The Illusion of Simplicity: The Dramatic Failure of Koopmans Theorem for Antioxidants in Solvents -- The Ascorbic Acid Paradigm

TL;DR

This study shows that solvent effects profoundly reshape the redox properties of antioxidants, using ascorbic acid as a paradigmatic case. By combining high-level CBS-QB3 calculations with DFT (M06-2X and B3LYP) across six solvents, the authors demonstrate that polar solvents dramatically stabilize charged species, lowering $IP$ by ~3 eV and raising $EA$, which narrows the gap $E_g$ from ~8.7 eV in vacuum to ~4.8 eV in water. They expose a catastrophic breakdown of Koopmans' theorem in solution, where KT yields solvent-insensitive estimates that miss essential dielectric screening and nuclear relaxation, advocating adiabatic $ riangle$SCF approaches with explicit solvent. The work also highlights that the choice of functional matters (with M06-2X performing best among tested DFAs), but the central lesson is that solvent-inclusive, geometry-relaxed calculations are mandatory for meaningful antioxidant predictions. Practically, this reframes how redox diagnostics should be performed in biological contexts and provides a rigorous framework for predicting antioxidant behavior in aqueous and polar environments.

Abstract

Antioxidants operate in biological environments where solvent effects dramatically alter their redox properties. Using ascorbic acid (vitamin C) as a paradigmatic example, we present a comprehensive quantum-chemical investigation of its global chemical reactivity indices -- ionization potential, electron affinity, HOMO-LUMO gap, hardness, softness, electronegativity, electrophilicity, and electrodonating/accepting powers -- computed at the compound chemistry CBS-QB3 and various DFT levels in vacuo and across six solvents. The results demonstrate that solvation stabilizes charged species so strongly that reactivity indices shift by several electronvolts, following a roughly Born-like dependence on dielectric constant. Most importantly, we show unequivocally that Koopmans' theorem, often used to estimate these indices from orbital energies, fails catastrophically in solution: it predicts solvent-independent values that are qualitatively and quantitatively wrong, missing the essential physics of dielectric screening and geometric relaxation. We therefore conclude that Koopmans' theorem must be abandoned for antioxidant studies in condensed phases; adiabatic calculations with solvent are mandatory for meaningful predictions.

Figures (7)

• Figure 1: (a) Optimized geometry of ascorbic acid with IUPAC atom numbering (indistinguishable within drawing accuracy across all methods employed). (b) HOMO spatial distribution (also indistinguishable within drawing accuracy across all methods), concentrated along the C2=C3 bond, with significant contributions from the adjacent oxygen atoms O3 and O4, and to a lesser extent from O1 (bonded to C1). LUMO spatial distributions computed at (c) B3LYP/6-31+G(d,p), (d) M062X/6-31+G(d,p), and (e) HF/6-31+G(d,p). Note the marked contrast: the B3LYP LUMO shows substantial delocalization over the lactone-enediol conjugated system (major contributions from C1-C2 and C3), whereas the M062X LUMO is nonphysically dominated by the side chain, as is also the case for the Hartree-Fock LUMO.
• Figure 2: Adiabatic quantities plotted against $1 - 1/\varepsilon$: (a) ionization potential IP, (b) electron affinity EA, (c) HOMO-LUMO gap, and (d) electronegativity $\chi$ using data for vacuum and six solvents spanning a broad spectrum which confirm by and large the Born-like Bard:01AtkinsBook effect of the solvents. (e--h) Their counterparts obtained by subtracting the electron solvation enthalpy from IP and EA calculated according to the standard prescription (eqs (\ref{['eq-IP']}) and (\ref{['eq-EA']})) exhibiting a nearly perfect linearity suggest either an observable deviation from Born picture or the need to re-consider electron solvation data available in the literature Markovic:16 and used in the present calculations. Shown here are results of CBS-QB3 calculations and two extreme DFT flavors, M06-2X/6-31+G(d,p) and B3LYP/6-31+G(d,p), which exhibit the smallest and the largest from CBS-QB3 (cf. \ref{['tab:ip_dev', 'tab:ea_dev', 'tab:eta_dev', 'tab:sigma_dev', 'tab:omega_dev', 'tab:omegap_dev', 'tab:omegam_dev', 'tab:solvation_dev', 'tab:sol_neutral_dev', 'tab:sol_cation_dev', 'tab:sol_anion_dev']}). See the main text for details.
• Figure 3: Gibbs free energy of solvation $\Delta G_{\text{sol}}$ plotted against $1 - 1/\varepsilon$ for (a) neutral, (c) cationic, and (c) anionic species. Notice the nearly perfect linear dependence for the charged species which contrasts to the neutral molecules, a behavior which might be related to the deviation from linearity visible both in \ref{['fig:ip-ea-eg-chi']}a,b,d and in the present panel (d), which depicts the electron enthalpy of solvation taken from literature.Markovic:16
• Figure 4: Vertical and adiabatic (a) ionization potential IP and (b) electron affinity EA and the quantities (c) $E_g$ and (d) $\chi$ depending linearly on them plotted versus $1 - 1/\varepsilon$. Notice that the approximately linear vertical IP and EA are less inclined than the adiabatic ones, reflecting a similar dependence of the reorganization energies, which are equal to the difference between them. (e--h) Counterpart of the quantities shown in panels (a--d) but adding the electron's solvation enthalpy to the Koopmans' estimates.
• Figure 5: Cation and anion reorganization energies $\Lambda$ plotted versus $1 - 1/\varepsilon$ computed by using (left to right): B3LYP/6-31+G(d,p), B3LYP/6-311++G(3df,3pd), M06-2X/6-31+G(d,p), and M06-2X/6-311++G(3df,3pd). These results show a series of contrasts (cation versus anion, B3LYP versus M06-2X, smaller basis set 6-31+G(d,p) versus larger basis set 6-311++G(3df,3pd)) discussed in the main text.