Influence of Hartree−Fock Exchange on the Calculated Mössbauer Isomer Shifts and Quadrupole Splittings in Ferrocene Derivatives Using Density Functional Theory

Extensive reference set and refined computational protocol for calculations of 57Fe Mössbauer parameters

Mössbauer spectroscopy is a powerful technique for probing the local electronic structure of iron compounds, because it reports in an element-selective manner on both the oxidation state and coordination environment of the Fe ion. Computational prediction of the two main Mössbauer parameters, isomer shift (δ) and quadrupole splitting (ΔEQ), has long been targeted by quantum chemical studies, and useful protocols based on density functional theory have been proposed. Here we present an extensive curated reference set of Fe compounds that is considerably larger and more diverse than literature precedents. We make a distinction between low-temperature and high-temperature experimental subgroups. This set is employed for optimizing a refined computational protocol utilizing the scalar version of the exact 2-component (X2C) Hamiltonian with the finite nucleus approximation. Attention is devoted to having an accurate and flexible all-electron basis set for Fe. We assess the performance of several DFT methods that cover all representative families and rungs of functionals and find that hybrid functionals with ca. 25-30% exact exchange offer the best accuracy for isomer shifts. The work establishes a refined general protocol of wide applicability that achieves good performance for the prediction of isomer shifts in a wider variety of systems than before, but the limitations of DFT for quadrupole splittings are also highlighted. Finally, comparison of calculated values with high-temperature experimental results shows that the use of an empirical correction factor is required to account for the second-order Doppler shift and to achieve the same quality of correlation as with the low-temperature data.

Calculation of electric field gradients with the exact two-component (X2C) quasi-relativistic method and its local approximations

When calculating electric field gradients (EFGs), relativistic and electron correlation effects are crucial for obtaining accurate results, and the commonly used density functional methods produce unsatisfactory results, especially for heavy elements and/or strongly correlated systems. In this work, a stand-alone program is presented, which enables calculation of EFGs from the molecular orbitals supplied by an external high accuracy quantum chemical calculation and includes relativistic effects through the exact two-component (X2C) formalism and efficient local approximations to it. Application to BiN and BiP molecules shows that a high precision can be achieved in the calculation of nuclear quadrupole coupling constants of 209Bi by combining advanced ab initio methods with the X2C approach. For seventeen iron compounds, the Mössbauer nuclear quadrupole splittings (NQS) of 57Fe calculated using a double-hybrid functional method are in very good agreement with the experimental values. It is shown that, for strongly correlated molecules, the double-hybrid functionals are much more accurate than the commonly used hybrid functionals. The computer program developed in this study furnishes a useful utility for obtaining EFGs and related nuclear properties with high accuracy.

The fascinating story of axial ligand dependent spectroscopy and redox-properties in iron(II) phthalocyanines

Iron phthalocyanines play crucial fundamental and applied roles ranging from bulk colorants to components of advanced materials. In this Frontier article, we discuss four aspects concerning the influence of the axial ligands on spectroscopic and redox properties of iron(II) phthalocyanines: (i) iron versus macrocycle oxidation cite as a function of Lever's EL parameter; (ii) energy of the metal-to-ligand charge-transfer transitions as a function of Lever's EL parameter; (iii) iron versus macrocycle reduction in iron(II) phthalocyanines; (iv) Mössbauer quadrupole splitting as a function of axial ligand binding through the prism of dz2 orbital population.

Magnetically Induced Binary Ferrocene with Oxidized Iron

Ferrocene is perhaps the most popular and well-studied organometallic molecule, but our understanding of its structure and electronic properties has not changed for more than 70 years. In particular, all previous attempts of chemically oxidizing pure ferrocene by binding directly to the iron center have been unsuccessful, and no significant change in structure or magnetism has been reported. Using a metal organic framework host material, we were able to fundamentally change the electronic and magnetic structure of ferrocene to take on a never-before observed physically stretched/bent high-spin Fe(II) state, which readily accepts O2 from air, chemically oxidizing the iron from Fe(II) to Fe(III). We also show that the binding of oxygen is reversible through temperature swing experiments. Our analysis is based on combining Mößbauer spectroscopy, extended X-ray absorption fine structure, in situ infrared, SQUID, thermal gravimetric analysis, and energy dispersive X-ray fluorescence spectroscopy measurements with ab initio modeling.

