This journal is c the Owner Societies 2013 Phys. Chem. Chem. Phys., 2013, 15, 20911--20920 20911 Cite this: Phys. Chem. Chem. Phys., 2013, 15, 20911 High-resolution molybdenum K-edge X-ray absorption spectroscopy analyzed with time-dependent density functional theory† Frederico A. Lima,zy a Ragnar Bjornsson,y a Thomas Weyhermu ¨ller, a Perumalreddy Chandrasekaran, b Pieter Glatzel, c Frank Neese a and Serena DeBeer* ad X-ray absorption spectroscopy (XAS) is a widely used experimental technique capable of selectively probing the local structure around an absorbing atomic species in molecules and materials. When applied to heavy elements, however, the quantitative interpretation can be challenging due to the intrinsic spectral broadening arising from the decrease in the core–hole lifetime. In this work we have used high-energy resolution fluorescence detected XAS (HERFD-XAS) to investigate a series of molybdenum complexes. The sharper spectral features obtained by HERFD-XAS measurements enable a clear assignment of the features present in the pre-edge region. Time-dependent density functional theory (TDDFT) has been previously shown to predict K-pre-edge XAS spectra of first row transition metal compounds with a reasonable degree of accuracy. Here we extend this approach to molybdenum K-edge HERFD-XAS and present the necessary calibration. Modern pure and hybrid functionals are utilized and relativistic effects are accounted for using either the Zeroth Order Regular Approximation (ZORA) or the second order Douglas–Kroll–Hess (DKH2) scalar relativistic approximations. We have found that both the predicted energies and intensities are in excellent agreement with experiment, independent of the functional used. The model chosen to account for relativistic effects also has little impact on the calculated spectra. This study provides an important calibration set for future applications of molybdenum HERFD- XAS to complex catalytic systems. 1 Introduction Molybdenum is an important element, playing crucial roles in biological and geochemical cycles and catalysis. 1–9 Enzymatic systems which require molybdenum as a cofactor are responsible for catalyzing oxygen transfer reactions, for the metabolism of nitrogen, sulfur and carbon compounds and for intramolecular electron transfer, among other functions. 3,4 X-ray absorption spectroscopy (XAS) provides a selective tool to probe the changes that occur in Mo in a wide range of diverse systems. It is for this reason that Mo K-edge XAS has long been used to characterize the structure of metalloenzymes, catalysts and model compounds. 1,5,9–14 However, the interpretation of the Mo K-edge region has generally been very empirical in nature. This is in contrast to the interpretation of first row transition metal K-edges XAS, in which resolved 1s to 3d pre-edge features allow for quantitative interpretation of the low energy edge region based on ligand field theory and molecular orbital considerations. Recently, we and others have shown that time-dependent density functional theory (TDDFT) approaches can be used with reasonably high accuracy to predict both the energies and intensities of metal (manganese, iron, copper) 15–20 and ligand (chlorine, sulfur) 21–25 K-pre-edge features. We note, however, that the analogous 1s to 4d feature, which corresponds to the lowest unoccupied level on a Mo absorber, is generally absent at the Mo K-edge, as well as all other second row transition metal K-edges. The poor resolution of a standard Mo K-edge XAS spectrum can be understood in terms of the Heisenberg uncertainty principle, which states that the energy uncertainty in the core–hole (created in the photo-absorption process) is inversely proportional to its lifetime. In the case of transition metal a Max-Planck-Institut fu ¨r Chemische Energiekonversion, Stiftstrasse 34-36, D- 45470, Mu ¨lheim an der Ruhr, Germany. E-mail: [email protected]; Fax: +49 (208) 306 3951; Tel: +49 (208) 306 3605 b Department of Chemistry and Biochemistry, Lamar University, Beaumont, TX 77710, USA c European Synchrotron Radiation Facility, 6 Rue Jules Horowitz, 38043 Grenoble Cedex, France d Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA † Electronic supplementary information (ESI) available. See DOI: 10.1039/c3cp53133c ‡ Present address: Centro Nacional de Pesquisa em Energia e Materiais, Brazilian Synchrotron Light Laboratory – LNLS, CP 6192, 13084-971 Campinas, SP, Brazil. § These authors have contributed equally to the work presented in this manuscript. Received 25th July 2013, Accepted 14th October 2013 DOI: 10.1039/c3cp53133c www.rsc.org/pccp PCCP PAPER Published on 07 November 2013. Downloaded by St. Petersburg State University on 01/01/2014 18:58:59. View Article Online View Journal | View Issue
