Calibration of Modern Density Functional Theory Methods for the Prediction of <sup>57</sup>Fe Mössbauer Isomer Shifts: Meta-GGA and Double-Hybrid Functionals

Römelt, Michael; Ye, Shengfa; Neese, Frank

doi:10.1021/ic801535v

Cited by 226 publications

(345 citation statements)

References 33 publications

(21 reference statements)

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“…Also here, we see significant deviations, but systematically on the order of 10%. This feature suggests that a calibration approach similar to that of Neese [24,25] can be employed, thus justifying the use of contact densities for the determination of Mössbauer isomer shifts for elements as heavy as mercury. However, we will demonstrate in the next section that a DFT scheme, such as proposed by Neese [24,25], does not even qualitatively reproduce the trends observed in relative contact densities between the fluorides of mercury.…”

Section: Justification Of the Use Of Contact Densitiesmentioning

confidence: 99%

“…This feature makes it possible to derive corrections that scale non-relativistic contact densities, calculated with a GTO basis set and a point nucleus model, towards the true values. Such a useful pragmatic approach to the isomer shift has been suggested by Neese [24,25] who employed non-relativistic density functional theory to capture valenceshell effects on the contact density, while the difficult-tocapture atomic contributions were absorbed in fit parameters upon parametrization against experimental results.…”

Section: Introductionmentioning

confidence: 99%

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Mössbauer spectroscopy for heavy elements: a relativistic benchmark study of mercury

Knecht

Fux

Meer³

et al. 2011

Theor Chem Acc

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The electrostatic contribution to the Mössbauer isomer shift of mercury for the series HgF n (n = 1, 2, 4) with respect to the neutral atom has been investigated in the framework of four-and two-component relativistic theory. Replacing the integration of the electron density over the nuclear volume by the contact density (that is, the electron density at the nucleus) leads to a 10% overestimation of the isomer shift. The systematic nature of this error suggests that it can be incorporated into a correction factor, thus justifying the use of the contact density for the calculation of the Mössbauer isomer shift. The performance of a large selection of density functionals for the calculation of contact densities has been assessed by comparing with finite-field four-component relativistic coupled-cluster with single and double and perturbative triple excitations [CCSD(T)] calculations. For the absolute contact density of the mercury atom, the Density Functional Theory (DFT) calculations are in error by about 0.5%, a result that must be judged against the observation that the change in contact density along the series HgF n (n = 1, 2, 4), relevant for the isomer shift, is on the order of 50 ppm with respect to absolute densities. Contrary to previous studies of the 57 Fe isomer shift (F Neese, Inorg Chim Acta 332:181, 2002), for mercury, DFT is not able to reproduce the trends in the isomer shift provided by reference data, in our case CCSD(T) calculations, notably the non-monotonous decrease in the contact density along the series HgF n (n = 1, 2, 4). Projection analysis shows the expected reduction of the 6s 1/2 population at the mercury center with an increasing number of ligands, but also brings into light an opposing effect, namely the increasing polarization of the 6s 1/2 orbital due to increasing effective charge of the mercury atom, which explains the nonmonotonous behavior of the contact density along the series. The same analysis shows increasing covalent contributions to bonding along the series with the effective charge of the mercury atom reaching a maximum of around ?2 for HgF 4 at the DFT level, far from the formal charge ?4 suggested by the oxidation state of this recently observed species. Whereas the geometries for the linear HgF 2 and square-planar HgF 4 molecules were taken from previous computational studies, we optimized the equilibrium distance of HgF at the four-component Fock-space CCSD/aug-cc-pVQZ level, giving spectroscopic constants r e = 2.007 Å and x e = 513.5 cm -1 .Dedicated to Professor Pekka Pyykkö on the occasion of his 70th birthday and published as part of the Pyykkö Festschrift Issue.Electronic supplementary material The online version of this article

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Section: Justification Of the Use Of Contact Densitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mössbauer spectroscopy for heavy elements: a relativistic benchmark study of mercury

Knecht

Fux

Meer³

et al. 2011

Theor Chem Acc

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“…7 which led to results similar to quasi-relativistic ZORA calculations. 23,24 The use of effective densities and the inclusion of relativity has also been considered by others and both effects have been shown to be of quantitative importance for heavier nuclei. 25,26 On the contrary, for iron both the role of relativity and the use of effective densities rather than contact densities remains less clear.…”

mentioning

confidence: 99%

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

Hedegård

Knecht

Ryde

et al. 2014

Phys. Chem. Chem. Phys.