Influence of the ligand-field on EPR parameters of cis- and trans-isomers in MoV systems relevant to molybdenum enzymes: Experimental and density functional theory study

The electron paramagnetic resonance (EPR) investigation of mononuclear cis- and trans-(L1O)MoOCl2 complexes [L1OH = bis(3,5-dimethylpyrazolyl)-3-tert-butyl-2-hydroxy-5-methylphenyl)methane] reveals a significant difference in their spin Hamiltonian parameters which reflect different equatorial and axial ligand fields created by the heteroscorpionate donor atoms. Density functional theory (DFT) was used to calculate the values of principal components and relative orientations of the g and A tensors, and the molecular framework in four pairs of isomeric mononuclear oxo‑molybdenum(V) complexes (cis- and trans-(L1O)MoOCl2, cis,cis- and cis,trans-(L-N2S2)MoOCl [L-N2S2H2 = N,N'-dimethyl-N,N'-bis(mercaptophenyl)ethylenediamine], cis,cis- and cis,trans-(L-N2S2)MoO(SCN), and cis- and trans-[(dt)2MoO(OMe)]2- [dtH2 = 2,3-dimercapto-2-butene]). Scalar relativistic DFT calculations were conducted using three different exchange-correlation functionals. It was found that the use of hybrid exchange-correlation functional with 25% of the Hartree-Fock exchange leads to the best quantitative agreement between theory and experiment. A simplified ligand-field approach was used to analyze the influence of the ligand fields in all cis- and trans-isomers on energies and contributions of molybdenum d-orbital manifold to g and A tensors and relative orientations. Specifically, contributions that originated from the spin-orbit coupling of the dxz, dyz, and dx2-y2 orbitals into the ground state have been discussed. The new findings are discussed in the context of the experimental data of mononuclear molybdoenzyme, DMSO reductase.

Charge-Transfer Spectroscopy of Bisaxially Coordinated Iron(II) Phthalocyanines through the Prism of the Lever's EL Parameters Scale, MCD Spectroscopy, and TDDFT Calculations

The position of the experimentally observed (in the UV-vis and magnetic circular dichroism (MCD) spectra) low-energy metal-to-ligand charge-transfer (MLCT) band in low-spin iron(II) phthalocyanine complexes of general formula PcFeL₂, PcFeL'L″, and [PcFeX₂]^2- (L, L', or L″ are neutral and X^- is an anionic axial ligand) was correlated with the Lever's electrochemical E_L scale values for the axial ligands. The time-dependent density functional theory (TDDFT)-predicted UV-vis spectra are in very good agreement with the experimental data for all complexes. In the majority of compounds, TDDFT predicts that the first degenerate MLCT band that correlates with the MCD A-term observed between 360 and 480 nm is dominated by an e_g (Fe, d_π) → b_1u (Pc, π*) single-electron excitation (in traditional D_4h point group notation) and agrees well with the previous assignment discussed by Stillman and co-workers[ Inorg. Chem. 1994, 33, 573-583]. The TDDFT calculations also suggest a small energy gap for b_1u/b_2u (Pc, π*) orbital splitting and closeness of the MLCT₁ e_g (Fe, d_π) → b_1u (Pc, π*) and MLCT₂ e_g (Fe, d_π) → b_2u (Pc, π*) transitions. In the case of the PcFeL₂ complexes with phosphines as the axial ligands, additional degenerate charge-transfer transitions were observed between 450 and 500 nm. These transitions are dominated by a_2u (Pc + L, π) → e_g (Pc, π*) single-electron excitations and are unique for the PcFe(PR₃)₂ complexes. The energy of the phthalocyanine-based a_2u orbital has large axial ligand dependency and is the reason for a large energy deviation for B1 a_2u (Pc + L, π) → e_g (Pc, π*) transition. The energies of the axial ligand-to-iron, axial ligand-to-phthalocyanine, iron-to-axial ligand, and phthalocyanine-to-axial ligand charge-transfer transitions were discussed on the basis of TDDFT calculations.

