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CCC01063.0005 X-ray Absorption Spectroscopy
J. E. PENNER-HAHN
1.59.1 PHYSICS OF X-RAY ABSORPTION
CCC01063.0010 X rays are ionizingradiation and thus, by definition, have sufficient energy to eject a core election from an atom. Each core shell has a distinct bindingenergy, and thus if one plots X-ray absorption as a function of energy, the spectrum for any atom resembles the X-ray absorption spectrum for Pb, shown in Figure 1.1–4^ When the X-ray energy is scanned through the binding energy of a core shell, there is an abrupt increase in absorption cross-section. This gives rise to a
- 1.59.1 PHYSICS OF X-RAY ABSORPTION The University of Michigan, Ann Arbor, MI, USA
- 1.59.1.1 X-ray Absorption Edges
- 1.59.1.2 X-ray Fluorescence
- 1.59.1.3 Measurement of X-ray Absorption Spectra
- 1.59.2 EXTENDED X-RAY ABSORPTION FINE STRUCTURE
- 1.59.2.1 Theoretical Description of EXAFS Spectra
- 1.59.2.1.1 Single scattering
- 1.59.2.1.2 Multiple scattering
- 1.59.2.1.3 Other corrections to the EXAFS equation
- 1.59.2.2 Programs for Calculating and Analyzing EXAFS
- 1.59.2.2.1 Fourier transforms
- 1.59.2.2.2 Curve fitting
- 1.59.2.3 Limitations of EXAFS
- 1.59.2.4 Applications of EXAFS to Coordination Chemistry
- 1.59.2.4.1 De novo structure determination
- 1.59.2.4.2 Solution structure determination
- 1.59.2.4.3 Resolution of crystallographic disorder
- 1.59.2.4.4 Time-dependent structural evolution
- 1.59.3 X-RAY ABSORPTION NEAR EDGE STRUCTURE
- 1.59.3.1 Sensitivity of XANES to Oxidation State
- 1.59.3.2 Multiple Scatteringand XANES
- 1.59.3.3 Bound State Transitions in XANES
- 1.59.3.4 Multi-electron Transitions in XANES
- 1.59.3.5 Applications of XANES to Coordination Chemistry
- 1.59.4 HIGHER RESOLUTION XAS
- 1.59.4.1 Polarization-dependent Measurements
- 1.59.4.1.1 Linearly polarized measurements
- 1.59.4.1.2 X-ray MCD
- 1.59.4.1.3 Natural circular dichroism
- 1.59.4.2 High-resolution X-ray Fluorescence
- 1.59.4.2.1 Elimination of lifetime broadening in XANES
- 1.59.4.2.2 Site-selective XAS
- 1.59.4.3 Spatially Resolved Measurements
- 1.59.4.3.1 Methods for focusing X rays
- 1.59.4.3.2 Applications of X-ray microprobes
- 1.59.5 REFERENCES
so-called absorption edge, with each edge representing a different core–electron binding energy. The edges are named according to the principle quantum number of the electron that is excited: K for n ¼ 1, L for n ¼ 2, M for n ¼ 3, etc. The core–electron bindingenergy increases with increasing atomic number, ranging from 284 eV for the C K edge to 115,606 eV for the U K edge, with the L edges at significantly lower energies than the corresponding K edge (e.g., 270 eV for the Cl L (^1) edge, 20,948 eV and 17,166 eV for the U L 2 and L 3 edges). CCC01063.0015 Closer examination of Figure 1 (see inset) shows that the L edge is in fact three distinct L edges, named L 1 , L 2 , and L 3 in order of decreasingenergy. L 1 corresponds to excitation of a 2s electron. The 2p excitation is split into two edges, L 2 and L 3 , as a consequence of the spin–orbit coupling energy of the 2p^5 configuration that is created when a 2p electron is excited. The higher energy of the 2p^5 excited states is the 2 P1/2 term; This gives rise to the L 2 edge. At lower energy is the L 3 edge, correspondingto the 2 P (^) 3/2 excited state. Due to degeneracy, the L 3 edge has twice the edge jump of the L 2 and L 1 edges. In contrast with valence electron shells where spin–orbit coupling energies are relatively small, the spin–orbit couplingfor core shells can be quite large. For Pb, the L 2 L (^3) splittingis 2,165 eV (1 eV ¼ 8,066 cm^1 ). Analogous, albeit smaller, splitting occurs for the lower- energy edges, with 5 M edges, 7 N edges, etc. X-ray absorption spectroscopy (XAS) refers to the measurement of X-ray absorption cross-section in the vicinity of one or more absorbingedges.
1.59.1.1 X-ray Absorption Edges
CCC01063.0020 An absorption edge by itself is of little value beyond elemental identification.5,6^ However, if one examines any of the edges in Figure 1 in more detail, they are found to contain a wealth of information. This is illustrated by the schematic absorption edge shown in Figure 2. The absorp- tion edge is not simply a discontinuous increase in absorption, as suggested by Figure 1, but in
Energy (ke V)
Absorbance (
cm
g
M
L
K
L
3
L
2
L
1
Figure 1 Low-resolution X-ray absorption spectrum for Pb. Three major transitions are seen (K, L, and M edges), corresponding to excitation of an electron from n ¼ 1, 2, and 3 shells, respectively. At higher resolution (inset) both the L and the M edges are split (see text for details).
