Synchrotron X-ray Absorption Spectroscopy - Stanford Synchrotron ...

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 

Near-edge spectra 

Nomenclature 

Today… 

Selection rules and spectra 

What are near-edge spectra sensitive to? 

Pseudo Voigt peak fitting analysis 


X-ray Absorption Spectroscopy 

EXAFS oscillations (k 3 -weighted) 

Near-edge spectrum 

I. J. Pickering and G. N. George GEOL 498.3/898.3

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) 


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 


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 

White Line 

photographic film 

spectrum 


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. 

hν 

2s, l=0 

1s, 

l=0 

vacant orbital 

2p, l=1 

nucleus 

electron 

electron-hole 


Core level 

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 

Threshold, E 0 


µ ( ) = ∑ ψ i H 

Near-edge spectra 

X-ray absorption is given by Fermi’s Golden Rule: 

E ψ 

f 

2 

ψ i - the initial state wavefunction 

ψ f - 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. 


σ* 

LUMO+1 

π* 

LUMO 

What is a near-edge spectrum? 

Molecular orbital approach - transitions to boundstate 

molecular orbitals. 

S1s →π* 

S1s → σ* 


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: 

1 

∆E∆t ≥ 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. 



Example – aqueous solution of molybdate [MoO 4 ] 2- measured at the K-edge (1s 

excitation) and the L I 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 L I edge, and has corresponding broader linewidths. 

L I edge 

K edge 


S 

OH 

O

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. 


Near-edge Spectra 

We can write Fermi’s Golden Rule as: 

µ ∝ 

∑ 

2 

i( 

k⋅r 

) 

i ( e⋅ 

p) 

e ψ f 

ψ 

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. 

ψ i - the initial state wavefunction 

ψ f - the final state wavefunction 

e - the X-ray electric vector 

p - the electron momentum vector 

k - the X-ray forward propagation 

vector 

r - the transition operator (x, y or z) 

in the molecular axis system 


Dipole and Quadrupole Transitions 

Dipole transitions are described by: 

∑ 

µ D ∝ ψ i ( e⋅ 

p) 

ψ f 

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: 

∑ 

µ Q ∝ ψ i ( e⋅ 

p)( 

k ⋅r) 

ψ f 

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. 


2 

2

Transition 

Dipole 

Quadrupole 

Transition 

Dipole 

Quadrupole 

Selection Rules for X-ray absorption 

near-edge spectra 

Selection rule 

∆l=±1 

∆l=±2 

K, L I , M I 

ns →n´p 

ns →n´d 

Strength 

Intense 

Weak 

K-edge 

np →n´d 

np →n´f 

1s →np 

1s →nd 

L II , L III , M II , M III 

LIII-edge 2p →nd 

2p →nf 

M IV , M V 

nd →n´f 

nd →n´g 


Tungsten L-edges – Selection Rules 

XAS L-edge spectra of Na 2 WO 4 –W(VI) is 5d 0 , so we expect strong dipole 

allowed transitions to the 5d manifold at the L III and L II edges from the 

2p 3/2 and 2p 1/2 , respectively. No such intense transitions are expected at 

the L I near-edge (2s excitation). 

W L III W L II 

W L I 


Uranium M-edges – Selection Rules 

XAS M-edge spectra of UO 2 (CH 3 CO 2 ) 2 (H 2 O) 2 –U(VI) is 5f 0 , so we expect 

strong dipole-allowed transitions to the 5f manifold at the M V and M IV edges 

from the 3d 3/2 and 3d 1/2 , respectively. No such intense transitions are 

expected at the M III , M II (3p 3/2 and 3p 1/2 excitation, respectively) or M I (3s 

excitation) near-edges. 

M V 

M IV MIII 

O O OH2 O U 

O 

H2O O 

O 


M II 

M I

Dipole and Quadrupole transitions 

Cu K-edge spectrum of [Cu(Imidazole) 4](NO 3) 2 is 3d 9 . 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 

x20 

Dipole 1s→4p transitions 


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 Co 2+ K near-edge 

spectra correspond optical spittings observed in the iso-structural 

Fe 2+ compound. 


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. 


Influence of core hole on electronic structure 

Ejection of metal core-electron causes outer metal orbitals to relax to 

lower energies. 

