Bridging Quantum Chemical Predictions of Excitation Energies with Experimental Data for Voltage-Sensitive Fluorescent Dyes

Voltage-sensitive dyes (VSDs) are fluorescent molecules that detect changes in the membrane potential, making them invaluable for studying electrical activity in neurons, cardiac cells, and other excitable tissues. They are widely used in neuroscience and physiology to visualize and measure real-time voltage dynamics in cellular networks and whole tissues. VSDs exhibit a high sensitivity to their surrounding environment, which leads to notable solvation relaxation and a substantial Stokes shift upon excitation. Accurate prediction of their fluorescence spectra requires an advanced solvation model that captures these dynamic effects. In this work, we extend the Similarity Transformed Equation-of-Motion Domain-Based Local Pair Natural Orbital Coupled Cluster with Singles and Doubles (STEOM-DLPNO-CCSD) method, a computationally efficient approach for vertical excitation energies, to predict fluorescence spectra for VSDs. While the default perturbative solvation correction at the Hartree-Fock level has proven effective for some excited state calculations, it fails to account for the electron correlation effects that are crucial for accurate fluorescence spectra predictions. To address this, we incorporate a time-dependent density functional theory-based perturbative solvation correction, which improves the accuracy of the methods by better capturing the necessary correlation effects. The methodology is validated through studies of two carefully selected VSDs, (<i>E</i>)-3-(4-(2-(6-(dibutylamino)naphthalen-2-yl)vinyl)pyridin-1-ium-1-yl)propane-1-sulfonate (di-4-ANEPPS) and 4-((<i>E</i>)-4-((<i>E</i>)-4-(diethylamino)-2-methoxystyryl)styryl)-2-(6-(dimethylamino)-3-(dimethyliminio)-3<i>H</i>-xanthen-9-yl)benzenesulfonate (sRhoVR-1). The developed quantum chemical protocol allows for accurate prediction of fluorescence maxima for dyes with a predominant excited state and can accommodate computational constraints without greatly compromising precision. However, the study also highlights the need for further improvements for the prediction of peak intensity, suggesting that explicit solvent models or hybrid quantum mechanics/molecular mechanics (QM/MM) approaches could be valuable for future work. The proposed method provides a powerful tool for the design of VSDs optimized for specific environments and applications.