Energy (e V)
Absorption
XANES EXAFS
Figure 2 Schematic illustration of an X-ray absorption spectrum, showingthe structured absorption that is seen both within ca. 50 eV of the edge (the XANES) and for several hundred to >1,000 eV above the edge (the EXAFS).
ionization chamber^12 in front of and behind the sample, usingBeer’s law to convert to absorption coefficient. This approach is limited to moderately concentrated samples (greater than ca. 10 mM or 500 ppm) and, depending on the energy of the absorption edge, even these concentrations may not be accessible. For example, sulfur or chlorine containingsolvents are nearly opaque to lower- energy X rays and thus interfere with XAS measurements. CCC01063.0035 To avoid the limitations of absorption, XAS spectra are frequently measured as fluorescence excitation spectra.^13 This is particularly important for dilute samples such as catalysts, biological samples, or environmental samples. The basic experimental geometry is illustrated in Figure 4. Providingthe sample is dilute (absorbance due to the element of interest is much smaller than the background absorbance) or thin (total absorbance <<1), the intensity of the fluorescence X rays is proportional to the X-ray absorption cross-section (see Figure 4).^14 In most cases, the sample will emit a variety of X rays, both the fluorescence X rays of interest and a background of scattered X rays. In order to have good sensitivity, the fluorescence detector needs some kind of energy resolution to distinguish between the signal and background X rays. In some cases, energy resolution can be provided by a simple low-pass filter15,16^ although for the ultimate sensitivity it is necessary to use higher resolution in order to more effectively exclude background radiation. This is typically an energy-resolving solid-state fluorescence detector,17–19^ although recent advances with wavelength- resolving detectors (i.e., multilayer diffraction gratings) may be important in special cases.20, CCC01063.0040 In principle, any physical property that changes in proportion to X-ray absorption could be used to measure XAS spectra. In addition to X-ray fluorescence, properties that have been used include photoconductivity,^22 optical luminescence,22–24^ and electron yield, 25,26^ although only the latter is widely used. Electron yield detection of XAS is particularly important for studies of surfaces. Since the penetration depth of an electron through matter is quite small, electron yield can be used to make XAS measurements surface sensitive. 27, CCC01063.0045 Although XAS can be studied for virtually any X-ray absorption edge, experiments are simplest when they can be performed at atmospheric pressure. This limits the accessible X-ray energies to those greater than approximately 5 keV (for air) or 2 keV (for a He atmosphere). Lower energy measurements (i.e., measurements of the K edges for elements lighter than phosphorus) require that the sample be in vacuum in order to avoid excessive attenuation of the incident X-ray beam. Similarly, it is difficult, although not impossible, to make XAS measurements at energies above approximately 30 keV (K edge energy for Sn ¼ 30.5 keV). However, this does not limit XAS significantly, since elements that are heavy enough to have K edge energies >30 keV have readily accessible L edge energies (the L 3 edge for Sn is at 4 keV). This means that XAS spectra can be measured for virtually every element, although measurements for elements lighter than phos- phorus generally require that the sample be made vacuum compatible. X-ray absorption spectra can be measured for solids, liquids, or gases and do not require that samples have long-range order (i.e., be crystalline) or that samples possess particular magnetic properties (e.g., non-zero electron spin or specific isotopes). Measurements can be made at low temperature for studies of unstable samples, or at high temperature and/or pressure, for example for studies of catalysts under reaction conditions or of geochemical samples under conditions that approximate the inner mantle. This flexibility, combined with near universality, has made XAS a widely utilized technique in all areas of coordination chemistry.
Monochromatic Beam
fluorescence detector
IF
I0 Ion chamber I1Ion chamber
sample
Transmission: A = ln I^0 I
IF
I
Fluorescence: A =^
Figure 4 Typical experimental apparatus for XAS measurements. Incident and transmitted intensities are typically measured usingan ion chamber; a variety of detectors can be used to measure X-ray fluorescence intensity for dilute samples (see text).
CCC01063.0050 The critical experimental detail that limits the utility of XAS, and that accounts for XAS havingbeen an obscure technique prior to about 1975, is the need for an intense, tunable X-ray source. Conventional X-ray sources work much the same as the X-ray tube that was invented by Ro¨ ntgen:^29 an electron beam strikes a target which emits both ‘‘characteristic’’ radiation (X-ray fluorescence lines) and a broad continuous background of bremsstrahlung radiation. Only the latter is useful for XAS, since XAS measurements require a broad band of X-ray energies. The intensity of monochromatic radiation that can be obtained from the bremsstrahlungradiation is too low for most XAS measurements. CCC01063.0055 The development that allowed XAS to become a routine analytical tool was the recognition that the electron storage rings that are used in high-energy physics can serve as an extremely intense X-ray source. When an electron beam is accelerated, for example by usinga magnetic field to cause the beam to follow the curvature of a storage ring, the electron beam radiates a broad spectrum of ‘‘synchrotron’’ radiation. From modest beginnings in the early 1970s, synchrotron radiation laboratories have grown enormously to the point that there are now over 75 labora- tories, either planned, under construction, or in operation, devoted to the production of synchro- tron radiation in one form or another, located in 23 countries.^30 A selection of some of the more important sources for XAS is given in Table 1. Other countries that will soon join this list include Armenia, Canada, Jordan, Spain, Thailand, and the Ukraine. Each of these laboratories is based around an electron (or positron) storage ring. Ring sizes vary, but modern synchrotrons typically have a circumference of approximately one kilometer. This size is large enough to accommodate anywhere from 10 to perhaps 100 independent ‘‘beamlines’’ (the hardware that transports the X rays from the synchrotron source to the experimental apparatus) at each synchrotron laboratory. CCC01063.0060 The importance of synchrotron radiation can be seen by comparingthe X-ray flux that is available from X-ray tubes with that available from synchrotron sources (Figure 5). The spectral brightness (X-ray flux normalized by area that is irradiated and divergence of the beam) of the most powerful sources is more than 10 orders of magnitude greater than that available from X-ray tubes. Another advantage of synchrotron sources is that the synchrotron X-ray beam is polarized, thus permittingorientation-dependent measurements for ordered samples. In addition,
Table 1 Major synchrotron sources for XAS.