Accurate 57Fe Mössbauer Parameters from General Gaussian Basis Sets

The prediction of isomer shifts in ⁵⁷Fe Mossbauer spectra is typically achieved by building calibration lines using the values of the density at the nuclear position. Using Slater-type orbital basis or large and specific Gaussian-type orbital basis has been thus far mandatory to achieve accurate predictions with density functional theory methods. In this work, we show that replacing the value of the density at the nucleus by the density integrated in a sphere of radius 0.06 au centered on the Fe nuclei yields excellent calibration lines (r² = 0.976) with a high predictive power (q² = 0.975, MAE = 0.055 mm·s^–1) while using the conventional def2-TZVP basis set and X-ray geometrical parameters. Our data set comprises 69 ⁵⁷Fe-containing compounds and 103 signals. We also find B3LYP performing significantly better than the PW91 functional.

Application of Lever's EL Parameter Scale toward Fe(II)/Fe(III) versus Pc(2-)/Pc(1-) Oxidation Process Crossover Point in Axially Coordinated Iron(II) Phthalocyanine Complexes

The electronic structures and, particularly, the nature of the HOMO in a series of PcFeL₂, PcFeL'L″, and [PcFeX₂]^2- complexes (Pc = phthalocyaninato(2-) ligand; L = NH₃, n-BuNH₂, imidazole (Im), pyridine (Py), PMe₃, PBu₃, t-BuNC, P(OBu)₃, and DMSO; L' = CO; L″ = NH₃ or n-BuNH₂; X = NCO^-, NCS^-, CN^-, imidazolate (Im^-), or 1,2,4-triazolate(Tz^-)) were probed by electrochemical, spectroelectrochemical, and chemical oxidation as well as theoretical (density functional theory, DFT) studies. In general, energies of the metal-centered occupied orbitals in various six-coordinate iron phthalocyanine complexes correlate well with Lever Electrochemical Parameter E_L and intercross the phthalocyanine-centered a_1u orbital in several compounds with moderate-to-strong π-accepting axial ligands. In these cases, an oxidation of the phthalocyanine macrocycle (Pc(2-)/Pc(1-)) rather than the central metal ion (Fe(II)/Fe(III)) was theoretically predicted and experimentally confirmed.

Accurate Prediction of Mössbauer Hyperfine Parameters in Bis-Axially Coordinated Iron(II) Phthalocyanines Using Density Functional Theory Calculations: A Story of a Single Orbital Revealed by Natural Bond Orbital Analysis

Density Functional Theory (DFT) calculations coupled with several exchange-correlation functionals were used for the prediction of Mössbauer hyperfine parameters of 36 bis-axially coordinated iron(II) phthalocyanine complexes with the general formulas PcFeL₂, PcFeL'L″, and [PcFeX₂]^2-, including four new compounds. Both gas-phase and PCM calculations using BPW91 and MN12L exchange-correlation functionals were found to accurately predict both Mössbauer quadrupole splittings and the correct trends in experimentally observed isomer shifts. In comparison, hybrid exchange-correlation functionals underestimated quadrupole splittings, while still accurately predicted isomer shifts. Out of ∼40 exchange-correlation functionals tested, only MN12L was found to correctly reproduce quadrupole splitting trends in the PcFeL₂ complexes coordinated with phosphorus-donor axial ligands (i.e., P(OnBu)₃ ≈ P(OEt)₃ < PMe₃ < P[(CH₂O)₂CH₂]-p-C₆H₄NO₂ < PEt₃ ≈ PnBu₃). Natural Bond Orbital (NBO) analysis was successfully used to explain the general trends in the observed quadrupole splitting for all compounds of interest. In particular, the general trends in the quadrupole splitting correlate well with the axial ligand dependent, NBO-predicted population of the 3d_z2 orbital of the Fe ion and are reflective of the hypothesis proposed by Ohya and co-workers ( Inorg. Chem., 1984, 23, 1303) on the adaptability of the phthalocyanine's π-system toward Fe-L_ax interactions. The first X-ray crystal structure of a PcFeL₂ complex with axial phosphine ligands is also reported.