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This journal is c the Owner Societies 2013 Phys. Chem. Chem. Phys., 2013, 15, 20911--20920 20911
Cite this: Phys. Chem.Chem.Phys.,2013,15, 20911
High-resolution molybdenum K-edge X-ray absorptionspectroscopy analyzed with time-dependent densityfunctional theory†
Frederico A. Lima,zya Ragnar Bjornsson,ya Thomas Weyhermuller,a
Perumalreddy Chandrasekaran,b Pieter Glatzel,c Frank Neesea andSerena DeBeer*ad
X-ray absorption spectroscopy (XAS) is a widely used experimental technique capable of selectively
probing the local structure around an absorbing atomic species in molecules and materials. When
applied to heavy elements, however, the quantitative interpretation can be challenging due to the
intrinsic spectral broadening arising from the decrease in the core–hole lifetime. In this work we have
used high-energy resolution fluorescence detected XAS (HERFD-XAS) to investigate a series of molybdenum
complexes. The sharper spectral features obtained by HERFD-XAS measurements enable a clear assignment
of the features present in the pre-edge region. Time-dependent density functional theory (TDDFT) has
been previously shown to predict K-pre-edge XAS spectra of first row transition metal compounds with
a reasonable degree of accuracy. Here we extend this approach to molybdenum K-edge HERFD-XAS
and present the necessary calibration. Modern pure and hybrid functionals are utilized and relativistic
effects are accounted for using either the Zeroth Order Regular Approximation (ZORA) or the second
order Douglas–Kroll–Hess (DKH2) scalar relativistic approximations. We have found that both the
predicted energies and intensities are in excellent agreement with experiment, independent of the
functional used. The model chosen to account for relativistic effects also has little impact on the calculated
spectra. This study provides an important calibration set for future applications of molybdenum HERFD-
XAS to complex catalytic systems.
1 Introduction
Molybdenum is an important element, playing crucial roles inbiological and geochemical cycles and catalysis.1–9 Enzymaticsystems which require molybdenum as a cofactor are responsiblefor catalyzing oxygen transfer reactions, for the metabolism ofnitrogen, sulfur and carbon compounds and for intramolecularelectron transfer, among other functions.3,4 X-ray absorptionspectroscopy (XAS) provides a selective tool to probe the changes
that occur in Mo in a wide range of diverse systems. It is for thisreason that Mo K-edge XAS has long been used to characterize thestructure of metalloenzymes, catalysts and model compounds.1,5,9–14
However, the interpretation of the Mo K-edge region has generallybeen very empirical in nature. This is in contrast to the interpretationof first row transition metal K-edges XAS, in which resolved 1s to 3dpre-edge features allow for quantitative interpretation of the lowenergy edge region based on ligand field theory and molecularorbital considerations. Recently, we and others have shown thattime-dependent density functional theory (TDDFT) approaches canbe used with reasonably high accuracy to predict both the energiesand intensities of metal (manganese, iron, copper)15–20 and ligand(chlorine, sulfur)21–25 K-pre-edge features. We note, however, thatthe analogous 1s to 4d feature, which corresponds to the lowestunoccupied level on a Mo absorber, is generally absent at the MoK-edge, as well as all other second row transition metal K-edges.
The poor resolution of a standard Mo K-edge XAS spectrumcan be understood in terms of the Heisenberg uncertaintyprinciple, which states that the energy uncertainty in thecore–hole (created in the photo-absorption process) is inverselyproportional to its lifetime. In the case of transition metal
a Max-Planck-Institut fur Chemische Energiekonversion, Stiftstrasse 34-36, D- 45470,
Fax: +49 (208) 306 3951; Tel: +49 (208) 306 3605b Department of Chemistry and Biochemistry, Lamar University, Beaumont,
TX 77710, USAc European Synchrotron Radiation Facility, 6 Rue Jules Horowitz,
38043 Grenoble Cedex, Franced Department of Chemistry and Chemical Biology, Cornell University, Ithaca,
New York 14853, USA
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c3cp53133c‡ Present address: Centro Nacional de Pesquisa em Energia e Materiais, BrazilianSynchrotron Light Laboratory – LNLS, CP 6192, 13084-971 Campinas, SP, Brazil.§ These authors have contributed equally to the work presented in this manuscript.
