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High-resolution molybdenum K-edge X-ray absorption spectroscopy analyzed with time-dependent density functional theory† Frederico A. Lima,zya Ragnar Bjornsson,ya Thomas Weyhermu ¨ ller,a b c Perumalreddy Chandrasekaran, Pieter Glatzel, Frank Neesea 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
Received 25th July 2013, Accepted 14th October 2013
order Douglas–Kroll–Hess (DKH2) scalar relativistic approximations. We have found that both the
DOI: 10.1039/c3cp53133c
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-
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XAS to complex catalytic systems.
predicted energies and intensities are in excellent agreement with experiment, independent of the
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 a
¨r Chemische Energiekonversion, Stiftstrasse 34-36, D- 45470, Max-Planck-Institut fu ¨lheim an der Ruhr, Germany. E-mail: [email protected]; Mu 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.
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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
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K-edge XAS, this means that the energy uncertainty increases almost 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, often resulting in the absence of fine structure in the pre-edge and edge regions and thus limiting quantitative spectral interpretation.28 ¨ma ¨la ¨inen et al. proposed a measurement scheme based In 1991, Ha on an emission spectrometer which was capable of reducing the apparent broadening in XAS spectra caused by core–hole lifetime effects.27 The experiment involves the measurement of the fluorescent photon intensity as a function of the incident energy. By using a high-resolution crystal analyzer, it was demonstrated that the resultant spectra are dominated by the core–hole-lifetime of the intermediate state, rather than that of the initial state. This was later demonstrated theoretically by Tanaka et al.29 For a more detailed derivation of the lifetime contribution to the HERFD-XAS spectrum, we refer the interested reader to ref. 30 and for discussions of secondary processes in XAS, including resonant XAS and HERFD-XAS, the reader is referred to ref. 31–33. Since then, many applications of the so-called High Energy Resolution Fluorescence Detected XAS (HERFD-XAS) to the study of the electronic structure of materials can be found in the literature.33–44 Herein we focus on the increased pre-edge resolution resulting from HERFD Mo K-edge XAS. Molybdenum HERFD-XAS data have been obtained for a series of structurally characterized Mo monomers and dimers, and subsequently interpreted using a TDDFT approach. We note that previous HERFD-XAS studies have utilized either multiple-scattering based or multiplet-based approaches; hence to our knowledge, the present study represents the first detailed TDDFT study of heavy element HERFD-XAS. The methodology presented here provides a framework for future quantitative studies of Mo HERFD-XAS spectra within complex catalytic systems.
2 Materials and methods A total of eight molybdenum complexes were selected to serve the TDDFT calibration presented in this study. These compounds 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; L 0 = 1,4,7-trimethyl-1,4,7-triazacyclononane; Pdt = 1,2-diphenyl-1,2-dithiolate. A schematic representation of the structures of the measured compounds is shown in Fig. 1. 2.1
Sample preparation
XAS samples were finely ground and mixed with boron nitride to a dilution corresponding to 1–2 absorbances. The samples were then pressed in PEEK sample holders with 2 mm path length and sealed with 38 mm thick Kapton tape. 2.2
XAS measurements
XAS data were obtained at the ID26 beamline at the European Synchrotron Radiation Facility (ESRF). The storage ring operated at 6.04 GeV and 200 mA current. A double-crystal monochromator
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with Si(311) crystals was used to select the incoming X-ray energy. Standard XAS data were collected in transmission and total fluorescence yield (TFY) modes. HERFD-XAS data were collected concomitantly with the standard XAS measurements. The [999] reflection of five Ge(111) crystals from the multicrystal spectrometer installed at ID26 was used to select the Mo Ka emission line (approximately 17.4 keV). The energy resolution of the HERFD-XAS data was estimated to be approximately 3.5–4 eV. Energy calibration of the incoming radiation was performed prior to the measurements by recording the K-edge transmission spectrum of a Mo foil and assigning the maximum of the white line to 20 016.4 eV. All samples were maintained at approximately 40 K using a liquid helium cryostat. The data were monitored for signs of X-ray damage. During the course of the measurements no apparent changes in the XANES region of the spectrum were found. Several successive scans (18–20, depending on the sample) were averaged in order to improve the data quality. Background subtraction and normalization were performed using the ATHENA package.52 Finally, the energy position and intensity of the pre-edge features were determined by a fitting procedure using the Blueprint XAS software.53,54 Details of the fitting procedure and the results of the individual fits of the 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 performed using the ORCA program package version 2.9.55 Relativistic effects were taken into account by either the zeroth-order regular approximation (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 functions from the most recent def2 versions60 were used throughout. A set of nine different functionals were used in the calculation of the XAS spectra (see Table 2). All the spectral calculations used dense integration 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 crystal structures as a starting point, all-electron ZORA geometry optimizations were carried out for all eight model compounds. They were done at the RI-BP86/def2-TZVP level (ZORA recontraction and using a decontracted auxiliary basis set) in the presence of an infinite dielectric using the conductor-like screening model (COSMO)61 and including DFT-D3BJ dispersion correction.62,63 No X-ray structure of compound (7) ([MoIV(CO)2(Pdt)2]0) was available. 2.3.2 Calculation of the XAS spectra. TDDFT calculations were carried out using the Tamm–Dancoff approximation64 as implemented 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 Dielectric field contributions using COSMO (infinite dielectric) were included in TDDFT calculations as well. Up to 60 roots were calculated (making sure to cover the whole range of transitions in the pre-edge region), allowing only for transitions from molybdenum 1s donor orbitals. Calculated intensities include electric dipole, magnetic dipole and quadrupole contributions.
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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 the Mo 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 the identification of the transitions and correlation with experiment. A constant shift of 60.9 eV has been applied to the calculated energies
Experiment Energy (eV)
Intensity
Ref.b
Energyc (eV)
Intensity
Aread
(1) – [LMo (O)3]
1 2 Ave.
