Prediction of EPR <b>g</b> Tensors in Simple d¹ Metal Porphyrins with Density Functional Theory

Electron paramagnetic resonance (EPR) g tensors of 20 five- or six-coordinated d 1 metal porphyrins following the [M E(P)]−L structural motif (M = V(IV), Nb(IV), Cr(V), Mo(V); E = N, O, S, Se; P = porphyrin dianion; L = F -, Cl -, Br -, ClO 4 -, OH -, OCH 3 -, H 2 O, or not present) were computed using density functional theory (DFT). For all complexes, the singly occupied molecular orbital (SOMO) is dominated by the metal d xy orbitals. Qualitative trends in Δ g components are determined by magnetic-field-induced coupling of the SOMO with three classes of molecular orbitals (MOs): (a) β-spin σ MOs formed by the metal d x 2 - y 2 atomic orbital (AO) and the porphyrin ligand; (b) the corresponding vacant α-spin σ* MOs; and (c) pairs of unoccupied α-spin π* MOs formed between the metal d xz (d yz ) AOs, p x (p y ) AOs of the axial ligands, and the porphyrin π system. The rich orbital system of the porphyrin ligand usually gives rise to multiple contributions of each type. As a consequence, electronic structure of the entire porphyrin ligand must be taken into account for the analysis of experimental g tensors. Values of the theoretical Δ g tensor components are systematically too positive compared to experiment. Once the systematic errors are accounted for, changes in the calculated g tensor components for complexes of metals from the same transition row are in good quantitative agreement with experiment. In oxomolybdenum porphyrinates [Mo O(P)]−L, the sixth ligand L influences g tensors both through geometrical distortion of the invariant part of the complex and by direct electronic interactions. Changes in the orientation of g tensors upon coordination of the sixth ligand arise mostly due to the electronic effects. The importance of the direct contribution increases for more covalent ligands L. The g tensor components of the isolated [Cr O(P)] + cation, which has not been characterized by EPR so far, are predicted to be Δ g ∥ = −15 and Δ g ⊥ = −20 ppt. The Δ g ∥ and Δ g ⊥ values for the [Mo O(P)] + complex are predicted to be −29 and −35 ppt.

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