Density functional theory calculations on Mössbauer parameters of nonheme iron nitrosyls

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.

Low-Coordinate Iron Hydride Chemistry at an N,N,C-Heteroscorpionate Platform

Locally high-spin iron hydrides are proposed to play a critical role as intermediates in iron-molybdenum cofactor (FeMoco)-catalyzed N2 fixation. Inspired by these biological systems, we report herein our initial investigations into low-coordinate iron hydride chemistry supported by our N,N,C-heteroscorpionate ligands. Those ligands with smaller steric profiles are unable to completely suppress the formation of a binuclear [Fe(μ2-H)]2 complex; however, the incorporation of more substantial steric bulk allows for the isolation of a rare example of a terminal, high-spin (S = 2) Fe2+ hydride. Fourier transform infrared spectroscopy suggests an unusually weak Fe-H bond in the latter molecule. Mössbauer spectroscopies, coupled with density functional theory calculations, highlights the substantial influence of the terminal hydride ligand on 57Fe isomer shift.

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.

Local Oxidation States in {FeNO}6-8 Porphyrins: Insights from DMRG/CASSCF-CASPT2 Calculations

A first DMRG/CASSCF-CASPT2 study of a series of paradigmatic {FeNO}6, {FeNO}7, and {FeNO}8 heme-nitrosyl complexes has led to substantial new insight as well as uncovered key shortcomings of the DFT approach. By virtue of its balanced treatment of static and dynamic correlation, the calculations have provided some of the most authoritative information available to date on the energetics of low- versus high-spin states of different classes of heme-nitrosyl complexes. Thus, the calculations indicate low doublet-quartet gaps of 1-4 kcal/mol for {FeNO}7 complexes and high singlet-triplet gaps of ≳20 kcal/mol for both {FeNO}6 and {FeNO}8 complexes. In contrast, DFT calculations yield widely divergent spin state gaps as a function of the exchange-correlation functional. DMRG-CASSCF calculations also help calibrate DFT spin densities for {FeNO}7 complexes, pointing to those obtained from classic pure functionals as the most accurate. The general picture appears to be that nearly all the spin density of Fe[P](NO) is localized on the Fe, while the axial ligand imidazole (ImH) in Fe[P](NO)(ImH) pushes a part of the spin density onto the NO moiety. An analysis of the DMRG-CASSCF wave function in terms of localized orbitals and of the resulting configuration state functions in terms of resonance forms with varying NO(π*) occupancies has allowed us to address the longstanding question of local oxidation states in heme-nitrosyl complexes. The analysis indicates NO(neutral) resonance forms [i.e., Fe(II)-NO0 and Fe(III)-NO0] as the major contributors to both {FeNO}6 and {FeNO}7 complexes. This finding is at variance with the common formulation of {FeNO}6 hemes as Fe(II)-NO+ species but is consonant with an Fe L-edge XAS analysis by Solomon and co-workers. For the {FeNO}8 complex {Fe[P](NO)}-, our analysis suggests a resonance hybrid description: Fe(I)-NO0 ↔ Fe(II)-NO-, in agreement with earlier DFT studies. Vibrational analyses of the compounds studied indicate an imperfect but fair correlation between the NO stretching frequency and NO(π*) occupancy, highlighting the usefulness of vibrational data as a preliminary indicator of the NO oxidation state.

Simulations of the Aqueous "Brown-Ring" Complex Reveal Fluctuations in Electronic Character

Ab initio molecular dynamics (AIMD) simulations of the aqueous [Fe(H2O)5(NO)]2+ "brown-ring" complex in different spin states, in combination with multiconfigurational quantum chemical calculations, show a structural dependence on the electronic character of the complex. Sampling in the quartet and sextet ground states show that the multiplicity is correlated with the Fe-N distance. This provides a motivation for a rigid Fe-N scan in the isolated "brown-ring" complex to investigate how the multiconfigurational wave function and the electron density change around the FeNO moiety. Our results show that subtle changes in the Fe-N distance produce a large response in the electronic configurations underlying the quartet wave function. However, while changes in spin density and potential energy are pronounced, variations in charge are negligible. These trends within the FeNO moiety are preserved in structural sampling of the AIMD simulations, despite distortions present in other degrees of freedom in the bulk solution.

