and Double-Electron Excitation (KLII&III, KLI) - American Chemical

Jun 2, 2015 - and Tricia D. Smurthwaite. ∥. †. Physical Sciences Division,. ‡. Environmental Molecular Sciences Laboratory,. §. Institute for I...
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Electronic and Chemical State of Aluminum from the Single- (K) and Double-Electron Excitation (KLII&III, KLI) X‑ray Absorption Near-Edge Spectra of α‑Alumina, Sodium Aluminate, Aqueous Al3+·(H2O)6, and Aqueous Al(OH)4− John L. Fulton,*,† Niranjan Govind,*,‡ Thomas Huthwelker,⊥ Eric J. Bylaska,‡ Aleksei Vjunov,§ Sonia Pin,⊥ and Tricia D. Smurthwaite∥ †

Physical Sciences Division, ‡Environmental Molecular Sciences Laboratory, §Institute for Integrated Catalysis, and ∥Energy Processes and Materials, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352, United States ⊥ Swiss Light Source, Laboratory for Catalysis and Sustainable Chemistry (LSK), Paul Scherrer Institut (PSI), 5232 Villigen, Switzerland ABSTRACT: We probe, at high energy resolution, the double electron excitation (KLII&II) X-ray absorption region that lies approximately 115 eV above the main Al K-edge (1566 eV) of α-alumina and sodium aluminate. The two solid standards, αalumina (octahedral) and sodium aluminate (tetrahedral), are compared to aqueous species that have the same Al coordination symmetries, Al3+·6H2O (octahedral) and Al(OH)4− (tetrahedral). For the octahedral species, the edge height of the KLII&III-edge is approximately 10% of the main K-edge; however, the edge height is much weaker (3% of K-edge height) for Al species with tetrahedral symmetry. For the α-alumina and aqueous Al3+·6H2O the KLII&III spectra contain white line features and extended absorption fine structure (EXAFS) that mimics the K-edge spectra. The KLII&III-edge feature interferes with an important region in the EXAFS spectra of the crystalline and aqueous standards. The K-edge spectra and K-edge energy positions are predicted using time-dependent density functional theory (TDDFT). The TDDFT calculations for the K-edge X-ray absorption nearedge spectra (XANES) reproduce the observed transitions in the experimental spectra of the four Al species. The KLII&II and KLI onsets and their corresponding chemical shifts for the four standards are estimated using the delta self-consistent field (ΔSCF) method.

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INTRODUCTION X-ray absorption fine structure (XAFS) spectroscopy probes the chemical state and structure of atoms in their condensed phase through a single-photon, single-electron excitation process. An XAFS spectrum is typically divided into two regions. In the region up to approximately 50 eV above the absorption edge, the X-ray absorption near-edge spectrum (XANES) contains the electronic transitions from core to bound states that are overlapped increasingly at higher k with photoelectron single- and multiple-scattering processes. The extended X-ray absorption fine structure spectrum (EXAFS), in the region up to about 1200 eV above the absorption edge, arises primarily from photoelectron backscattering of nearby atoms. The high specificity of the XAFS method results from the ability to select specific X-ray energies that excite only the core electron from the atomic species of interest. The absorption spectrum may also contain single-photon, double-electron excitations whose absorption edge height occurs as a few percent of the single-electron process. These double-electron excitations appear as peaks and edge-like features in the atomic absorption background function over a region up to about 1000 eV above the main edge of the single© 2015 American Chemical Society

electron absorption. A reasonable approximation for the position of these double-electron edges is derived from the Z + 1 rule, which states that the energy required to eject the second electron after creation of a core−hole vacancy is equal to the binding energy of that electron for the next higher element.1,2 Qualitatively, the double-electron features include both electron “shake-up” to discrete resonances of unoccupied states and “shake-off” of the electron into the continuum. The double-electron process has thus far eluded a fully quantitative theoretical treatment although there is recent progress.3−6 There are several reasons that the double-electron spectra are important. Foremost, these spectra contain an independent set of electronic- and chemical-state information that is thus far underutilized because of the relatively weak transition and the lack of a comprehensive theory describing these transitions. These limitations are diminishing with improved X-ray optics at synchrotron sources and by advances in X-ray absorption theory. There is also renewed interest in double-electron Received: November 19, 2014 Revised: May 26, 2015 Published: June 2, 2015 8380

