A quantitative relationship between electron localization function and the strength of physical binding

The electron localization function (ELF) measures electron localization in matter and provides insights into bonds in materials and molecules. This study examines the relationship between ELF and binding energy in bimolecular systems, focusing on van der Waals (vdW) interactions such as Keesom, Debye, and London dispersion forces. These interactions play significant roles in crystalline molecular materials. This work addresses the challenge of accurately calculating binding energies in molecular materials and supramolecular synthons by exploring their correlation with ELF. We use density functional theory and have evaluated seven exchange-correlation functionals to identify which functional provides the most accurate binding energies in comparison to values obtained with coupled cluster. The findings revealed that rev-vdW-DF2 offers high precision, whereas Perdew-Burke-Ernzerhof-D3(BJ) is computationally efficient. These functionals were utilized to demonstrate how ELF can be employed to accurately determine binding energies. By analyzing the ELF and its correlation with binding energies in 95 bimolecular systems held together with physical bindings ranging from weak to strong interactions, we demonstrate a strong linear correlation, with a coefficient of determination (<i>R</i>²) reaching 0.960. These findings suggest that ELF can effectively differentiate between weak and strong vdW interactions, providing a reliable quantitative metric for evaluating interaction strengths. The results indicate that ELF can be used as method to determine the strength of intermolecular interactions, with potential applications in materials science. Especially as a method for analyzing and predicting molecular interaction strengths within molecular materials and supramolecular synthons. This work opens up the possibility to derive all directional physical binding energies of molecular materials within the unit cell directly from the ELF, which has the potential to simplify practical calculations. Furthermore, the study revealed a possible systematic error for current xc-functionals in describing systems with two neighboring O-H⋯O hydrogen bonds between interacting molecules.