The Elusive Mononitrosylated [Fe4 S4 ] Cluster in Three Redox States

Iron-sulfur clusters are well-established targets in biological nitric oxide (NO) chemistry, but the key intermediate in these processes-a mononitrosylated [Fe4 S4 ] cluster-has not been fully characterized in a protein or a synthetic model thereof. Here, we report the synthesis of a three-member redox series of isostructural mononitrosylated [Fe4 S4 ] clusters. Mononitrosylation was achieved by binding NO to a 3 : 1 site-differentiated [Fe4 S4 ]+ cluster; subsequent oxidation and reduction afforded the other members of the series. All three clusters feature a local high-spin Fe3+ center antiferromagnetically coupled to 3 [NO]- . The observation of an anionic NO ligand suggests that NO binding is accompanied by formal electron transfer from the cluster to NO. Preliminary reactivity studies with the monocationic cluster demonstrate that exposure to excess NO degrades the cluster, supporting the intermediacy of mononitrosylated intermediates in NO sensing/signaling.

Evidence for Low-Valent Electronic Configurations in Iron-Sulfur Clusters

Although biological iron-sulfur (Fe-S) clusters perform some of the most difficult redox reactions in nature, they are thought to be composed exclusively of Fe²⁺ and Fe³⁺ ions, as well as mixed-valent pairs with average oxidation states of Fe^2.5+. We herein show that Fe-S clusters formally composed of these valences can access a wider range of electronic configurations─in particular, those featuring low-valent Fe¹⁺ centers. We demonstrate that CO binding to a synthetic [Fe₄S₄]⁰ cluster supported by N-heterocyclic carbene ligands induces the generation of Fe¹⁺ centers via intracluster electron transfer, wherein a neighboring pair of Fe²⁺ sites reduces the CO-bound site to a low-valent Fe¹⁺ state. Similarly, CO binding to an [Fe₄S₄]⁺ cluster induces electron delocalization with a neighboring Fe site to form a mixed-valent Fe^1.5+Fe^2.5+ pair in which the CO-bound site adopts partial low-valent character. These low-valent configurations engender remarkable C-O bond activation without having to traverse highly negative and physiologically inaccessible [Fe₄S₄]⁰/[Fe₄S₄]^- redox couples.

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.

Antiferromagnetic Exchange and Metal-Metal Bonding in Roussin's Black Sulfur and Selenium Salts

Atom-efficient syntheses of the tetraethylammonium Roussin black sulfur and selenium salts ((Et₄N)[Fe₄E₃(NO)₇], E = S, Se) as well as their ¹⁵N-labeled counterparts are described herein. Broken-symmetry DFT calculations were conducted on both complexes to model an antiferromagnetic interaction between the apical {FeNO}⁷ unit, S_ap = 3/2, and the three basal {Fe(NO)₂}⁹ units, S_bas = 1/2. The calculated J values are -1813 and -1467 cm^-1 for the sulfur and selenium compounds, respectively. The mechanism for antiferromagnetic exchange in both compounds was deduced to be direct exchange on the basis of the partially overlapping magnetic orbitals with orbital density only residing on the Fe-centers. The obtained Mössbauer parameters are most consistent with the calculated M_S = 0 broken-symmetry state for both complexes. The values for J have been determined with variable-temperature ¹⁵N NMR experiments. Values of -1660 and -1430 cm^-1 for the sulfur and selenium compounds, respectively, were obtained by fits to the variable-temperature NMR data, further validating the broken-symmetry M_S = 0 model of the electronic structure.

