BioPHYSICAL chemistry

For a free metal, as the energy of the X-rays is varied, the

intensity of the beam undergoes an abrupt shift when it

matches a transition energy (Figure 15.26). If another atom

is nearby then the transmission of the X-rays immediately

after the transition is found to have features that are iden-

tified as extended X-ray absorption fine structure (EXAFS).

The absorption of the photon leads to the emission of an

electron from the atom, which has wavelength determined

by the de Broglie relationship. This wave can be back-

scattered from a nearby second atom, and the backscattered

wave consequently contributes to the initial wave in either

a constructive or destructive manner that is dependent upon

the pathlength, 2d, where dis the distance between the atoms,

relative to the wavelength:

(15.10)

In a typical EXAFS experiment, the angles are fixed and

the energy of the incident photon is varied. As the photon

energy is varied the energy of the emitted electron can be

calculated according to:

(15.11)

where Eionis the energy required to remove the electron from the atom.

The phase will change as the energy of the photon changes due to the

changes in the wavelength of the electron, which are found by using

the de Broglie relationship (Chapter 9) and eqn 15.11:

(15.12)

The change in phase as the energy of the photon, h 9 , changes gives rise

to the ripples in the EXAFS signal. The phase is proportional to the bond

distance d, so a Fourier transform can be used to determine the bond

distance.

This technique is sensitive only to those atoms that have transition

energies in the appropriate energy region, namely transition metals. Thus,

for a protein, the signals will provide a direct measure of the coordina-

tion of the metal cofactors. As an example, there are many iron-containing

Phase

()

()

()

== = ( −

4

4

4

2

π

λ

π

π

ν

d

d

p

h

d

h

mhe Eiion)

Eh E

p

ion me

=− =ν

2

2

Phase=

⎛

⎝

⎜⎜

⎞

⎠

2 ⎟⎟

2

π

λ

d

340 PART 2 QUANTUM MECHANICS AND SPECTROSCOPY

μ

Figure 15.26The absorption of
X-rays shows a transition at a
metal site followed by oscillations
due to reflections from nearby
atoms.