20 004.0 20 006.5 20 006.0
0.490 2.232 2.722
45
20 003.4 20 006.6 20 006.4
0.249 5.143 5.392
0.193 2.574 2.696
(2) – [L 0 MoVI(O)2(OCH3)](PF6)
1 2 Ave.
20 004.4 20 006.8 20 006.2
0.525 1.649 2.174
46 and 47
20 003.3 20 006.7 20 006.4
0.382 4.379 4.761
0.258 2.203 2.389
(3) – [L 0 MoV(O)(OCH3)2](PF6)
1 2 Ave.
20 003.6 20 005.8 20 005.3
0.320 1.104 1.424
47
20 002.4 20 005.4 20 005.3
0.171 3.280 3.451
0.155 1.668 1.751
(4) – [L 0 (MoIII)(m-O)(m-OAc)2(MoIII)L 0 ](PF6)2
1 2e Ave.e
20 003.4 20 007.1 20 004.3
0.445 0.146 0.592
48
20 000.4 20 002.5 20 002.3
0.041 0.361 0.402
0.092 0.248 0.267
(5) – [L 0 (MoIII)(m-OH)(m-OAc)(MoIII)(L 0 )](PF6)3
1 2 Ave.
20 000.2 20 002.3 20 001.6
0.075 0.100 0.175
48
20 000.3 20 002.3 20 001.5
0.039 0.057 0.095
0.091 0.100 0.118
(6) – [MoIV(OPh)(Pdt)2](NEt4)
1 2e Ave.e
20 002.9 20 005.7 20 003.5
1.732 0.456 2.188
49
20 001.8 — 20 001.8
2.351 — 2.351
1.216 — 1.216
(7) – [MoIV(CO)2(Pdt)2]
1 2 Ave.
20 001.3 20 003.7 20 001.4
0.580 0.029 0.609
20 002.1 — 20 002.1
1.188 — 1.188
0.650 — 0.650
(8) – [MoVI(Pdt)3]
1 2 Ave.
20 001.0 — 20 001.0
0.511 — 0.511
20 002.0 — 20 002.0
1.304 — 1.304
0.706 — 0.706
VI
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Calculation
Peaka
Compound
51
a
Individual peaks as determined by the fit procedure. Ave. refers to the intensity-weighted averaged energy and total intensity of both peaks. Synthesis and crystallographic structure references. c Intensity-weighted average energies. The calculated energies have been shifted by 60.9 eV to higher energies. d The predicted experimental areas, Acalc, are obtained from the calculated intensities, Icalc, using the linear regression obtained from the 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. b
Fig. 1
Schematic representation of the model compounds investigated in this study.
3 Results and discussion The HERFD-XAS spectra of all the eight model compounds investigated in this study are shown in Fig. 2. The formal oxidation state of the compounds, used throughout this work
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in their description, varies systematically from III to VI with differing coordination environments, thus representing a broad test set of models to study the contributions of the oxidation state, the coordination environment and geometry to the XAS spectra. As described above, the use of HERFD-XAS as opposed
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Table 2 Computational protocol used in the calculation of the XAS spectra in the present work
Functional
Basis set
Structure
Rel. approx.
Solvation
BP86
TZVP TZVP TZVP TZVP TZVP TZVP TZVP TZVP TZVP TZVP TZVP TZVP TZVP
X-ray Optimized Optimized Optimized Optimized Optimized Optimized Optimized Optimized Optimized Optimized Optimized Optimized
DKH2 DKH2 ZORA None DKH2 ZORA ZORA ZORA ZORA ZORA ZORA ZORA ZORA
COSMO COSMO COSMO COSMO COSMO COSMO COSMO COSMO COSMO COSMO COSMO COSMO COSMO
B3LYP PBE PBE0 TPSS TPSSh revTPSS revTPSSh BHLYP
to regular TFY- or transmission-detected XAS allows us to obtain higher resolution XAS spectra – a comparison of standard TFY and HERFD XAS is shown in the next section. The HERFD-XAS data exhibit rich features in the pre-edge and near-edge regions, with the edge position (here defined as the zero crossing of the second 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-edge features, with the most intense peak reaching approximately 0.9 normalized units (all the spectra have been normalized to one absorber atom such that at the EXAFS region m(E) = IHERFD/I0 = 1). The number of oxo groups in each complex correlates with the peak intensity at about 20 006 eV. As the geometries of these three compounds are similar, all having a distorted octahedral environment around the Mo atom, it appears that the pre-edge intensity is largely mediated through the short, highly covalent Mo-oxo bonds which enhance metal 4d–5p mixing via increased Mo–O 4d–2p hybridization.70 Replacement of the oxo group by a longer, less covalent methoxy ligand thus diminishes the observed intensity. The identification of an ‘‘oxo feature’’ in the Mo K preedge was first qualitatively observed by Cramer et al.28,71 Later, Kutzler et al. confirmed this observation via polarized XAS measurements and presented calculations which made the assignment of covalency in a class of molybdates possible.
Kutzler’s analysis inferred the origins of the electronic transitions responsible for the pre-edge features in molybdates and made the correlation of the strength (intensity) and the position (energy) of the pre-edge features with the bond length.72,73 This approach has been subsequently applied to assess the number of oxo groups in both proteins and model complexes, using the second derivative as a fingerprint.74–76 The present data indicate that the increased energy resolution of HERFDXAS data should aid in more quantitative assessments of oxo ligand contributions. Additionally, the edge position of compounds (1)–(3) varies by approximately 1 eV. This variation is correlated 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. The reduced spectral broadening due to HERFD detection greatly aids in accurate determination of the edge position. The HERFD-XAS spectra of the molybdenum dithiolene complexes [MoIV(OPh)(Pdt)2]1 (compound (6)), [MoIV(CO)2(Pdt)2]0 (compound (7)) and [MoIV(Pdt)3]0 (compound (8)) also show strong pre-edge features. The peak intensities vary from approximately 0.25 to about 0.5 normalized units and the pre-edge energies shift over an B2 eV range. An empirical assessment of these trends is complicated by the non-innocent nature of the dithiolene ligands – which may make the Mo effectively more reduced – together with the p-accepting character of the carbonyl ligands in complex (7) – which would make the metal appear more oxidized. Nonetheless, it is clear that symmetry factors do contribute to the pre-edge intensity, with the 5-coordinate complex (6) having greater pre-edge intensity than either 6-coordinate trigonal prismatic complexes. The molybdenum dimers present the lowest intensity preedges of all the compounds studied, consistent with the approximately octahedral local symmetry. However, despite the fact that both compounds are formally MoIII, there are differences in both the energies and intensities. Namely the pre-edge of compound (4) appears at higher energy and has greater intensity than that of complex (5). This can be understood in part by a more careful analysis of the structures. The Mo–Mo distance in compound (4) (2.715 Å) is notably smaller than in the protonated compound (5) (3.521 Å), suggesting a bonding interaction in the
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 sharp resonances above the edge (a) and zoom in the pre-edge region (b). The edge position varies by approximately 6.5 eV across the series.
