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Synchrotron X-ray Absorption Spectroscopy Near-edge Spectra (I) Graham N. George Ingrid J. Pickering I. J. Pickering and G. N. George GEOL 498.3/898.3 Today… Near-edge spectra Nomenclature Selection rules and spectra What are near-edge spectra sensitive to? Pseudo Voigt peak fitting analysis I. J. Pickering and G. N. George GEOL 498.3/898.3 X-ray Absorption Spectroscopy EXAFS oscillations (k3-weighted) Near-edge spectrum I. J. Pickering and G. N. George GEOL 498.3/898.3 1 Nomenclature There are a large number of names and acronyms in use – they all refer to the same thing or are closely related… Edge Spectra Near-Edge Spectra Near-Edge X-ray Absorption Fine Structure (NEXAFS) X-ray Absorption Near-Edge Structure (XANES) I. J. Pickering and G. N. George GEOL 498.3/898.3 Nomenclature Sometimes, but not always, “XANES” is used to refer to the region just above the edge, which is more readily calculable using multiple scattering theory. } near-edge } XANES EXAFS I. J. Pickering and G. N. George GEOL 498.3/898.3 Nomenclature What is a “White Line”? The term “white line” refers to an intense absorption in the near-edge. The nomenclature dates from the days when spectra were recorded on strips of photographic film, and such intense absorption peaks showed up as a heavily exposed line on the developed film. White Line photographic film White Line I. J. Pickering and G. N. George spectrum GEOL 498.3/898.3 2 X-ray absorption near-edge spectra Intense features arise due excitation of transitions from the core level to vacant levels, close to the highest occupied molecular orbital. nucleus vacant orbital electron 2p, l=1 hν electron-hole 1s, l=0 2s, l=0 I. J. Pickering and G. N. George GEOL 498.3/898.3 What is a near-edge spectrum The photoelectron is excited to a variety of bound states lying below the threshold energy. Transitions to bound states observed spectrum Core level Threshold, E0 I. J. Pickering and G. N. George GEOL 498.3/898.3 Near-edge spectra X-ray absorption is given by Fermi’s Golden Rule: µ (E ) = ∑ ψ i H ψ f 2 ψi - the initial state wavefunction ψf - the final state wavefunction H - the interaction If we wish to quantify spectra, we have two alternatives – evaluate the integral as completely as possible (molecular orbital approach) or use multiple scattering theory. Molecular orbital approach. A chemistry perspective – the X-ray excites transitions between the core level and a molecular orbital. Quantification is non-trivial, but this approach is highly successful in understanding spectra. Multiple scattering approach. A physics perspective – the X-ray excites a lowenergy photo-electron which undergoes extensive multiple scattering by nearby atoms. This success of this approach is limited (to date). It usually cannot model features due to low-lying bound-state transitions. I. J. Pickering and G. N. George GEOL 498.3/898.3 3 What is a near-edge spectrum? Molecular orbital approach - transitions to boundstate molecular orbitals. σ* S1s → σ* LUMO+1 S1s →π* S O OH π* LUMO I. J. Pickering and G. N. George GEOL 498.3/898.3 Spectral linewidths Two components contribute to the spectral linewidth – the core-hole lifetime and the optical resolution. Core-hole lifetime. Heisenberg’s uncertainty principal states that: ∆E∆t ≥ 1 h 2 Thus, comparing high and low energy edges, we expect the higher energy edge to have shorter core hole lifetimes (∆t) and correspondingly broader experimental linewidth (∆E) (assuming that the spectroscopic resolution is not limiting). This adds a Lorentzian component to the lineshape. I. J. Pickering and G. N. George GEOL 498.3/898.3 Spectral linewidths Example – aqueous solution of molybdate [MoO4]2- measured at the K-edge (1s excitation) and