Quantum Mechanics Calculations on Rhodamine Dyes Require Inclusion of Solvent Water for Accurate Representation of the Structure

DFT studies of structural and electrostatic properties of two rhodamines are reported. For one compound, a
sulforhodamine, a crystallographic structure determination was used to validate the computational approach.
For the other compound, N,N,N‘,N‘-tetramethylrhodamine, we considered both its lactone and quinonoid forms.
Geometry optimization of the quinonoid form required inclusion of solvent effects to prevent its collapse into
the lactone. Best agreement with the experimental preference for the quinonoid form in solvents of high
polarity was obtained when explicit water molecules were added to a continuous solvent model. The quinonoid
structures of both rhodamines are rather rigid molecules, with a strong charge separation mostly localized
around the N atoms (positive pole) and around the sulfonate or carboxylate groups (negative pole). In the
quinonoid structures, rotation around the N−C(xanthene) bond is considerably restricted by extensive
conjugation of the N atoms with the xanthene ring. The lactone form is characterized by reduced charge
separation and a much lower barrier for the rotation around the N−C(xanthene) bond. The calculated energy
barrier for the interconversion between the quinonoid and lactone forms is low, in good agreement with the
experimentally observed easy interconversion between the two forms.