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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 mixing and thus the greater pre-edge intensity in the pre-edge of compound (4) relative to (5). A more quantitative analysis of these 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 two model compounds are used here to illustrate the effect of increased energy resolution in the HERFD-XAS. However, the same conclusions apply for all models investigated. Fig. 3 also shows the first and second spectral derivatives, the latter smoothed by a three-point binomial algorithm in order to obtain a better definition of the peaks. The XAS of compound (1) exhibits a strong pre-edge feature which is clearly observed in both spectra recorded using HERFD and TFY. The energy position of the pre-edge and the rising edge can be estimated by inspecting the spectral derivatives. In the pre-edge region two minima separated by almost 4 eV are observed in the second derivative of the HERFD-XAS spectrum, indicating that the pre-edge is actually composed of two features. Despite a clear asymmetry visible in the TFY data, the second derivative does not clearly indicate the position of the first peak. This translates in a large uncertainty in the energy position of this feature, which can lead to ambiguous interpretation. In addition, all the features in the XANES region are suppressed in the TFY data. In the case of the XAS of compound (4) the interpretation of the near-edge region is more prone to ambiguity due to the relatively weak pre-edge feature. The HERFD-XAS spectrum shows a clear feature at around 20 003.5 eV, which is confirmed by the single minimum in the second derivative. The TFY spectrum of this model does not show any clear feature in the pre-edge and even analyzing the 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 compounds studied here collected using HERFD and TFY is relevant to show that using high-energy resolution is important in order to extract accurate quantitative information from the spectra. The determination of the Mo-oxo coordination number discussed above represents just one example. Further, the spectral sharpening obtained by HERFD-XAS measurements is essential for a more quantitative assessments of the pre-edge region using computational approaches, as detailed in the next section. 3.2
TDDFT calibration
The experimental intensities and energies of the molybdenum HERFD-XAS K-pre-edge features of the eight studied compounds are reported in Table 1. Also listed are the corresponding calculated parameters using the BHLYP functional following the computational model described in Section 2.3. A table containing the calculated parameters using the other functionals employed in this study can be found in the ESI† (Table S1). Fig. 4 shows the correlations between the experimental and calculated energies and intensities. To produce the correlations only peaks originating from transitions which could clearly be assigned as belonging to the pre-edge region, i.e., transitions with significant acceptor d-character, were taken into account. Peaks due mainly to transitions with the metal-to-ligand or the metal-to-metal charge transfer (MLCT and MMCT, respectively) origin were not included in the correlations as these have been previously shown to dependent strongly on the amount of Hartree–Fock (HF) exchange present in a specific functional.17 The calculated energies are intensityweighted average values. The reported intensities are the sum of the squares of transition moments – electric dipole, magnetic dipole and electric quadrupole – of all states contributing to a given pre-edge feature. Calculated intensities were determined after application of a Gaussian broadening of 1.75 eV, mainly to help 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), first derivatives (middle) and second derivatives (bottom).
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Fig. 4 Correlations between the experimental and calculated Mo K-pre-edge intensity-weighted average energies (a) and intensities (b) obtained using the BHLYP functional. The linear least-square fits result in the following relations: Ecal = 953.7 + 0.949(Eexp) and Intcal = 0.148 + 2.055(Intexp).
spectra and to correlate individual peaks derived from the fit procedure in the experimental data and groups of transitions in the calculated spectra. This, however, does not affect the calculated energies of the transitions since changing the broadening results only in constant scaling of the intensities. However, the visual comparison between the predicted and experimental spectra is more realistic when using a larger value for the broadening. Based on the estimate of the experimental resolution, we have used a broadening of 3.5 eV for plotting the
calculated spectra. The relationship between calculated intensity and oscillator strength is given by: X 2 eq 2 ed md 2 I ¼c fosc þ fosc þ fosc c¼
pffiffiffiffiffiffiffiffi 1 1 2 ln 2 p ffiffiffi 4:33 109 p FWHM
(1)
in which FWHM is the full-width-half-maximum of the Gaussian broadening applied to the spectrum.
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 measured HERFD-XAS spectra subtracted from all the contributions except the pre-edge features (derived from the fits). The calculations used the BHLYP functional with DKH2 relativity 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 produce similar results.