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K-edge position and XANES spectra was achieved using Gaussian basis restricted-excitation window time-dependent density functional theory (REW-TDDFT).30−32

excitation processes with the advent of X-ray free electron lasers7,8 that not only have the intensities required to doubly ionize single atom sites but also have the capability to detect the far weaker cross sections of double-electron excitations from two different atom sites. The double electron features are also important because they interfere with the interpretation of the absorption spectra for the conventional single-electron process that is the backbone of modern EXAFS. In this respect doubleelectron edges distort the single-electron K- or L-edge spectra by adding new spectral features to the atomic background function.9 Often the intensity of the double-electron features are comparable to the intensity of the relatively weak photoelectron backscattering signals (i.e., EXAFS signal). In addition, the height of the double-electron edge affects the value of the amplitude reduction factor, S02, for the singleelectron process.10−12 S02 is used to normalize the amplitude of the EXAFS oscillations and thus any uncertainty in S02 directly affects the estimates of atom coordination numbers. Double electron features are present in absorption spectra of all elements to a greater or lesser extent. For ordered systems, their presence is generally ignored in conventional EXAFS analysis because the double electron features represent only a small fraction of the strong EXAFS backscattering signal. For amorphous or disordered systems this is not the case because the photoelectron backscattering signal is quite weak due to phase cancellation of the scattering from many similar atom− atom length scales. Multiple illustrative examples are provided by ions in aqueous solution that have only a moderately ordered first solvation shell and largely disordered higher shells. Double-electron excitations have been observed for the aqueous ions of the alkali and alkaline earth metals,13−17 the aqueous halides,18−22 aqueous lanthanides,23 and aqueous actinides.24,12 In this work we extend these observations to a light element cation, Al3+, and find that Al has an especially strong double-electron feature that we show is also prominent in a highly ordered crystalline solid such as α-alumina as well as aqueous systems. The two objectives of this work are first to identify and characterize the Al double-electron transitions and then to employ electronic structure calculations to predict the positions of these double-electron transitions as well as to calculate the K-edge XANES spectra using TDDFT. Results are presented for the double-electron spectra (KLII&III and KLI (ls2p and ls2s states, respectively)), to provide a comprehensive analysis following a recent report identifying the existence of these features in the Al EXAFS spectra of zeolites.25 The Al doubleelectron features are found to be relatively strong and they occur in a region that significantly interferes with the K-edge EXAFS spectra. Furthermore, the position, structure and intensity of the transitions are found to be strongly dependent upon the first-shell symmetry of the ligands at the Al center. The existence of double-electron features in the Al K-edge spectra is similar to early reports of structure for the Si K-edge spectra of SiH426 and other gas-phase silicon molecules.27 A comprehensive study28 of double electron excitations has been reported for the light elements of the series Si, P, S, and Cl although the existence of these features for Al has only been reported in X-ray photoelectron spectra.29 Two different theoretical approaches are used to predict features of these electronic transitions. The ΔSCF method (delta self-consistent field) was used to estimate the onsets of the K single-electron edge and the KLII&III and KLI doubleelectron edges, whereas a more complete analysis of both the

