Density Functional Theory Study of Redox Pairs: 2. Influence of Solvation and Ion-Pair Formation on the Redox Behavior of Cyclooctatetraene and Nitrobenzene

A study of the electrochemical behavior of cyclooctatetraene (COT) and nitrobenzene with Density Functional Theory and the conductor like solvation model (COSMO) is reported. The two-electron reduction of the tub-shaped COT molecule is accompanied by a structural change to a planar structure of D(4)(h)() symmetry in the first electron addition step, and to a fully aromatic structure of D(8)(h)() symmetry in the second electron addition step. Theoretical models are examined that are aimed at understanding the electrolyte- and solvent-dependent redox behavior of COT, in which a single 2e(-) redox wave is observed with KI electrolyte in liquid ammonia solution (DeltaDeltaE(disp) = [E(-2) - E(-1)] - [E(-1) - E(0)] < 0, inverted potential), while two 1e(-) redox waves are observed (DeltaDeltaE(disp) > 0) with NR(4)(+)X(-) (R = butyl, propyl; X(-) = perchlorate) electrolyte in dimethylformamide solution. In all cases, the computed reaction energy profiles are in fair agreement with the experimental reduction potentials. A chemically intuitive theoretical square scheme method of energy partitioning is introduced to analyze in detail the effects of structural changes and ion-pair formation on the relative energies of the redox species. The structural relaxation energy for conversion of tub-COT to planar-COT is mainly apportioned to the first reduction step, and is therefore a positive contribution to DeltaDeltaE(disp). The effect of the structural change on the disproportionation energy for COT is counteracted by the substantially more positive reduction potential for planar-(COT)(-1) in comparison to tub-(COT)(-1). Ion pairing of alkali metal counterions with the anionic reduction products gives rise to a negative contribution to DeltaDeltaE(disp) because the second ion-pairing step is more exothermic than the first, and the reduction of [KA] (A = COT, NB) is more exothermic than the reduction of A(-1). For COT, this negative energy differential term as a result of ion pairing predicts the experimentally observed inversion in the two 1e(-) potentials (DeltaDeltaE(disp) < 0). Nitrobenzene is treated with the same computational protocol to provide a system for comparison that is not complicated by the major structural change that influences the COT energy profile.