Country Location Synchrotron source
Brazil Campinas LNLS China (PRC) BeijingBSRF Hefei NSRL China (ROC-Taiwan) Hsinchu SRRC Denmark Aarhus ASTRID France Grenoble ESRF Orsay LURE Germany Berlin BESSY HamburgHASYLAB/DESY India Indore INDUS Italy Trieste ELETTRA Japan Nishi Harima Spring- Tsukuba Photon Factory ht SourceKorea Lig PohangPohang Russia Moscow Siberia 1 Novosibirsk VEPP Singapore Singapore SSLS Sweden Lund MAX Switzerland Villigen SLS UK Daresbury SRS USA Argonne, IL APS Baton Rouge, LA CAMD Berkeley, CA ALS Ithaca, NY CHESS Stanford, CA SSRL Stoughton, WI Aladdin Upton, NY NSLS
is comparable to the interatomic distances. The EXAFS photoexcitation cross-section is modu- lated by the interference between the outgoing and the back-scattered photoelectron waves as illustrated schematically in Figure 6. At energy E 1 , the outgoing and the back-scattered X rays are in phase, resultingin constructive interference and a local maximum in the X-ray photoabsorp- tion cross section. At higher X-ray energy, the photoelectron has greater kinetic energy and thus a shorter wavelength, resulting in destructive interference and a local minimum in photoabsorption cross section (energy E 2 ). The physical origin of EXAFS is thus electron scattering, and EXAFS can be thought of as a spectroscopically detected scattering method, rather than as a more conventional spectroscopy. CCC01063.0075 For a single absorber–scatterer pair (for example, in a diatomic gas) this alternating interfer- ence will give rise to sinusoidal oscillations in the absorption coefficient if the energy is given in units proportional to the inverse photoelectron wavelength (the photoelectron wavevector, or k, defined as in Equation (1)). In Equation (1), the threshold energy, E 0 , is the bindingenergy of the photoelectron.
k ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 me ðE E 0 Þ=h^2
q ð 1 Þ
CCC01063.0080 In XAS analyses, it is typical to define the EXAFS, (k), as the fractional modulation in the X-ray absorption coefficient as in Equation (2), where is the observed absorption coefficient and 0 is the absorption that would be observed in the absence of EXAFS effects. Since 0 cannot be directly measured, it is approximated, typically by fittinga smooth spline function through the data. Division by 0 normalizes the EXAFS oscillations ‘‘per atom,’’ and thus the EXAFS represents the average structure around the absorbing atoms.
ðkÞ ¼
0 0
ð 2 Þ
CCC01063.0085 When plotted as (k), EXAFS oscillations have an appearance similar to that shown in Figure 7. The amplitude of the EXAFS oscillations is proportional to the number of scatteringatoms, the frequency of the oscillations is inversely proportional to the absorber–scatterer distance, and the shape of the oscillations is determined by the energy dependence of the photoelectron scattering, which depends on the identity of the scatteringatom. For quantitative analyses, the EXAFS can be described31–33^ by an equation such as Equation (3), with the summation taken over all of the scatteringatoms near the absorber.
ðkÞ ¼
X
s
N (^) s A (^) sðkÞS (^20) kR^2 as
expð2R (^) as=ðkÞÞexpð 2 k^2 as^2 Þ sinð 2 kR (^) as þ asðkÞÞ ð 3 Þ
CCC01063.0090 In Equation (3), the parameters that are of principal interest for coordination chemistry are the number of scatteringatoms, Ns and the absorber–scatterer distance, Ras. However, there are a variety of other parameters that must either be determined or be defined in order to extract the chemically relevant information. Chief amongthese are As (k) and as (k). These represent, respect- ively, the energy dependence of the photoelectron scattering, and the phase shift that the photo- electron wave undergoes when passing through the potential of the absorbing and scattering atoms. These amplitude and phase parameters contain the information necessary to identify the scatteringatom. Thus, for example, sulfur and oxygen introduce phase shifts, as (k), that differ by approximately . Unfortunately, both As (k) and as (k) depend only weakly on scatterer identity, and thus it is difficult to identify the scatterer with precision. This means that O and N, or S and Cl, typically cannot be distinguished, while O and S can. CCC01063.0095 The EXAFS amplitude falls off as 1/R^2. This reflects the decrease in photoelectron amplitude per unit area as one moves further from the photoelectron source (i.e., from the absorbingatom). The main consequence of this dampingis that the EXAFS information is limited to atoms in the near vicinity of the absorber. There are three additional dampingterms in Equation (2). The S 02 term is introduced to allow for inelastic loss processes and is typically not refined in EXAFS analyses. The first exponential term is a dampingfactor that arises from the mean free path of the photoelectron ((k)). This serves to limit further the distance range that can be sampled by EXAFS. The second exponential term is the so-called ‘‘Debye–Waller’’ factor. This dampingreflects the fact that if there is more than one absorber–scatterer distance, each distance will contribute EXAFS oscillations of a
slightly different frequency. The destructive interference between these different frequencies leads to dampingin the EXAFS amplitude. The Debye–Waller factor, as, is the root-mean-square devia- tion in absorber–scatterer distance. This dampingis always present due to zero-point thermal motion, and may, for polyatomic systems, also occur as a consequence of structural disorder. As a consequence of the dampingterms in Equation (3), EXAFS oscillations are typically only observed for atoms within approximately 5 A˚ of the absorbingatom. CCC01063.0100 In Equation (3) the backscatteringamplitude and phase are assumed to depend only on the identity of the absorber and the scatterer. This derives from the so-called plane wave approxima- tion, in which the curvature in the photoelectron wave is neglected and the photoelectron is treated as a plane wave.34–36^ For energies well above the X-ray edge (high k, short photoelectron wavelength) or for long absorber–scatterer distances this is a fairly reasonable assumption. It is not, however, a good assumption for most of the useful EXAFS region. Modern approaches to calculatingamplitude and phase parameters (see Section 1.59.2.2) include spherical wave correc- tions to the amplitude and phase, thus introducinga distance dependence to As and as.
