Chapter 8.11. EXAFS applications in coordination chemistry

A metal complex with strongly coordinated ligands does not always crystallize into the dominant solution structure. For example, with D-penicillamine (3,3′-dimethylcysteine; H₂Pen), lead(II) crystallizes as the 1:1 Pb(S,N,O-Pen) complex even when a combination of Pb L₃-edge EXAFS and ²⁰⁷Pb NMR shows that two 1:2 [Pb(S,N,O-Pen)(S-H_nPen)]²⁻ⁿ (n = 0, 1) species with PbS₂NO coordination prevail in solution, with average Pb–2S and Pb–2(N/O) distances of 2.64 ± 0.04 and 2.45 ± 0.04 Å, respectively (Freeman et al., 1974; Schell et al., 2012; Sisombath et al., 2014). This result highlights that the same system can be examined in solution, powder and crystalline states to explore solution equilibria and phase-related structural differences. This particular strength of EXAFS is now widely exploited to probe catalysts in operando (Bordiga et al., 2013; Weiher et al., 2005).

Despite nearly 70 years of study, the structure of dissolved d⁹ [Cu(aq)]²⁺ remains under active investigation, with a focus on the axial Jahn–Teller (JT) distortion. At the time of writing, the Cambridge Crystal Structure Database included 20 [Cu(aq)]²⁺ structures, including 17 [Cu(H₂O)₆]²⁺ structures, two [Cu(H₂O)₄]²⁺ structures and one [Cu(H₂O)₅]²⁺ structure (Dudev et al., 2006). Among the first-row transition-metal aqua ions, only copper(II) shows such structural variability, and has a similar heterogeneity in other ligand systems (Gray et al., 2000). Crystalline [Cu(H₂O)₆](ClO₄)₂ displays the standard JT-distorted octahedron, but [Cu(H₂O)₆](BrO₃)₂ does not [six Cu–O distances of 2.079 (4) Å], while crystalline [Cu(H₂O)₆](SiF₆) includes both regular and JT-distorted octahedral structures in a 1:3 ratio (Blackburn et al., 1991; Cotton et al., 1993; Gallucci & Gerkin, 1989; Ray et al., 1973). With such heterogeneity of copper(II), the crystal structures cannot support inferences of solution structure.

Cu K-edge EXAFS of dissolved copper(II) complexes typically cannot resolve the five- and six-coordinate ligand alternatives because the axial ligands are weakly bound, distant and subject to rapid exchange (Helm & Merbach, 2005). EXAFS studies on [Cu(aq)]²⁺ in water have generally converged to a structural consensus describing a Jahn–Teller axially elongated octahedron with four Cu–O_eq distances of 1.95 ± 0.01 Å and two Cu–O_ax distances of 2.29 ± 0.03 Å (D'Angelo et al., 1997; Persson et al., 2002; Tajiri & Wakita, 1986). Persson and coworkers combined Cu K-edge EXAFS (k ≃ 12 Å⁻¹) with WAXS data and excluded the elongated square-pyramidal model on the grounds that the fitted single axial bond included an excessively small mean displacement (σ²; Persson et al., 2002).

Cu K-edge EXAFS to k = 18 Å⁻¹ was attained with an aqueous copper(II) solution prepared using ultralow-zinc CuO (Frank et al., 2015). Analysis resolved two different axial Cu–O distances, Cu–O_ax1 = 2.19 ± 0.01 Å and Cu–O_ax2 = 2.33 ± 0.01 Å, along with four Cu–O_eq distances of 1.97 ± 0.01 Å. This model was extended with MINUIT XANES (MXAN) analysis (Benfatto et al., 2005), yielding a C_4v axially elongated square-pyramidal [Cu(H₂O)₅]²⁺ structure (Fig. 1), with four Cu–O_eq distances of 1.97 ± 0.02 Å, one Cu–O_ax distance of 2.09 ± 0.03 Å and a nonbonded water molecule with a Cu–O distance of 3.0 ± 0.1 Å.

Figure 1 Left: Fourier-filtered K-edge EXAFS spectrum of copper(II) in 1 M HClO4 (circles). Fits: JT octahedral, blue; elongated square pyramidal, green; elongated square pyramidal including a distant sixth oxygen scatterer, red. The vertical dotted line shows the k = 13.4 Å−1 zinc cutoff. Inset: the best fit is unique only above k = 13 Å−1. Right: the [Cu(H2O)5]2+ structural model (Frank et al., 2015).