X-Ray structures, Mössbauer hyperfine parameters, and molecular orbital descriptions of the phthalocyaninato iron(II) azole complexes

The electronic structures of a set of PcFe(azole)2 complexes (azole = imidazole, [Formula: see text]-methylimidazole, pyrazole, isoxazole, thiazole, 1,2,4-triazole, 3-amino-1,2,4,-triazole, and 5-amino-1,2,3,4-tetrazole) were examined by Mössbauer spectroscopy and Density Functional Theory (DFT) calculations. In addition, the geometric distortions in these compounds were elucidated by X-ray crystallography for imidazole, pyrazole, and thiazole-containing compounds. Predicted by DFT calculations, Mössbauer hyperfine parameters for all compounds are in reasonable agreement with experimental results, and the influence of the [Formula: see text]-donor and [Formula: see text]-acceptor properties of the axial azoles on the electronic structure of the PcFe(azole)2 complexes is demonstrated by comparison with the reference PcFePy2 compound.

Mössbauer isomer shifts and effective contact densities obtained by the exact two-component (X2C) relativistic method and its local variants

A standalone program to calculate scalar relativistic effective contact densities.

Density Functional Calculations for Prediction of 57Fe Mössbauer Isomer Shifts and Quadrupole Splittings in β-Diketiminate Complexes

The relative ease of Mössbauer spectroscopy and of density functional theory (DFT) calculations encourages the use of Mössbauer parameters as a validation method for calculations, and the use of calculations as a double check on crystallographic structures. A number of studies have proposed correlations between the computationally determined electron density at the iron nucleus and the observed isomer shift, but deviations from these correlations in low-valent iron β-diketiminate complexes encouraged us to determine a new correlation for these compounds. The use of B3LYP/def2-TZVP in the ORCA platform provides an excellent balance of accuracy and speed. We provide here not only this new correlation and a clear guide to its use but also a systematic analysis of the limitations of this approach. We also highlight the impact of crystallographic inaccuracies, DFT model truncation, and spin states, with intent to assist experimentalists to use Mössbauer spectroscopy and calculations together.

Reliable Estimation of Prediction Uncertainty for Physicochemical Property Models

One of the major challenges in computational science is to determine the uncertainty of a virtual measurement, that is the prediction of an observable based on calculations. As highly accurate first-principles calculations are in general unfeasible for most physical systems, one usually resorts to parameteric property models of observables, which require calibration by incorporating reference data. The resulting predictions and their uncertainties are sensitive to systematic errors such as inconsistent reference data, parametric model assumptions, or inadequate computational methods. Here, we discuss the calibration of property models in the light of bootstrapping, a sampling method that can be employed for identifying systematic errors and for reliable estimation of the prediction uncertainty. We apply bootstrapping to assess a linear property model linking the ⁵⁷Fe Mössbauer isomer shift to the contact electron density at the iron nucleus for a diverse set of 44 molecular iron compounds. The contact electron density is calculated with 12 density functionals across Jacob's ladder (PWLDA, BP86, BLYP, PW91, PBE, M06-L, TPSS, B3LYP, B3PW91, PBE0, M06, TPSSh). We provide systematic-error diagnostics and reliable, locally resolved uncertainties for isomer-shift predictions. Pure and hybrid density functionals yield average prediction uncertainties of 0.06-0.08 mm s^-1 and 0.04-0.05 mm s^-1, respectively, the latter being close to the average experimental uncertainty of 0.02 mm s^-1. Furthermore, we show that both model parameters and prediction uncertainty depend significantly on the composition and number of reference data points. Accordingly, we suggest that rankings of density functionals based on performance measures (e.g., the squared coefficient of correlation, r², or the root-mean-square error, RMSE) should not be inferred from a single data set. This study presents the first statistically rigorous calibration analysis for theoretical Mössbauer spectroscopy, which is of general applicability for physicochemical property models and not restricted to isomer-shift predictions. We provide the statistically meaningful reference data set MIS39 and a new calibration of the isomer shift based on the PBE0 functional.