the LI edge (2s excitation). These are very similar ground states, and no significant differences in the nature of the near-edge transitions are expected. The spectra have been offset by 20008.70 eV and 2869.95 eV, respectively. The K edge is has a much shorter core-hole lifetime than the LI edge, and has corresponding broader linewidths. LI edge K edge I. J. Pickering and G. N. George GEOL 498.3/898.3 4 Spectral linewidths Spectrometer Resolution In a modern EXAFS beamline this is usually only a function of the monochromator. Each monochromator material has an inherent energy resolution - the Darwin width of the crystal. This adds a Gaussian component to the overall experimental lineshape function. The experimental lineshape is expected to be approximated by a convolution of a Gaussian and a Lorenztian due to monochromator and lifetime broadening, respectively. This is known as a Voigt lineshape function – in practice it can be approximated by the sum of a Gaussian and Lorenztian – a pseudo Voigt lineshape function. I. J. Pickering and G. N. George GEOL 498.3/898.3 Near-edge Spectra We can write Fermi’s Golden Rule as: µ ∝ ∑ ψ i (e ⋅ p)e i (k ⋅r ) ψ f If we use a series expansion of the exponential, and examine just the first term, we get what is called the “dipole-allowed” transitions. These are the most intense transitions observed, and can be thought of as being stimulated by an oscillating electric field. 2 ψi ψf e p k - the initial state wavefunction r - the transition operator (x, y or z) in the molecular axis system - the final state wavefunction - the X-ray electric vector - the electron momentum vector - the X-ray forward propagation vector I. J. Pickering and G. N. George GEOL 498.3/898.3 Dipole and Quadrupole Transitions Dipole transitions are described by: µ D ∝ ∑ ψ i (e ⋅ p) ψ f 2 These are the most intense transitions observed, and can be thought of as being stimulated by an oscillating electric field, and have ∆l= ±1. Including the next term in the series expansion gives “quadrupole transitions”, which have ∆l= ±2, and these are described by: µQ ∝ ∑ ψ i (e ⋅ p)(k ⋅ r ) ψ f 2 Quadrupole transitions are of low intensity and can be thought of as being stimulated by the electric field gradient, which is significant due to the short wavelength of the X-radiation being used. I. J. Pickering and G. N. George GEOL 498.3/898.3 5 Selection Rules for X-ray absorption near-edge spectra Transition Selection rule LIII-edge Strength K-edge Dipole ∆l=±1 Intense 1s →np 2p →nd Quadrupole ∆l=±2 Weak 1s →nd 2p →nf MIV, MV Transition K, LI, MI LII, LIII, MII, MIII Dipole ns →n´p np →n´d nd →n´f Quadrupole ns →n´d np →n´f nd →n´g I. J. Pickering and G. N. George GEOL 498.3/898.3 Tungsten L-edges – Selection Rules XAS L-edge spectra of Na2WO4 – W(VI) is 5d0, so we expect strong dipole allowed transitions to the 5d manifold at the LIII and LII edges from the 2p3/2 and 2p1/2, respectively. No such intense transitions are expected at the LI near-edge (2s excitation). W LIII W LII W LI I. J. Pickering and G. N. George GEOL 498.3/898.3 Uranium M-edges – Selection Rules XAS M-edge spectra of UO2(CH3CO2)2(H2O)2 – U(VI) is 5f0, so we expect strong dipole-allowed transitions to the 5f manifold at the MV and MIV edges from the 3d3/2 and 3d1/2, respectively. No such intense transitions are expected at the MIII, MII (3p3/2 and 3p1/2 excitation, respectively) or MI (3s excitation) near-edges. O O O OH 2 O U H2O O O MI MIV MIII MII MV I. J. Pickering and G. N. George GEOL 498.3/898.3 6 Dipole and Quadrupole transitions Cu K-edge spectrum of [Cu(Imidazole)4](NO3)2 is 3d9. Spectra arise from 1s excitation, so we expect strong dipole allowed transitions to orbitals with a lot of 4p character, and a single weak quadrupole allowed