Ambidentate ligands can bind at either or both of two internal sites and include cyanide (CN⁻; C, N), cyanate (OCN⁻; N, O), thiocyanate (SCN⁻; N, S), nitrite (; N, O) and sulfite (; S, O). Cadmium(II) can bind to either end of the thiocyanate ion. Crystalline octahedral Cd(SCN)₂ includes two Cd–N (2.24 Å) and four Cd–S (2.76 Å) distances (Cannas et al., 1976). EXAFS, ¹¹³Cd NMR and X-ray diffraction studies of cadmium(II) complexation with NH₄SCN or (C₂H₅)₄N(SCN) revealed the formation of [Cd(NSC)₂(SCN)₂]²⁻ and [Cd(NSC)₃(SCN)]²⁻ complexes in water or N,N-dimethyl­formamide (DMF), respectively (Ozutsumi et al., 1992). In dimethylsulfoxide (DMSO) with added NH₄SCN or (C₂H₅)₄NSCN, the solvent enters the coordination environment of cadmium(II), producing five-coordinate [Cd(NCS)₃(SCN)(DMSO)]²⁻ or [Cd(NCS)₄(DMSO)]²⁻ complexes, respectively. In the former complex, ⋯NCS–Cd hydrogen bonding was ascribed to the S-bound thiocyanate.

The use of K-edge EXAFS, {¹H}¹³C NMR and IR spectroscopies to examine (Bu₄N)[Y(NCS)₆], both crystalline and in aceto­nitrile solution, confirmed the Y–NCS linkage and O_h symmetry (Díaz-Moreno et al., 1998). The focused multiple scattering of linear Y–N–C–S units allowed the determination of distances to the third coordination shell. The best-fit EXAFS model had three single and 22 multiple scattering paths (up to six legs), limiting the refined Debye–Waller factors to four, which resulted in the following bond distances: Y–N = 2.36 ± 0.01 Å, Y–C = 3.5 ± 0.01 Å and Y–S = 5.1 ± 0.02 Å.

A combined WAXS and EXAFS study found that the gallium(III) ion in acidic aqueous solution binds six water molecules with Ga–O distances of 1.959 ± 0.006 Å, with 12 hydrogen-bonded water molecules in a second shell (Lindqvist-Reis et al., 1998). Careful analysis of EXAFS data measured at different OH⁻:Ga³⁺ ratios (designated r) showed that hydrolysis eventually leads to the formation of the Ga₁₃ Keggin ion (Michot et al., 2000). At r ≤ 1.8, the first coordination shell of gallium(III) consists of six O atoms (Ga–O = 1.95 ± 0.01 Å), which at high r (∼2.0–2.2) with nearly 100% Ga₁₃ polycation is resolved into two subshells with four Ga–O distances of 1.92 ± 0.01 Å and two Ga–O distances of 2.03 ± 0.01 Å. Three sets of Ga⋯Ga distances occur at 3.01–3.05, 3.47–3.53 and 3.90–3.95 Å, although the latter could reflect multiple scattering. The full hydrolysis process was then described based on the formation and condensation of dimers, trimers and tetramers at different OH⁻:Ga³⁺ ratios.

In dimethylsulfoxide solution, [Ga(O-DMSO)₆]³⁺ ions dominate with a mean Ga–O distance of 1.955 ± 0.002 Å (Molla-Abbassi et al., 2003). Addition of twofold thiocyanate produced the five-coordinated complex [Ga(O-DMSO)₄(SCN)]²⁺, with four Ga–O distances of 1.902 ± 0.006 Å and a Ga–S distance of 2.198 ± 0.006 Å. The shorter Ga–O distance is consistent with the change in gallium(III) ionic radius in six- and five-coordinated environments: 0.62 Å versus 0.55 Å (Shannon, 1976).