Calculated Mechanism of Cyanobacterial Aldehyde-Deformylating Oxygenase: Asymmetric Aldehyde Activation by a Symmetric Diiron Cofactor

Cyanobacterial aldehyde-deformylating oxygenase (cADO) is a nonheme diiron enzyme that catalyzes the conversion of aldehyde to alk(a/e)ne, an important transformation in biofuel research. In this work, we report a highly desired computational study for probing the mechanism of cADO. By combining our QM/MM results with the available ⁵⁷Fe Mössbauer spectroscopic data, the gained detailed structural information suggests construction of asymmetry from the symmetric diiron cofactor in an aldehyde substrate and O₂ activation. His₁₆₀, one of the two iron-coordinate histidine residues in cADO, plays a pivotal role in this asymmetric aldehyde activation process by unprecedented reversible dissociation from the diiron cofactor, a behavior unknown in any other nonheme dinuclear or mononuclear enzymes. The revealed intrinsically asymmetric interactions of the substrate/O₂ with the symmetric cofactor in cADO are inspirational for exploring diiron subsite resolution in other nonheme diiron enzymes.

Calibration of 57Fe Mössbauer constants by first principles

Ab initio periodic esimate of Mössbauer isomer shift and quadrupolar moment for iron: hybrid functional approach in a GTO basis set.

A High-Valent Iron(IV) Peroxo Core Derived from O2

Dioxygen-tolerant [NiFe] hydrogenases catalyze not only the conversion of H2 into 2 H(+) and 2 e(-) but also the reduction of O2 to H2O. Chemists have sought to mimic such bifunctional catalysts with structurally simpler compounds to facilitate analysis and improvement. Herein, we report a new [NiFe]-based catalyst for O2 reduction via an O2 adduct. Structural investigations reveal the first example of a side-on iron(IV) peroxo complex.

Chloride ion-aided self-assembly of pseudoclathrochelate metal tris-pyrazoloximates

Chloride ion-aided one-pot template self-assembly of a mixed pyrazoloxime ligand with phenylboronic acid on a corresponding metal(II) ion as a matrix afforded the first boron-capped zinc, cobalt, iron, and manganese pseudoclathrochelate tris-pyrazoloximates. The presence of a pseudocross-linking hydrogen-bonded chloride ion is critical for their formation, as the same chloride-capped complexes were isolated even in the presence of large excesses of bromide and iodide ions. As revealed by X-ray diffraction, all complexes are capped with a chloride ion via three N-H···Cl hydrogen bonds that stabilize their pseudomacrobicyclic frameworks. The MN6 coordination polyhedra possess a distorted trigonal prismatic geometry, with the distortion angles φ between their nonequivalent N3 bases of approximately 0°. Temperature dependences of the effective magnetic moment for the paramagnetic complexes showed the encapsulated metal(II) ions to be in a high-spin state in the temperature range of 2-300 K. In the case of the iron(II) pseudoclathrochelate, density functional theory (DFT) and time-dependent DFT calculations were used to assess its spin state as well as the (57)Fe Mössbauer and UV-vis-NIR parameters. Cyclic voltammetry studies performed for these pseudomacrobicyclic complexes showed them to undergo irreversible or quasi-reversible metal-localized oxidations and reductions. As no changes are observed in the presence of a substantial excess of bromide ion, no anion-exchange reaction occurs, and thus the pseudoclathrochelates have a high affinity toward chloride anions in solution.

