Reduction of CO₂ with Hydrated Electrons: Ab Initio Computational Studies for Finite-Size Cluster Models

In the present work, the mechanisms of the reduction of the CO₂ molecule with hydrated electrons to the hydroxyl-formyl (HOCO) radical were studied with ab initio computational methods. Hydrated hydronium radicals, H₃O(H₂O) (n = 0,3,6), are considered as finite-size models of the hydrated electron in liquid water. The investigation of cluster models allows the application of high-accuracy electronic-structure methods, which are not computationally feasible in condensed-phase simulations. Reaction paths and potential-energy (PE) profiles of the proton-coupled electron-transfer reaction from hydrated H₃O radicals to the CO₂ molecule were explored on the ground-state PE surface. The computationally efficient unrestricted second-order Møller-Plesset method is employed, and its accuracy has been carefully benchmarked in comparison with complete-active-space self-consistent-field and multi-reference second-order perturbation calculations. The results provide insights into the interplay of electron transfer from the diffuse Rydberg-type unpaired electron of H₃O to the CO₂ molecule, the contraction of the electron cloud by the re-hybridization of the carbon atom of CO₂, and proton transfer from the nearest water molecule to the CO₂^- anion, followed by Grotthus-type proton rearrangements to form stable clusters. Starting from local energy minima of hydrogen-bonded CO₂-H₃O(H₂O) complexes, the reaction to form HOCO-(H₂O) complexes is exothermic by about 1.3 eV (125 kJ/mol). The reaction is barrier controlled with a barrier of the order of a few tenths of an electron volt, depending on size and conformation of the water cluster. This barrier is at least an order of magnitude lower than the barrier of the reaction of CO₂ with any closed-shell partner molecule. The HOCO radicals can recombine by H-atom transfer (disproportionation), resulting in formic acid or a dihydroxycarbene product, as well as by the formation of a C-C bond, resulting in oxalic acid. The strong exothermicity of these radical-radical recombination reactions likely results in the fragmentation of the closed-shell products formic acid and oxalic acid, which explains the strong specificity for CO formation observed in recent experiments of Hamers and co-workers.