New formulation for non-equilibrium solvation:: Spectral shifts and cavity radii of 6-propanoyl-2(N,N-dimethylamino) naphthalene and 4-(N,N-dimethylamino) benzonitrile

In the present work, the new formulations describing spectral shifts by the authors have been introduced and employed to investigate two dye molecules, 6-propanoyl-2(N,N-dimethylamino) naphthalene and 4-(N,N-dimethylamino) benzonitrile. From the viewpoints of the authors, the cavity radii were overestimated owing to the errors existing in the traditional models. Slightly differing from the results by other authors in the past, this work fits the cavity radii to the values of similar to 4.5 angstrom for 6-propanoyl-2-(N,N-dimethylamino) naphthalene and similar to 3.2 angstrom for 4-(N,N-dimethylamino) benzonitrile. In the fittings, both point dipole approximation and multipole expansion methods are employed. The calculations of the excited states are performed by means of the time-dependent density functional theory. Comparing the fitted cavity radii from the experimental spectra with those estimated from the molecular volumes by some well-known procedures such as COSMO and PCM, we find that the new formulations give fairly satisfactory results. By taking an atomic ion as an example, the authors argue that the Onsager radii recommended by some popular procedures are greatly exaggerated. The cavity radius derived simply from the volume encompassed by the solvent-accessible surface, without any addition of other parts, is suggested for application.