1.59.2.1.2 Multiple scattering
CCC01063.0105 The discussion above assumed that the X-ray excited photoelectron was scattered only by a single scattering atom before returning to the absorbing atom (e.g., Figure 6). In fact, the X-ray excited photoelectron can be scattered by two (or more) atoms prior to returningto the absorbingatom. Multiple scatteringis particularly important at low k where the photoelectron has a very low energy and consequently a long mean-free path, allowing it to undergo extensive multiple scattering. Multiple scattering is particularly strong if the two scattering atoms are nearly collinear since the photoelectron is strongly scattered in the forward direction. In this case, the EXAFS oscillations due to the multiple scatteringpathway (absorber! scatterer 1! scatterer 2! scatterer 1! absorber in Figure 8) can be as much as an order of magnitude stronger than that due to the single scattering pathway (absorber! scatterer 2! absorber).37–39^ Failure to account for multiple scatteringcan lead to serious errors in both EXAFS amplitude and phase, with consequent errors in the apparent coordination number and bond length. CCC01063.0110 Multiple scattering is extremely angle dependent. For scattering angles less than ca. 150^ (the angle A–S 1 S 2 in the example above), multiple scatteringis weak and can often be neglected. However, for angles between 150^ and 180, multiple scatteringmust be considered. The angle dependence of multiple scatteringmeans that EXAFS can, at least in principle, provide direct information about bond angles. Even when accurate angular information cannot be obtained (see below), multiple scattering is still important because it gives certain coordinating groups unique EXAFS signatures. These include both linear ligands such as CO and CN, as well as rigid cyclic ligands such as pyridine or imidazole. This can, in some cases, improve the limited sensitivity of EXAFS to scatterer identity. For example, in biological systems water and the imidazole group of
Absorption
E 1
E 2
A
A
S
S
Energy (eV)
6400 6500 6600 6700 6800 6900
Figure 6 Schematic illustration of the physical basis of EXAFS oscillations. The X-ray excited photo- electron is represented by concentric circles around the absorbingatom (A), with the spacingbetween circles representing the de Broglie wavelength of the photoelectron. The photoelectron is scattered by surrounding atoms (indicated by a single atom S in the figure). At energy E 1 , the out-going and back-scattered waves are in phase, resultingin constructive interference and a local maximum in photoabsorption cross-section. At a slightly higher energy E 2 (shorter photoelectron wavelength) the absorber–scatterer distance gives destructive interference and a local minimum in absorbance.
(2)) and conversion to k space (Equation (1)). Data analysis is, at least in principle, a relatively straightforward problem of optimizing the variable parameters in Equation (3) so as to give the best fit to the observed data usingsome sort of non-linear least-squares fittingprocedure. Over 20 programs are available to accomplish the data reduction and analysis.^56 Most are quite similar in their functionality. CCC01063.0125 In order to fit EXAFS data, it is first necessary to determine the parameters that define the scattering( As (k), S 02 , as (k), and (k)). This can be done using ab initio calculations or from model compounds of known structure. In recent years, the available theoretical methods for quickly and accurately calculatingthese parameters have improved dramatically. Ab initio calculations are now relatively straightforward, with three main programs that are in wide use: FEFF39,57,58, EXCURVE41,59, and GNXAS60–62. Although these differ in the particulars of their approach to EXAFS, all give approximately the same structural parameters.^63 In contrast, older approaches, particularly those usingthe earliest plane-wave parameters 34–36^ often fail to give accurate structural results. Despite these well-known errors,^64 publications usingthese parameters continue to appear occasionally in the literature. Regardless of what theoretical parameters are used, careful comparison with model compounds remains important for proper calibration of the calculated parameters.^65 CCC01063.0130 Usingcarefully calibrated parameters to determine S^20 and E 0 , it is possible to obtain excellent accuracy for EXAFS bond length determinations. Typical values, determined by measuring data for structurally defined complexes, are 0.01–0.02 A˚ for nearest-neighbor distances and somewhat worse for longer distance interactions. The precision of bond-length determinations is even better, with experimentally determined reproducibilities as good as 0.004 A˚.^66 Coordination number is less well defined, due in part to correlation between N and ^2 (see Equation (3)). In many cases, EXAFS coordination numbers cannot be determined to better than 1. As noted above, EXAFS has only weak sensitivity to atomic type. Typically it is only possible to determine the atomic number of the scatteringatom to 10. Despite these limitations, the ability to provide structural information, particularly highly accurate bond lengths, for non-crystalline systems, has made EXAFS an extremely important tool in coordination chemistry.
