Aqueous-Phase Single-Electron Transfer Calculations for Carbonate Radicals Using the Validated Marcus Theory

Abstract

Single-electron transfer is a major aqueous-phase reaction mechanism commonly used in environmental engineering and natural processes such as aquatic photochemistry and advanced oxidation processes. While the Marcus theory is frequently used to analyze single-electron transfers, many previous studies appear to have overlooked its application, with uncertain energy values being reported without validation. Herein, using the carbonate radical as the oxidant, we analyze the validity of the Marcus theory to aqueous-phase reactions involving aromatic compounds. We highlight the impact of charged targeted molecules by comparing the reactivity with phenolate and aniline. Further, we expand the validated methodology to a wide range of structurally diverse organic compounds and reveal the underlying reaction mechanisms, such as outer-/inner-sphere single-electron transfer and proton coupled electron transfer. Our research outlines the next steps to be taken in Marcus theory calculations to investigate aqueous-phase environmental reactions.

Competition between C–C and C–H Bond Fluorination: A Continuum of Electron Transfer and Hydrogen Atom Transfer Mechanisms

“…Here, the Gibbs free energy of the electron-transfer reaction (Δ G ET o ) is readily determined by ∑ G products – ∑ G reactants following straightforward geometry optimizations, and the total reorganization energy (λ tot ) accounts for both inner-sphere (λ in ) and outer-sphere (λ out ) reorganization energy components, as per eq : λ normaltot = λ normalin + λ normalout normal2 …”

“…The inner-sphere reorganization energy term (λ in ) is associated with molecular structural distortions that occur following SET to reach the lowest energy ground states of the products. It can be calculated using Nelsen’s four-point method, as per eq : λ normalin = normalΔ italicE normalaq , normalET normalreact − normalΔ italicE normalaq , normalcalc , normalET normalreact …”

“…Lastly, the outer-sphere reorganization energy term (λ out ) is associated with changes in the solvent environment that accompany SET. It can be calculated using a modified two-sphere model, as per eq : , λ normalout = normalΔ italice normal2 italicN normalA ( 1 2 r D + 1 2 r A − 1 R ) ( 1 ε o − 1 ε s ) …”

“…Here, the Gibbs free energy of the electron-transfer reaction (ΔG ET o ) is readily determined by ∑G products − ∑G reactants following straightforward geometry optimizations, and the total reorganization energy (λ tot ) accounts for both innersphere (λ in ) and outer-sphere (λ out ) reorganization energy components, as per eq 3: 84 Table 1. Competitive Formation of C−H Fluorination Byproducts Observed under C−C Bond Fluorination (SET) Conditions Yields were determined by 19 The inner-sphere reorganization energy term (λ in ) is associated with molecular structural distortions that occur following SET to reach the lowest energy ground states of the products.…”

Predicting Transformation Products during Aqueous Oxidation Processes: Current State and Outlook

“…Quantitative structure–activity relationships (QSARs) are well-known approaches for correlating physical-chemical and structural properties of entire or fragmented parts of organic compounds with k values . The parameters used to correlate with k values can be Hammett- or Taft-type constants (classical), or parameters obtained by quantum chemical (QC) computations. ,,− Because correlations between properties and k values can be nonlinear, machine learning (ML) approaches have been recently applied for such QSARs . Assessment of the predictability of such tools is important when combined with mechanistic information to predict transformation products.…”