Received 25th July 2013,Accepted 14th October 2013
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K-edge XAS, this means that the energy uncertainty increasesalmost exponentially as a function of the atomic number Z.26,27
This effect leads to a spectral broadening of the near-edge region,which is particularly noticeable in the case of heavy elements, oftenresulting in the absence of fine structure in the pre-edge and edgeregions and thus limiting quantitative spectral interpretation.28
In 1991, Hamalainen et al. proposed a measurement scheme basedon an emission spectrometer which was capable of reducing theapparent broadening in XAS spectra caused by core–hole lifetimeeffects.27 The experiment involves the measurement of the fluores-cent photon intensity as a function of the incident energy. By usinga high-resolution crystal analyzer, it was demonstrated that theresultant spectra are dominated by the core–hole-lifetime of theintermediate state, rather than that of the initial state. This waslater demonstrated theoretically by Tanaka et al.29 For a moredetailed derivation of the lifetime contribution to the HERFD-XASspectrum, we refer the interested reader to ref. 30 and for discus-sions of secondary processes in XAS, including resonant XAS andHERFD-XAS, the reader is referred to ref. 31–33. Since then, manyapplications of the so-called High Energy Resolution FluorescenceDetected XAS (HERFD-XAS) to the study of the electronic structureof materials can be found in the literature.33–44
Herein we focus on the increased pre-edge resolution resultingfrom HERFD Mo K-edge XAS. Molybdenum HERFD-XAS datahave been obtained for a series of structurally characterized Momonomers and dimers, and subsequently interpreted using aTDDFT approach. We note that previous HERFD-XAS studieshave utilized either multiple-scattering based or multiplet-basedapproaches; hence to our knowledge, the present study representsthe first detailed TDDFT study of heavy element HERFD-XAS.The methodology presented here provides a framework forfuture quantitative studies of Mo HERFD-XAS spectra withincomplex catalytic systems.
2 Materials and methods
A total of eight molybdenum complexes were selected to servethe TDDFT calibration presented in this study. These com-pounds were synthesized following published procedures.45–51
The corresponding molecular formulas are listed in Table 1.The following abbreviations have been used for the ligands:L = 1,4,7-triazacyclononane; L0 = 1,4,7-trimethyl-1,4,7-triazacyclo-nonane; Pdt = 1,2-diphenyl-1,2-dithiolate. A schematic represen-tation of the structures of the measured compounds is shownin Fig. 1.
2.1 Sample preparation
XAS samples were finely ground and mixed with boron nitrideto a dilution corresponding to 1–2 absorbances. The sampleswere then pressed in PEEK sample holders with 2 mm pathlength and sealed with 38 mm thick Kapton tape.
2.2 XAS measurements
XAS data were obtained at the ID26 beamline at the EuropeanSynchrotron Radiation Facility (ESRF). The storage ring operatedat 6.04 GeV and 200 mA current. A double-crystal monochromator
with Si(311) crystals was used to select the incoming X-rayenergy. Standard XAS data were collected in transmission andtotal fluorescence yield (TFY) modes. HERFD-XAS data werecollected concomitantly with the standard XAS measurements.The [999] reflection of five Ge(111) crystals from the multi-crystal spectrometer installed at ID26 was used to select theMo Ka emission line (approximately 17.4 keV). The energy resolu-tion of the HERFD-XAS data was estimated to be approximately3.5–4 eV. Energy calibration of the incoming radiation wasperformed prior to the measurements by recording the K-edgetransmission spectrum of a Mo foil and assigning the maximumof the white line to 20 016.4 eV. All samples were maintained atapproximately 40 K using a liquid helium cryostat. The data weremonitored for signs of X-ray damage. During the course of themeasurements no apparent changes in the XANES region of thespectrum were found. Several successive scans (18–20, dependingon the sample) were averaged in order to improve the dataquality. Background subtraction and normalization were per-formed using the ATHENA package.52 Finally, the energy positionand intensity of the pre-edge features were determined by afitting procedure using the Blueprint XAS software.53,54 Detailsof the fitting procedure and the results of the individual fits ofthe pre-edge features up to approximately 50 eV above the edge(Fig. S2–S9) are given in the ESI.†
