Theoretical Study of Reactivity Indices and Rough Potential Energy Curves for the Dissociation of 59 Fullerendiols in the Gas Phase and in Aqueous Solution with an Implicit Solvent Model

Buckminsterfullerene, C₆₀, has not only a beautiful truncated icosahedral (soccer ball) shape but also simple Hückel calculations that predict a 3-fold degenerate lowest unoccupied molecular orbital, which can accommodate up to six electrons, making it a good electron acceptor. Experiments have confirmed that C₆₀ is a radical sponge, and it is now sold for use in topical cosmetics. Further medical uses require functionalization of C₆₀ to make it soluble, and one of the simplest functionalizations is to make C₆₀(OH)_<i>n</i> fullerenols. A previous article [<i>Adv. Quantum Chem.</i> <b>88</b>, 351 (2023)] studied reactivity indices for the successive addition of the ^•OH radical to (^•)C₆₀(OH)_<i>n</i> in the gas phase [(^•)C₆₀(OH)_<i>n</i> is a radical only when <i>n</i> is an odd number]. This present article extends this previous work by examining various aspects of how the reaction, ^•C₆₀OH + ^•OH → C₆₀(OH)₂ (R1) changes in aqueous solution. One obvious difference between C₆₀ and their various isomers of C₆₀(OH)₂ is the presence of a dipole. As fullerendiols are nearly spherical, their change in dipole moment in going from the gas to aqueous phase may be estimated using back-of-the-envelope calculations with the Onsager model. The result is remarkably similar to what is obtained using density functional theory (DFT) with an implicit solvation model (surface molecular density, SMD). Calculation of fullerendiol C-O bond energies and reactivity indices using the SMD approach confirms that the general conclusions from the earlier work regarding gas-phase reactivity still hold in the aqueous phase. A major difference between the present work and the earlier work is the calculation of potential energy curves (PECs) for reaction R1 in the gas and aqueous phases. This is done in exploratory work for all 59 possible fullerendiols in both the gas phase and in aqueous solution with the SMD approach using spin-unrestricted DFT calculations with symmetry breaking. Surprisingly little change is found between the gas- and aqueous-phase PECs. However, it was discovered that the majority of C₆₀(OH)₂ shows radicaloid character, as might have been expected from trying to draw resonance structures. Spin-contamination curves are also remarkably similar for gas- and aqueous-phase results. Although our calculations do not include a dispersion correction, it was noticed that all calculated PECs have a 1/<i>R</i>⁶ behavior over a significant <i>R</i> = <i>R</i>(C-O) distance, underlying the need to be careful of double counting when including dispersion corrections in DFT. A shortcoming of our SMD approach is the lack of explicit water molecules, which can form hydrogen bonds with the OH groups and dissociating radicals.