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It has been previously established that a constant shift needs to be applied to the calculated energies in order to account for many of the systematic errors inherent to present density functional approximations, as well as due to basis set incompleteness and use of different relativistic approximations.15–17,21,22 The magnitude of the shift is dependent on the specific computational protocol employed, thus it needs to be determined for each individual combination of functional, basis set and relativistic correction. In the case of the BHLYP functional the value for the average energy shift was determined to be 60.9 0.8 eV. As can be seen in Fig. 4, both calculated energies and intensities show a linear relationship with respect to the experimental values, with correlation constants RE = 0.936 and RInt = 0.961. To attest the quality of the TDDFT prediction of the K pre-edge spectra it is useful to visually inspect the experimental data with calculations. Here we opt for showing the experimental data subtracted from all the contributions except the pre-edge features of interest. Fig. 5 shows the comparison of the experimental (top) and calculated (bottom) pre-edges of the compounds investigated in this study, evidencing the excellent agreement between the experiment and calculation. For clarity, the spectra from the monomers (compounds (1), (2), (3), (6), (7) and (8)) are plotted separately from those of the dimers (compounds (4) and (5)). A complete comparison between the experimental and calculated spectra of all the other functionals used in this work (see Table 2) can be found in the ESI.† Similar to our results using the BHLYP functional presented here, our calculations using other functionals were able to accurately reproduce the measured spectra, both in terms of energies and intensities. Fig. 6 shows the predicted energies and intensities of all eight compounds using different functionals. The energies of the HERFD-XAS pre-edge features of all eight investigated compounds are well reproduced, independently of the functional used. The smallest uncertainty in the energy is found when using the revTPSSh functional (0.56 eV) and the largest one when using the PBE functional (0.92 eV). A table with the average energy shift and their corresponding standard deviations is given in Table S1 in the ESI.† Similarly, the predicted intensities do not show a strong dependence on the functional used in the calculations. With the exception of compound (5) which has the lowest intensity pre-edge of the whole series, the relative variation of the calculated pre-edge intensities of all the other compounds is less than 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 are related to the geometric and electronic structures of transition metal compounds.15–17 The strong agreement between theory and experiment thus serves as a means of experimentally validating a given electronic structure. In general terms, most of the transitions in the pre-edge region are dominated by electric dipole contributions, with a few weak ones having predominant electric quadrupole character. These transitions gain intensity due to the covalently mediated metal p + d mixing and also by symmetry distortions. Interestingly, in the case of compound (4) we observe a calculated (BHLYP/DKH2)
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Fig. 6 Calculated standard deviations in the energy shift for each functional (top) and relative intensity variation for each compound (bottom) of the transitions in the pre-edge region. The intensities are obtained from the peaks with transitions 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 each functional is listed in Table S1 in the ESI.†
strong transition at ca. 20 006 eV which can be described as due to metal-to-metal charge transfer (MMCT). The presence of MMCT transitions in (4) but not in (5) may be attributed to the presence of a metal–metal bond in the former, but not in the latter. However, as noted previously by Roemelt et al.17 the calculated energy at which these charge transfer transitions occur depends on the system under investigation and the amount of HF in the functional used. Therefore, caution must be exercised in ascribing this feature to a direct MMCT feature. 3.3
Relativistic effects
The effects of the relativistic corrections on the calculated TDDFT spectra were tested by calculating the spectra using either DKH2 or ZORA relativistic approximations, or without inclusion of relativistics, as described in Section 2.3. At the BP86 and B3LYP levels, calculations using either ZORA or DKH2 corrections nicely reproduced the experimental spectra. As expected, the calculated absolute energies of the transitions in the pre-edge region vary depending on the relativistic correction applied. However, the important parameter in a TDDFT calibration is the uncertainty in the energy shift and not the absolute magnitude. Using the BP86 functional in combination with DKH2 correction resulted in slightly better predicted absolute energies and a smaller energy shift uncertainty
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as compared with BP86/ZORA combination (DE ¼ 210:13 0:68 eV with a correlation constant RE = 0.947, and
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ZORA
DE 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 is different. The use of ZORA to account for relativity, despite still resulting in worse absolute transition energies, provides the smallest energy shift uncertainty compared to the calculations using DKH2 correction (DE E
DKH2
¼ 152:86 0:64 eV with a correZORA
lation constant R = 0.954, and DE ¼ 342:79 0:58 eV with RE = 0.963). As in the case of the BP86 functional, the transition intensities calculated using B3LYP are predicted to the same accuracy independent of the relativistic correction model employed (RInt = 0.963). Surprisingly, when excluding the relativistic correction, our calculations still reasonably reproduced the experimental spectra. Using the BP86 functional and no relativistic correction the no-rel average energy shift is DE ¼ 672:54 0:68 eV, with a correlation constant RE = 0.947. This uncertainty in the energy shift is comparable to the ones using either ZORA or DKH2 to account for relativity. In this case, the error in the prediction of the transition intensities (RInt = 0.972) is also comparable with the ones using either relativistic correction. Contrary to the results reported previously for the case of iron K-edge spectra,15 our calculated molybdenum K- pre-edge HERFD-XAS spectra do not depend strongly on the relativistic model employed.
4 Conclusions In this work, we have presented experimental HERFD-XAS data for a series of Mo complexes. The enhanced energy resolution allows for better resolved pre-edge features, which have been correlated to the oxidation state, the ligation environment and geometry. The better resolution also allows the Mo K-edge data to be quantitatively interpreted within a TDDFT framework. Our results show linear correlation between the experimental and calculated energies and intensities. The effects of different functionals and relativistic corrections have been investigated. We have found a general good agreement between the experimental and calculated Mo HERFD-XAS spectra, independent of the functional used. Accounting for the effects of relativity in the spectra by either the ZORA or DKH2 approximations leads to equivalent results, after calibration. The present work extends the application of previous TDDFT methodology for the calculation of pre K-edge XAS15–17,21,22 to the second transition series of metal complexes, and in particular to high-energy resolution XAS data. The improved information provided by the combination of HERFD-XAS experiments and TDDFT calculations should allow for a more quantitative interpretation of the near-edge region of K-edge XAS spectra of all compounds containing heavy elements. The present calibration sets the foundations for future studies of Mo in complex systems. This is of particular interest for biological and chemical systems where the Mo may play a
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functional role in catalysis. Furthermore, the same protocols presented here should be readily extendable to the rest of the second or even third transition series.
Acknowledgements The authors acknowledge the European Synchrotron Radiation Facility (ESRF) and the ID26 staff for the technical assistance during the experiments. SD and FN acknowledge the Max Planck Society for funding. SD also acknowledges the Sloan Foundation for a fellowship.
