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