Cu K-edge EXAFS spectra are typically limited to k ≤ 13.4 Å⁻¹ because of spurious intensity at the Zn K edge imposed by trace zinc impurities. EXAFS analyses of Cu^IX (X = Cl⁻, Br⁻, I⁻) in acetonitrile, DMSO, pyridine (py) or aqueous solution with added excess halide salts showed dimerization dependent both on concentration and halide size (Table 1). Linear [CuCl₂]^– and planar [CuCl₃]^2– complexes are formed in non-aqueous and aqueous solutions, respectively (Persson et al., 1991). In aqueous solution at high temperature (100–325°C), [CuCl₂]⁻ with a Cu–Cl distance of 2.13 ± 0.01 Å dominates in excess chloride (Fulton et al., 2000). Double-bridged [Cu₂X₄]^2– (X = Br⁻, I⁻) complexes are observed in DMSO solutions, while [Cu₂I₄]²⁻ dominates in concentrated copper(I) acetonitrile solution (Persson et al., 1991).

Table 1 Coordination chemistry of the cuprous halides The typical Cu–X distance (R) error is ±0.03 Å (Persson et al., 1991).   Chloride R (Å) Bromide R (Å) Iodide R (Å) Acetonitrile 2.10 † 2.21 ‡ 2.59 DMSO 2.11 ( and )§ 2.24, 2.36 ¶ 2.54 Pyridine 2.12 CuBr(py)3†† 2.41 — — H2O (excess Cl−) 2.21 — — — — †Copper concentration (CCu) = 88 mM. ‡CCu = 1 M, Cu–Cu distance of 2.73 Å. §CCu = 1.5 M, Cu–Cu distance of 2.72 Å for the dimeric complex. ¶CCu = 1.5 M, Cu–Cu distance of 2.77 Å. ††CCu = 0.4 M, three Cu–N distances of 2.06 Å.

Studies of the solvation of lead(II) in water and several organic solvents further highlight the utility of EXAFS. Combined with WAXS, EXAFS revealed six Pb–O distances of 2.54 ± 0.01 Å for [Pb(aq)]²⁺ in dilute acidic solution (Persson et al., 2011). The fitted σ² of 0.027 ± 0.001 Ų, indicating a large distribution of Pb–O distances (±0.16 Å), follows a theoretical prediction that electron density in antibonding lead 6s/ligand np molecular orbitals produces a distorted hemidirected structure and a spatial gap in the coordination sphere (Shimoni-Livny et al., 1998; Walsh & Watson, 2005). However, when dissolved in 1,1,3,3-tetramethylurea (TMU), a space-demanding ligand, the lead(II) ion organizes with six Pb–O distances of 2.517 ± 0.007 Å, now with a fitted σ² of 0.009 ± 0.001 Ų, indicating only a ±0.09 Å spread in Pb–O distances and implying a symmetrical holodirected coordination induced by increased ligand–ligand interactions in a [Pb(TMU)₆]²⁺ complex.

The +3 oxidation state is most common for the heavier actinides, while the lighter actinide(III) ions are redox-unstable. The reported [An(aq)]³⁺ crystal structures, [M(H₂O)₉](CF₃SO₃)₃ (M = U to Cm, Cf), all show tricapped trigonal prismatic hydration (Apostolidis et al., 2010; Lind­qvist-Reis et al., 2007; Matonic et al., 2001; Skanthakumar et al., 2007). EXAFS analyses of aqueous solutions reveal that the An–O distance shortens from 2.54 ± 0.02 Å for uranium(III) to 2.42 ± 0.01 Å for californium(III), consistent with ionic contraction across the actinide series (Brendebach et al., 2009; David et al., 1998; Galbis et al., 2010). This occurred without any specific trend in the coordination number (CN), which varies between eight and ten (Antonio & Soderholm, 2006). Analysis of a good-quality (k = 2–16 Å⁻¹) L₃-edge EXAFS spectrum for an acidic aqueous curium(III) solution resolved two distances: six (Cm–O)_prism distances of 2.470 ± 0.006 Å and three (Cm–O)_cap distances of 2.63 ± 0.02 Å (Skanthakumar et al., 2007), while for californium(III) neither a square antiprism (CN = 8) nor a tricapped trigonal prism (CN = 9) model could be ruled out (Galbis et al., 2010). Ab initio Monte Carlo quantum-mechanical models indicated that the EXAFS computed from a BP86 DFT (Rotzinger, 2005) simulation best reproduced the experimental EXAFS spectrum (CN ≃ 8 and R = 2.43 Å), implying eight first-shell water molecules for dissolved [Cf(aq)]³⁺ (Galbis et al., 2010). Assessing EXAFS in a more limited k range (2–10.3 Å⁻¹), D'Angelo and coworkers found no decrease in coordination number in the actinide(III) series from uranium(III) to californium(III), and also found that dissolved [Cf(aq)]³⁺ is tricapped trigonal prismatic. They estimated the ionic radii of the dissolved uranium(III) to californium(III) ions in the actinide series by analyzing previously reported EXAFS spectra using a single-shell model for An–O with fixed CN = 9, finding a contraction from 2.527 ± 0.009 to 2.422 ± 0.007 Å (Δ = 0.1 Å; D'Angelo et al., 2013). The actinide(III) ionic radii in aqueous solution, obtained by subtracting the Shannon radius of a coordinated O atom (1.350 Å; David et al., 2001), are longer than the actinide(III) crystal structure radii but are similar to the lanthanide(III) counterparts.