2.3 Computational details
All DFT calculations presented in this work were performedusing the ORCA program package version 2.9.55 Relativistic effectswere taken into account by either the zeroth-order regular approxi-mation (ZORA)56,57 or the second-order Douglas–Kroll–Hess(DKH2) Hamiltonian58 and relativistically recontracted versions59
of the all-electron Karlsruhe basis sets with polarization functionsfrom the most recent def2 versions60 were used throughout. A setof nine different functionals were used in the calculation of theXAS spectra (see Table 2). All the spectral calculations used denseintegration grids at the molybdenum atom (ORCA GridIntAcc 7).Examples of the ORCA input files are available in the ESI.†
2.3.1 Geometry optimizations. Using the available crystalstructures as a starting point, all-electron ZORA geometry optimiza-tions were carried out for all eight model compounds. They weredone at the RI-BP86/def2-TZVP level (ZORA recontraction and usinga decontracted auxiliary basis set) in the presence of an infinitedielectric using the conductor-like screening model (COSMO)61 andincluding DFT-D3BJ dispersion correction.62,63 No X-ray structureof compound (7) ([MoIV(CO)2(Pdt)2]0) was available.
2.3.2 Calculation of the XAS spectra. TDDFT calculations werecarried out using the Tamm–Dancoff approximation64 as imple-mented in ORCA. Pure functionals used the RI-J approximation,while hybrid functionals used the RIJCOSX approximation,65–67
which considerably speeds up TD-DFT calculations.68,69 Dielectricfield contributions using COSMO (infinite dielectric) were includedin TDDFT calculations as well. Up to 60 roots were calculated(making sure to cover the whole range of transitions in the pre-edgeregion), allowing only for transitions from molybdenum 1s donororbitals. Calculated intensities include electric dipole, magneticdipole and quadrupole contributions.
This journal is c the Owner Societies 2013 Phys. Chem. Chem. Phys., 2013, 15, 20911--20920 20913
3 Results and discussion
The HERFD-XAS spectra of all the eight model compoundsinvestigated in this study are shown in Fig. 2. The formaloxidation state of the compounds, used throughout this work
in their description, varies systematically from III to VI withdiffering coordination environments, thus representing a broadtest set of models to study the contributions of the oxidationstate, the coordination environment and geometry to the XASspectra. As described above, the use of HERFD-XAS as opposed
Table 1 Comparison of the experimental and calculated (BHLYP/DKH2) energies, intensities and areas of the pre-edge peaks in the Mo K-edge HERFD-XAS for theMo compounds (1)–(8) used in the calibration study. A Gaussian broadening of 1.75 eV has been applied to the calculated spectra in order to facilitate theidentification of the transitions and correlation with experiment. A constant shift of 60.9 eV has been applied to the calculated energies
Compound Peaka
Experiment Calculation
Energy (eV) Intensity Ref.b Energyc (eV) Intensity Aread
a Individual peaks as determined by the fit procedure. Ave. refers to the intensity-weighted averaged energy and total intensity of both peaks.b Synthesis and crystallographic structure references. c Intensity-weighted average energies. The calculated energies have been shifted by 60.9 eV tohigher energies. d The predicted experimental areas, Acalc, are obtained from the calculated intensities, Icalc, using the linear regression obtained fromthe fit of the curve shown in Fig. 4, i.e., Icalc = �0.14813 + 2.0554Acalc.
e Peaks in the experimental spectra not included in the correlations.
Fig. 1 Schematic representation of the model compounds investigated in this study.
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to regular TFY- or transmission-detected XAS allows us to obtainhigher resolution XAS spectra – a comparison of standard TFYand HERFD XAS is shown in the next section. The HERFD-XASdata exhibit rich features in the pre-edge and near-edge regions,with the edge position (here defined as the zero crossing of thesecond derivative) spanning an interval of approximately 6.5 eV.