1.59.2.2.1 Fourier transforms
CCC01063.0135 Although Equation (3) provides a complete description of the EXAFS oscillations, it is not a particularly convenient form for visualizingthe information content of an EXAFS spectrum. As with NMR spectroscopy, Fourier transformation can be used to decompose a k-space signal into its different constituent frequencies.^67 This is illustrated usingthe EXAFS data 68 for a THF solution of CuCN2LiCl. The EXAFS spectrum (Figure 9) clearly contains more than one frequency, based on the complex variation in amplitude. For EXAFS, the canonical variables are k (in A˚ ^1 ) and R (in A˚), and the Fourier transform (FT) of an EXAFS spectrum gives a
Cu–C–N–Cu
Fourier Transform Magnitude
EXAFS
· K
(^3)
6 5 4 3 2 1 0 0
0
1.5 3 4.5 6 7.
4
2
2.5 4.5 6.5 8.5 10.5 12. K (Å–^1 ) R +^ α^ (Å) Figure 9 EXAFS data (left) and its Fourier transform (right) for a THF solution of CuCN.^ 2LiCl.^68 The Fourier transform clearly shows three distinct peaks, reflectingthe presence of three distinct absorber– scatterer interactions, as indicated above the Fourier transform.
pseudo-radial distribution function. The Fourier transform of the data in Figure 9 shows that there are three principal frequencies that contribute to this spectrum. These are due to scattering from the Cu nearest neighbors (C from the cyanide), the next-nearest neighbors (N from the cyanide), and the next-next-nearest neighbors (an additional Cu coordinated to the distal end of the cyanide). The third peak thus clearly shows formation of a (CuCN)n oligomer under these conditions. The FT amplitude is not a true radial distribution function since the amplitude cannot be related directly to electron density around the absorber due to the As (k) factor and the dampingfactors in Equation (3), and the apparent distances in the FT are shifted by about 0.5 A˚ due to the phase shift as (k). The unusually high intensity of the second and third peaks in Figure 9 is due to the near linearity of the CuCNCu unit, which leads to intense multiple scattering. CCC01063.0140 The FT is useful for obtaininga qualitative understandingof a system. However, Fourier transforms are subject to several potential artifacts and cannot be used for quantitative data analysis. Dependingon the resolution of the data (see below), multiple shells of scatterers do not necessarily give rise to multiple peaks in the FT.^69 Perhaps more important, two peaks may appear to be well-resolved despite the fact that they have substantial overlap. This is illustrated in Figure 10, where the top FT is for the sum of two EXAFS spectra (simulated for MnO distances of 1.9 A˚ and 2.1 A˚) while the bottom shows the FTs of the two individual components. Although the two peaks appear to be well resolved, each peak, in fact, contains significant contributions from the other scatterer. This phenomenon is due to the fact that the FT is a complex function, includingboth real and imaginary components. Typically (e.g., Figure 10) what is plotted is the modulus of the Fourier transform, thus losingall phase information. In Figure 10, the Fourier components from the two different scatterers interfere destructively, leadingto the minimum in the modulus. CCC01063.0145 Interference such as that in Figure 10 is particularly important if the data are Fourier filtered. Fourier filteringinvolves selectingcertain frequencies in R space to use for a back Fourier transform (back into k space). Filteringcan greatly simplify the curve-fittingproblem, since the filtered data contains only a single shell of scatterers (this amounts to dropping the summation in Equation (3)). However, as illustrated by Figure 10, filtering can have unexpected consequences. Neither of the peaks in the top panel actually represents the scatteringfrom a single atom, despite the apparent resolution of the data; attempts to fit these as though they represent single shells leads to erroneous conclusions.^69
1.59.2.2.2 Curve fitting
CCC01063.0150 A typical coordination complex might have six different nearest-neighbor distances, together with a larger number of longer distance interactions. Although each of these contributes a slightly different signal to the overall EXAFS, it is not realistic to refine all of the different absorber–
Fourier transform magnitude
R + α (Å)
40 35 30 25 20 15 10 5 0 0 1 2 3 4
Figure 10 Fourier transform of the simulated EXAFS for two shells of scatterers. Data calculated for MnO distances of 1.9 and 2.1 A˚. (top) FT of the sum of the EXAFS signals of each shell. (bottom) FTs of the two individual components. Although there is significant overlap in the two shells, the FT of the sum appears to show baseline separation as a consequence of phase differences in the Fourier terms.
the ability of EXAFS to probe structure. One involves the ability of EXAFS to resolve contributions from two different scatterers. The best resolution that can be achieved^73 is given in Equation (8).