The systematic changes in the coordination environment of aqueous neptunium ions (²³⁷Np; t_1/2 = 2.14 × 10⁶ years) in 1.0 M HClO₄ solution were investigated using EXAFS as the oxidation state of neptunium was varied in situ using an X-ray spectroelectrochemical cell (Antonio et al., 2001). [Np^III(H₂O)₉]³⁺ and [Np^IV(H₂O)₉]⁴⁺ ions were produced with mean Np–O distances of 2.48 ± 0.02 and 2.37 ± 0.02 Å, respectively. Further oxidation yielded the trans-dioxoneptunyl species [Np^VO₂(H₂O)₅]⁺ and [Np^VIO₂(H₂O)₅]²⁺ with Np=O_ax bond lengths of 1.80 ± 0.02 and 1.73 ± 0.02 Å and average equatorial Np–O_eq(H₂O) bond distances of 2.44 ± 0.03 and 2.36 ± 0.03 Å, respectively. Each pair of hydrated species, Np^III→Np^IV and Np^V→Np^VI, exhibited contraction of the bond distances with increasing oxidation state.

However, the above results are somewhat parameter-dependent. An independent analysis of high-quality (k ≃ 19.5 Å⁻¹) L₃-edge EXAFS spectra of hydrated neptunium(IV), neptunium(V) and neptunium(VI) ions in 1.0 M HClO₄ proposed [Np^IV(H₂O)₁₀]⁴⁺ species (mean Np–O distance of 2.40 ± 0.01 Å, CN = 10.4 ± 1 with amplitude reduction factor = 0.9 or CN = 9.7 ± 1 with = 1.0; Ikeda-Ohno et al., 2008). The EXAFS spectra of neptunium(V) and neptunium(VI) were fitted with [Np^VO₂(H₂O)_5–6]⁺ and [Np^VIO₂(H₂O)₅]²⁺ models with Np=O_ax bond distances of 1.84 ± 0.01 and 1.76 ± 0.01 Å and with average Np–O_eq(H₂O) bond lengths of 2.49 ± 0.01 and 2.42 ± 0.01 Å, respectively, all of which are nominally longer than in the above 2001 study. This average Np^V–O_eq(H₂O) distance of 2.49 ± 0.01 Å is intermediate between the bond lengths of 2.46 or 2.55 Å for five or six equatorial water ligands, respectively, from crystal structures with [NpO₂(aq)]⁺ ions. Therefore, the authors suggested that both [Np^VO₂(H₂O)₅]⁺ and [Np^VO₂(H₂O)₆]⁺ are present in aqueous solution (Ikeda-Ohno et al., 2008). Comparing bond distances for solvated species with those in crystal structures is generally more reliable in order to obtain coordination numbers (especially at high CN) than a value from EXAFS model refinement, which is affected by additional uncertainty from an assumed amplitude reduction factor ; see Section 3.8.

