On Predicting Mössbauer Parameters of Iron-Containing Molecules with Density-Functional Theory

The performance of six frequently used density functional theory (DFT) methods (RPBE, OLYP, TPSS, B3LYP, B3LYP*, and TPSSh) in the prediction of Mössbauer isomer shifts(δ) and quadrupole splittings (ΔEQ) is studied for an extended and diverse set of Fe complexes. In addition to the influence of the applied density functional and the type of the basis set, the effect of the environment of the molecule, approximated with the conducting-like screening solvation model (COSMO) on the computed Mössbauer parameters, is also investigated. For the isomer shifts the COSMO-B3LYP method is found to provide accurate δ values for all 66 investigated complexes, with a mean absolute error (MAE) of 0.05 mm s–1 and a maximum deviation of 0.12 mm s–1. Obtaining accurate ΔEQ values presents a bigger challenge; however, with the selection of an appropriate DFT method, a reasonable agreement can be achieved between experiment and theory. Identifying the various chemical classes of compounds that need different treatment allowed us to construct a recipe for ΔEQ calculations; the application of this approach yields a MAE of 0.12 mm s–1 (7% error) and a maximum deviation of 0.55 mm s–1 (17% error). This accuracy should be sufficient for most chemical problems that concern Fe complexes. Furthermore, the reliability of the DFT approach is verified by extending the investigation to chemically relevant case studies which include geometric isomerism, phase transitions induced by variations of the electronic structure (e.g., spin crossover and inversion of the orbital ground state), and the description of electronically degenerate triplet and quintet states. Finally, the immense and often unexploited potential of utilizing the sign of the ΔEQ in characterizing distortions or in identifying the appropriate electronic state at the assignment of the spectral lines is also shown

Experimental and Theoretical Evidence for an Unusual Almost Triply Degenerate Electronic Ground State of Ferrous Tetraphenylporphyrin

Iron porphyrins exhibit unrivalled catalytic activity for electrochemical CO2-to-CO conversion. Despite intensive experimental and computational studies in the last 4 decades, the exact nature of the prototypical square-planar [FeII(TPP)] complex (1; TPP2– = tetraphenylporphyrinate dianion) remained highly debated. Specifically, its intermediate-spin (S = 1) ground state was contradictorily assigned to either a nondegenerate 3A2g state with a (dxy)2(dz2)2(dxz,yz)2 configuration or a degenerate 3Egθ state with a (dxy)2(dxz,yz)3(dz2)1/(dz2)2(dxy)1(dxz,yz)3 configuration. To address this question, we present herein a comprehensive, spectroscopy-based theoretical and experimental electronic-structure investigation on complex 1. Highly correlated wave-function-based computations predicted that 3A2g and 3Egθ are well-isolated from other triplet states by ca. 4000 cm–1, whereas their splitting ΔA–E is on par with the effective spin–orbit coupling (SOC) constant of iron(II) (≈400 cm–1). Therefore, we invoked an effective Hamiltonian (EH) operating on the nine magnetic sublevels arising from SOC between the 3A2g and 3Egθ states. This approach enabled us to successfully simulate all spectroscopic data of 1 obtained by variable-temperature and variable-field magnetization, applied-field 57Fe Mössbauer, and terahertz electron paramagnetic resonance measurements. Remarkably, the EH contains only three adjustable parameters, namely, the energy gap without SOC, ΔA–E, an angle θ that describes the mixing of (dxy)2(dxz,yz)3(dz2)1 and (dz2)2(dxy)1(dxz,yz)3 configurations, and the ⟨rd–3⟩ expectation value of the iron d orbitals that is necessary to estimate the 57Fe magnetic hyperfine coupling tensor. The EH simulations revealed that the triplet ground state of 1 is genuinely multiconfigurational with substantial parentages of both 3A2g (3Eg (>12%), owing to their accidental near-triple degeneracy with ΔA–E = +950 cm–1. As a consequence of this peculiar electronic structure, 1 exhibits a huge effective magnetic moment (4.2 μB at 300 K), large temperature-independent paramagnetism, a large and positive axial zero-field splitting, strong easy-plane magnetization (g⊥ ≈ 3 and g∥ ≈ 1.7) and a large and positive internal field at the 57Fe nucleus aligned in the xy plane. Further in-depth analyses suggested that g⊥ ≫ g∥ is a general spectroscopic signature of near-triple orbital degeneracy with more than half-filled pseudodegenerate orbital sets. Implications of the unusual electronic structure of 1 for CO2 reduction are discussed

Experimental and Theoretical Evidence for an Unusual Almost Triply Degenerate Electronic Ground State of Ferrous Tetraphenylporphyrin.