57Fe Mössbauer isomer shift of pure iron and iron oxides at high pressure-An experimental and theoretical study

The ⁵⁷Fe isomer shift (IS) of pure iron has been measured up to 100 GPa using synchrotron Mössbauer spectroscopy in the time domain. Apart from the expected discontinuity due to the α → ε structural and spin transitions, the IS decreases monotonically with increasing pressure. The absolute shifts were reproduced without semi-empirical calibrations by periodic density functional calculations employing extensive localized basis sets with several common density functionals. However, the best numerical agreement is obtained with the B1WC hybrid functional. Extension of the calculations to 350 GPa, a pressure corresponding to the Earth's inner core, predicted the IS range of 0.00 to -0.85 mm/s, covering the span from Fe(0) to Fe(VI) compounds measured at ambient pressure. The calculations also reproduced the pressure trend from polymorphs of prototypical iron oxide minerals, FeO and Fe₂O₃. Analysis of the electronic structure shows a strong donation of electrons from oxygen to iron at high pressure. The assignment of formal oxidation to the Fe atom becomes ambiguous under this condition.

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.

Nature of the copper-nitrosyl intermediates of copper nitrite reductases during catalysis

The design and synthesis of copper complexes that can reduce nitrite to NO has attracted considerable interest. They have been guided by the structural information on the catalytic Cu centre of the widespread enzymes Cu nitrite reductases but the chemically novel side-on binding of NO observed in all crystallographic studies of these enzymes has been questioned in terms of its functional relevance. We show conversion of NO₂⁻ to NO in the crystal maintained at 170 K and present ‘molecular movies’ defining events during enzyme turnover including the formation of side-on Cu-NO intermediate. DFT modelling suggests that both true {CuNO}¹¹ and formal {CuNO}¹⁰ states may occur as side-on forms in an enzymatic active site with the stability of the {CuNO}¹⁰ side-on form governed by the protonation state of the histidine ligands. Formation of a copper-nitrosyl intermediate thus needs to be accommodated in future design templates for functional synthetic Cu-NiR complexes.

Observation of side-on copper-nitrosyl intermediate and its confirmation by DFT during catalysis of copper nitrite reductases.

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.

Structural and Optical Properties of Metal-Nitrosyl Complexes

The electronic, structural and optical properties (including Spin–Orbit Coupling) of metal nitrosyl complexes [M(CN)₅(NO)]²⁻ (M = Fe, Ru or Os) are investigated by means of Density Functional Theory, TD-DFT and MS-CASPT2 based on an RASSCF wavefunction. The energy profiles connecting the N-bound (η¹-N), O-bound (η¹-O) and side-on (η²-NO) conformations have been computed at DFT level for the closed shell singlet electronic state. For each structure, the lowest singlet and triplet states have been optimized in order to gain insight into the energy profiles describing the conformational isomerism in excited states. The energetics of the three complexes are similar—with the N-bound structure being the most stable—with one exception, namely the triplet ground state of the O-bound isomer for the iron complex. The conformation isomerism is highly unfavorable in the S₀ electronic state with the occurrence of two energy barriers higher than 2 eV. The lowest bands of the spectra are assigned to MLCT_NO/LLCT_NO transitions, with an increasing MLCT character going from iron to osmium. Two low-lying triplet states, T1 (MLCT_NO/LLCT_NO) and T2 (MLCT_NO/IL_NO), seem to control the lowest energy profile of the excited-state conformational isomerism.

Density functionalized [RuII(NO)(Salen)(Cl)] complex: Computational photodynamics and in vitro anticancer facets