Another EXAFS study of hydrated neptunium(IV) ions proposed [Np^IV(H₂O)_11.2±1.1]⁴⁺ complexes (Np–O distance of 2.40 ± 0.01 Å, = 0.9; Allen et al., 1997), which can be compared with the EXAFS models for hydrated uranium(IV): [U^IV(H₂O)_8.7±1.3]⁴⁺ (U–O = 2.41 ± 0.02 Å, = 1.0; Hennig et al., 2007) or [U^IV(H₂O)_10±1]⁴⁺ (U–O = 2.42 ± 0.01 Å, = 1.0; Moll et al., 1999).

The low energy of the F K-edge, 696.7 eV, presently forestalls aqueous-phase EXAFS analysis. A K-edge EXAFS study of aqueous Cl⁻, limited to k = 8 Å⁻¹ due to a multi-electron excitation at 8.1 Å⁻¹, revealed a shell of 6.4 hydrogen-bonded water molecules with a mean Cl⋯H distance of 2.23 ± 0.04 Å and Cl⋯O distance of 3.14 ± 0.02 Å, and a Cl–H–O angle of 156° (Fulton & Balasubramanian, 2010), consistent with previous neutron diffraction metrics of Cl⋯H = 2.28 ± 0.03 Å and Cl⋯O = 3.1 ± 0.1 Å (Powell et al., 1993).

Combined Br K-edge EXAFS analysis and Monte Carlo simulation revealed an asymmetrical shell of 6.0 ± 0.5 water molecules at a mean Br⋯O distance of 3.44 ± 0.07 Å (Merkling et al., 2003), which is in good agreement with the previously found solvation shell (seven Br⋯O distances of 3.4 Å) using X-ray anomalous scattering (Ramos et al., 2000). Concurrent iodine multiple-edge (K, L₁, L₃) EXAFS analysis revealed an asymmetric solvation shell of 6.3 water molecules with a mean I⋯H distance of 2.65 ± 0.03 Å and I⋯O distance of 3.50 ± 0.02 Å, corresponding to an I–H–O angle of 148° (Fulton et al., 2010).

EXAFS combined with MXAN produced 3D solvation models for aqueous Cl⁻, Br⁻ and I⁻ (Antalek et al., 2016). Bromide and iodide exhibited globally symmetric solvation spheres, while chloride uniquely required a second shell with seven Cl⋯H–OH distances of 4.14 Å. EXAFS fitting parameters for halide hydration are given in Table 2.

Table 2 EXAFS fitting parameters for halide hydration Halide CN X⋯H (Å) X⋯O (Å) X–H–O (°) Reference Cl− 6.4† 2.23 (4)‡ 3.14 (2) 156 Fulton & Balasubramanian (2010) 6.4 (1.0)‡   3.11 (3)   Dang et al. (2006) 6.0 (1.7)   3.05 (4)   Tongraar et al. (2010) 7.0§ 2.18 (2) 3.15 (2) 166 (2) Antalek et al. (2016) Br− 6.9   3.34   D'Angelo et al. (1994) 5.1 (5)   3.29 (4)   Simonet et al. (2002) 6.0 (5)   3.44 (7)¶   Merkling et al. (2003)     3.40   Filipponi et al. (2003) 10.7   3.33 (3)   Feiters et al. (2005) 8 (1)§ 2.48 (2) 3.40 (2) 159 (2) Antalek et al. (2016) I− 6.3 (9) 2.65 (3) 3.50 (2) 148 Fulton et al. (2010) 10.0   3.56 (3)   Feiters et al. (2005) 8 (1)§ 2.67 (2) 3.59 (2) 159 (2) Antalek et al. (2016) †Fixed value from aqueous and crystalline standards (Dang et al., 2006). ‡Uncertainties in the last digit are given parenthetically. §Refined EXAFS parameters: four Cl⋯O distances of 2.91 (1) Å, three Cl⋯O distances of 3.11 (1) Å, ten Br⋯O distances of 3.26 (3) Å and nine I⋯O distances of 3.50 (3) Å. ¶Refined EXAFS distance of 3.34 (3) Å.

