Theoretical Basis for Refractive Index Changes Resulting from Solution Phase Molecular Interaction

Abstract

Refractive index (RI) is a fundamental optical property widely used to investigate the physical and chemical characteristics of materials. Here, we build on our previous work to refine the framework for RI sensing in solution-phase chemical and biochemical interactions. Starting from the Clausius–Mossotti relation, we present a first-principles derivation of a relationship for the RI signal resulting from chemical binding. We then demonstrate how the binding-induced conformational and hydration changes of interacting species relate to their estimated change in dielectric and thus the solution-phase change in refractive index (ΔRI). By varying the model parameters, such as solvation shell size and polarizability, we investigate the RI changes for two interactions: Ca²⁺ with the protein Recoverin and benzenesulfonamide with carbonic anhydrase 2 (CAII). These examples show that our theory predicts that even for small changes in binding-induced polarizability (relative to previous literature values), a quantifiable RI change is produced within the detectable range of RI detectors operating at ca. 10^–6 RIU. Empirical observations confirm our theoretical predictions. Surprisingly, theory and experiment yield a decrease in ΔRI for the benzenesulfonamide-CAII interaction. We attribute this observation to shielding of charged residues and water molecule displacement during the binding event. Our approach is generalized, enabling it to be extended to other binding systems, as well as those undergoing nonbinding conformational changes, and facilitates the exploration of diverse biological and chemical processes by solution-phase RI sensing.