Photodynamic therapy (PDT) is a treatment that uses photosensitizing agents to kill cancer cells. Scientific community has been eager for decades to design an efficient PDT drug. Under such purview, the current report deals with the computational photodynamic behavior of ruthenium(II) nitrosyl complex containing N, N'-salicyldehyde-ethylenediimine (SalenH₂), the synthesis and X-ray crystallography of which is already known [Ref. 38,39]. Gaussian 09W software package was employed to carry out the density functional (DFT) studies. DFT calculations with Becke-3-Lee-Yang-Parr (B3LYP)/Los Alamos National Laboratory 2 Double Z (LanL2DZ) specified for Ru atom and B3LYP/6-31G(d,p) combination for all other atoms were used using effective core potential method. Both, the ground and excited states of the complex were evolved. Some known photosensitizers were compared with the target complex. Pthalocyanine and porphyrin derivatives were the compounds selected for the respective comparative study. It is suggested that effective photoactivity was found due to the presence of ruthenium core in the model complex. In addition to the evaluation of theoretical aspects in vitro anticancer aspects against COLO-205 human cancer cells have also been carried out with regard to the complex. More emphasis was laid to extrapolate DFT to depict the chemical power of the target compound to release nitric oxide. A promising visible light triggered nitric oxide releasing power of the compound has been inferred. In vitro antiproliferative studies of [RuCl₃(PPh₃)₃] and [Ru(NO)(Salen)(Cl)] have revealed the model complex as an excellent anticancer agent. From IC₅₀ values of 40.031mg/mL in former and of 9.74mg/mL in latter, it is established that latter bears more anticancer potentiality. From overall study the DFT based structural elucidation and the efficiency of NO, Ru and Salen co-ligands has shown promising drug delivery property and a good candidacy for both chemotherapy as well as light therapy.

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.

Comment on “Calibration of 57Fe Mössbauer constants by first principles” Phys. Chem. Chem. Phys., 2016, 18, 10201–10206

The proportionality constant between the iron-57 Mössbauer isomer shift and the electron probablility density at the nucleus is reevaluated from the correct experimental isomer shifts.

Recent advances in biosynthetic modeling of nitric oxide reductases and insights gained from nuclear resonance vibrational and other spectroscopic studies

This Forum Article focuses on recent advances in structural and spectroscopic studies of biosynthetic models of nitric oxide reductases (NORs). NORs are complex metalloenzymes found in the denitrification pathway of Earth’s nitrogen cycle where they catalyze the proton-dependent two-electron reduction of nitric oxide (NO) to nitrous oxide (N₂O). While much progress has been made in biochemical and biophysical studies of native NORs and their variants, a clear mechanistic understanding of this important metalloenzyme related to its function is still elusive. We report herein UV–vis and nuclear resonance vibrational spectroscopy (NRVS) studies of mononitrosylated intermediates of the NOR reaction of a biosynthetic model. The ability to selectively substitute metals at either heme or nonheme metal sites allows the introduction of independent ⁵⁷Fe probe atoms at either site, as well as allowing the preparation of analogues of stable reaction intermediates by replacing either metal with a redox inactive metal. Together with previous structural and spectroscopic results, we summarize insights gained from studying these biosynthetic models toward understanding structural features responsible for the NOR activity and its mechanism. The outlook on NOR modeling is also discussed, with an emphasis on the design of models capable of catalytic turnovers designed based on close mimics of the secondary coordination sphere of native NORs.

New insights into nitric oxide reductases (NORs) are obtained. Using nuclear resonance vibrational spectroscopy, we probe both iron atoms in mononitrosylated intermediates of the NOR reaction in a biosynthetic protein model that reveal new insights into the structural and electronic features responsible for the NOR activity and its likely mechanism.

Use of Broken-Symmetry Density Functional Theory To Characterize the IspH Oxidized State: Implications for IspH Mechanism and Inhibition

With current therapies becoming less efficacious due to increased drug resistance, new inhibitors of both bacterial and malarial targets are desperately needed. The recently discovered methylerythritol phosphate (MEP) pathway for isoprenoid synthesis provides novel targets for the development of such drugs. Particular attention has focused on the IspH protein, the final enzyme in the MEP pathway, which uses its [4Fe-4S] cluster to catalyze the formation of the isoprenoid precursors IPP and DMAPP from HMBPP. IspH catalysis is achieved via a 2e-/2H+ reductive dehydroxylation of HMBPP; the mechanism by which catalysis is achieved, however, is highly controversial. The work presented herein provides the first step in assessing different routes to catalysis by using computational methods. By performing broken-symmetry density functional theory (BS-DFT) calculations that employ both the conductor-like screening solvation model (DFT/COSMO) and a finite-difference Poisson-Boltzmann self-consistent reaction field methodology (DFT/SCRF), we evaluate geometries, energies, and Mössbauer signatures of the different protonation states that may exist in the oxidized state of the IspH catalytic cycle. From DFT/SCRF computations performed on the oxidized state, we find a state where the substrate, HMBPP, coordinates the apical iron in the [4Fe-4S] cluster as an alcohol group (ROH) to be one of two, isoenergetic, lowest-energy states. In this state, the HMBPP pyrophosphate moiety and an adjacent glutamate residue (E126) are both fully deprotonated, making the active site highly anionic. Our findings that this low-energy state also matches the experimental geometry of the active site and that its computed isomer shifts agree with experiment validate the use of the DFT/SCRF method to assess relative energies along the IspH reaction pathway. Additional studies of IspH catalytic intermediates are currently being pursued.