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High-resolution molybdenum K-edge X-ray absorption spectroscopy analyzed with time-dependent density functional theory† Frederico A. Lima,zya Ragnar Bjornsson,ya Thomas Weyhermu ¨ ller,a b c Perumalreddy Chandrasekaran, Pieter Glatzel, Frank Neesea 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
Received 25th July 2013, Accepted 14th October 2013
order Douglas–Kroll–Hess (DKH2) scalar relativistic approximations. We have found that both the
DOI: 10.1039/c3cp53133c
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-
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XAS to complex catalytic systems.
predicted energies and intensities are in excellent agreement with experiment, independent of the
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 a
¨r Chemische Energiekonversion, Stiftstrasse 34-36, D- 45470, Max-Planck-Institut fu ¨lheim an der Ruhr, Germany. E-mail: [email protected]; Mu 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.
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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
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K-edge XAS, this means that the energy uncertainty increases almost 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, often resulting in the absence of fine structure in the pre-edge and edge regions and thus limiting quantitative spectral interpretation.28 ¨ma ¨la ¨inen et al. proposed a measurement scheme based In 1991, Ha on an emission spectrometer which was capable of reducing the apparent broadening in XAS spectra caused by core–hole lifetime effects.27 The experiment involves the measurement of the fluorescent photon intensity as a function of the incident energy. By using a high-resolution crystal analyzer, it was demonstrated that the resultant spectra are dominated by the core–hole-lifetime of the intermediate state, rather than that of the initial state. This was later demonstrated theoretically by Tanaka et al.29 For a more detailed derivation of the lifetime contribution to the HERFD-XAS spectrum, we refer the interested reader to ref. 30 and for discussions of secondary processes in XAS, including resonant XAS and HERFD-XAS, the reader is referred to ref. 31–33. Since then, many applications of the so-called High Energy Resolution Fluorescence Detected XAS (HERFD-XAS) to the study of the electronic structure of materials can be found in the literature.33–44 Herein we focus on the increased pre-edge resolution resulting from HERFD Mo K-edge XAS. Molybdenum HERFD-XAS data have been obtained for a series of structurally characterized Mo monomers and dimers, and subsequently interpreted using a TDDFT approach. We note that previous HERFD-XAS studies have utilized either multiple-scattering based or multiplet-based approaches; hence to our knowledge, the present study represents the first detailed TDDFT study of heavy element HERFD-XAS. The methodology presented here provides a framework for future quantitative studies of Mo HERFD-XAS spectra within complex catalytic systems.
2 Materials and methods A total of eight molybdenum complexes were selected to serve the TDDFT calibration presented in this study. These compounds 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; L 0 = 1,4,7-trimethyl-1,4,7-triazacyclononane; Pdt = 1,2-diphenyl-1,2-dithiolate. A schematic representation of the structures of the measured compounds is shown in Fig. 1. 2.1
Sample preparation
XAS samples were finely ground and mixed with boron nitride to a dilution corresponding to 1–2 absorbances. The samples were then pressed in PEEK sample holders with 2 mm path length and sealed with 38 mm thick Kapton tape. 2.2
XAS measurements
XAS data were obtained at the ID26 beamline at the European Synchrotron Radiation Facility (ESRF). The storage ring operated at 6.04 GeV and 200 mA current. A double-crystal monochromator
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with Si(311) crystals was used to select the incoming X-ray energy. Standard XAS data were collected in transmission and total fluorescence yield (TFY) modes. HERFD-XAS data were collected concomitantly with the standard XAS measurements. The [999] reflection of five Ge(111) crystals from the multicrystal spectrometer installed at ID26 was used to select the Mo Ka emission line (approximately 17.4 keV). The energy resolution of the HERFD-XAS data was estimated to be approximately 3.5–4 eV. Energy calibration of the incoming radiation was performed prior to the measurements by recording the K-edge transmission spectrum of a Mo foil and assigning the maximum of the white line to 20 016.4 eV. All samples were maintained at approximately 40 K using a liquid helium cryostat. The data were monitored for signs of X-ray damage. During the course of the measurements no apparent changes in the XANES region of the spectrum were found. Several successive scans (18–20, depending on the sample) were averaged in order to improve the data quality. Background subtraction and normalization were performed using the ATHENA package.52 Finally, the energy position and intensity of the pre-edge features were determined by a fitting procedure using the Blueprint XAS software.53,54 Details of the fitting procedure and the results of the individual fits of the 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 performed using the ORCA program package version 2.9.55 Relativistic effects were taken into account by either the zeroth-order regular approximation (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 functions from the most recent def2 versions60 were used throughout. A set of nine different functionals were used in the calculation of the XAS spectra (see Table 2). All the spectral calculations used dense integration 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 crystal structures as a starting point, all-electron ZORA geometry optimizations were carried out for all eight model compounds. They were done at the RI-BP86/def2-TZVP level (ZORA recontraction and using a decontracted auxiliary basis set) in the presence of an infinite dielectric using the conductor-like screening model (COSMO)61 and including DFT-D3BJ dispersion correction.62,63 No X-ray structure of compound (7) ([MoIV(CO)2(Pdt)2]0) was available. 2.3.2 Calculation of the XAS spectra. TDDFT calculations were carried out using the Tamm–Dancoff approximation64 as implemented 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 Dielectric field contributions using COSMO (infinite dielectric) were included in TDDFT calculations as well. Up to 60 roots were calculated (making sure to cover the whole range of transitions in the pre-edge region), allowing only for transitions from molybdenum 1s donor orbitals. Calculated intensities include electric dipole, magnetic dipole and quadrupole contributions.
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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 the Mo 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 the identification of the transitions and correlation with experiment. A constant shift of 60.9 eV has been applied to the calculated energies
Experiment Energy (eV)
Intensity
Ref.b
Energyc (eV)
Intensity
Aread
(1) – [LMo (O)3]
1 2 Ave.
