Simple and Accurate Computations of Solvatochromic Shifts in pi -> pi* Transitions of Aromatic Chromophors
A new approach is introduced for calculating the spectral shifts of the most bathochromic pi -> pi* transition of an aromatic chromophore in apolar environments. As an example, perylene in solid and liquid n-alkane matrices was chosen, and all shifts are calculated relative to one well-defined solid-inclusion system. It is shown that a simple two-level treatment of the solute using Huckel theory yields spectral shifts in excellent agreement with experimental results for the most prominent inclusion sites of perylene in solid n-alkane surroundings and for the dilute solutions in liquid n-alkanes. The idea is general enough to be applied to any aromatic chromophore in a nonpolar solvent matrix. In contrast to earlier treatments, this approach is based on geometry-dependent polarizabilities, employs a r^-4 dependence for the dispersion energy, is conceptually simple and computationally efficient. Different simple models based on our general approach to compute the UV spectral shifts due to solvation indicate that the dispersive part of the van-der-Waals energy, which stabilizes the LUMO of perylene more than the HOMO, falls off with a distance dependence of r^-4 in a range up to ~1 nm and not as r^-6, as has been assumed for a long time. This finding corresponds to the interpretation of temporary dipoles as being equivalent to weak permanent dipoles with fluctuating orientation.