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.

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.

Geometric and electrostatic study of the [4Fe-4S] cluster of adenosine-5'-phosphosulfate reductase from broken symmetry density functional calculations and extended X-ray absorption fine structure spectroscopy

Adenosine-5'-phosphosulfate reductase (APSR) is an iron-sulfur protein that catalyzes the reduction of adenosine-5'-phosphosulfate (APS) to sulfite. APSR coordinates to a [4Fe-4S] cluster via a conserved CC-X(~80)-CXXC motif, and the cluster is essential for catalysis. Despite extensive functional, structural, and spectroscopic studies, the exact role of the iron-sulfur cluster in APS reduction remains unknown. To gain an understanding into the role of the cluster, density functional theory (DFT) analysis and extended X-ray fine structure spectroscopy (EXAFS) have been performed to reveal insights into the coordination, geometry, and electrostatics of the [4Fe-4S] cluster. X-ray absorption near-edge structure (XANES) data confirms that the cluster is in the [4Fe-4S](2+) state in both native and substrate-bound APSR while EXAFS data recorded at ~0.1 Å resolution indicates that there is no significant change in the structure of the [4Fe-4S] cluster between the native and substrate-bound forms of the protein. On the other hand, DFT calculations provide an insight into the subtle differences between the geometry of the cluster in the native and APS-bound forms of APSR. A comparison between models with and without the tandem cysteine pair coordination of the cluster suggests a role for the unique coordination in facilitating a compact geometric structure and "fine-tuning" the electronic structure to prevent reduction of the cluster. Further, calculations using models in which residue Lys144 is mutated to Ala confirm the finding that Lys144 serves as a crucial link in the interactions involving the [4Fe-4S] cluster and APS.

Comparative assessment of the composition and charge state of nitrogenase FeMo-cofactor

A significant limitation in our understanding of the molecular mechanism of biological nitrogen fixation is the uncertain composition of the FeMo-cofactor (FeMo-co) of nitrogenase. In this study we present a systematic, density functional theory-based evaluation of spin-coupling schemes, iron oxidation states, ligand protonation states, and interstitial ligand composition using a wide range of experimental criteria. The employed functionals and basis sets were validated with molecular orbital information from X-ray absorption spectroscopic data of relevant iron-sulfur clusters. Independently from the employed level of theory, the electronic structure with the greatest number of antiferromagnetic interactions corresponds to the lowest energy state for a given charge and oxidation state distribution of the iron ions. The relative spin state energies of resting and oxidized FeMo-co already allowed exclusion of certain iron oxidation state distributions and interstitial ligand compositions. Geometry-optimized FeMo-co structures of several models further eliminated additional states and compositions, while reduction potentials indicated a strong preference for the most likely charge state of FeMo-co. Mössbauer and ENDOR parameter calculations were found to be remarkably dependent on the employed training set, density functional, and basis set. Overall, we found that a more oxidized [Mo(IV)-2Fe(II)-5Fe(III)-9S(2-)-C(4-)] composition with a hydroxyl-protonated homocitrate ligand satisfies all of the available experimental criteria and is thus favored over the currently preferred composition of [Mo(IV)-4Fe(II)-3Fe(III)-9S(2-)-N(3-)] from the literature.