20 004.0 20 006.5 20 006.0
0.490 2.232 2.722
45
20 003.4 20 006.6 20 006.4
0.249 5.143 5.392
0.193 2.574 2.696
(2) – [L 0 MoVI(O)2(OCH3)](PF6)
1 2 Ave.
20 004.4 20 006.8 20 006.2
0.525 1.649 2.174
46 and 47
20 003.3 20 006.7 20 006.4
0.382 4.379 4.761
0.258 2.203 2.389
(3) – [L 0 MoV(O)(OCH3)2](PF6)
1 2 Ave.
20 003.6 20 005.8 20 005.3
0.320 1.104 1.424
47
20 002.4 20 005.4 20 005.3
0.171 3.280 3.451
0.155 1.668 1.751
(4) – [L 0 (MoIII)(m-O)(m-OAc)2(MoIII)L 0 ](PF6)2
1 2e Ave.e
20 003.4 20 007.1 20 004.3
0.445 0.146 0.592
48
20 000.4 20 002.5 20 002.3
0.041 0.361 0.402
0.092 0.248 0.267
(5) – [L 0 (MoIII)(m-OH)(m-OAc)(MoIII)(L 0 )](PF6)3
1 2 Ave.
20 000.2 20 002.3 20 001.6
0.075 0.100 0.175
48
20 000.3 20 002.3 20 001.5
0.039 0.057 0.095
0.091 0.100 0.118
(6) – [MoIV(OPh)(Pdt)2](NEt4)
1 2e Ave.e
20 002.9 20 005.7 20 003.5
1.732 0.456 2.188
49
20 001.8 — 20 001.8
2.351 — 2.351
1.216 — 1.216
(7) – [MoIV(CO)2(Pdt)2]
1 2 Ave.
20 001.3 20 003.7 20 001.4
0.580 0.029 0.609
20 002.1 — 20 002.1
1.188 — 1.188
0.650 — 0.650
(8) – [MoVI(Pdt)3]
1 2 Ave.
20 001.0 — 20 001.0
0.511 — 0.511
20 002.0 — 20 002.0
1.304 — 1.304
0.706 — 0.706
VI
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Calculation
Peaka
Compound
51
a
Individual peaks as determined by the fit procedure. Ave. refers to the intensity-weighted averaged energy and total intensity of both peaks. Synthesis and crystallographic structure references. c Intensity-weighted average energies. The calculated energies have been shifted by 60.9 eV to higher energies. d The predicted experimental areas, Acalc, are obtained from the calculated intensities, Icalc, using the linear regression obtained from the 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. b
Fig. 1
Schematic representation of the model compounds investigated in this study.
3 Results and discussion The HERFD-XAS spectra of all the eight model compounds investigated in this study are shown in Fig. 2. The formal oxidation state of the compounds, used throughout this work
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in their description, varies systematically from III to VI with differing coordination environments, thus representing a broad test set of models to study the contributions of the oxidation state, the coordination environment and geometry to the XAS spectra. As described above, the use of HERFD-XAS as opposed
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Table 2 Computational protocol used in the calculation of the XAS spectra in the present work
Functional
Basis set
Structure
Rel. approx.
Solvation
BP86
TZVP TZVP TZVP TZVP TZVP TZVP TZVP TZVP TZVP TZVP TZVP TZVP TZVP
X-ray Optimized Optimized Optimized Optimized Optimized Optimized Optimized Optimized Optimized Optimized Optimized Optimized
DKH2 DKH2 ZORA None DKH2 ZORA ZORA ZORA ZORA ZORA ZORA ZORA ZORA
COSMO COSMO COSMO COSMO COSMO COSMO COSMO COSMO COSMO COSMO COSMO COSMO COSMO
B3LYP PBE PBE0 TPSS TPSSh revTPSS revTPSSh BHLYP
to regular TFY- or transmission-detected XAS allows us to obtain higher resolution XAS spectra – a comparison of standard TFY and HERFD XAS is shown in the next section. The HERFD-XAS data exhibit rich features in the pre-edge and near-edge regions, with the edge position (here defined as the zero crossing of the second 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-edge features, with the most intense peak reaching approximately 0.9 normalized units (all the spectra have been normalized to one absorber atom such that at the EXAFS region m(E) = IHERFD/I0 = 1). The number of oxo groups in each complex correlates with the peak intensity at about 20 006 eV. As the geometries of these three compounds are similar, all having a distorted octahedral environment around the Mo atom, it appears that the pre-edge intensity is largely mediated through the short, highly covalent Mo-oxo bonds which enhance metal 4d–5p mixing via increased Mo–O 4d–2p hybridization.70 Replacement of the oxo group by a longer, less covalent methoxy ligand thus diminishes the observed intensity. The identification of an ‘‘oxo feature’’ in the Mo K preedge was first qualitatively observed by Cramer et al.28,71 Later, Kutzler et al. confirmed this observation via polarized XAS measurements and presented calculations which made the assignment of covalency in a class of molybdates possible.
Kutzler’s analysis inferred the origins of the electronic transitions responsible for the pre-edge features in molybdates and made the correlation of the strength (intensity) and the position (energy) of the pre-edge features with the bond length.72,73 This approach has been subsequently applied to assess the number of oxo groups in both proteins and model complexes, using the second derivative as a fingerprint.74–76 The present data indicate that the increased energy resolution of HERFDXAS data should aid in more quantitative assessments of oxo ligand contributions. Additionally, the edge position of compounds (1)–(3) varies by approximately 1 eV. This variation is correlated 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. The reduced spectral broadening due to HERFD detection greatly aids in accurate determination of the edge position. The HERFD-XAS spectra of the molybdenum dithiolene complexes [MoIV(OPh)(Pdt)2]1 (compound (6)), [MoIV(CO)2(Pdt)2]0 (compound (7)) and [MoIV(Pdt)3]0 (compound (8)) also show strong pre-edge features. The peak intensities vary from approximately 0.25 to about 0.5 normalized units and the pre-edge energies shift over an B2 eV range. An empirical assessment of these trends is complicated by the non-innocent nature of the dithiolene ligands – which may make the Mo effectively more reduced – together with the p-accepting character of the carbonyl ligands in complex (7) – which would make the metal appear more oxidized. Nonetheless, it is clear that symmetry factors do contribute to the pre-edge intensity, with the 5-coordinate complex (6) having greater pre-edge intensity than either 6-coordinate trigonal prismatic complexes. The molybdenum dimers present the lowest intensity preedges of all the compounds studied, consistent with the approximately octahedral local symmetry. However, despite the fact that both compounds are formally MoIII, there are differences in both the energies and intensities. Namely the pre-edge of compound (4) appears at higher energy and has greater intensity than that of complex (5). This can be understood in part by a more careful analysis of the structures. The Mo–Mo distance in compound (4) (2.715 Å) is notably smaller than in the protonated compound (5) (3.521 Å), suggesting a bonding interaction in the
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 sharp resonances above the edge (a) and zoom in the pre-edge region (b). The edge position varies by approximately 6.5 eV across the series.