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EXPERIMENTAL METHODS

The Al XAFS spectra were acquired at the PHOENIX I beamline at the Swiss Light Source (SLS) at the Paul Scherrer Institute. Calibration of the monochromator was achieved by setting the inflection point of an Al foil spectrum to 1559.6 eV. We used a KTiOPO4 (011) double-crystal monochromator to provide an energy resolution of about 0.6 eV over a scan range from 1500 to 2100 eV. In addition, the core−hole lifetime broadening for aluminum is expected to be about 0.42 eV.33 Upstream of I0, two Ni-coated mirrors were set at an angle of 1.45° to remove higher harmonics from the reflected beam. The unfocused 1.0 × 1.0 mm beam had a flux of approximately 109 photons/s. For the solid samples, the sample chamber pressure was maintained at approximately 2.5 × 10−4 mbar whereas for the aqueous-phase sample, the sample chamber was held at 800 mbar He. Measurements were typically performed in fluorescence mode although several total electron yield and transmission measurements were obtained to ascertain the magnitude of the self-absorption corrections. I0 was measured as total electron yield signal taken from a 0.5 μm thin polyester foil, which was coated with 50 nm of Ni. This device was held in a miniaturized vacuum chamber (2.9 × 10−6 mbar), which is separated by a thin Kapton foil from the measurement chamber itself. The X-ray fluorescence was detected using a four-element Si-drift diode detector (manufacturer: Vortex). For transmission measurement a Si-diode was used. For the liquid samples a membrane-window cell was used that has been previously described.34 Briefly, this cell uses two membrane windows, one of which is connected to a steppermotor drive. The stepper motor is controlled to remotely define a range of path lengths from 1 to 500 μm. A set of either 200 nm Si3N4 or 800 nm thick CVD diamond (Applied Diamond, Inc.) membrane windows were used. The selection of the CVD diamond windows significantly reduces the artifacts in the Al EXAFS from the Si3N4 windows originating from the Si-edge at 1839 eV. These features could not be completely eliminated due to other Si sources in the beamline optics. Any residual Si-edge defects in the Al EXAFS spectra were removed by background correction. The cell was mounted at 45° to the beam so that both the transmission and fluorescence signals could simultaneously be collected. The combined use of transmission and fluorescence measurements allowed minimization of self-absorption effects in the fluorescence measurements. Liquid transfer lines extended outside of the vacuum chamber for ease of sample transfer. AlCl3 (99.999% anhydrous), α-Al2O3 (99%) (octahedral-Al), and Na2Al2O4 (99.95% anhydrous) (tetrahedral-Al) were obtained from Sigma-Aldrich and were used without further processing. Subsequent XRD analysis of the Na2Al2O4 sample showed the presence of approximately 15% of the hydrate, Na4Al4O8·5H2O, as an impurity. The aqueous Al3+ was prepared from a stock solution of 0.03 M HCl, and the final pH was adjusted to 1.5 to eliminate hydrolysis species. The aqueous Al(OH)4− was prepared according to a method previously reported.35 8381

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Generating AIMD Configurations for the Aqueous Systems. A set of molecular configurations or snapshots generated from molecular dynamics were used as the basis for calculating the TDDFT-XANES spectra of the two aqueous systems. The clusters for the aqueous systems were extracted from periodic plane-wave ab initio molecular dynamics (AIMD) simulations performed with the NWChem program.36 These simulations were performed with the PBE exchange− correlation functional51 and norm-conserving Hamann pseudopotentials52,53 modified into a separable form suggested by Kleinman and Bylander.54 These methods were used for all atoms. The original pseudopotential parameters suggested by Hamann were too “hard”, and softer pseudopotentials were constructed by increasing the core radii (H rcs = 0.8 au, rcp = 0.8 au; O rcs = 0.7 au, rcp = 0.7 au, rcd = 0.7 au; Al rcs = 1.241 au, rcp = 1.577 au, rcd = 1.577 au). A uniform charge background was applied to neutralize the charged simulation cell. For the aqueous octahedral Al3+ simulations, which were previously published,55 we used a simulation cell consisting of one Al3+ ion and 128 waters in a periodic cubic box (length = 15.64 Å). For the aqueous tetrahedral Al(OH)4− simulations, we used a simulation cell consisting of one Al(OH)4− and 64 water molecules in a periodic cubic box (length = 12.56 Å). Other calculation parameters included an energy cutoff of 100 Ry, density cutoff of 200 Ry, a simulation time step of 0.121 fs, and a fictitious electron mass of 600 au. The simulation temperature was set at 300 K and controlled using a Nose−Hoover thermostat.56 Approximately 10 ps of dynamics were collected for the simulations. In our sampling, the first 3 ps were considered the equilibration phase and ignored. A total of 100 snapshots were averaged from the AIMD trajectory to form the final spectra for the aqueous systems.