S K-edge X-ray absorption spectroscopy and density functional theory studies of high and low spin {FeNO}7 thiolate complexes: exchange stabilization of electron delocalization in {FeNO}7 and {FeO2}8

S K-edge X-ray absorption spectroscopy (XAS) is a direct experimental probe of metal ion electronic structure as the pre-edge energy reflects its oxidation state, and the energy splitting pattern of the pre-edge transitions reflects its spin state. The combination of sulfur K-edge XAS and density functional theory (DFT) calculations indicates that the electronic structures of {FeNO}(7) (S = 3/2) (S(Me2)N4(tren)Fe(NO), complex I) and {FeNO}(7) (S = 1/2) ((bme-daco)Fe(NO), complex II) are Fe(III)(S = 5/2)-NO(-)(S = 1) and Fe(III)(S = 3/2)-NO(-)(S = 1), respectively. When an axial ligand is computationally added to complex II, the electronic structure becomes Fe(II)(S = 0)-NO•(S = 1/2). These studies demonstrate how the ligand field of the Fe center defines its spin state and thus changes the electron exchange, an important factor in determining the electron distribution over {FeNO}(7) and {FeO2}(8) sites.

Modeling the MoFe nitrogenase system with broken symmetry density functional theory

Density functional theory (DFT) represents a unified framework for gaining molecular level insight into molybdenum-iron (MoFe) nitrogenase. However, accurately describing the electronic structure of the spin-polarized and spin-coupled iron-molybdenum cofactor (FeMo-co) where N(2) reduction occurs within MoFe nitrogenase is challenging. Therefore, the enhancement of DFT to include broken symmetry (BS-DFT) plus approximate spin projection has proven valuable because it provides a procedure to compute reliable geometries, energies, redox potentials, and quantities relevant to Mössbauer and ENDOR spectroscopies. After describing the theoretical tools necessary to obtain this information, we show by way of examples how BS-DFT is a very powerful partner to experiment. We expect that quantitative quantum chemical theory of this type will play an ever-increasing role in helping to decipher complex bioinorganic systems like those found in MoFe nitrogenase.

Experimental and theoretical Mössbauer study of an extended family of [Fe8(μ4-O)4(μ-4-R-px)12X4] clusters

Six [Fe(8)(μ(4)-O)(4)(μ-4-R-pyrazolato)(12)X(4)] complexes containing an identical Fe(8)(μ(4)-O)(4) core have been structurally characterized and studied by Mössbauer spectroscopy. In each case, an inner μ(4)-O bridged Fe(III) cubane core is surrounded by four trigonal bipyramidal iron centers, the two distinct sites occurring in a 1:1 ratio. The Mössbauer spectrum of each of the clusters consists of two quadrupole doublets, which, with one exception (X = NCS, R = H), overlap to give three absorption lines. The systematic variation of X and R causes significant changes in the Mössbauer spectra. A comparison with values for the same clusters computed using density functional theory allows us to establish an unequivocal assignment of these peaks in terms of a nested model for the overlapping doublets. The changes in Mössbauer parameters (both experimental and computed) for the 1-electron reduced species [Fe(8)(μ(4)-O)(4)(μ-4-Cl-pyrazolato)(12)Cl(4)](-) are consistent with a redox event that is localized within the cubane core.