The HERFD-XAS spectra of the molybdenum oxide compounds,i.e., [MoVI(O)3L]0, [MoVI(O)2(OCH3)L0]+ and [MoV(O)(OCH3)2L0]2+
(compounds (1)–(3), respectively) present the strongest pre-edgefeatures, with the most intense peak reaching approximately 0.9normalized units (all the spectra have been normalized to oneabsorber atom such that at the EXAFS region m(E) = IHERFD/I0 = 1).The number of oxo groups in each complex correlates with thepeak intensity at about 20 006 eV. As the geometries of thesethree compounds are similar, all having a distorted octahedralenvironment around the Mo atom, it appears that the pre-edgeintensity is largely mediated through the short, highly covalentMo-oxo bonds which enhance metal 4d–5p mixing via increasedMo–O 4d–2p hybridization.70 Replacement of the oxo group by alonger, less covalent methoxy ligand thus diminishes the observedintensity. The identification of an ‘‘oxo feature’’ in the Mo K pre-edge was first qualitatively observed by Cramer et al.28,71 Later,Kutzler et al. confirmed this observation via polarized XASmeasurements and presented calculations which made theassignment of covalency in a class of molybdates possible.
Kutzler’s analysis inferred the origins of the electronic transi-tions responsible for the pre-edge features in molybdates andmade the correlation of the strength (intensity) and the posi-tion (energy) of the pre-edge features with the bond length.72,73
This approach has been subsequently applied to assess thenumber of oxo groups in both proteins and model complexes,using the second derivative as a fingerprint.74–76 The presentdata indicate that the increased energy resolution of HERFD-XAS data should aid in more quantitative assessments of oxoligand contributions. Additionally, the edge position of com-pounds (1)–(3) varies by approximately 1 eV. This variation iscorrelated to the change in the oxidation state; i.e., for the MoVI
complexes (1) and (2), the edge position is located at 20 014.1 eV,whereas for the MoV compound (3), the edge is at 20 013.2 eV. Thereduced spectral broadening due to HERFD detection greatly aidsin accurate determination of the edge position.
The HERFD-XAS spectra of the molybdenum dithiolene com-plexes [MoIV(OPh)(Pdt)2]1� (compound (6)), [MoIV(CO)2(Pdt)2]0
(compound (7)) and [MoIV(Pdt)3]0 (compound (8)) also showstrong pre-edge features. The peak intensities vary from approxi-mately 0.25 to about 0.5 normalized units and the pre-edgeenergies shift over an B2 eV range. An empirical assessment ofthese trends is complicated by the non-innocent nature of thedithiolene ligands – which may make the Mo effectively morereduced – together with the p-accepting character of the carbonylligands in complex (7) – which would make the metal appear moreoxidized. Nonetheless, it is clear that symmetry factors do con-tribute to the pre-edge intensity, with the 5-coordinate complex (6)having greater pre-edge intensity than either 6-coordinate trigonalprismatic complexes.
The molybdenum dimers present the lowest intensity pre-edges of all the compounds studied, consistent with the approxi-mately octahedral local symmetry. However, despite the fact thatboth compounds are formally MoIII, there are differences inboth the energies and intensities. Namely the pre-edge ofcompound (4) appears at higher energy and has greater inten-sity than that of complex (5). This can be understood in part bya more careful analysis of the structures. The Mo–Mo distance incompound (4) (2.715 Å) is notably smaller than in the protonatedcompound (5) (3.521 Å), suggesting a bonding interaction in the
Table 2 Computational protocol used in the calculation of the XAS spectra inthe present work
Functional Basis set Structure Rel. approx. Solvation
Fig. 2 HERFD-XAS of the model compounds investigated in this work. The XANES region showing the presence of well defined pre-edge features and sharpresonances above the edge (a) and zoom in the pre-edge region (b). The edge position varies by approximately 6.5 eV across the series.
This journal is c the Owner Societies 2013 Phys. Chem. Chem. Phys., 2013, 15, 20911--20920 20915
former case.48 The average Mo–Ooxo bond lengths in (4) (1.941 Å)are also notably smaller than the Mo–Ohydroxo bond lengths in (5)(2.135 Å). This should give rise to an increase in Mo–Ooxo
covalency providing a mechanism for increased Mo 4p–5d mixingand thus the greater pre-edge intensity in the pre-edge ofcompound (4) relative to (5). A more quantitative analysis ofthese assessments will follow in the computational section.