EXAFS investigations of metal complexes in ionic liquids have been reviewed (Estager et al., 2014; Hardacre, 2005). M(BF₄)₂·6H₂O (M = Co²⁺, Cu²⁺) salts dissolved in [EMIm][BF₄] (EMIm = 1-ethyl-3-methylimidazolium) produce unusual tetrahedral M(H₂O)₄]²⁺ aqua ions (Takao et al., 2012). Likewise, tetrahedral [CuCl₄]²⁻ complexes form when dissolving anhydrous CuCl₂ in [EMIm][Cl] (Li et al., 2010). Copper(II) and nickel(II) hydrates dissolved in [C₆MIm][Cl] (C₆MIm = 1-hexyl-3-methylimidazolium) were found to form [CuCl₃]⁻ and [NiCl₃]⁻ complexes, governed by the large size of the [C₆MIm]⁺ cation, while in [EMIm][SCN] solvent [Cu(NCS)₂(SCN)]⁻ is formed. Chromium(III) chloride hydrate forms [CrCl₄(H₂O)₂]²⁻ and [Cr(NCS)₆]³⁻ complexes in the ionic liquids [C₆MIm][Cl] and [EMIm][SCN], respectively (Hartley et al., 2014).

Multi-electron excitations can impact EXAFS fits, influencing coordination numbers and bond distances. For example, the L₃-edge EXAFS spectra of light lanthanide(III) complexes exhibit double-electron excitations (2p4d→5d²) in the k range 5–7 Å⁻¹ (Solera et al., 1995). For lanthanide ions and third-row transition metals, the short core-hole lifetime of high-energy K-edge EXAFS broadens double-electron features into negligible intensity. The long k range available from lanthanide K-edge EXAFS can compensate for the loss of information from spectral broadening and larger core-hole width (Γ) relative to the L edges (D'Angelo et al., 2008).

Multi-electron excitations are also prominent in the Ca K-edge EXAFS of calcium(II) aqueous solutions at k = 2.7, 3.7 and 10.3 Å⁻¹, which correspond to [1s3p], [1s3s] and [1s2p] double-electron excitations, respectively (Fulton et al., 2003), and in yttrium(III) K-edge EXAFS (Chaboy et al., 2001; Díaz-Moreno et al., 2000). In a background-correction procedure relying on the Z-dependent similarity of the multi-electron background, the Ar K-edge XAS was used to remove the multi-electron features of dissolved [Ca(aq)]²⁺, finding (7.2 ± 1.2) Ca–O_ave distances of 2.437 ± 0.01 Å ( ± 20%) and back-scattering from 16 Ca⋯H distances of 2.97 ± 0.02 Å (Fulton et al., 2003). Alternatively, double-electron excitations can be fitted rather than omitted, as in analysis of the K-edge EXAFS of dissolved [Ca(aq)]²⁺ (eight Ca–O distances of 2.42 Å in a disordered shell and Ca⋯H = 3.10 Å; D'Angelo et al., 2004).

The double-electron excitations [1s4s], [1s3d] and [1s3p] were observed in the K-edge EXAFS of aqueous strontium(II). EXAFS analysis using an atomic background model to account for these transitions yielded a solvation sphere with (10.3 ± 0.1) Sr–O_ave distances of 2.643 ± 0.002 Å, while ignoring this model produced underestimated coordination numbers: 6.3 Sr–O_ave at 2.62 Å (D'Angelo, Nolting et al., 1996) and (7.3 ± 0.5) Sr–O_ave at 2.62 ± 0.03 Å (Pfund et al., 1994).

For dissolved [Ba(aq)]²⁺, disregarding the respective L_3,2- and L₁-edge [2p4d]→[5d]² and [2s4d]→[6p5d] double-electron excitations yielded R_Ba–O = 2.780 ± 0.003 Å and systematically underestimated the Ba–O coordination number, i.e. CN_Ba–O = 6.9 rather than 7.8 ± 0.3 (D'Angelo, Pavel et al., 1996). However, it is not clear why the same corrected EXAFS method produced a higher hydration number of 10.3 ± 0.1 for the smaller strontium(II) cation. Combined EXAFS and WAXS results suggested the same hydration number of 8.1 ± 0.3 for both metal ions, with R_Sr–O = 2.63 ± 0.02 Å and R_Ba–O = 2.81 ± 0.03 Å (Persson et al., 1995).

