Photoelectron Spectroscopy
• Lecture 8 – probability of photoionization– Cross-sections– Gelius model– Asymmetry parameters
Ionization is still a transition between states
• Initial State: Neutral (or anion)• Final State: Atom/Molecule/Anion after an electron
is removed, plus the ejected electron• M → M+ + e-
init = M final = M+ + e-• Transition Probability = ∫ init m final d• For direct photoionization, transition probability is
always > 0• Photoionization probability is typically described in
terms of a cross-section (much more on this later)
Photoionization Cross-section• The probability per unit area, per unit time that a photon of a given
energy can be absorbed by an atom to excite the photoelectrons.– Fictitious area representing the fraction of incoming photons that will
be absorbed in the photoionization process.
– Unit: barn (10-24 cm2) or megabarn (10-18 cm2)
)(
)()(
hI
hPh cross-section
# photons absorbed per unit time
incident photon flux
Partial Photoionization Cross-sections
• If more than one orbital level is excited, then the cross-section becomes the summation of partial photoionization cross-sections (PPCS)
– PPCSs are a function of the photoelectron’s kinetic energies, and therefore are a function of the incident photon energies.
• When PPCS is measured at a specific angle, it is called a differential cross-section, dσ/d, which is related to σnl by an asymmetry parameter, (h)
– This specific equation is for a randomly-oriented ensemble of atoms in an unpolarized field.
nl
nltot
)]1cos3)((4
11[
4
)( 2
hv
d
hvd nlnl
J.J. Yeh and I. Lindau, At. Data Nucl. Data Tables 1985, 21, 1.
Calculated atomic orbital ionization cross-sections
So far we’ve only talked about atoms; what about molecules?
Gelius model: cross-section behavior of molecular orbitals is dependent on the atomic orbital character from which the MO is comprised.
(Gelius and Siegbahn, Faraday Discuss. Chem. Soc., 1972, 257.)
Branching Ratios:
Ratio of band intensities as afunction of photon energy.
“Photoionization Cross-Sections: A Guide to Electronic Structure”, J. C. Green and P. Decleva, Coord. Chem. Rev. 2005, 249, 209-228.
Variable photon synchrotron studies: Green has collected data on ferrocene at 25 different photon energies from 20-120 eV.
Ionization Energy (eV)7111315 9
He I
He II
Ferrocene
2E2g2A1g
2E1u
2E1g
Fe
Electronic Structure of Ferrocene
What is the point group?
Looking down the Cp-Fe-Cp vector:Cp’s can lie in two extreme conformations:
staggeredeclipsed
D5h D5d
d orbitals transform as:a1g, e1g, e2g
d orbitals transform as:a1’, e1’, e2’
We’re going to use these labels
Metallocene Ligand Group Orbitals
Cp- (D5h)
e "1
e "2
a "2
(Cp)22- (D5d)
a1g a2u
e1ge1u
e2g e2u
Cp-
a 2"
e 1"
e 2 "
a1g
a2u
e1u
e1g
e2g
e2u
a1g
a2u
e1u
e1g
e2g
a1g
e1g*
e2u
a1g
e2g*a2u
e1u
a1g
4s
4p
3d
(a2u+e1u)
(a1g+e1g
+e2g)
(Cp)22- M2+(Cp)2M
Asymmetry Parameters
=2
=1
=0
=-1
= 90°
= 0° = 180°
= 54.73°
Photoelectron Imaging
800 nm
400 nm
CS2 photoelectron images
(Abel inverted)
54.73
=2
=1
=0
=-1