4p 

3d 

1s 

metal ligand 

Ground state 

3p 

1s 

metal ligand 


4p 

3d 

Final state 


Oxidation State 


3p 

Pyrococcus furiosus rubredoxin 

Fe 2+ 

Fe 3+ 


Nature of the Ligands 

Ferric ions with sulfur and oxygen donors 

[Fe 3+ (SR) 4 ] - 

[Fe 3+ (OR) 4 ] - 



Nature of the Ligands 

P 4 O 10 and P 4 S 10 are isostructural, both with P(V) oxidation state 

P 4 O 10 

P 4 S 10 

Covalency of sulfur means that phosphorus appears more reduced than its 

formal oxidation state 



Coordination Geometry 

Oxygen coordinated ferric ions – octahedral vs. tetrahedral 

octahedral 

tetrahedral 

1s→3d region 


Transition metal MO 4 anions 

Similar chemical environments give rise to similar spectra 

K 

K 

K 

K 

L I 

K 

VO 4 2- 

K 2 CrO 4 

KMnO 4 

K 2 FeO 4 

Na 2 WO 4 

Na 2 MoO 4 

Spectra have been offset to align the lowest energy transition 


Edge energy


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 

Cu 

SR 

- 

SR 

2- 

RS Cu 

SR 

Cuprous thiolate metalloproteins form a very large group of diverse 

function. Both two and three coordinate examples are known. 


atom 

Isolated atom – degenerate 

p-orbital energies 

Ligand Field Splitting 

p x p y p z 

energy 

Molecule – ligand-field splitting, 

p-orbital degeneracy lifted 




Cu(I) is 3d 10 , 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. 

x 

z 

digonal 

SR 

y Cu 

SR 

p x 

p z 

p y 

RS 

trigonal 

Cu 

SR 

SR 


p y 

p x 

p z 

RS 

p x 

Cu 

p y 

SR 

SR 

p z 

energy 

distorted trigonal 

p x 

pz py

Cu K near-edge spectra of digonal and 

trigonal cuprous thiolates 

Cu 1s→4p x,y 

Cu 1s→4p x 

digonal 

trigonal 


Cu K near-edge spectra of digonal and 

trigonal cuprous thiolates 


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 

RS 

SR 

Cu 

SR 


1s→3d transitions of transition metal ions 

Octahedral Fe 3+ 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 


Octahedrally coordinated 

metal atom 

Energy 

Ligand Field Splitting 

Ligand atom 

∆ 

d 2 

z 

Those d-orbitals with lobes 

directed towards the ligand atoms 

will possess higher energies than 

those with lobes directed in 

between the ligands. 

d − 

2 2 

x y 

d xy d d 

xz 

yz 

The energy separation of the orbitals ∆ is known as the ligand field splitting 


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. 


d − 

2 2 

x y 

d 2 

z 

d xy d xz d yz 

d − 

2 2 

x y 

High-Spin vs. Low-Spin Ferrous 

d 2 

z 

d xy d xz d yz 


e g 

t2 g 

e g 

t2 g 

∆ 

Low spin, R ion=0.92 Å 

High spin, R ion=0.75 Å 

Low-spin Fe 2+ occurs with larger ∆, and gives rise to one peak of 

relatively increased intensity.

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. 


Analysis by peak deconvolution 

The experimental spectrum is fitted to a calculated spectrum 

comprised of a sum of pseudo Voigt peaks (I V) plus a step function 

for the edge (I 0). 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) = a0I 

0( 

E) 

+ ∑ aiIVi 

( E) 

i 

I Vi -psudo-Voigt peak i 

I 0 -edge function 

a 0 - amplitude for edge function 

a i - amplitude for peak i 

This method allows quantitative analysis of quite subtle changes in 

near-edge spectra. 

V 


I = mI + 1− 

G 

⎛ 

I ⎜ 

G = exp 

⎜ 

⎝ 

I 

L 

= 


( m) 

I L 

( ) 

[ ( ( ) ) ] ⎟⎟ 

2 

− ln 2 E − E ⎞ m 

W + E − E η ξ 

[ ( ) ] 

[ ( ) ] ( ) 2 

2 

2 

W + E − Em 

η 

W + E − E η + E − E 

m 

m 

⎠ 

m 

I V - the psudo-Voigt function 

I G - Gaussian peak-shape function 

I L - Lorentzian peak-shape function 

m -mixing factor 

E m -peak position 

W –half-width of peak 

η - peak skew 

ξ - ratio of Gaussian to Lorentzian 

widths 




Sulfur K-edge X-ray 

absorption near-edge 

spectra 

Sulfur K Near-edge spectra of 

biological model compounds. 

The spectra are very sensitive 

to the chemical form of sulfur 

and can be used to “fingerprint” 

forms of sulfur present. 

SO 4 2- 

RSO 3 - 

SO 3 2- 

RSO 2 - 

RS=O 

R3S + 

RS-Me 

RS-H 

RS-SR 

S8 Fe 4S 4 


x2 

x2 

x2 

x2 

x2

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