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Mössbauer spectroscopy is an indispensable technique and analytical tool in iron coordination chemistry. The linear correlation between the electron density at the nucleus ("contact density") and experimental isomer shifts has been used to link calculated contact densities to experimental isomer shifts. Here we have investigated for the first time relativistic methods of systematically increasing sophistication, including the eXact 2-Component (X2C) Hamiltonian and a finite-nucleus model, for the calculation of isomer shifts for iron compounds.While being of similar accuracy as the full four-component treatment, X2C calculations are far more efficient. We find that effects from spin orbit coupling can safely be neglected, leading to further speed up. Linear correlation plots using effective densities rather than contact densities versus experimental isomer shift leads to a correlation constant a = −0.32 a −3 0 mm s −1 (PBE functional) which is in close agreement to experimental findings. Isomer shifts of similar quality can thus be obtained both with and without fitting, which is not the case if one pursues a priori a non-relativistic model approach. As an application for a biologically relevant system, we have studied three recently proposed [Fe]-hydrogenase intermediates. The structures for these intermediates were extracted from QM/MM calculations using large QM regions surrounded by the full enzyme and a solvation shell of water molecules. We show that a comparison between calculated and experimentally observed isomer shifts can be used to discriminate between the different intermediates, whereas calculated atomic charges do not necessarily correlate with Mössbauer isomer shifts. Detailed analysis shows that the difference in isomer shifts between two intermediates is due to an overlap effect.

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“…[16] The predictions of the quadrupole splitting are remarkably accurate within 0.04 mm s -1 in all cases. These calculations also illustrate the trend discussed in the main text in which lower spin states are associated with low isomer shifts.…”

Section: Ir Spectramentioning

confidence: 72%

A Triad of Highly Reduced, Linear Iron Nitrosyl Complexes: {FeNO}^8–10

Chalkley

Peters

2016

Angewandte Chemie

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Given the importance of Fe–NO complexes in both human biology and the global nitrogen cycle, there has been interest in understanding their diverse electronic structures. Herein a redox series of isolable iron nitrosyl complexes stabilized by a tris(phosphine)borane (TPB) ligand is described. These structurally characterized iron nitrosyl complexes reside in the following highly reduced Enemark–Feltham numbers: {FeNO}8, {FeNO}9, and {FeNO}10. These {FeNO}8–10 compounds are each low‐spin, and feature linear yet strongly activated nitric oxide ligands. Use of Mössbauer, EPR, NMR, UV/Vis, and IR spectroscopy, in conjunction with DFT calculations, provides insight into the electronic structures of this uncommon redox series of iron nitrosyl complexes. In particular, the data collectively suggest that {TPBFeNO}8–10 are all remarkably covalent. This covalency is likely responsible for the stability of this system across three highly reduced redox states that correlate with unusually high Enemark–Feltham numbers.

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Calibration of Modern Density Functional Theory Methods for the Prediction of ⁵⁷Fe Mössbauer Isomer Shifts: Meta-GGA and Double-Hybrid Functionals

Cited by 226 publications

References 33 publications

Mössbauer spectroscopy for heavy elements: a relativistic benchmark study of mercury

Mössbauer spectroscopy for heavy elements: a relativistic benchmark study of mercury

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

A Triad of Highly Reduced, Linear Iron Nitrosyl Complexes: {FeNO}^8–10

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Calibration of Modern Density Functional Theory Methods for the Prediction of 57Fe Mössbauer Isomer Shifts: Meta-GGA and Double-Hybrid Functionals

Cited by 226 publications

References 33 publications

Mössbauer spectroscopy for heavy elements: a relativistic benchmark study of mercury

Mössbauer spectroscopy for heavy elements: a relativistic benchmark study of mercury

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

A Triad of Highly Reduced, Linear Iron Nitrosyl Complexes: {FeNO}8–10

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Calibration of Modern Density Functional Theory Methods for the Prediction of ⁵⁷Fe Mössbauer Isomer Shifts: Meta-GGA and Double-Hybrid Functionals

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

A Triad of Highly Reduced, Linear Iron Nitrosyl Complexes: {FeNO}^8–10