R = 2 k ð 8 Þ
This gives R 0.13 A˚ for data to kmax¼12 A˚ ^1. However, this estimate is generally too optimis- tic as illustrated by Figure 11, which shows pairs of simulated EXAFS spectra for one shell (dashed lines) and two shells (solid lines).^69 The top trace shows the simulation for a pair of scatterers separated by 0.25 A˚ (R 1 ¼1.75, R 2 ¼2.00 A˚ ). There is an obvious ‘‘beat’’ in the EXAFS amplitude at k 8 A˚ ^1 which distinguishes these data from the EXAFS for a single shell at the same average distance (1.875 A˚ ). The middle simulation shows that there is still a beat when R decreases to 0.15 A˚, although the beat has moved close to kmax. It is straightforward to distinguish between two shells and a single shell at the average distance (1.925 A˚, dashed line). However, if the single-shell simulation is damped with an exponential damping factor (lower traces) it is now nearly impossible to distinguish between one shell (dashed line) and two shells (solid line). It is only at high k, where the noise in an experimental spectrum is the largest, that the one- and two- shell simulations are distinguishable. It is unlikely that these spectra could be distinguished for
R 1 = 1.75 Å, R 2 = 2.00 Å
R 1 = 1.85 Å, R 2 = 2.00 Å
R 1 = 1.85 Å, R 2 = 2.00 Å
R = 1.875 Å
R = 1.925 Å
R = 1.925 Å,
damped
k ( Å^ – 1 )
EXAFS
• K
3
Figure 11 Simulated EXAFS data for one-shell (dashed line) and two-shell (solid line) models. In each case, the one-shell simulation has a distance equal to the average of the two-shell simulation. For the top and middle simulations, both one-shell and two-shell data use the same Debye–Waller factor. For the bottom simulation, the one-shell Debye–Waller factor has been increased to give the best agreement with the two- shell data. Two shells with a small Debye–Waller factor are, for any realistic noise level, indistinguishable from a single shell with a large Debye–Waller factor.
real (i.e., noisy) data, even though R > /2k. This is because the Debye–Waller factor (^2 in Equation (3)) can mimic the dampingthat is caused by the presence of two shells of scatterers. This illustrates the fact that although the resolution limit of EXAFS is much better than those of most crystallography, it is nevertheless sufficiently poor that it is often not possible to resolve the contributions from different nearest neighbors, even when they are known chemically to be present at different distances. CCC01063.0170 The definition of resolution is more complicated if there is more than one type of scattering atom. The presence of two different kinds of scatteringatoms may increase the effective resolu- tion. For example, the EXAFS signals for F and Cl have quite different As (k) and as (k). This means that F and Cl EXAFS signals can be resolved even if the distances are identical, although this can be complicated by destructive interference between the O and Cl signals.^65 Conversely, the presence of several different scatterers at about the same distance can change the apparent amplitude of an EXAFS feature, thus leadingto misassignment of the chemical identity of the scatterer. For example, a Cu–Cu shell in the CuA site of cytochrome oxidase^74 was initially assigned as a Cu–S interaction75–77^ due to interference and the limited k range of the data.
1.59.2.4 Applications of EXAFS to Coordination Chemistry
CCC01063.0175 There are over 15,000 papers dealingwith the application of X-ray absorption spectroscopy. Since the development of intense, readily accessible synchrotron sources in about 1980, there has been a steady growth in the applications of EXAFS (see Figure 12). Although the applications cover all areas of science, a significant fraction of these address questions of interest to coordination chemistry. Given the size of this literature, it is not realistic to report on all of the applications of EXAFS. In selectingthe examples below, no attempt has been made to provide a comprehensive survey of the literature; a number of excellent reviews exist that survey different field-specific applications of EXAFS27,78–91^ together with several monographs on the subject.86,92–94^ Rather, the examples below have been selected to illustrate important types of applications.
1.59.2.4.1 De novo structure determination
CCC01063.0180 For de novo structure determination, one measures the EXAFS spectra for one or more of the atoms in a sample and uses this information to determine the structure around the absorbing atom. In principle this is straightforward, although in practice the analysis is often complicated by the limitations discussed above. It is seldom the case that EXAFS can provide reliable informa- tion for scatterers that are more than 5 A˚ from the absorbingatom and in most cases EXAFS provides little or no angular information. Despite these limitations, de novo structure determin- ation remains one of the most important applications for EXAFS. The areas in which de novo structure determination are most important are those in which crystallography cannot be used. One key area is bioinorganic chemistry. It has been estimated that one-third of all proteins bind
Figure 12 Number of XAS papers published per year. Solid line is a polynomial fit to the data.
EXAFS with crystallography thus provides a more detailed structural characterization than would be possible from either measurement alone.
1.59.2.4.4 Time-dependent structural evolution
CCC01063.0205 An excitingnew development in XAS is the ability to measure time-resolved spectra. This provides a powerful tool for investigating the reactivity of solids in catalysis and solid-state chemistry.129,130^ To date, most studies have been limited to a time resolution of seconds although this can, in principle, extend into the femtosecond regime.130,131^ The latter offers the possibility of probingdirectly the structure of photoexcited states, thus followingdirectly the structural changes that accompany a chemical.132,133^ Before this can be widely applied, more intense femtosecond X-ray sources are needed.^134 At present, time-resolved studies in the second to millisecond times are becomingrelatively straightforward, and are providingimportant new chemical information. CCC01063.0210 Although other probes may be substantially easier to use, XAS is sometimes the only method that is sensitive to the structures of interest, particularly for solid-state samples and in situ studies of catalysts.135–138^ For example, in a study of the reduction of NiO, time-resolved X-ray diffrac- tion had shown that the catalyst went directly from NiO! Ni without a well-ordered intermedi- ate phase,^137 but could not rule out the existence of an amorphous NiOxphase, since the diffraction was not sensitive to disordered phases. However, the formation of an intermediate phase could be ruled out by time-resolved EXAFS. A similar situation exists for spectroscopically ‘‘silent’’ metals (d^10 systems), which are difficult to probe with methods other than XAS. Exam- ples that are important in bioinorganic chemistry include Cuþ^1 and Zn^2 þ. For carboxypeptidase, time-resolved XAS could be used to determine the rate of change of the native Zn 2 þ^ site, while conventional UV-visible methods could only be used on the Co 2 þ^ substituted enzyme.