Theoretical 57Fe Mössbauer Spectroscopy for Structure Elucidation of [Fe] Hydrogenase Active Site Intermediates

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.

Theoretical Evaluation of Metal-Ligand Bonding in Neptunium Compounds in Relation to 237Np Mössbauer Spectroscopy

The ²³⁷Np Mössbauer isomer shift and quadrupole splitting (QS) are powerful probes for the metal-ligand bonding of neptunium, a 5f-element of vital importance in the nuclear fuel cycle. A large set of Np compounds with different oxidation states (III) to (VII) is studied to investigate, by first-principles calculations, isomer shifts and the QS trends in relation to the Np oxidation state. Natural Bond Orbital analysis reveals that in addition to donation bonding to the 5f shell, participation of the 6d and 7s neptunium shells in covalent (donation) bonding substantially impacts the isomer shifts. The isomer shift cannot be interpreted solely by the 5f shell electron count. The isomer shift for Np(II) compounds is estimated to be in the range of 31-34 mm/s, less positive than for Np(III) compounds. For the QS, density functional calculations fail to reproduce the quadrupole splitting for some Np(VI) ionic solids. A multiconfigurational wave function approach reproduces the observed QS trends. The calculations give a semiquantitative interpretation of the trends for Np oxidation states (V) to (VII). The contrasting QS for standard and "reverse" neptunyl(VI), at the opposite extremes of the observed QS scale, arises predominantly from the different crystal environments.

237Np Mössbauer Isomer Shifts: A Lesson About the Balance of Static and Dynamic Electron Correlation in Heavy Element Complexes

A large set of neptunium compounds with different oxidation states (III to VII) was assembled to study the Mössbauer isomer shift by wave function calculations and better understand covalency in f-elements complexes. The contact density approach was used to calculate the isomer shift using complete active space self-consistent field (CASSCF) multiconfiguration wave functions, as well as matrix product states [from Density Matrix Renormalization Group (DMRG) algorithms] for large active spaces. Dynamic correlation effects for the isomer shifts were treated via CASPT2 energy derivatives with respect to the nuclear radius. The CASSCF calculations appear to produce different orbital overlocalization errors for low and high Np oxidation states. For compounds with low Np oxidation numbers, the errors can be attributed to the overlocalization of the 5f orbitals. For the compounds with high Np oxidation numbers, the main errors arise from an overlocalization of ligand orbitals and concomitant to weak donation bonding. Attempts to mitigate the overlocalization errors with large active spaces using DMRG were only partially successful, showing that explicit treatment of dynamic correlation is necessary for accurate predictions of Mössbauer isomer shifts. The CASPT2 calculations perform very satisfactorily. For a subset of Np compounds, both static and dynamic correlation effects were substantial. A rational active space selection based on orbital entanglement diagrams proved beneficial for determining the optimal reference wave function.

Theoretical Prediction and Interpretation of 237Np Mössbauer Isomer Shifts

Different theoretical approaches for the calculation of ²³⁷Np Mössbauer isomer shifts are investigated. The traditional contact density route is compared to a previously proposed alternative approach that uses energy derivatives with respect to the nuclear radius. Both approaches yield similar results as long as suitable basis sets augmented with large exponents and relativistic methods are used. Density functional theory (DFT) calculations do not show a strong dependency of the ²³⁷Np isomer shift on the chosen functional. Wavefunction calculations show that dynamic electron correlation can be important when covalent bonding influences the isomer shift. Effects from spin-orbit coupling are small. The isomer shifts of ionic solids and Np(III) organometallic complexes are largely governed by the oxidation state of Np. Isomer shifts of organometallic Np(IV) complexes are strongly affected by donation bonding. Detailed analysis of the wavefunction results with different active spaces demonstrates that correlation among the outer core Np and occupied ligand frontier orbitals contributes significantly to isomer shifts of Np(IV) compounds.

Successes, challenges, and opportunities for quantum chemistry in understanding metalloenzymes for solar fuels research

Overview of the rich and diverse contributions of quantum chemistry to understanding the structure and function of the biological archetypes for solar fuel research, photosystem II and hydrogenases.

Scaffold-Based Functional Models of [Fe]-Hydrogenase (Hmd): Building the Bridge between Biological Structure and Molecular Function

The well-known dinuclear [FeFe] and [NiFe] hydrogenase enzymes are redox-based proton reduction and H₂ oxidation catalysts. In comparison, the structural and functional aspects of the mononuclear nonredox hydrogenase, known as [Fe]-hydrogenase or Hmd, have been less explored because of the relatively recent crystallographic elucidation of the enzyme active site. Additionally, the synthetic challenges posed by the highly substituted and asymmetric coordination environment of the iron guanylylpyridinol (FeGP) cofactor have hampered functional biomimetic modeling studies to a large extent. The active site contains an octahedral low-spin Fe(II) center with the following coordination motifs: a bidentate acyl-pyridone moiety (C,N) and cysteinyl-S in a facial arrangement; two cis carbonyl ligands; and a H₂O/H₂ binding site. In [Fe]-hydrogenase, heterolytic H₂ activation putatively by the pendant pyridone/pyridonate-O base serving as a proton acceptor. Following H₂ cleavage, an intermediate Fe-H species is thought to stereoselectively transfer a hydride to the substrate methenyl-H₄MPT⁺, thus forming methylene-H₄MPT. In the past decade, chemists, inspired by the elegant organometallic chemistry inherent to the FeGP cofactor, have synthesized a number of faithful structural models. However, functional systems are still relatively limited and often rely on abiological ligands or metal centers that obfuscate a direct correlation to nature's design.Our group has developed a bioinspired suite of synthetic analogues of Hmd to better understand the effects of structure on the stability and functionality of the Hmd active site, with a special emphasis on using a scaffold-based ligand design. This systematic approach has contributed to a deeper understanding of the unique ligand array of [Fe]-hydrogenase in nature and has ultimately resulted in the first functional synthetic models without the aid of abiological ligands. This Account reviews the reactivity of the functional anthracene-scaffolded synthetic models developed by our group in the context of current mechanistic understanding drawn from both protein crystallography and computational studies. Furthermore, we introduce a novel thermodynamic framework to place the reactivity of our model systems in context and provide an outlook on the future study of [Fe]-hydrogenase synthetic models through both a structural and functional lens.

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.

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.

DFT study of the mechanism of hydrogen evolution catalysed by molecular Ni, Co and Fe catalysts containing a diamine–tripyridine ligand

Electrolysis of water to obtain hydrogen is a practical way to transform surplus electrical power into clean and sustainable hydrogen fuels.

Toward functional type III [Fe]-hydrogenase biomimics for H2 activation: insights from computation

The chemistry of [Fe]-hydrogenase has attracted significant interest due to its ability to activate molecular hydrogen. The intriguing properties of this enzyme have prompted the synthesis of numerous small molecule mimics aimed at activating H2. Despite considerable effort, a majority of these compounds remain nonfunctional for hydrogenation reactions. By using a recently synthesized model as an entry point, seven biomimetic complexes have been examined through DFT computations to probe the influence of ligand environment on the ability of a mimic to bind and split H2. One mimic, featuring a bidentate diphosphine group incorporating an internal nitrogen base, was found to have particularly attractive energetics, prompting a study of the role played by the proton/hydride acceptor necessary to complete the catalytic cycle. Computations revealed an experimentally accessible energetic pathway involving a benzaldehyde proton/hydride acceptor and the most promising catalyst.

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.

Hydrogen-activation mechanism of [Fe] hydrogenase revealed by multi-scale modeling

A complete atomistic model of [Fe] hydrogenase reveals important details of its mechanism.