Iron porphyrins exhibit unrivalled catalytic activity for electrochemical CO2-to-CO conversion. Despite intensive experimental and computational studies in the last 4 decades, the exact nature of the prototypical square-planar [FeII(TPP)] complex (1; TPP2– = tetraphenylporphyrinate dianion) remained highly debated. Specifically, its intermediate-spin (S = 1) ground state was contradictorily assigned to either a nondegenerate 3A2g state with a (dxy)2(dz2)2(dxz,yz)2 configuration or a degenerate 3Egθ state with a (dxy)2(dxz,yz)3(dz2)1/(dz2)2(dxy)1(dxz,yz)3 configuration. To address this question, we present herein a comprehensive, spectroscopy-based theoretical and experimental electronic-structure investigation on complex 1. Highly correlated wave-function-based computations predicted that 3A2g and 3Egθ are well-isolated from other triplet states by ca. 4000 cm–1, whereas their splitting ΔA–E is on par with the effective spin–orbit coupling (SOC) constant of iron(II) (≈400 cm–1). Therefore, we invoked an effective Hamiltonian (EH) operating on the nine magnetic sublevels arising from SOC between the 3A2g and 3Egθ states. This approach enabled us to successfully simulate all spectroscopic data of 1 obtained by variable-temperature and variable-field magnetization, applied-field 57Fe Mössbauer, and terahertz electron paramagnetic resonance measurements. Remarkably, the EH contains only three adjustable parameters, namely, the energy gap without SOC, ΔA–E, an angle θ that describes the mixing of (dxy)2(dxz,yz)3(dz2)1 and (dz2)2(dxy)1(dxz,yz)3 configurations, and the ⟨rd–3⟩ expectation value of the iron d orbitals that is necessary to estimate the 57Fe magnetic hyperfine coupling tensor. The EH simulations revealed that the triplet ground state of 1 is genuinely multiconfigurational with substantial parentages of both 3A2g (3Eg (>12%), owing to their accidental near-triple degeneracy with ΔA–E = +950 cm–1. As a consequence of this peculiar electronic structure, 1 exhibits a huge effective magnetic moment (4.2 μB at 300 K), large temperature-independent paramagnetism, a large and positive axial zero-field splitting, strong easy-plane magnetization (g⊥ ≈ 3 and g∥ ≈ 1.7) and a large and positive internal field at the 57Fe nucleus aligned in the xy plane. Further in-depth analyses suggested that g⊥ ≫ g∥ is a general spectroscopic signature of near-triple orbital degeneracy with more than half-filled pseudodegenerate orbital sets. Implications of the unusual electronic structure of 1 for CO2 reduction are discussed

A fluorescence model of the C[SUB]3[/SUB] radical in comets

Theoretical resonance fluorescence calculations are presented of the triatomic C[SUB]3[/SUB] radical and are compared with observations of the C[SUB]3[/SUB] emission in comets Hale-Bopp and de Vico. A theoretical model of the C[SUB]3[/SUB] vibration-rotational structure in the A[SUP]1[/SUP]Pi[SUB]u[/SUB] - X[SUP]1[/SUP]Sigma[SUB]g[/SUB] [SUP]+[/SUP] electronic system is introduced. The model takes into account the detailed structure of the bending mode nu[SUB]2[/SUB] which is responsible for the emission of the 4050 à group. A total of 1959 levels are considered, with 515 levels in the ground state. The main effort is to model high-resolution spectra of the 4050 à emission in comets C/1995 O1 Hale-Bopp and 122P/1995 S1 de Vico. The agreement between observed and theoretical spectra is good for a value of the dipole moment derivative of dmu/dr ~ 2.5 Debye à [SUP]-1[/SUP]. The modeled C[SUB]3[/SUB] emission exhibits a pronounced Swings effect. Based on observations made with William Herschel Telescope operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias, and on observations made at the McDonald Observatory, which is operated by the University of Texas at Austin, USA