Theoretical 57Fe Mössbauer spectroscopy: isomer shifts of [Fe]-hydrogenase intermediates

A computational protocol for ⁵⁷Fe isomer shifts, based on the relativistic eXact 2-Component Hamiltonian (X2C), is applied to discriminate between proposed intermediates of [Fe]-hydrogenase. Detailed analysis reveals that the difference in isomer shifts between two intermediates is due to an overlap effect.

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.

Insight into the electronic structure, optical properties, and redox behavior of the hybrid phthalocyaninoclathrochelates from experimental and density functional theory approaches

An insight into the electronic structure of several hafnium(IV), zirconium(IV), and lutetium(III) phthalocyaninoclathrochelates has been discussed on the basis of experimental UV-vis, MCD, electro- and spectroelectrochemical data as well as density functional theory (DFT) and time-dependent DFT (TDDFT) calculations. On the basis of UV-vis and MCD spectroscopy as well as theoretical predictions, it was concluded that the electronic structure of the phthalocyninoclathrochelates can be described in the first approximation as a superposition of the weakly interacting phthalocyanine and clathrochelate substituents. Spectroelectrochemical data and DFT calculations clearly confirm that the highest occupied molecular orbital (HOMO) in all tested complexes is localized on the phthalocyanine ligand. X-ray crystallography on zirconium(IV) and earlier reported hafnium(IV) phthalocyaninoclathrochelate complexes revealed a slightly distorted phthalocyanine conformation with seven-coordinated metal center positioned ∼1 Å above macrocyclic cavity. The geometry of the encapsulated iron(II) ion in the clathrochelate fragment was found to be between trigonal-prismatic and trigonal-antiprismatic.

Photoinduced charge transfer in short-distance ferrocenylsubphthalocyanine dyads

Two new ferrocenylsubphthalocyanine dyads with ferrocenylmethoxide (2) and ferrocenecarboxylate (3) substituents directly attached to the subphthalocyanine ligand via the axial position have been prepared and characterized using NMR, UV-vis, and magnetic circular dichroism (MCD) spectroscopies as well as X-ray crystallography. The redox properties of the ferrocenyl-containing dyads 2 and 3 were investigated using the cyclic voltammetry (CV) approach and compared to those of the parent subphthalocyanine 1. CV data reveal that the first reversible oxidation is ferrocene-centered, while the second oxidation and the first reduction are localized on the subphthalocyanine ligand. The electronic structures and nature of the optical bands observed in the UV-vis and MCD spectra of all target compounds were investigated by a density functional theory polarized continuum model (DFT-PCM) and time-dependent (TD)DFT-PCM approaches. It has been found that in both dyads the highest occupied molecular orbital (HOMO) to HOMO-2 are ferrocene-centered molecular orbitals, while HOMO-3 as well as lowest unoccupied molecular orbital (LUMO) and LUMO+1 are localized on the subphthalocyanine ligand. TDDFT-PCM data on complexes 1-3 are consistent with the experimental observations, which indicate the dominance of π-π* transitions in the UV-vis spectra of 1-3. The excited-state dynamics of the dyads 2 and 3 were investigated using time-correlated single photon counting, which indicates that fluorescence quenching is more efficient in dyad 3 compared to dyad 2. These fluorescence lifetime measurements were interpreted on the basis of DFT-PCM calculations.

Mössbauer properties of the diferric cluster and the differential iron(II)-binding affinity of the iron sites in protein R2 of class Ia Escherichia coli ribonucleotide reductase: a DFT/electrostatics study

