Diffusion and Aggregation of Sodium Fluorescein in Aqueous Solutions

The diffusion and aggregation of sodium fluorescein in aqueous solutions was investigated adopting density functional theory (DFT) and molecular dynamics (MD) simulations. First, DFT calculations in implicit water were used to determine minimum energy structure and atomic charges of the solute, which were then used as input for explicit water MD simulations. The self-diffusion coefficient of sodium fluorescein was calculated using the Einstein equation, computing the mean square displacement from 24 ns trajectories. The calculated diffusion coefficient, 0.42 · 10–5 cm2 s–1, is in good agreement with literature experimental data. The simulations confirmed the tendency of fluorescein to form dimers. In order to achieve a deeper understanding of aggregation phenomena, the dimer geometry was investigated through DFT calculations both in vacuo and in implicit water using different functionals and solvation theories. The results showed that dimerization does not occur in vacuo, as charge repulsion dominates, and that the minimum energy dimer structure is symmetric and stabilized by edge-to-face π–π interactions. The interaction energy was computed both at the DFT level and through MD simulations using Umbrella Sampling. The free interaction energy calculated with the WHAM and Umbrella Integration protocol, −1.3 kcal/mol, is in good agreement with experimental data, while the value determined using DFT calculations is significantly smaller and depends largely from the chosen functional and the computational methodology used to determine the solute–solvent boundary surface.