transition to the half-filled 3d level. Quadrupole 1s→3d transition Dipole 1s→4p transitions x20 I. J. Pickering and G. N. George GEOL 498.3/898.3 What do we expect about near-edge spectra? • Intense features due to dipole-allowed ∆l=±1 transitions • Weak features due to quadrupole-allowed ∆l=±2 transitions • For hard X-ray spectra (i.e. E > 1500 eV) the core-hole lies deep within the atom. One consequence of this is that the final state of an absorber with atomic number Z approximates to that of Z+1 – i.e. the next element in the periodic table. This can be important when comparing splittings measured from UV-visible electronic spectroscopy with X-ray near-edge spectra – e.g splittings of Co2+ K near-edge spectra correspond optical spittings observed in the iso-structural Fe2+ compound. I. J. Pickering and G. N. George GEOL 498.3/898.3 What do we expect about near-edge spectra? • For hard X-ray spectra (i.e. E > 1500 eV) the ejection of a core electron will cause the outer orbitals to relax to lower energies (e.g. by about 10 eV for Cu K-edge spectra). This causes a corresponding shrinkage of the wave function, and thus reduction in the overlap integrals for molecular orbitals. We therefore expect the spectra to be very “atomic” in some of their properties. I. J. Pickering and G. N. George GEOL 498.3/898.3 7 Influence of core hole on electronic structure Ejection of metal core-electron causes outer metal orbitals to relax to lower energies. 4p 4p 3d 3p 3p 3d metal 1s ligand Ground state metal 1s ligand Final state I. J. Pickering and G. N. George GEOL 498.3/898.3 What are near-edge spectra sensitive to? Oxidation State Pyrococcus furiosus rubredoxin Fe2+ Fe3+ I. J. Pickering and G. N. George GEOL 498.3/898.3 What are near-edge spectra sensitive to? Nature of the Ligands Ferric ions with sulfur and oxygen donors [Fe3+(SR)4]- [Fe3+(OR)4]- I. J. Pickering and G. N. George GEOL 498.3/898.3 8 What are near-edge spectra sensitive to? Nature of the Ligands P4O10 and P4S10 are isostructural, both with P(V) oxidation state P4S10 P4O10 Covalency of sulfur means that phosphorus appears more reduced than its formal oxidation state I. J. Pickering and G. N. George GEOL 498.3/898.3 What are near-edge spectra sensitive to? Coordination Geometry Oxygen coordinated ferric ions – octahedral vs. tetrahedral octahedral 1s→3d region tetrahedral I. J. Pickering and G. N. George GEOL 498.3/898.3 Transition metal MO4 anions Similar chemical environments give rise to similar spectra VO42K K K LI K K2CrO4 KMnO4 K2FeO4 Na2WO4 Edge energy K Na2MoO4 Spectra have been offset to align the lowest energy transition I. J. Pickering and G. N. George GEOL 498.3/898.3 9 What are near-edge spectra sensitive to? Trigonal vs. Digonal cuprous thiolate compounds Inspection of the chemical literature indicates that Cu(I) prefers two distinct coordination environments – linear two-coordinate (digonal) and planar three-coordinate (trigonal) coordination geometries, e.g. with thiolate ligands: SR - SR RS Cu 2- Cu SR SR Cuprous thiolate metalloproteins form a very large group of diverse function. Both two and three coordinate examples are known. I. J. Pickering and G. N. George GEOL 498.3/898.3 Ligand Field Splitting Isolated atom – degenerate p-orbital energies Molecule – ligand-field splitting, p-orbital degeneracy lifted pz px py energy energy atom pz px I. J. Pickering and G. N. George py GEOL 498.3/898.3 What are near-edge spectra sensitive to? Trigonal vs. Digonal cuprous thiolate compounds Cu(I) is 3d10, so we expect no quadrupole transitions to the 3d manifold, and the lowest energy features in the near-edge should be 1s→4p transitions. Let us consider the ligand field splitting of the 4p orbitals. digonal SR z y x Cu SR trigonal pz px py