3.1 HERFD vs. TFY
Fig. 3 shows a comparison of the XAS spectra of compounds (1)and (4) collected using HERFD and TFY detection. Only twomodel compounds are used here to illustrate the effect ofincreased energy resolution in the HERFD-XAS. However, thesame conclusions apply for all models investigated. Fig. 3 alsoshows the first and second spectral derivatives, the lattersmoothed by a three-point binomial algorithm in order toobtain a better definition of the peaks.
The XAS of compound (1) exhibits a strong pre-edge featurewhich is clearly observed in both spectra recorded usingHERFD and TFY. The energy position of the pre-edge and therising edge can be estimated by inspecting the spectral deriva-tives. In the pre-edge region two minima separated by almost4 eV are observed in the second derivative of the HERFD-XASspectrum, indicating that the pre-edge is actually composed oftwo features. Despite a clear asymmetry visible in the TFY data,the second derivative does not clearly indicate the position ofthe first peak. This translates in a large uncertainty in theenergy position of this feature, which can lead to ambiguousinterpretation. In addition, all the features in the XANES regionare suppressed in the TFY data. In the case of the XAS ofcompound (4) the interpretation of the near-edge region ismore prone to ambiguity due to the relatively weak pre-edgefeature. The HERFD-XAS spectrum shows a clear feature ataround 20 003.5 eV, which is confirmed by the single minimumin the second derivative. The TFY spectrum of this model doesnot show any clear feature in the pre-edge and even analyzingthe derivatives can be misleading. Moreover, the XANES region
lacks the fine structure found in the HERFD-XAS spectrum.The comparison between the XAS of the Mo-based compoundsstudied here collected using HERFD and TFY is relevantto show that using high-energy resolution is important inorder to extract accurate quantitative information from thespectra. The determination of the Mo-oxo coordination numberdiscussed above represents just one example. Further, thespectral sharpening obtained by HERFD-XAS measurementsis essential for a more quantitative assessments of the pre-edgeregion using computational approaches, as detailed in the nextsection.
3.2 TDDFT calibration
The experimental intensities and energies of the molybdenumHERFD-XAS K-pre-edge features of the eight studied com-pounds are reported in Table 1. Also listed are the corre-sponding calculated parameters using the BHLYP functionalfollowing the computational model described in Section 2.3.A table containing the calculated parameters using the otherfunctionals employed in this study can be found in the ESI†(Table S1). Fig. 4 shows the correlations between the experi-mental and calculated energies and intensities. To produce thecorrelations only peaks originating from transitions whichcould clearly be assigned as belonging to the pre-edge region,i.e., transitions with significant acceptor d-character, weretaken into account. Peaks due mainly to transitions with themetal-to-ligand or the metal-to-metal charge transfer (MLCTand MMCT, respectively) origin were not included in thecorrelations as these have been previously shown to dependentstrongly on the amount of Hartree–Fock (HF) exchange presentin a specific functional.17 The calculated energies are intensity-weighted average values. The reported intensities are the sumof the squares of transition moments – electric dipole, magneticdipole and electric quadrupole – of all states contributing to agiven pre-edge feature. Calculated intensities were determinedafter application of a Gaussian broadening of 1.75 eV, mainly tohelp in the identification of the transitions present in the
Fig. 3 Comparison of the molybdenum K-edge XAS spectra of compounds (1) and (4) measured using HERFD and TFY modes. Normalized spectra (top), firstderivatives (middle) and second derivatives (bottom).
20916 Phys. Chem. Chem. Phys., 2013, 15, 20911--20920 This journal is c the Owner Societies 2013
spectra and to correlate individual peaks derived from the fitprocedure in the experimental data and groups of transitionsin the calculated spectra. This, however, does not affect thecalculated energies of the transitions since changing thebroadening results only in constant scaling of the intensities.However, the visual comparison between the predicted andexperimental spectra is more realistic when using a larger valuefor the broadening. Based on the estimate of the experimentalresolution, we have used a broadening of 3.5 eV for plotting the
calculated spectra. The relationship between calculated inten-sity and oscillator strength is given by:
I ¼ cX
f edosc
� �2þ f mdosc
� �2þ f eqosc
� �2
c ¼ 1
4:33� 10�91ffiffiffipp 2
ffiffiffiffiffiffiffiffiln 2p
FWHM
(1)
in which FWHM is the full-width-half-maximum of the Gaussianbroadening applied to the spectrum.