THEORETICAL METHODS Calculating K-, KLII&III-, and KLI-Edge Energies Using ΔSCF. Two approaches were used to simulate and analyze the spectra. The ΔSCF method was used to approximately estimate the onsets of the K single-electron edge and the KLII&III and KLI double-electron edges. These calculations are performed by setting the occupations of the relevant molecular orbitals and then the corresponding energies are subtracted. Specifically, we estimate the K-edge onset as the SCF energy difference between the ground-state energy and the energy needed to promote a 1s electron to the LUMO, the KL1 onset as the energy difference between the K-edge onset energy and the energy to promote a 1s and 2s electrons to the LUMO, and the KLII&III onset as the energy difference between the K-edge onset energy and the energy to promote a 1s and 2p electrons to the LUMO. Even though the ΔSCF approach provides an approximate way to calculate the double excitation energy onsets for the 4- and 6-coordinated species, we found that the approach is not accurate enough to provide a quantitative argument for the origin of the intensity differences between the species. So, this issue remains an open question and requires further analysis. Calculating K-Edge Energies and XANES Spectra Using TDDFT. A more complete analysis of both the K-edge position and XANES spectra was performed by using the REWTDDFT approach30−32 as implemented in the NWChem program.36 This approach involves defining a model subspace of single excitations from the relevant core orbitals. This ansatz is valid as excitations from the core orbitals are well-separated from pure valence−valence excitations and the method is reliable to approximately 20−30 eV in the pre- and near-edge region of the X-ray absorption spectrum.30−32 We have recently applied this approach successfully to several studies including the K-edges of oxygen, carbon, and fluorine in a number of molecular systems (CO, H2O, fluorobenzenes),30 ruthenium L3-edge in [Ru(NH3)6]3+, ruthenium L3-edge in a series of model Ru(II) and Ru(III) complexes and mixed-valence metal (Ru/Fe) dimers,31 the K-edges spectra of oxygen, nitrogen, and sulfur in cysteine,32 dissolved lithium polysulfide species in Li− S batteries,37 Al K-edge studies of the aluminum distribution in zeolites,25 and Cl K-edge spectra in actinide hexachloride complexes.38 XANES calculations were performed at the Al K-edge for the aqueous octahedral Al3+, α-Al2O3, aqueous tetrahedral Al(OH)4−, and tetrahedral sodium aluminate (NaAlO2) systems, respectively. Previous studies of the Al K-edge XANES have used a plane-wave pseudopotential method39,40 for Al, AlN, and α-Al2O3, and studies of aqueous Al(H2O)63+ clusters using both “transition state” DFT41 and a discrete variational (DV) molecular orbital methods.42,43 In all the ΔSCF and XANES calculations the Sapporo-QZP2012 all electron basis set44 was used for the single absorbing Al site, whereas the surrounding O and H atoms were treated with the 6-311G** basis set45 and the Stuttgart RLC ECPs46 were used to treat the surrounding Al atoms in the solid-state αAl2O3, and tetrahedral sodium aluminate systems, respectively. The exchange−correlation was treated with the BHLYP functional.47,48 For comparison with experimental values, the spectra were Lorentzian broadened by γ = 1 eV. Experimental crystal structures were used to construct finite hydrogen capped clusters for the solid systems (α-Al2O3 and NaAlO2).49,50

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RESULTS AND DISCUSSION Comparing the Experimental K- and KLII&III-Edge Spectra. Figure 1 presents the normalized X-ray absorption spectra, μ(E), spanning the region from the onset of the K-edge until just beyond the KLII&III-edge for two crystalline standards, α-alumina and sodium aluminate, and for aqueous 3 m Al3+ and 0.5 m Al(OH)4−. In the expanded K-edge XANES spectra of Figure 1b, the tetrahedral sodium aluminate and aqueous Al(OH)4− have similar edge energies as do those of the octahedral of α-alumina and aqueous Al3+. There are also similarities in the positions of many of the spectral transitions. The region about the KLII&III-edge, which was scanned using a higher energy resolution, is shown in the expanded plot of Figure 1c. As for the K-edge spectra the two octahedral samples and the two tetrahedral samples share some similar features. For all four samples the amplitudes of the KLII&III-edge XANES spectra were normalized to the K-edge height. Thus, the relative edge heights of the KLII&III-edge for the tetrahedral samples shown in Figure 1c are much lower than for the octahedral samples. Figure 2 provides a series of overlay plots of the K- and KLII&III-edges for the sodium aluminate, α-alumina, aqueous Al3+ (3 m AlCl3), aqueous Al(OH)4−. For all plots in Figure 2 the KLII&III-edge spectra have been scaled by a factor of 10 for direct comparison to the K-edge spectra. In addition, a constant E0 offset has been applied to all the K-edge and KLII&III-edge spectra of 1567.7 and 1680.3 eV, respectively, to normalize the positions to the α-alumina standard. As shown in Figure 2a, the α-alumina has a KLII&III-edge height that represents about 10% of the height of the K-edge. 8382