The R2 subunit of class-Ia ribonucleotide reductase (RNR) from Escherichia coli (E. coli) contains a diiron active site. Starting from the apo-protein and Fe(II) in solution at low Fe(II)/apoR2 ratios, mononuclear Fe(II) binding is observed indicating possible different Fe(II) binding affinities for the two alternative sites. Further, based on their Mössbauer spectroscopy and two-iron-isotope reaction experiments, Bollinger et al. (J. Am. Chem. Soc., 1997, 119, 5976-5977) proposed that the site Fe1, which bonds to Asp84, should be associated with the higher observed (57)Fe Mössbauer quadrupole splitting (2.41 mm s(-1)) and lower isomer shift (0.45 mm s(-1)) in the Fe(III)Fe(III) state, site Fe2, which is further from Tyr122, should have a greater affinity for Fe(II) binding than site Fe1, and Fe(IV) in the intermediate X state should reside at site Fe2. In this paper, using density functional theory (DFT) incorporated with the conductor-like screening (COSMO) solvation model and with the finite-difference Poisson-Boltzmann self-consistent reaction field (PB-SCRF) methodologies, we have demonstrated that the observed large quadrupole splitting for the diferric state R2 does come from site Fe1(III) and it is mainly caused by the binding position of the carboxylate group of the Asp84 sidechain. Further, a series of active site clusters with mononuclear Fe(II) binding at either site Fe1 or Fe2 have been studied, which show that with a single dielectric medium outside the active site quantum region, there is no energetic preference for Fe(II) binding at one site over another. However, when including the explicit extended protein environment in the PB-SCRF model, the reaction field favors the Fe(II) binding at site Fe2 rather than at site Fe1 by ~9 kcal mol(-1). Therefore our calculations support the proposal of the previous Mössbauer spectroscopy and two-iron-isotope reaction experiments by Bollinger et al.

Calibration of DFT Functionals for the Prediction of Fe Mössbauer Spectral Parameters in Iron-Nitrosyl and Iron-Sulfur Complexes: Accurate Geometries Prove Essential

Six popular density functionals in conjunction with the conductor-like screening (COSMO) solvation model have been used to obtain linear Mössbauer isomer shift (IS) and quadrupole splitting (QS) parameters for a test set of 20 complexes (with 24 sites) comprised of nonheme nitrosyls (Fe-NO) and non-nitrosyl (Fe-S) complexes. For the first time in an IS analysis, the Fe electron density was calculated both directly at the nucleus, ρ(0)(N), which is the typical procedure, and on a small sphere surrounding the nucleus, ρ(0)(S), which is the new standard algorithm implemented in the ADF software package. We find that both methods yield (near) identical slopes from each linear regression analysis but are shifted with respect to ρ(0) along the x-axis. Therefore, the calculation of the Fe electron density with either method gives calibration fits with equal predictive value. Calibration parameters obtained from the complete test set for OLYP, OPBE, PW91, and BP86 yield correlation coefficients (r(2)) of approximately 0.90, indicating that the calibration fit is of good quality. However, fits obtained from B3LYP and B3LYP* with both Slater-type and Gaussian-type orbitals are generally found to be of poorer quality. For several of the complexes examined in this study, we find that B3LYP and B3LYP* give geometries that possess significantly larger deviations from the experimental structures than OLYP, OPBE, PW91 or BP86. This phenomenon is particularly true for the di- and tetranuclear Fe complexes examined in this study. Previous Mössbauer calibration fit studies using these functionals have usually included mononuclear Fe complexes alone, where these discrepancies are less pronounced. An examination of spin expectation values reveals B3LYP and B3LYP* approach the weak-coupling limit more closely than the GGA exchange-correlation functionals. The high degree of variability in our calculated S(2) values for the Fe-NO complexes highlights their challenging electronic structure. Significant improvements to the isomer shift calibrations are obtained for B3LYP and B3LYP* when geometries obtained with the OLYP functional are used. In addition, greatly improved performance of these functionals is found if the complete test set is grouped separately into Fe-NO and Fe-S complexes. Calibration fits including only Fe-NO complexes are found to be excellent, while those containing the non-nitrosyl Fe-S complexes alone are found to demonstrate less accurate correlations. Similar trends are also found with OLYP, OPBE, PW91, and BP86. Correlations between experimental and calculated QSs were also investigated. Generally, universal and separate Fe-NO and Fe-S fit parameters obtained to determine QSs are found to be of good to excellent quality for every density functional examined, especially if [Fe(4)(NO)(4)(μ(3)-S)(4)](-) is removed from the test set.

