Computational Analysis of Electron Transfer Kinetics for CO₂ Reduction with Organic Photoredox Catalysts

Abstract

We present a fundamental description of the electron transfer (ET) step from substituted oligo(p-phenylene) (OPP) radical anions to CO2, with the larger goal of assessing the viability of underexplored, organic photoredox routes for utilization of anthropogenic CO2. This work varies the electrophilicity of para-substituents to OPP and probes the dependence of rate coefficients and interfragment interactions on the substituent Hammett parameter, σp, using constrained density functional theory (CDFT) and energy decomposition analysis (EDA). Large electronic coupling elements across substituents indicate an adiabatic electron transfer process for reactants at contact. As one might intuitively expect, free energy changes dominate trends in ET rate coefficients in most cases, and rates increase with substituent electron-donating ability. However, we observe an unexpected dip in rate coefficients for the most electron-donating groups, due to the combined impact of flattening free energies and a steep increase in reorganization energies. Our analysis shows that flattening OPP LUMO levels lower the marginal increase in free energy with decreasing σp. Reorganization energies do not exhibit a direct dependence on σp. They are higher for substituents containing lone pairs of electrons since substituent orientation varies with OPP charge. EDA reveals that interfragment orbital relaxation, or charge transfer interaction, plays a critical role in stabilizing the vertically excited charge transfer state. Subsequent relaxation to the final state geometry lowers charge transfer stabilization. A concurrent increase in long-range electrostatic interactions is observed, which are more favorable for electron-withdrawing substituents. Our study therefore suggests that while a wide range of ET rates are observed, there is an upper limit to rate enhancements achievable by tuning substituent electrophilicity. File list (2) download file view on ChemRxiv Manuscript.pdf (1.52 MiB) download file view on ChemRxiv Supporting Info.docx (115.25 KiB)

Consistent Inclusion of Continuum Solvation in Energy Decomposition Analysis: Theory and Application to Molecular CO2 Reduction Catalysts

“…In our previous study, the ALMO-EDA calculations were performed in vacuum at the B3LYP-D3(BJ)/6-311G(d,p) level of theory, and the CT component was identified as another main contributor to the stabilization of the product complexes relative to the reactant ones and also to the trend in substituent effect. 101 This differs from the gas-phase ALMO-EDA results that we obtained here with ωB97X-V/def2-TZVPD, where CT only makes a minimal contribution to each complex's ∆∆E INT (see the comparison between Tables S7 and S8 in the Supporting Information). We ascribe this discrepancy to the delocalization error associated with the B3LYP functional, 109,110 which, as shown in Ref.…”

“…•− is of only minimal strength (less favorable than −1 kJ/mol), while with EWGs (−Br, −CF 3 , and −NO 2 ) the interaction becomes increasingly more favorable with the increase in substituent's electron-withdrawing ability (σ p ). Note that the resulting interaction energy for the NMe 2 -substituted product complex is net repulsive (+1.96 kJ/mol), which most likely arises from the distinct levels of theory that were used in CDFT geometry optimizations 101 and ALMO-EDA(solv) calculations in the present paper. Similar to the reactant complexes, the substituent effects on the total interaction strength in the product state is also dominated by the ELEC component, where the EWGs are shown to strengthen the binding by reducing the electrostatic repulsion between CO 2…”

Consistent inclusion of continuum solvation in energy decomposition analysis: theory and application to molecular CO2 reduction catalysts

“…•− is of only minimal strength (less favorable than −1 kJ/mol), while with EWGs (−Br, −CF 3 , and −NO 2 ) the interaction becomes increasingly more favorable with the increase in substituent's electron-withdrawing ability (σ p ). Note that the resulting interaction energy for the NMe 2 -substituted product complex is net repulsive (+1.96 kJ/mol), which most likely arises from the distinct levels of theory that were used in CDFT geometry optimizations 101 and ALMO-EDA(solv) calculations in the present paper. Similar to the reactant complexes, the substituent effects on the total interaction strength in the product state is also dominated by the ELEC component, where the EWGs are shown to strengthen the binding by reducing the electrostatic repulsion between CO 2 •− and the π electrons on the p-terphenyl moiety.…”

“…The geometries of the reactant and product complexes are directly taken from our previous work, 101 which were optimized on their respective diabatic PESs constructed from constrained DFT (CDFT) 103,104 calculations at the B3LYP-D3(BJ)/6-311G(d,p) [105][106][107] level of theory with C-PCM. As illustrative examples, in Fig.…”

“…14 demonstrate the attenuation of substituent effects on the differential interaction energies due to solvent screening. In our previous study 101 where the ALMO-EDA calculations were performed in vacuum at the B3LYP-D3(BJ)/6-311G(d,p) level of theory, we identified CT as another main contributor to the stabilization of the product complexes relative to the reactant ones and also to the trend in substituent effects. This contradicts the gas-phase ALMO-EDA results obtained here with ωB97X-V/def2-TZVPD, according to which CT only makes a minimal contribution to each complex's ∆∆E INT (see the comparison between Tables S7 and S8 in the ESI †).…”