Extending the Marcus μ-Scale of Solvent Softness Using Conceptual Density Functional Theory and the Orbital Overlap Distance: Method and Application to Ionic Liquids

The chemical hardness of a solvent can play a decisive role in solubility and reactivity in solution. Several empirical scales quantifying solvent softness have been proposed. We explore whether computed properties of solvent molecules can reproduce these experimental scales. Our “orbital overlap distance” quantifying the size of orbitals at a molecule’s surface effectively reproduces the Marcus μ-scale of solvent softness. The orbital overlap distance predicts that the surface of chemically hard solvent molecules is dominated by compact orbitals possessing a small orbital overlap distance. In contrast, the surface of chemically soft solvent molecules has a larger contribution from diffuse orbitals and a larger orbital overlap distance. Other conceptual density functional theory descriptors, including the global hardness and electronegativity, can also reproduce the Marcus scale. We further introduce a “solvent versatility” RMSD Dsurf scale quantifying variations in the surface orbital overlap distance. “Good” solvents such as DMSO, which combine chemically “hard” and “soft” sites within a single molecule, possess a large RMSD Dsurf. We conclude by applying this approach to predict the Marcus μ-parameters for widely-used ionic liquids and ionic liquid–cosolvent systems.