence, D2BIA) has (have) an excellent correlation with FLU according to the MP3 method. In this work, by using DFT calculations for a series involving several six-membered and five-membered heteroaromatic rings, only D2BIA and NICS have very good correlation. All other well known aromaticity indexes used in this work (FLU, HOMA and ELF) gave poor correlations. As to homoaromatic systems, only D2BIA vs NICS and D2BIA vs FLU plots have excellent correlations. HOMA has the worst results in this series. Thus, D2BIA proved to be flexible and effective for the analysis of heteroaromatic rings of different sizes and for caged homoaromatic systems. Moreover, D2BIA has better correlations than D3BIA for planar aromatic systems, and same correlations for caged-homoaromatic systems. Graphical abstract D2BIA-an effective and improved version of the D3BIA aromaticity index.