Fig. 4 Correlations between the experimental and calculated Mo K-pre-edge intensity-weighted average energies (a) and intensities (b) obtained using the BHLYPfunctional. The linear least-square fits result in the following relations: Ecal = 953.7 + 0.949(Eexp) and Intcal = �0.148 + 2.055(Intexp).
Fig. 5 Experimental (top) and calculated (bottom) Mo K-pre-edge of the various compounds investigated in this study. For clarity, the plots show the measuredHERFD-XAS spectra subtracted from all the contributions except the pre-edge features (derived from the fits). The calculations used the BHLYP functional with DKH2relativity correction. A constant shift of 60.9 eV and a broadening of 3.5 eV were applied to all calculated spectra. The calculations using other functionals producesimilar results.
This journal is c the Owner Societies 2013 Phys. Chem. Chem. Phys., 2013, 15, 20911--20920 20917
It has been previously established that a constant shiftneeds to be applied to the calculated energies in order toaccount for many of the systematic errors inherent to presentdensity functional approximations, as well as due to basis setincompleteness and use of different relativistic approxima-tions.15–17,21,22 The magnitude of the shift is dependent onthe specific computational protocol employed, thus it needs tobe determined for each individual combination of functional,basis set and relativistic correction. In the case of the BHLYPfunctional the value for the average energy shift was deter-mined to be 60.9 � 0.8 eV. As can be seen in Fig. 4, bothcalculated energies and intensities show a linear relationshipwith respect to the experimental values, with correlation con-stants RE = 0.936 and RInt = 0.961. To attest the quality of theTDDFT prediction of the K pre-edge spectra it is useful tovisually inspect the experimental data with calculations. Herewe opt for showing the experimental data subtracted from allthe contributions except the pre-edge features of interest. Fig. 5shows the comparison of the experimental (top) and calculated(bottom) pre-edges of the compounds investigated in thisstudy, evidencing the excellent agreement between the experi-ment and calculation. For clarity, the spectra from the mono-mers (compounds (1), (2), (3), (6), (7) and (8)) are plottedseparately from those of the dimers (compounds (4) and (5)).
A complete comparison between the experimental and cal-culated spectra of all the other functionals used in this work(see Table 2) can be found in the ESI.† Similar to our resultsusing the BHLYP functional presented here, our calculationsusing other functionals were able to accurately reproduce themeasured spectra, both in terms of energies and intensities.Fig. 6 shows the predicted energies and intensities of all eightcompounds using different functionals. The energies of theHERFD-XAS pre-edge features of all eight investigated com-pounds are well reproduced, independently of the functionalused. The smallest uncertainty in the energy is found whenusing the revTPSSh functional (0.56 eV) and the largest one whenusing the PBE functional (0.92 eV). A table with the averageenergy shift and their corresponding standard deviations is givenin Table S1 in the ESI.† Similarly, the predicted intensities do notshow a strong dependence on the functional used in the calcula-tions. With the exception of compound (5) which has the lowestintensity pre-edge of the whole series, the relative variation of thecalculated pre-edge intensities of all the other compounds is lessthan 12%. For the compounds with strong pre-edges features,e.g., compounds (1) or (6), it is as low as 4%.
Often, the overall K pre-edge spectral shape and intensity arerelated to the geometric and electronic structures of transitionmetal compounds.15–17 The strong agreement between theoryand experiment thus serves as a means of experimentallyvalidating a given electronic structure. In general terms, mostof the transitions in the pre-edge region are dominated byelectric dipole contributions, with a few weak ones havingpredominant electric quadrupole character. These transitionsgain intensity due to the covalently mediated metal p + dmixing and also by symmetry distortions. Interestingly, in thecase of compound (4) we observe a calculated (BHLYP/DKH2)
strong transition at ca. 20 006 eV which can be described as dueto metal-to-metal charge transfer (MMCT). The presence ofMMCT transitions in (4) but not in (5) may be attributed tothe presence of a metal–metal bond in the former, but not inthe latter. However, as noted previously by Roemelt et al.17 thecalculated energy at which these charge transfer transitionsoccur depends on the system under investigation and theamount of HF in the functional used. Therefore, caution mustbe exercised in ascribing this feature to a direct MMCT feature.
