Density Functional Theory (DFT) Computations

Electronic-structure calculations were carried out using the ORCA 3.0 software package developed by Dr. F. Neese (MPI for Chemical Energy Conversion).⁵⁴ Computational models of 2 and 4 were obtained via unrestrained DFT geometry optimizations, using the X-ray crystal structures as starting points. For calculations involving 2, the ^Ph2TIP ligand was truncated by replacing the 4,5-diphenyl-1-methylimidazole donors with 4-methylimidazole rings; similarly, in calculations for 4 employed the ^Ph,MeTp⁻ ligand was modeled as ^Me,HTp⁻. Numerical frequency calculations verified that all structures corresponded to a local minimum with only real vibrational frequencies. The zero-point energies, thermal corrections, and entropy terms (vibrational, rotational, translational) were obtained from these frequency calculations. All calculations were carried out spin-unrestricted and utilized Ahlrichs’ valence triple-ζ basis set (TZV) and TZV/J auxiliary basis set, in conjunction with polarization functions on main-group and transition-metal elements (default-basis 3 in ORCA).^55–57 Solvent effects were accounted for using the conductor-like screening model (COSMO)⁵⁸ with a dielectric constant (ε) of 9.08 for CH₂Cl₂.

The DFT calculations employed different functionals depending on the nature of the species under examination and the property being computed. Geometric structures for the Fe(II) complexes and Fe/O₂ adducts were optimized using the Perdew-Burke-Ernzerhof (PBE) functional⁵⁹ with 10% Hartree-Fock exchange. The “spin-flip” feature of ORCA was employed to generate broken-symmetric wavefunctions for the S_tot = 2 and 1 states of Fe/O₂ adducts containing high-spin Fe centers. The transition state for the S-O_d bond forming reaction (where O_d is the distal oxygen atom of the iron-superoxo unit) was located by performing a relaxed surface scan along the S···O_d distance. The existence of the transition state was confirmed by the presence of one imaginary frequency, corresponding to the ν(S–O_d) mode.

Calculations of the Fe/NO adducts employed either the Becke-Perdew (BP86)^60–61 or TPSSh^62–63 functionals. In calculations of EPR parameters, the “core properties” with extended polarization [CP(PPP)] basis set⁶⁴ was used for the Fe atom and Kutzelnigg’s NMR/EPR (IGLO-III) basis set⁶⁵ for the NO ligand. The contribution of spin-orbit coupling to the g- and A-tensors was evaluated by solving the coupled-perturbed self-consistent field (CP-SCF) equations.^66–69 To compute the hyperfine coupling constants, a high resolution grid with an integration accuracy of 7.0 was used for the Fe and N atoms. Time-dependent DFT (TD-DFT) calculations employed the cam-B3LYP range-separated hybrid functional,⁷⁰ previously shown to yield good agreement between experimental and TD-DFT computed absorption spectra for CDO.⁷¹ Absorption energies and intensities were computed for 40 excited states with the Tamm-Dancoff approximation.^72–73 Isosurface plots of molecular orbitals were prepared using the ChemCraft program.