I. J. Pickering and G. N. George SR RS distorted trigonal SR pz py RS Cu SR px Cu SR pz py px GEOL 498.3/898.3 10 Cu K near-edge spectra of digonal and trigonal cuprous thiolates Cu 1s→4px,y digonal trigonal Cu 1s→4px I. J. Pickering and G. N. George GEOL 498.3/898.3 Cu K near-edge spectra of digonal and trigonal cuprous thiolates Trigonal vs. Digonal cuprous thiolate compounds The ~8983 eV peak is diagnostic of digonal Cu(I) coordination. It can be used as a fingerprint of this kind of metal coordination. SR Cu SR I. J. Pickering and G. N. George SR RS Cu SR GEOL 498.3/898.3 1s→3d transitions of transition metal ions Octahedral Fe3+ with oxygen coordination – a small quadrupoleallowed, dipole-forbidden 1s→3d peak is observed. The transition has structure is due to the ligand field splitting of the 3d manifold. 1s→3d 1s→3d I. J. Pickering and G. N. George GEOL 498.3/898.3 11 Ligand Field Splitting Octahedrally coordinated metal atom Ligand atom Those d-orbitals with lobes directed towards the ligand atoms will possess higher energies than those with lobes directed in between the ligands. Energy dz2 d x2 − y2 ∆ d xy d xz d yz The energy separation of the orbitals ∆ is known as the ligand field splitting I. J. Pickering and G. N. George GEOL 498.3/898.3 1s→3d transitions of transition metal ions The size of the ligand field splitting ∆ (remember this is an excited state splitting) can tell us about the nature of the metal site. ∆ I. J. Pickering and G. N. George GEOL 498.3/898.3 High-Spin vs. Low-Spin Ferrous d x2 − y2 d z2 eg d xy d xz d yz t2g d x2 − y2 d z2 eg d xy d xz d yz t2g Low spin, Rion=0.92 Å High spin, Rion=0.75 Å Low-spin Fe2+ occurs with larger ∆, and gives rise to one peak of relatively increased intensity. I. J. Pickering and G. N. George GEOL 498.3/898.3 12 1s→3d transitons – octahedral vs. tetrahedral geometry Centrosymmetric (e.g. octahedral symmetry) mixing of metal 4p and 3d orbitals forbidden, and the transition is pure quadrupole. Non-centrosymmetric (e.g. tetrahedral symmetry) mixing of metal 4p and 3d orbitals allowed, and the transition is quadrupole, plus dipole-allowed intensity from admixture of metal 4p levels. I. J. Pickering and G. N. George GEOL 498.3/898.3 Analysis by peak deconvolution The experimental spectrum is fitted to a calculated spectrum comprised of a sum of pseudo Voigt peaks (IV) plus a step function for the edge (I0). This is usually done by iteratively minimizing the sum-of-squares of the differences between calculated and measured spectra. Each peak should comprise a single transition (or group of transitions) to a particular bound state (or states). µ calc (E ) = a0 I 0 (E ) + ∑ ai IVi (E ) i IVi I0 a0 ai - psudo-Voigt peak i - edge function - amplitude for edge function - amplitude for peak i This method allows quantitative analysis of quite subtle changes in near-edge spectra. I. J. Pickering and G. N. George GEOL 498.3/898.3 Analysis by peak deconvolution IV = mI G + (1 − m )I L − ln 2(E − Em )2 I G = exp [(W + (E − Em )η )ξ ] IL = [W + (E − Em )η ]2 [W + (E − Em )η ]2 + (E − Em )2 I. J. Pickering and G. N. George IV - the psudo-Voigt function IG - Gaussian peak-shape function IL - Lorentzian peak-shape function m - mixing factor Em - peak position W – half-width of peak η - peak skew ξ - ratio of Gaussian to Lorentzian widths GEOL 498.3/898.3 13 Analysis by peak deconvolution I. J. Pickering and G. N. George GEOL 498.3/898.3 Sulfur K-edge X-ray absorption near-edge spectra SO42RSO3- Sulfur K Near-edge spectra of biological model compounds. SO32RSO2RS=O The spectra are very sensitive to the chemical form of sulfur and can be used to “fingerprint” forms of sulfur present. R3S+ x2 x2 x2 x2 x2 I. J. Pickering and G. N. George RS-Me RS-H RS-SR S8 Fe4S4 GEOL 498.3/898.3 14