(509db) Developing Linear Free Energy Relationships for Transition Metal Chemistry

Linear free energy relationships (LFERs) are quantitative structure-activity relationships that are linear when the reaction mechanism is invariant. While LFERs are invaluable tools guiding catalyst design, their applications have been largely limited to organic aromatic chemistry and heterogeneous catalysis. In transition metal chemistry, one long-standing challenge of establishing LFERs is isolation and quantification of ligand effects because ligands play a role in both electronic tuning of catalytic activity as well as spatial configuration.

This study aims to construct LFERs for transition metal chemistry by quantifying barrier trends obtained upon systematic catalyst design. The selected probe reaction is a one-step oxo-insertion mechanism of CH₄ hydroxylation with bio-inspired N-donor-bound [Cu₂O₂]²⁺ complexes. Quantum chemistry package, Q-Chem, is used to carry out density functional theory simulations. We adopt activation strain model to decompose barriers to interaction and strain energies. A LFER is developed by (1) quantifying interaction and strain energies by electronic and steric descriptors, respectively and (2) combining these descriptors to extend LFERs for barriers.

Our analysis shows both oxo-insertion barrier and interaction energy are lowered with electron-withdrawing groups. Hence, Hammett parameter (σ_p) describing N-donor electrophilicity is a reasonable descriptor for interaction energy. We then identify descriptors for strain energy via N-donors of varying bulk and prove that Sterimol parameters (B1) and bite angles (Θ) are essential for describing strain energy. These two LFERs are capable of describing interaction and strain energies, respectively. Lastly, we demonstrate that the combined (interaction + strain) LFER (Eqn. 1) performs reliably for CH activation barriers (Figure 1) and possesses transferability across different levels of theory.

This study bridges a gap between the need of high throughput catalyst screening for transition-metal complexes and the challenge of accurate characterization of reaction barriers. Going forward, this work will focus on expanding this approach across metal-oxo active centers for CH activation.