Theoretical study on the molecular structures of X-, α-, and β-types of lithium phthalocyanine dimer

We report here the results from theoretical calculations of the potential energy curves, the geometry optimizations, and the electronic structures for three dimers of lithium phthalocyanine (LiPc) by using three types of functional systems: PBE1PBE, B3LYP, and M06. The results were discussed in comparison with those obtained for the dimers of magnesium phthalocyanine (MgPc). The long-range dispersive interactions were considered in part using these functional systems in the increasing order of PBE1PBE, B3LYP, and M06. The mechanism whereby the dispersive interactions affect the geometric and electronic structures of the LiPc and MgPc dimers is discussed. The calculated results provide insight into the computational methods for both open- and closed-shell metal phthalocyanine (MPc) dimers: Although the PBE1PBE and B3LYP functional systems cannot evaluate a weak dispersion interaction appropriately, the M06 functional can estimate a weak dispersion interaction well in both open- and closed-shell MPc dimers. Basis set superposition error (BSSE) corrections play an important role for the quantitative analysis; however, the calculation results without BSSE corrections may be sufficient for the qualitative discussion on the properties of these dimers such as geometries, stabilities, electronic structures, and so on.

The prediction of Fe Mössbauer parameters by the density functional theory: a benchmark study

We report the performance of eight density functionals (B3LYP, BPW91, OLYP, O3LYP, M06, M06-2X, PBE, and SVWN5) in two Gaussian basis sets (Wachters and Partridge-1 on iron atoms; cc-pVDZ on the rest of atoms) for the prediction of the isomer shift (IS) and the quadrupole splitting (QS) parameters of Mössbauer spectroscopy. Two sources of geometry (density functional theory-optimized and X-ray) are used. Our data set consists of 31 iron-containing compounds (35 signals), the Mössbauer spectra of which were determined at liquid helium temperature and where the X-ray geometries are known. Our results indicate that the larger and uncontracted Partridge-1 basis set produces slightly more accurate linear correlations of electronic density used for the prediction of IS and noticeably more accurate results for the QS parameter. We confirm and discuss the earlier observation of Noodleman and co-workers that different oxidation states of iron produce different IS calibration lines. The B3LYP and O3LYP functionals have the lowest errors for either IS or QS. BPW91, OLYP, PBE, and M06 have a mixed success whereas SVWN5 and M06-2X demonstrate the worst performance. Finally, our calibrations and conclusions regarding the best functional to compute the Mössbauer characteristics are applied to candidate structures for the peroxo and Q intermediates of the enzyme methane monooxygenase hydroxylase (MMOH), and compared to experimental data in the literature.

Comparative calculation of EPR spectral parameters in [Mo(V)OX4]-, [Mo(V)OX5]2-, and [Mo(V)OX4(H2O)]- complexes

The EPR spectral parameters, i.e. g-tensors and molybdenum hyperfine couplings, for several d(1) systems of the general formula [Mo(V)EX(4)](n-), [Mo(V)OX(5)](2-), and [Mo(V)OX(4)(H(2)O)](-) (E = O, N; X = F, Cl, Br; n = 1 or 2) were calculated using Density Functional Theory. The influence of basis sets, their contraction scheme, the type of exchange-correlation functional, the amount of Hartree-Fock exchange, molecular geometry, and relativistic effects on the calculated EPR spectra parameters have been discussed. The g-tensors and molybdenum hyperfine coupling parameters were calculated using a relativistic Hamiltonian coupled with several LDA, GGA, and 'hybrid' exchange-correlation functionals and uncontracted full-electron DGauss DZVP basis sets. The calculated EPR parameters are found to be sensitive to the Mo=E distance and E=Mo-Cl angle, and thus the choice of starting molecular geometry should be considered as an important factor in predicting the g-tensors and hyperfine coupling constants in oxo-molybdenum compounds. In the present case, the GGA exchange-correlation functionals provide a better agreement between the theory and the experiment.