^139 The importance of XAS in both of these examples is as a tool for measuringrate constants. CCC01063.0215 A second area where time-resolved EXAFS is important is for structural characterization of reactive intermediates. Reactive intermediates are difficult or impossible to crystallize. They may, however, be accessible to structural characterization by EXAFS. The difficulty is that a bulk technique such as EXAFS cannot easily be used to measure structure for minor components in a complex mixture. However, mathematical approaches such as principal component analysis140–142^ can be used to extract information about relatively minor components if a large enough number of individual spectra are measured. For example, in a study of the oxidation of n-butane over a V 2 O 5 catalyst, hundreds of XAS spectra were measured with 1 second time resolution.^143 No single spectrum gave sufficient information that could be used to distinguish the different species that were present. However, by usingprincipal component analysis, it was possible to identify contributions from three different species (one present at only ca. 20 mol.%) that contributed to the overall data variation. From comparison with standards, these components could be assigned to V^5 þ, V^4 þ, and V^3 þ. CCC01063.0220 Time-resolved studies frequently make use of a dispersive geometry in which the synchrotron beam is focused onto the sample usinga curved crystal, 144 as shown in Figure 13. In this geometry, the sample is illuminated with all X-ray energies simultaneously. The transmitted X rays are dispersed onto a position-sensitive detector, allowingmuch more rapid measurement of the spectrum. However, because this is a transmission geometry, dispersive measurements are limited to relatively concen- trated samples; dilute samples require the fluorescence geometry shown in Figure 4. For fluorescence, the time resolution is limited to the speed with which the monochromator can be scanned. This is typically several seconds per scan, although there are recent advances in rapid-scanning monochro- mators that can extend this to the millisecond regime.145,146^ Extremely fast time resolution (nanose- cond to femtosecond) requires a pump-probe experiment with a pulsed X-ray source.130,131,
1.59.3 X-RAY ABSORPTION NEAR EDGE STRUCTURE
CCC01063.0225 A typical XANES spectrum is shown in Figure 14 (this is an expansion of the edge shown in Figure 2). It is clear that the XANES region is more complex than simply an abrupt increase in absorption cross-section. There are several weak transitions below the edge (pre-edge transitions) together with structured absorption on the high energy side of the edge. Some XANES spectra show intense narrow transitions on the risingedge (these can be much more intense than the transition at the edge in Figure 14). These are often referred to as ‘‘white lines’’ in reference to the fact that when film was used to record X-ray absorption spectra, an intense transition would
absorb all of the incident X rays, thus preventingthe film from beingexposed and leavinga white line on the film. Above the edge, there are a variety of structures that show generally oscillatory behavior, ultimately becomingthe EXAFS oscillations. CCC01063.0230 The same physical principles govern both the EXAFS region and the XANES region. However, in the near edge region the photoelectron has low kinetic energy, giving it a long mean-free path. In addition, the exp(k^2 ) dependence of the Debye–Waller factor means that this dampingfactor is negligible in the XANES region. These effects combine to make the XANES region sensitive to longer distance absorber–scatterer interactions than are typically sampled by EXAFS. This greatly complicates simulation of XANES structure, since many interactions and a large number of multiple scatteringpathways need to be included. 147–149^ However, the sensitivity to multiple scatteringis, at least in principle, an advantage since it provides the possibility of extracting information about the three-dimensional structure from XANES spectra. Although much pro- gress has been made recently in the theoretical modeling of XANES,111,112,147–150^ most simula- tions of XANES structure remain qualitative. Nevertheless, the ability to make even qualitative fingerprint-like comparisons of XANES spectra can be important. If a representative library of reference spectra is available, spectral matchingcan be used to identify an unknown. Beyond this qualitative application, there are three main ways in which XANES spectra are used: to determine oxidation state, to deduce three-dimensional structure, and as a probe of electronic structure.
1.59.3.1 Sensitivity of XANES to Oxidation State
CCC01063.0235 The energy of an absorption edge is not well-defined. It can be taken as the energy at half-height or, more commonly, as the maximum in the first derivative with respect to energy. However, as
Energy (eV)
(^6500 )
Absorption
Pre-edge transitions
White line
Figure 14 Expansion of the XANES region for the data shown in Figure 2, showing different features within the XANES region.
Bent monochromator crystal
High energy
Low energy
Sample
Position sensetive detector
“white” synchrotron beam Figure 13 Dispersive XAS geometry. A broad band of X-ray energies is focused onto the sample using a curved crystal and detected usinga position-sensitive detector. Time resolution is limited only by the readout time of the detector (microseconds in principle) but samples are limited to those accessible by transmission.
complexes, as shown in Figure 15.164,165^ and thus can be used to deduce geometry. The greater intensity for square–planar complexes may be due to decreased mixingbetween the empty 4 p orbital (4p (^) z) and the ligand orbitals. This intensity of the 1s! 4 p transition is even more dramatic for 2-coordinate Cu I^.^166 CCC01063.0260 An alternative, complementary, approach to electronic structure information is to use ligand XANES rather than metal XANES. This is particularly promisingas a tool for investigatingsulfur or chlorine ligands167–169^ and has been used to quantitate the amount of metal–ligand orbital mixing (i.e., the covalency) of different complexes.^170 For example, excitation at the Cl K edge gives rise to an allowed 1 s! 3 p transition. Since the Cl 3p orbitals are bondingorbitals in metal chlorides, the lowest energy transition at the Cl edge is actually a 1s(Cl)! HOMO transition, where the HOMO has both metal 3 d and Cl 3p character. The intensity of this transition is a direct measure of the percent 3p character of this orbital (i.e., the covalency of the complex). Ligand XANES can be more useful than metal XANES due to the fact that the transitions of interest from a bondingperspective are 1 s! 3 p for S or Cl ligands and 1s! 3 d for a metal from the first transition series. The former is an allowed transition while the latter is forbidden by dipole selection rules, and consequently much weaker and harder to detect.