K-edge EXAFS and X-ray powder diffraction were combined to structurally characterize several microcrystalline M′[MIO₆]·xH₂O complexes (M′ = Na⁺–Cs⁺, and M^IV = Ni, Pb, Sn, Ge, Mn; Levason, 1997). Sodium persulfate (Na₂S₂O₈) oxidation of dissolved NiSO₄ plus Na₃H₂IO₆ produced solid Na[NiIO₆], for which Ni and I K-edge EXAFS spectra were collected. X-ray powder diffraction data showed that Na[NiIO₆] belongs to space group P312 with layered edge-sharing NiO₆ and IO₆ octahedra and intercalated sodium ions. EXAFS analyses (fixed coordination numbers) yielded an Ni–O distance of 1.863 ± 0.002 Å, an I–O distance of 1.868 ± 0.001 Å and an Ni⋯I distance of 2.85–2.86 Å (Currie et al., 1994). The refined Ni⋯Ni distance of 4.969 ± 0.005 Å closely matched the unit-cell edge a from powder diffraction.

Cyanide as a ligand can promote M₁–CN–M₂ electronic delocalization (Giorgetti et al., 1997). [Pt(CN)₄]²⁻ and [Tl(CN)_n]³⁻ⁿ (n = 2–4) combine to form hetero-dimetallic [(NC)₅Pt–Tl(CN)_n]ⁿ⁻ (n = 0–3) complexes in solution. Pt and Tl L₃-edge EXAFS, vibrational and multinuclear (¹⁹⁵Pt, ²⁰⁵Tl, ¹³C) NMR spectroscopies characterized the complexes and the local structure around platinum and thallium (Jalilehvand, Maliarik et al., 2001). The EXAFS analysis revealed single and focused multiple scattering (up to four legs) of linear Pt–C–N and Tl–C–N units and short Pt–Tl distances (2.60–2.64 Å).

Slow evaporation of an acidic (HClO₄) [(NC)₅Pt–Tl(CN)]⁻ solution produced polycrystalline TlPt(CN)₅. X-ray powder diffraction revealed both proximate Pt–Tl = 2.627 ± 0.002 Å and TlPt(CN)₅ units forming linear –NC–Pt–Tl–NC–Pt–Tl– chains. Pt and Tl L₃-edge EXAFS analyses indicated extensive multiple scattering from the five linear axial and equatorial Pt–C–N bonds, but not from the four bent (149°) equatorial Tl–N–C bonds. The equatorial and axial Tl–N distances refined independently to 2.50 ± 0.01 and 2.31 ± 0.03 Å, respectively (Jalilehvand, Eriksson et al., 2001).

The complex [(NC)₄Pt–Tl(O-DMSO)₅]⁺, derived from mixing K₂[Pt(CN)₄]·3H₂O and [Tl(DMSO)₆](ClO₄)₃ in dimethylsulfoxide, was studied using Pt and Tl L₃-edge EXAFS, multinuclear NMR and DFT calculations. The unoccupied sixth coordination site of platinum generated a slightly longer Pt–Tl bond with a distance of 2.67 ± 0.01 Å, with a mean Tl–O distance of 2.282 ± 0.002 Å and a Tl–O–S angle of 120°. The metal–metal bond has been described as a →Tl(6s)⁰ donation (Purgel et al., 2011).

The advantages and limitations of multiple-edge EXAFS spectroscopy were analyzed in applications to mixed-metal iron(II)/cobalt(II)/nickel(II) hexacyanoferrates (Giorgetti & Berrettoni, 2008). Microcrystalline An^IVFe^II(CN)₆·xH₂O complexes, in the hexagonal space group P6₃/m (An = Th, Np, Pu), were studied using Fe K-edge and An L₃-edge EXAFS and X-ray powder diffraction. The iron EXAFS Fourier transforms showed enhanced multiple scattering focused along the linear Fe–C–N segments within the {Fe(CN)₆} units (Dumas et al., 2013). Cyano bridges connect An(IV) to {Fe(CN)₆}, producing {An(NC)₆(H₂O)₃} tricapped trigonal prisms with three equatorial water ligands. The An–N–C angle varies between 155° and 165°, reducing the multiple scattering along this path and damping the corresponding An L₃-edge EXAFS Fourier transform feature. The mean An–N distance decreases from 2.58 ± 0.03 Å for thorium(IV) to 2.45 ± 0.01 Å for neptunium(IV) to 2.42 ± 0.01 Å for plutonium(IV), reflecting the `actinide contraction'. The average An–H₂O distance (which is shorter than the An–N distance) follows the same trend. However, the EXAFS model fitting was performed over the range k = 0–12 Å⁻¹, thus mistakenly including the XANES region (k < ∼2 Å⁻¹), wherein the short wavelength of the photoelectron due to its low kinetic energy (5–150 eV) makes multiple-scattering events between neighbour atoms dominant over single scattering.

