Exploring the Solvatochromism of Betaine 30 with Ab Initio Tools: From Accurate Gas-Phase Calculations to Implicit and Explicit Solvation Models

Betaine 30 is known for the extraordinary solvatochromism of its visible absorption band that goes from λ=882 nm in tetrachloromethane to λ=453 nm in water (Δλ=-429 nm). This large blueshift partly originates from a dramatic decrease of the dipole moment upon excitation. Despite several decades of research, experimental works still disagree on the exact value of the excess dipole moment, the orientation of the dipole moment of the excited-state, the role and amplitude of the change of the polarisability upon excitation as well as on the gas-phase excitation energy. In this work, we present an in-depth theoretical investigation. First, we carefully tested several levels of theory on the model system and next calculated the electric properties of betaine 30 at the CC2 level. Our best estimates are Δμ=-7 D for the excess dipole moment, that is, a significant decrease but no change of direction, a Δα value of -120 a.u. and a gas-phase vertical excitation energy of 1.127 eV. The implicit solvation models are able to reproduce the experimental trends, with large correlation coefficients for non-hydrogen-bond-donating solvents, the smallest root-mean-square deviation error being reached with the vertical excitation model (VEM). The explicit effective fragment potential method combined with time-dependent density functional theory (TD-DFT) in a QM/MM framework provides accurate estimates for hydrogen-bond-donating solvents, whereas the addition of a dispersion correction is needed to restore the correct solvatochromic direction in tetrachloromethane.