3.3 Relativistic effects
The effects of the relativistic corrections on the calculatedTDDFT spectra were tested by calculating the spectra usingeither DKH2 or ZORA relativistic approximations, or withoutinclusion of relativistics, as described in Section 2.3. At theBP86 and B3LYP levels, calculations using either ZORA orDKH2 corrections nicely reproduced the experimental spectra.As expected, the calculated absolute energies of the transitionsin the pre-edge region vary depending on the relativistic correc-tion applied. However, the important parameter in a TDDFTcalibration is the uncertainty in the energy shift and notthe absolute magnitude. Using the BP86 functional in combi-nation with DKH2 correction resulted in slightly better pre-dicted absolute energies and a smaller energy shift uncertainty
Fig. 6 Calculated standard deviations in the energy shift for each functional(top) and relative intensity variation for each compound (bottom) of the transi-tions in the pre-edge region. The intensities are obtained from the peaks withtransitions containing dominant acceptor d-character, as detailed in Section 3.2.A broadening of 1.75 eV was applied to the calculation. The energy shift for eachfunctional is listed in Table S1 in the ESI.†
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as compared with BP86/ZORA combination (DEDKH2 ¼
210:13� 0:68 eV with a correlation constant RE = 0.947, and
DEZORA ¼ � 285:45� 0:74 eV with RE = 0.937). In both cases,
the error in the calculated intensities was the same (RInt =0.967). When using the B3LYP functional the situation isdifferent. The use of ZORA to account for relativity, despite stillresulting in worse absolute transition energies, provides thesmallest energy shift uncertainty compared to the calculations
using DKH2 correction (DEDKH2 ¼ 152:86� 0:64 eV with a corre-
lation constant RE = 0.954, and DEZORA ¼ � 342:79� 0:58 eV
with RE = 0.963). As in the case of the BP86 functional, thetransition intensities calculated using B3LYP are predicted to thesame accuracy independent of the relativistic correction modelemployed (RInt = 0.963).
Surprisingly, when excluding the relativistic correction, ourcalculations still reasonably reproduced the experimental spectra.Using the BP86 functional and no relativistic correction the
average energy shift is DEno-rel ¼ 672:54� 0:68 eV, with a corre-
lation constant RE = 0.947. This uncertainty in the energy shift iscomparable to the ones using either ZORA or DKH2 to accountfor relativity. In this case, the error in the prediction of thetransition intensities (RInt = 0.972) is also comparable with theones using either relativistic correction. Contrary to the resultsreported previously for the case of iron K-edge spectra,15 ourcalculated molybdenum K- pre-edge HERFD-XAS spectra do notdepend strongly on the relativistic model employed.
4 Conclusions
In this work, we have presented experimental HERFD-XAS datafor a series of Mo complexes. The enhanced energy resolutionallows for better resolved pre-edge features, which have beencorrelated to the oxidation state, the ligation environment andgeometry. The better resolution also allows the Mo K-edge datato be quantitatively interpreted within a TDDFT framework.Our results show linear correlation between the experimentaland calculated energies and intensities. The effects of differentfunctionals and relativistic corrections have been investigated.We have found a general good agreement between the experi-mental and calculated Mo HERFD-XAS spectra, independent ofthe functional used. Accounting for the effects of relativity inthe spectra by either the ZORA or DKH2 approximations leadsto equivalent results, after calibration.
The present work extends the application of previous TDDFTmethodology for the calculation of pre K-edge XAS15–17,21,22
to the second transition series of metal complexes, and inparticular to high-energy resolution XAS data. The improvedinformation provided by the combination of HERFD-XASexperiments and TDDFT calculations should allow for a morequantitative interpretation of the near-edge region of K-edgeXAS spectra of all compounds containing heavy elements. Thepresent calibration sets the foundations for future studies ofMo in complex systems. This is of particular interest forbiological and chemical systems where the Mo may play a
functional role in catalysis. Furthermore, the same protocolspresented here should be readily extendable to the rest of thesecond or even third transition series.
Acknowledgements
The authors acknowledge the European Synchrotron RadiationFacility (ESRF) and the ID26 staff for the technical assistanceduring the experiments. SD and FN acknowledge the MaxPlanck Society for funding. SD also acknowledges the SloanFoundation for a fellowship.
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