The Grignard reagent CH₃MgBr in di-n-butylether solution was examined by measuring both Mg and Br K-edge EXAFS spectra using a UHV-compatible cell for liquid samples (Abraham et al., 1996). The independent Mg⋯Mg and Br⋯Br distances allowed calculation of the internal angles within the dimeric species (Fig. 2). The bromide L₃-edge at 1550 eV limited the Mg EXAFS oscillation to k = 8 Å⁻¹.

Figure 2 The Mg and Br K-edge EXAFS spectra of CH3MgBr in (C4H9)2O solution at −85°C and the angular structure of the dimeric complex with a double Br bridge derived from independent distances around the Mg and Br atoms. The O atom of di-n-butylether coordinated to magnesium(II) is shown in light red. Reprinted from Abraham et al. (1996), with permission from Elsevier.

The Cd K-edge EXAFS spectrum of the white precipitate formed when Cd(OAc)₂ is added to twofold cysteine (H₂Cys) in aqueous solution consistently yielded a Cd–S distance of 2.52 ± 0.02 Å in either CdS₄ or CdS₃O coordination models. The CdS₃O model, with a Cd–O distance of 2.27 ± 0.04 Å consistent with crystalline CdS₃O compounds (Cd–O_ave = 2.240 Å), proved superior when compared against the Cd L₃-edge XANES spectra of Cd(HCys)₂·H₂O and crystalline Cd^IIS_x(N/O)_y thiolate complexes (Jalilehvand et al., 2009).

In EXAFS spectroscopy the sensitivity to back-scattering atoms is limited to ∼5 Å, because the EXAFS amplitude reduces with 1/R² and also with high mean displacement (σ²) of nonbonded absorber–scatterer pairs at distance R, especially in solution. Therefore, EXAFS analysis may be of limited utility in defining the structure of a loosely bound second hydration shell (Ohtaki & Radnai, 1993), as shown for cobalt(II), nickel(II) and zinc(II) in aqueous solution (D'Angelo et al., 2002). Exceptions include the well defined second hydration shells for the [Cr(H₂O)₆]³⁺ complex ion and its chloroaqua cognates, [CrCl_n(H₂O)_6−n]⁽³⁻ⁿ⁾⁺ (n = 1–3) (Díaz-Moreno et al., 1996; Munoz-Paez & Marcos, 1992), as well as for the [Cu(NH₃)₅]²⁺ complex ion (Frank et al., 2008).

Several examples in this chapter relate the EXAFS uncertainty (±20%) in coordination number and its correlation to the amplitude reduction factor, , describing inelastic losses due to multi-electron excitations (Bauer & Bertagnolli, 2007).

EXAFS analysis cannot distinguish between back-scattering atoms of adjacent Z, for example (N, O) or (S, Cl). However, additional information supplied by complementary techniques, including multinuclear NMR and UV–visible spectroscopy, can allow detailed speciation and structural characterization. For example, combined results from ¹³C, ²⁰⁷Pb NMR, UV–Vis spectroscopy and electrospray ionization mass spectrometry (ESI-MS) were required to unveil co-existing dithiolate [Pb(S,N,O-Cys)(S-HCys)]⁻, [Pb(S,N-Cys)₂]²⁻ and trithiolate [Pb(S,N-Cys)(S-HCys)₂]²⁻, [Pb(S-HCys)₃]⁻ (minor) complexes in lead(II)–cysteine solutions (Jalilehvand et al., 2015). As the Pb–S distances, 2.65 ± 0.03 Å, did not differ significantly in the above three- or four-coordinated lead(II) complexes, and separation of the O/N EXAFS contributions in the presence of heavy back-scatterers such as S was difficult, the information from complementary spectroscopic methods was essential in identifying the chemical species in solution.