Computing the Local Aromaticity of Benzenoids Thanks to Constraint Programming

Abstract

Benzenoids are a subfamily of hydrocarbons (molecules that are only made of hydrogen and carbon atoms) whose carbon atoms form hexagons. These molecules are widely studied in theoretical chemistry. Then, there is a lot of problems relative to this subject, like the benzenoid generation or the enumeration of all its Kekulé structures (i.e. all valid configurations of double bonds). In this context, the computation of the local aromaticity of a given benzenoid is an important problematic since the aromaticity cannot be measured. Nowadays, computing aromaticity requires quantum chemistry calculations that are too expensive to be used on medium to large-sized molecules. But, there exist some methods related to graph theory which can allow us to compute it. In this article, we describe how constraint programming can be useful in order to compute the aromaticity of benzenoids. Moreover we show that our method is much faster than the reference one, namely NICS.

BenzAI: A Program to Design Benzenoids with Defined Properties Using Constraint Programming

“…The geometries used for the topological aromaticity calculations are not optimized (all hexagons are considered regular), and the aromaticity indices as well as the bond orders are quantities which differ from the ones extracted from quantum chemical calculations. However, the trends are usually good, as shown in our recent work …”

“…The difficulty lies in obtaining all possible Kekulé structures and their set of conjugated circuits. The detailed implementation of this model using the approaches by the Lin and Fan method or the improved method by Lin with constraint programming is thoroughly described in a previous work . In short, this approach consists in enumerating all possible h -MCCs in all Kekulé structures of a benzenoid and attributing to each of them a “resonance energy”, R n , whose value is tabulated according to its size (4 n + 2).…”

“…However, the trends are usually good, as shown in our recent work. 28 Local Aromaticity. In our program, local aromaticity is computed following the work of Randićand Balaban 29 based on minimal conjugated circuits.…”

“…The detailed implementation of this model using the approaches by the Lin and Fan method 30 or the improved method by Lin 31 with constraint programming is thoroughly described in a previous work. 28 In short, this approach consists in enumerating all possible h-MCCs in all Kekuléstructures of a benzenoid and attributing to each of them a "resonance energy", R n , whose value is tabulated according to its size (4n + 2). The sum of all these energy contributions normalized to the number of Kekuléstructures gives the total resonance energyor global aromaticityof the benzenoid.…”

How constraint programming can help chemists to generate Benzenoid structures and assess the local Aromaticity of Benzenoids

“…[Randić, 2019, Ruiz-Morales, 2004). It corresponds to the set used in [Carissan et al, 2020a, Randić, 2019 augmented by the molecules used in [Ruiz-Morales, 2004].…”