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Figure 1. Normalized μ(E) spectra for sodium aluminate, α-alumina, aqueous Al3+ (3 m AlCl3, pH 1.5), aqueous Al(OH)4− (0.5 m Al(OH)3, 3 m NaOH) are shown. Different regions of the experimental spectra are shown including (a) the full μ(E), (b) the K-edge XANES and the (c) the KLII&III XANES. The positions of the calculated ΔSCF edges (with constant E0 offset corrections) for both edges are shown in (b) and (c). The E0 for the ΔSCF K- and KLII&IIIedges have been offset by constant values of −27.9 and −31.0 eV, respectively (to match the experimental α-alumina edge positions).

For α-alumina, the overall XANES spectra for the single- and double-electron excitations are remarkably similar. Both spectra have (i) a weak shoulder at −2.5 eV just prior to the onset of the main edge, (ii) a white-line resonance about 1 eV above the edge, and (iii) oscillations in the μ(E) beyond the edge that suggests an origin from photoelectron backscattering (i.e., EXAFS). This is in contrast to the KLII&III features for sodium aluminate (Figure 2b) that shows an edge height that is about 3 times weaker than for α-alumina. In addition, there is a

Figure 2. Overlay of the normalized μ(E) for both the Al K- and KLII&III-edges spectra of (a) α-alumina, (b) sodium aluminate, (c) aqueous Al3+ (3 m AlCl3), and (d) aqueous Al(OH)4− (0.5 m Al(OH)3, 3 m NaOH). In all cases, the KLII&III-edge height has been normalized by the K-edge height and then scaled by a factor of 10 in the plots for comparison. The same sets of E0 shifts were applied to all sets of spectra (K- and KLII&III-edges, 1567.7 and 1680.3 eV, respectively). 8383

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Figure 3. k2-weighted χ(k) plots showing results of fitting the Al K-edge spectra for (a) α-alumina and (b) sodium aluminate to FEFF9 structure models. The predicted positions of the KLII&III- and KLI-edges from ΔSCF calculations are also indicated.

Table 1. Calculated Values of the K, KLII&III, and KLI Transitions and the Energy Differences, ΔE, for the K-Edge between the Three Samples and the α-Alumina Standard (All Units Reported in eV) ΔSCFa system

K [1s]

α-Al2O3 NaAlO2 aq Al3+ aq Al(OH)4−

1595.62 1594.39 1595.94 1594.77

TDDFTb

ΔE

KLII&III [1s2p]

KLI [1s2s]

K [1s]

−1.2 0.3 −0.9

+115.65 +115.92 +116.60 +115.80

+149.99 +150.10 + 150.91 + 149.98

1551.0 1548.8 1551.6 1548.7

expb ΔE

K [1s]

ΔE

KLII&III [1s2p]

−2.2 0.6 −2.3

1567.7 1565.1 1568.1 1565.1

−2.6 0.4 −2.6

+112.6 +110.0 +113.2 +109.9

a ΔSCF energy onsets as defined earlier. bEdge energy defined as the position of the primary maximum in the first derivative (for TDDFT, γ = 1.0 eV).