Spin coupling in Roussin's red and black salts

Although DFT calculations have provided a first-order electronic-structural description for Roussin's red and black salts, a detailed study of spin coupling in these species has yet to be reported. Such an analysis is presented here for the first time, based on broken-symmetry density functional theory (DFT, chiefly OLYP/STO-TZP) calculations. Both the Noodleman and Yamaguchi formulas were used to evaluate the Heisenberg coupling constants (J). Three nitrosylated binuclear clusters were studied: [Fe(2)(NO)(2)(Et-HPTB)(O(2)CPh)](2+) (1; Et-HPTB=N,N,N',N'-tetrakis-(N-ethyl-2-benzimidazolylmethyl)-2-hydroxy-1,3-diaminopropane), [Fe(NO)(2){Fe(NO)(NS(3))}-S,S'] (2), and Roussin's red salt anion [Fe(2)(NO)(4)(μ-S)(2)](2-) (3). Although the Heisenberg J for 1 is small (≈10(2) cm(-1)), 2 and 3 exhibit J values that are at least an order of magnitude higher (≈10(3) cm(-1)), where the J values refer to the following Heisenberg spin Hamiltonian: ℋ=JS(A)⋅S(B). For Roussin's black salt anion, [Fe(4)(NO)(7)(μ(3)-S)(3)](-) (4), the Heisenberg spin Hamiltonian describing spin coupling between the {FeNO}(7) unit (S(A)=3/2) and the three {Fe(NO)(2)}(9) units (S(B)=S(C)=S(D)=1/2) in [Fe(4)(NO)(7)(μ(3)-S)(3)](-) was assumed to have the form: ℋ=J(12)(S(A)⋅S(B)+S(A)⋅S(C)+S(A)⋅S(D))+J(22)(S(B)⋅S(C)+S(B)⋅S(D)+S(C)⋅S(D)), in which J(12) corresponds to the interaction between the apical iron and a basal iron, and J(22) refers to that between any two basal iron centers. Although the basal-basal coupling constant J(22) was found to be small (≈10(2) cm(-1)), the apical-basal coupling constant J(12) is some forty times higher (≈4000 cm(-1)). Thus, the nitrosylated iron-sulfur clusters feature some exceptionally high J values relative to the non-nitrosylated {2Fe2S} and {4Fe4S} clusters. An analysis of spin-dependent bonding energies shed light on this curious feature. In essence, the energy difference between the high-spin (i.e., ferromagnetically coupled iron sites) and low-spin (i.e., maximum spin coupling) states of Roussin's salts are indeed rather similar to those of analogous non-nitrosylated iron-sulfur clusters. However, the individual Fe(NO)(x) (x=1, 2) site spins are lower in the nitrosylated systems, resulting in a smaller denominator in both the Noodleman and Yamaguchi formulas for J, which in turn translates into the very high J values.

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.

Revisiting the nitrosyl complex of myoglobin by high-field pulse EPR spectroscopy and quantum mechanical calculations

The binding of NO to reduced myoglobin in solution results in the formation of two paramagnetic nitrosyl myoglobin (MbNO) complexes: one with a rhombic g-factor and the other with an axial one, referred to as the R- and A-forms. In spite of past extensive studies of MbNO by crystallography, spectroscopy and quantum chemical calculations it is still not clear what factors determine the appearance of the two forms. In this work we applied a combination of state of the art quantum chemical calculations and high field pulsed EPR spectroscopy (W-band, 3.4 T/95 GHz) to further characterize the two forms. Specifically, we have used (1)H and (2)H electron-nuclear double resonance (ENDOR) spectroscopy to identify and characterize the H-bond to the NO, and hyperfine sub-level correlation (HYSCORE) spectroscopy to determine the hyperfine and quadrupole interactions of the Fe(ii) coordinated (14)N of the proximal histidine (14)N(His93). The calculations employed quantum mechanics (QM), particularly density functional theory (DFT) methods in combination with molecular mechanics (MM) force-field to model the protein environment. Through QM/MM calculations of the EPR parameters we have explored their dependence on several geometrical factors of the Fe-NO bond and found those that reproduce the best experimental results. The spread of the W-band EPR spectrum of MbNO due to the g-anisotropy is large and there is a significant part of the spectrum where the R-form is the sole contributor. This allowed us to resolve some new characteristics of the R-form: (i) a NO-H hydrogen bond has been detected and characterized and through QM/MM calculations has been unambiguously assigned to (epsilon2)H(His64). (ii) The complete hyperfine and quadrupole interactions of (14)N(His93) have been determined and correlated with structural parameters again using QM/MM calculations. The agreement between the experimental results and calculations varied between excellent and good, depending on the EPR parameter in question. As for the more elusive A-form, the results only suggest that it does have a (14)N(His93) ligand with a hyperfine comparable to that of the R-form and it has less hydrogen bonding interaction with His(64). The calculations also established the orientation of the principal g-values, finding that they are closely related to the orientation of the NO bond. This information is essential for deriving structural information from the experimental orientation selective HYSCORE and ENDOR data.