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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 mixing and thus the greater pre-edge intensity in the pre-edge of compound (4) relative to (5). A more quantitative analysis of these 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 two model compounds are used here to illustrate the effect of increased energy resolution in the HERFD-XAS. However, the same conclusions apply for all models investigated. Fig. 3 also shows the first and second spectral derivatives, the latter smoothed by a three-point binomial algorithm in order to obtain a better definition of the peaks. The XAS of compound (1) exhibits a strong pre-edge feature which is clearly observed in both spectra recorded using HERFD and TFY. The energy position of the pre-edge and the rising edge can be estimated by inspecting the spectral derivatives. In the pre-edge region two minima separated by almost 4 eV are observed in the second derivative of the HERFD-XAS spectrum, indicating that the pre-edge is actually composed of two features. Despite a clear asymmetry visible in the TFY data, the second derivative does not clearly indicate the position of the first peak. This translates in a large uncertainty in the energy position of this feature, which can lead to ambiguous interpretation. In addition, all the features in the XANES region are suppressed in the TFY data. In the case of the XAS of compound (4) the interpretation of the near-edge region is more prone to ambiguity due to the relatively weak pre-edge feature. The HERFD-XAS spectrum shows a clear feature at around 20 003.5 eV, which is confirmed by the single minimum in the second derivative. The TFY spectrum of this model does not show any clear feature in the pre-edge and even analyzing the 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 compounds studied here collected using HERFD and TFY is relevant to show that using high-energy resolution is important in order to extract accurate quantitative information from the spectra. The determination of the Mo-oxo coordination number discussed above represents just one example. Further, the spectral sharpening obtained by HERFD-XAS measurements is essential for a more quantitative assessments of the pre-edge region using computational approaches, as detailed in the next section. 3.2
TDDFT calibration
The experimental intensities and energies of the molybdenum HERFD-XAS K-pre-edge features of the eight studied compounds are reported in Table 1. Also listed are the corresponding calculated parameters using the BHLYP functional following the computational model described in Section 2.3. A table containing the calculated parameters using the other functionals employed in this study can be found in the ESI† (Table S1). Fig. 4 shows the correlations between the experimental and calculated energies and intensities. To produce the correlations only peaks originating from transitions which could clearly be assigned as belonging to the pre-edge region, i.e., transitions with significant acceptor d-character, were taken into account. Peaks due mainly to transitions with the metal-to-ligand or the metal-to-metal charge transfer (MLCT and MMCT, respectively) origin were not included in the correlations as these have been previously shown to dependent strongly on the amount of Hartree–Fock (HF) exchange present in a specific functional.17 The calculated energies are intensityweighted average values. The reported intensities are the sum of the squares of transition moments – electric dipole, magnetic dipole and electric quadrupole – of all states contributing to a given pre-edge feature. Calculated intensities were determined after application of a Gaussian broadening of 1.75 eV, mainly to help 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), first derivatives (middle) and second derivatives (bottom).
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Fig. 4 Correlations between the experimental and calculated Mo K-pre-edge intensity-weighted average energies (a) and intensities (b) obtained using the BHLYP functional. The linear least-square fits result in the following relations: Ecal = 953.7 + 0.949(Eexp) and Intcal = 0.148 + 2.055(Intexp).
spectra and to correlate individual peaks derived from the fit procedure in the experimental data and groups of transitions in the calculated spectra. This, however, does not affect the calculated energies of the transitions since changing the broadening results only in constant scaling of the intensities. However, the visual comparison between the predicted and experimental spectra is more realistic when using a larger value for the broadening. Based on the estimate of the experimental resolution, we have used a broadening of 3.5 eV for plotting the
calculated spectra. The relationship between calculated intensity and oscillator strength is given by: X 2 eq 2 ed md 2 I ¼c fosc þ fosc þ fosc c¼
pffiffiffiffiffiffiffiffi 1 1 2 ln 2 p ffiffiffi 4:33 109 p FWHM
(1)
in which FWHM is the full-width-half-maximum of the Gaussian broadening applied to the spectrum.
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 measured HERFD-XAS spectra subtracted from all the contributions except the pre-edge features (derived from the fits). The calculations used the BHLYP functional with DKH2 relativity 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 produce similar results.