resonance at about −4 eV; however, mostly, the spectrum has few structural features. In Figure 2a,c we observe an additional weak peak at approximately 7−8 eV below the main KLII&IIIedge for both α-alumina and aqueous Al3+. There is possibly a similar feature in the sodium aluminate spectrum in Figure 2b. Filipponi et al.28 observed a similar splitting in the KL transition that they assigned to the core−holes being coupled in either singlet or triplet configurations. For the series of Si, P, S, and Cl, they showed a splitting of the two primary KL peaks in the range from approximately 7 to 10 eV where the extent of splitting increased with the atomic number. For the Al KLII&IIIedge spectra in Figure 2, these two peaks can also be ascribed to this core−hole splitting process. For α-alumina, an earlier X-ray photoelectron spectrum (XPS) clearly shows the existence of a peak due to this double electron transition at the Al-edge and a splitting of this peak with one weak and one stronger feature.29 Parts c and d of Figure 2 provide the same types of overlay plots for the two aqueous samples, Al3+ and Al(OH)4−, that have octahedral and tetrahedral symmetry, respectively. Although the ligand symmetry about the Al atom is identical to that of α-alumina and sodium aluminate, the type of ligand is different being either H2O or OH−. As was observed for the solid standards, the KLII&III-edge spectra mimics the overall Kedge structure for a species with octahedral symmetry (Figure 2c) but not for the one with tetrahedral symmetry (Figure 2d). The edge step height of the KLII&III transition for the tetrahedral Al(OH)4− is again approximately 3 times lower than that for the octahedral Al3+. From the set of four samples shown in Figure 2, there are several main conclusions. First the KLII&III-edge is a relatively strong feature in the Al absorption spectra and it can interfere with the EXAFS structure for the K-

edge. Also, extended X-ray absorption features are observed within the KLII&III spectra. Finally, the intensity of the KLII&III transition is strongly dependent upon the local Al symmetry. KL-Edge Distortions of the Al-EXAFS Spectra. Figure 3 provides the EXAFS k2-weighted χ(k) plots for both (a) αalumina and (b) sodium aluminate. The plots also show the fits using the theoretical standard (FEFF9) that include contributions from the most important set of single- and multiplescattering paths that were derived from the crystalline standards. By comparison of the experimental spectra to the fitted spectra, the relative importance of the double electron excitation contributions are more clearly observed. It is clear that the magnitude of these features may significantly distort the EXAFS information. For α-alumina a very prominent feature of the KLII&III-edge at k = 5.4 Å−1 is observed whereas, in contrast, a rather weak feature is observed at the same position for sodium aluminate. The KLI-edge (+34 eV above KLII&III), if present, would be observed at approximately 6.3 Å−1 (the positions are determined from ΔSCF calculations). In Figure 3 there are features for both α-alumina and sodium aluminate that suggest the presence of KLI-edges. Previously, the KLI-transition (1s2s) was postulated for SiCl4 and Si(CH3)427 and Ne.57 Comparison of Calculated Single- and DoubleElectron Excitation Edges Energies. Table 1 reports the positions of both the experimental absorption edge energies and those calculated from ΔSCF (K-, KLII&III-, and KLI-edges) and TDDFT (K-edge). The position of the ΔSCF edges for the K-edge and KLII&III -transitions are also indicated as arrows in Figure 1b,c, respectively. The E0 values for all of these ΔSCF values shown in Figure 1 have been shifted by a constant value 8384

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Figure 4. Al K-edge μ(E) plots for α-alumina (a), sodium aluminate (b), aqueous Al3+ (1 m AlCl3) (c), and aqueous Al(OH)4− (0.5 m Al(OH)3, 3 m NaOH) (d) compared to the calculated values from TDDFT. Calculated curves are shown with and without 1 eV broadening.

to match the experimental E0 for α-alumina. For the four different samples, the ΔSCF values for the K-edge match the ordering of the chemical shift although the magnitude of the shift is somewhat underestimated. From the entries in Table 1 it is useful to compare the absolute K-edge and ΔKLII&III-edge errors. ΔSCF errors with respected to the measured E0 positions are about +1.8% for the K-edge (1595.6 vs 1567.7 ev for α-Al2O3) and +2.7% for the KLII&III-edge (+115.6 vs +112.6 eV). The K-edge error for TDDFT is only about −1.0% (the method to calculate the TDDFT energies is based upon a slightly different approach of spectral derivatives described below). TDDFT quite accurately predicts the chemical shifts of sodium aluminate, aqueous Al3+, and aqueous Al(OH)4− with respect to α-alumina (see ΔE’s in Table 1). The error in these cases is only a few tenths of an electronvolt when compared to the experimental values. In addition, the TDDFT chemical shift values are significantly better than those derived from ΔSCF. This is not surprising as excited states within TDDFT are linear combinations of singly excited determinants, whereas the ΔSCF edge estimates presented here just include single determinants for the K, KLI, and KLII&III excited states, respectively. Finally, it should be noted that whereas ΔSCF correctly predicts the ordering of the K-edge position for the octahedral versus tetrahedral standards, this is not the case for the KLII&III-edge. Thus, ΔSCF does not correctly predict the approximately 3% shift of the tetrahedral versus the octahedral species for the KLII&III-edge.