1.59.3.4 Multi-electron Transitions in XANES
CCC01063.0265 The single-electron bound-state transitions described above can be written as 1s (V) 1 , where the underline in 1s refers to a hole in the 1s orbital, and V is a valence orbital. At higher photon energies, the X-ray has sufficient energy to excite an extra electron into the valence band (e.g., V! V) resultingin double excitations such as 1 s V V^2. In this notation, excitation of the core electron to the continuum is described as 1s "p, where "p indicates a p-symmetry photoelectron, with variable energy ". The continuum states also have the possibility of multi-electron excita- tions, giving final states such as 1s V V*^1 "p. This class of multi-electron transition is sometimes referred to as shake-up transitions, to reflect the description of the excess energy as ‘‘shaking’’ a second electron into a higher-lying state.171, CCC01063.0270 In addition to shake-up transition, a second class of multi-electron transition is possible, as illustrated in Figure 16. Excitation of a core electron has the effect of converting an atom with atomic number Z into an atom with an apparent atomic number of Z þ 1. This means that, for example, in the 1s 4 p^1 state of Cu II, the valence electrons experience the effective nuclear charge of ZnII^. The increased nuclear charge lowers the energy of the Cu II^3 d orbitals so that they are now lower than the ligand orbitals (B and C in Figure 16). Two transitions are now possible: the direct 1 s 3 d^9 4 p^1 transition (Figure 16B) and the multielectron transition to 1s 3 d^10 4 p^1 L, in which a ligand electron has been transferred to the lower-energy Cu 3d orbital. The latter gives a lower-energy excited state, and is often referred to as a shake-down transition. Shake-down transitions are seen frequently in photoelectron spectroscopy but have not been invoked often in XANES. One prominent exception is Cu II^ , where polarized XANES spectra and theoretical calculations provide good evidence for shake-down transitions.157,173–175^ The large covalency of many Cu II^ complexes
1 s 4 p
1 s 3 d
Energy (eV) Figure 15 XANES spectra for 4-coordinate Ni II^ , redrawn from data in Ref. 164. (top) Ni(cyclam) (ClO 4 ) (^2) (square–planar) ; (bottom) (Me 4 N) 2 NiCl 4 (tetrahedral). Note the weaker 1s! 3 d transition and stronger 1 s! 4 p transition for the square–planar site.
makes shake-down transitions more important here, but it seems likely that shake-down and other multielectron transtions^176 contribute to many XANES spectra.
1.59.3.5 Applications of XANES to Coordination Chemistry
CCC01063.0275 XANES spectra are much easier to measure than EXAFS spectra since even weak transitions are considerably more intense than EXAFS oscillations at high k. A second advantage of XANES spectra is that they can often be treated spectroscopically—that is, that individual spectral features can be attributed to specific features in the electronic structure. In contrast, EXAFS spectra are spectroscopically detected scatteringpatterns; it is not possible to attribute a specific EXAFS oscillation to a specific structural feature. Despite these advantages, and the fact that the XANES region is inevitably scanned during the process of measuring EXAFS spectra, relatively little use has been made of XANES beyond qualitative comparisons of an unknown spectrum to reference spectra. The most common qualitative use is for oxidation state assignment, although near-edge features have also been used to distinguish metal-site geometry (e.g., Figure 15). CCC01063.0280 The complexity of XANES spectra, and in particular their sensitivity to multiple scattering from distant atoms, is largely responsible for the relatively limited attention that XANES spectra have received for quantitative analyses. With the development of new theoretical and computa- tional approaches to XANES,148,149,158,169,177^ the utility of XANES for investigating coordination complexes is likely to increase.
1.59.4 HIGHER RESOLUTION XAS
CCC01063.0285 Despite the numerous applications of XAS, XAS spectra have, in general, quite limited resolu- tion. For XANES, resolution limits are the consequence of relatively broad spectral lines and severe spectral overlap. Resolution can be improved, in some cases quite dramatically, by using polarization-dependent measurements to reduce spectral overlap (Section 1.59.4.1) or by using inelastic scattering(high-resolution fluorescence) to reduce line widths (Section 1.59.4.2). For EXAFS, one of the most serious resolution limitations results from the fact that EXAFS is sensitive to all of the absorber in a sample; if two different metal sites are present, EXAFS will give only the average structure. This can be addressed, in some cases, by using high-resolution fluorescence to
Direct 1 s 4 p 1 s 4 p + LMTC
4 p 4 p 4 p 3 p 3 p 3 p
3 d 3 d 3 d
1 s 1 s 1 s
Ground state 1 s core-hole excited state
( a ) ( b ) ( c ) Figure 16 Schematic illustration of the energy levels involved in bound-state XANES features for 3d transi- tion metals. For each diagram, metal orbitals (1s, 3d, 4p) are on the left and ligand orbitals (3p) are on the right. (a) Ground state; (b) 1s core-hole excited state showingdirect 1 s! 4 p transition; (c) 1s core-hole excited state showingmultielectron 1 s! 4 p plus ligand-to-metal charge transfer shake-down transition. Due to the higher effective charge of the core-hole excited state, the multielectron transition is at lower energy than the direct transition. The intensity of the shake-down transition is a measure of the covalency of the site (i.e., the metal 3 d þ ligand 3p mixing).