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It has been previously established that a constant shift needs to be applied to the calculated energies in order to account for many of the systematic errors inherent to present density functional approximations, as well as due to basis set incompleteness and use of different relativistic approximations.15–17,21,22 The magnitude of the shift is dependent on the specific computational protocol employed, thus it needs to be determined for each individual combination of functional, basis set and relativistic correction. In the case of the BHLYP functional the value for the average energy shift was determined to be 60.9 0.8 eV. As can be seen in Fig. 4, both calculated energies and intensities show a linear relationship with respect to the experimental values, with correlation constants RE = 0.936 and RInt = 0.961. To attest the quality of the TDDFT prediction of the K pre-edge spectra it is useful to visually inspect the experimental data with calculations. Here we opt for showing the experimental data subtracted from all the contributions except the pre-edge features of interest. Fig. 5 shows the comparison of the experimental (top) and calculated (bottom) pre-edges of the compounds investigated in this study, evidencing the excellent agreement between the experiment and calculation. For clarity, the spectra from the monomers (compounds (1), (2), (3), (6), (7) and (8)) are plotted separately from those of the dimers (compounds (4) and (5)). A complete comparison between the experimental and calculated spectra of all the other functionals used in this work (see Table 2) can be found in the ESI.† Similar to our results using the BHLYP functional presented here, our calculations using other functionals were able to accurately reproduce the measured spectra, both in terms of energies and intensities. Fig. 6 shows the predicted energies and intensities of all eight compounds using different functionals. The energies of the HERFD-XAS pre-edge features of all eight investigated compounds are well reproduced, independently of the functional used. The smallest uncertainty in the energy is found when using the revTPSSh functional (0.56 eV) and the largest one when using the PBE functional (0.92 eV). A table with the average energy shift and their corresponding standard deviations is given in Table S1 in the ESI.† Similarly, the predicted intensities do not show a strong dependence on the functional used in the calculations. With the exception of compound (5) which has the lowest intensity pre-edge of the whole series, the relative variation of the calculated pre-edge intensities of all the other compounds is less than 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 are related to the geometric and electronic structures of transition metal compounds.15–17 The strong agreement between theory and experiment thus serves as a means of experimentally validating a given electronic structure. In general terms, most of the transitions in the pre-edge region are dominated by electric dipole contributions, with a few weak ones having predominant electric quadrupole character. These transitions gain intensity due to the covalently mediated metal p + d mixing and also by symmetry distortions. Interestingly, in the case of compound (4) we observe a calculated (BHLYP/DKH2)
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Fig. 6 Calculated standard deviations in the energy shift for each functional (top) and relative intensity variation for each compound (bottom) of the transitions in the pre-edge region. The intensities are obtained from the peaks with transitions 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 each functional is listed in Table S1 in the ESI.†
strong transition at ca. 20 006 eV which can be described as due to metal-to-metal charge transfer (MMCT). The presence of MMCT transitions in (4) but not in (5) may be attributed to the presence of a metal–metal bond in the former, but not in the latter. However, as noted previously by Roemelt et al.17 the calculated energy at which these charge transfer transitions occur depends on the system under investigation and the amount of HF in the functional used. Therefore, caution must be exercised in ascribing this feature to a direct MMCT feature. 3.3
Relativistic effects
The effects of the relativistic corrections on the calculated TDDFT spectra were tested by calculating the spectra using either DKH2 or ZORA relativistic approximations, or without inclusion of relativistics, as described in Section 2.3. At the BP86 and B3LYP levels, calculations using either ZORA or DKH2 corrections nicely reproduced the experimental spectra. As expected, the calculated absolute energies of the transitions in the pre-edge region vary depending on the relativistic correction applied. However, the important parameter in a TDDFT calibration is the uncertainty in the energy shift and not the absolute magnitude. Using the BP86 functional in combination with DKH2 correction resulted in slightly better predicted absolute energies and a smaller energy shift uncertainty
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as compared with BP86/ZORA combination (DE ¼ 210:13 0:68 eV with a correlation constant RE = 0.947, and
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ZORA
DE 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 is different. The use of ZORA to account for relativity, despite still resulting in worse absolute transition energies, provides the smallest energy shift uncertainty compared to the calculations using DKH2 correction (DE E
DKH2
¼ 152:86 0:64 eV with a correZORA
lation constant R = 0.954, and DE ¼ 342:79 0:58 eV with RE = 0.963). As in the case of the BP86 functional, the transition intensities calculated using B3LYP are predicted to the same accuracy independent of the relativistic correction model employed (RInt = 0.963). Surprisingly, when excluding the relativistic correction, our calculations still reasonably reproduced the experimental spectra. Using the BP86 functional and no relativistic correction the no-rel average energy shift is DE ¼ 672:54 0:68 eV, with a correlation constant RE = 0.947. This uncertainty in the energy shift is comparable to the ones using either ZORA or DKH2 to account for relativity. In this case, the error in the prediction of the transition intensities (RInt = 0.972) is also comparable with the ones using either relativistic correction. Contrary to the results reported previously for the case of iron K-edge spectra,15 our calculated molybdenum K- pre-edge HERFD-XAS spectra do not depend strongly on the relativistic model employed.
4 Conclusions In this work, we have presented experimental HERFD-XAS data for a series of Mo complexes. The enhanced energy resolution allows for better resolved pre-edge features, which have been correlated to the oxidation state, the ligation environment and geometry. The better resolution also allows the Mo K-edge data to be quantitatively interpreted within a TDDFT framework. Our results show linear correlation between the experimental and calculated energies and intensities. The effects of different functionals and relativistic corrections have been investigated. We have found a general good agreement between the experimental and calculated Mo HERFD-XAS spectra, independent of the functional used. Accounting for the effects of relativity in the spectra by either the ZORA or DKH2 approximations leads to equivalent results, after calibration. The present work extends the application of previous TDDFT methodology for the calculation of pre K-edge XAS15–17,21,22 to the second transition series of metal complexes, and in particular to high-energy resolution XAS data. The improved information provided by the combination of HERFD-XAS experiments and TDDFT calculations should allow for a more quantitative interpretation of the near-edge region of K-edge XAS spectra of all compounds containing heavy elements. The present calibration sets the foundations for future studies of Mo in complex systems. This is of particular interest for biological and chemical systems where the Mo may play a
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functional role in catalysis. Furthermore, the same protocols presented here should be readily extendable to the rest of the second or even third transition series.
Acknowledgements The authors acknowledge the European Synchrotron Radiation Facility (ESRF) and the ID26 staff for the technical assistance during the experiments. SD and FN acknowledge the Max Planck Society for funding. SD also acknowledges the Sloan Foundation for a fellowship.
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