K-Edge XANES Calculation from TDDFT. Figure 4 compares the K-edge XANES spectra calculated from TDDFT to the experimental spectra for α-alumina and sodium aluminate, as well as for aqueous 1 m Al3+ and 0.5 m Al(OH)4−. For the crystalline solids, a cluster is extracted from a crystal of α-alumina (107 atoms) or sodium aluminate (43 atoms) that has been generated from their XRD values49,50 and capped with −O-H groups wherein the O−H vector is coincident with the O−Al vector in the starting solid. For the aqueous samples a different approach is required because the dynamic fluctuations in the ion−water structure lead to large changes in the bond lengths and angles in addition to distortions of the first-shell symmetry from that of either pure octahedral or tetrahedral Al species. Clusters including the first and second coordination shell waters were extracted from 100 evenly spaced snapshots from the AIMD trajectory (between 3 and 10 ps). The resulting averaged TDDFT XANES spectra for the aqueous Al3+ and aqueous Al(OH)4− systems are shown in Figure 4c,d. In Figure 4 all the primary features of the experimental spectra are reproduced for all four different samples. In general, each peak represents an assembly of dozens of closely related transitions. In the case of the aqueous samples a further contribution results from small changes in the transition energies that occur with the dynamical changes in bond lengths and angles. Approximate assignments for the electronic transitions of each of the labeled peaks in Figure 4 are listed in Table 2. An analysis of the effect of atomic vibrations on the 8385

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The Journal of Physical Chemistry B Table 2. Assignment of Electronic Transitions for Primary Al XANES Features in Figure 4a peak assignments (octahedral)

a

system

A

B

α-Al2O3 aq Al3+

Al 1s → Al (3s,3p) Al 1s → Al (3s,3p), H 1s

C

Al 1s → Al (3s,3p) Al 1s → Al (3s,3p) Al 1s → Al (3s,3p), H 1s Al 1s → Al (3s,3p), H 1s peak assignments (tetrahedral)

D Al 1s → Al (3s,3p) Al 1s → Al(3s,3p), H 1s

system

E

F

G

NaAlO2 aq Al(OH)4−

Al 1s → Na 3s, Al (3s, 3p) Al 1s → Al(3s,3p, 3d), H 1s

Al 1s → Na 3s, Al (3s, 3p) Al 1s → Al(3s, 3p), H 1s

Al 1s → Na 3s, Al(3s, 3p) Al 1s → Al(3s, 3p), H 1s

In all cases the ground state is from Al 1s.

Figure 5. Al K-edge μ(E) plots and their first derivatives for α-alumina (a) and aqueous Al3+ (1 m AlCl3) (b) compared to the calculated values from TDDFT. Red dashed lines represent the energy positions of the derivative peak maximums corresponding to the energies that are reported in Table 1. Theory curves are shown with 1 eV broadening.

pre-edge peak (A) in α-alumina is also presented in Figure 4a. For this, five clusters were extracted from a 3 ps AIMD trajectory of α-alumina and the averaged XANES spectrum (solid line) was compared with a spectrum of a cluster (dashed line) extracted from a pure unperturbed crystal. A diminished pre-edge peak is seen in the crystalline cluster, whereas the peak becomes more prominent in the structural dynamics averaged spectra. Because this pre-edge feature involves transitions from the 1s to empty 3s states of the absorbing Al atom, a system with centrosymmetry will not involve any 3p mixing and hence will be forbidden by the electric dipole approximation. The diminished peak in our calculations are also 1s to empty 3s dominant, but the cluster approximation breaks the centrosymmetry, resulting in weak mixing of the empty 3p states. This mixing becomes more pronounced in the AIMD snapshots, resulting in a stronger pre-edge peak. Similar findings have been reported by Manuel, Cabaret, and Brouder.58,59 In Figure 4c, the experimental AlCl3 concentration is 1 m whereas for the spectra in Figure 1 that contains the highresolution scans of the KLII&III, the concentration is 3 m. The more dilute sample (Figure 4c) shows a moderate peak at 1570 eV. An EXAFS structural analysis for both concentrations shows that the first-shell H2O structures about Al3+ are identical in both cases. The broadening of the peak at 1570 eV is thus tentatively assigned to the existence of the solvent-shared ion pair species, Al3+·H2O·Cl−. In Figure 4b, the features of the experimental spectrum are broader than the calculated spectrum. Subsequent XRD analysis showed the existence of 15% of the hydrate, Na4Al4O8·5H2O, in the sample, and this may be the cause of some broadening of the experimental

