An–imidophosphorane (An = U–Pu) bond covalency and proton-coupled electron transfer thermodynamics driven by orbital energy matching

Abstract

A series of mid-actinide (An = U–Pu) tetrahomoleptic complexes supported by highly electron-donating imidophosphorane ligands, NPC ([NP^tBu(pyrr)₂]⁻, where ^tBu = C(CH₃)₃; pyrr = pyrrolidinyl = N(C₄H₈)), are systematically investigated computationally and experimentally to elucidate the nature of actinide–ligand (An–L) covalency across the An^3+/4+/5+ oxidation states. Trends in An–L bonding and redox properties for these complexes, together with their protonated counterparts, are examined using orbital-, electron density-, and energy-decomposition-based methods. This integrated approach reveals progressively improved energy matching between α-spin An 5f and N_im 2p orbitals with increasing atomic number and oxidation state, becoming particularly pronounced in the ligand-dominant π-bonding orbitals of An⁴⁺ and An⁵⁺. In contrast to the An³⁺ species, the enhanced An 5f_π contributions in the higher-valent counterparts drive the increase in An–N_im covalency for later An, thereby inverting the covalency trend to U < Np < Pu. Redistribution of electron density towards the An and N_im atomic basins due to the growing energy-matching assisted covalency correlates with higher pK_a values and increased N_im–H bond dissociation free energies in protonated An⁴⁺ complexes. Electron density at N_im in An⁴⁺ shows a linear correlation with the pK_a values calculated via the Bordwell equation. Calculations predict a cathodic shift of 0.84–1.00 V in the redox couples upon protonation, a trend validated when experimentally accessible. These findings demonstrate an increasing role of covalency driven by orbital energy matching from U to Pu in tuning the thermodynamic driving force for proton-coupled electron transfer in the An⁵⁺ species.