Intrinsic Bond Strength Index as a halogen bond interaction energy predictor

Halogen bonds (XBs) have become increasingly popular over the past few years with numerous applications in catalysis, material design, anion recognition, and medicinal chemistry. To avoid a \textit{post factum} rationalization of XB trends, descriptors can be tentatively employed to predict the interaction energy of potential halogen bonds. These typically comprise the electrostatic potential maximum at the tip of the halogen, ${V_{S, max}}$, or properties based on the topological analysis of the electronic density. However, such descriptors either can only be used with confidence for specific families of halogen bonds or require intense computations and, therefore, are not particularly attractive for large datasets with diverse compounds or biochemical systems. Therefore, the development of a simple, widely applicable, and computationally cheap descriptor remains a challenge as it would facilitate the discovery of new XB applications while also improving the existing ones. Recently, the Intrinsic Bond Strength Index (IBSI) has been proposed as a new tool to evaluate any bond strength, however, it has not been extensively explored in the context of halogen bonding. In this work, we show that IBSI values linearly correlate with the interaction energy of diverse sets of closed-shell halogen-bonded in the ground state, and therefore, can be used to quantitatively predict this property. Although the linear fit models that use quantum-mechanics-based electron density provided MAEs typically below 1~kcal~mol$^{-1}$, this type of calculation might still be computationally heavy in large sets or systems. Therefore, we also explored the exciting possibility to use a promolecular density approach (\pro{}), which only requires the geometry of the complex as an input, being computationally cheap. Surprisingly, the performance was comparable to the QM-based methods, thus opening the door for the usage of \pro{} as a fast, yet accurate, XB energy descriptor in large datasets but also in biomolecular systems such as protein--ligand complexes. We also show that $\delta g^{pair}$ descriptor emerging from the Independent Gradient Model that leads to IBSI can be seen as a term proportional to the overlapping van der Waals volume of the atoms at a given interaction distance.