NaAlO2 spectra with respect to the calculated one. Further, a smaller cluster was used for the sodium aluminate (43 atoms) calculation versus a somewhat larger cluster for the α-alumina (107 atoms). The line width would be somewhat broadened with a larger cluster size. Defining the K-Edge Onset for TDDFT Derived from AIMD. For experimental spectra the K-edge energy, E0, is typically defined by the position of the primary maximum of the first derivative. As shown in Figure 5, the experimental values of E0 are 1567.7 and 1568.1 eV for α-alumina and aqueous Al3+, respectively. A similar methodology was applied to the theoretical spectra as shown in Figure 5 because it puts the definition of E0 on the same basis as the experimental one. For the TDDFT spectra there are tens of different electronic transitions (Figure 4a) that occur near the edge region of the αalumina. For the aqueous Al3+, this disordered system further includes hundreds of additional transitions (Figure 4c) from the structural dynamics. This method of derivative was used to establish the E0 positions for the TDDFT reported in Table 1.

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CONCLUSIONS The KLII&III double-electron transition, a prominent feature in Al XAFS spectra, has an edge height that ranges from about 3− 10% of the height of the K-edge. For these reasons it represents an important aspect in Al XAFS analysis. The intensity of the KLII&III transition is dependent upon the local symmetry about the Al atom. For octahedral symmetry the transition is strong whereas for tetrahedral symmetry it is approximately 3 times weaker. The XANES structure at the Al KLII&III-edge provides an independent set of information about the chemical and 8386

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electronic state of the core atom (Al). The extended-XAFS region (EXAFS) up to 20−40 eV above the KLII&III-edge mostly mimics the spectral structure for the K-edge spectra. Both ΔSCF and TDDFT methods predict the K-edge positions and their chemical shifts for the four different standard compounds, α-alumina, sodium aluminate, aqueous Al3+, and aqueous Al(OH)4−. The TDDFT method provides a much more accurate prediction of the E0 chemical shifts for this series of Al compounds than does the ΔSCF method. The ΔSCF method was used to calculate the positions of the KLII&III and KLI double electron transitions and thereby confirm the assignments of the experimentally observed edges. In comparison to the KLII&III-edge, the intensity of the KLI-edge is quite weak but it may contribute certain sharp features at high k in the K-edge EXAFS spectrum. The TDDFT method predicts the full K-edge XANES spectra for the four standard compounds. The primary spectral peaks in the pre-edge and XANES region (up to about 15 eV) are successfully reproduced. For the disordered aqueous systems, it is essential to generate an average TDDFT spectrum from a series of MD snapshots to reproduce the experimental spectrum. A full description of the K- and KLII&III-edge transition has the potential to expand the understanding of aqueous Al3+, Al(III) hydroxides, and Keggin ions and the structure and chemistry of zeolite Brønsted acid sites formed via Al incorporation in the silicate framework.

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AUTHOR INFORMATION

Corresponding Authors

*John L. Fulton. E-mail: [email protected]. *Niranjan Govind. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The Al XAFS measurements were performed at the PHOENIX beamline of the Swiss Light Source, Paul Scherrer Institute, Villigen, Switzerland. Research by J.L.F., N.G., E.J.B., A.V., and T.D.S. was supported by U.S. Department of Energy’s (DOE), Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Biosciences. N.G. thanks Amity Andersen for help with the α-Al2O3 and tetrahedral sodium aluminate (NaAlO2) clusters. All the calculations were performed using the Molecular Science Computing Capability at EMSL, a national scientific user facility sponsored by the U.S. Department of Energy’s Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory (PNNL). PNNL is a multiprogram national laboratory operated for DOE by Battelle Memorial Institute under Contract # DE-AC06-76RL0-1830.

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