Computer simulations of the solvatochromism of betaine-30

Monte Carlo simulations of the pyridinium N-phenolate dye "betaine-30" in 12 solvents (20 solvent representations) were performed in order to explore the molecular basis of the E_T(30) scale of solvent polarity. Ab initio (HF/6-31G*) and semiempirical (AM1 and INDO/S) electronic structure calculations were used to determine the geometry and charge distribution of betaine-30 in its S₀ and S₁ states. The solvent effect on the betaine absorption spectrum was assumed to derive from electrostatic interactions between the effective charge distributions of solvent molecules and the charge shift brought about by the S₀ → S₁ transition. Two models for this charge shift, one obtained from INDO/S calculations and the other an idealized two-site model, were used for the spectral calculations. Good agreement between simulated and observed ΔE_T shifts (E_T(30) values measured relative to the nonpolar standard tetramethylsilane) was found for both charge-shift models. In water and other hydroxylic solvents, the O atom of the betaine solute was observed to form moderately strong hydrogen bonds to between one and two solvent molecules. The contribution of these specifically coordinated molecules to the ΔE_T shift was found to be large, (30-60%) and comparable to experimental estimates. Additional simulations of acetonitrile and methanol in equilibrium with the S₁ state of betaine-30 were used to determine reorganization energies in these solvents and to decide the extent to which the solvent response to the S₀ ↔ S₁ transition conforms to linear response predictions. In both solvents, the spectral distributions observed in the S₀ state simulations were ∼15% narrower than those in the S₁ simulations, indicating only a relatively small departure from linear behavior. Reorganization energies were also estimated for a number of other solvents and compared to values reported in previous experimental and theoretical studies.