1. Photoelectron Spectroscopy Lecture 8 – probability of photoionization –Cross-sections –Gelius model –Asymmetry parameters

2. 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)

3. 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 cm 2 ) or megabarn (10 -18 cm 2 ) cross-section # photons absorbed per unit time incident photon flux

4. 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 σ nl by an asymmetry parameter,  (h ) –This specific equation is for a randomly-oriented ensemble of atoms in an unpolarized field.

5. J.J. Yeh and I. Lindau, At. Data Nucl. Data Tables 1985, 21, 1. Calculated atomic orbital ionization cross-sections

6. 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.)

7. Branching Ratios: Ratio of band intensities as a function 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.

9. 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: staggered eclipsed D 5h D 5d d orbitals transform as: a 1g, e 1g, e 2g d orbitals transform as: a 1 ’, e 1 ’, e 2 ’ We’re going to use these labels

10. Metallocene Ligand  Group Orbitals Cp - (D 5h ) e " 1 2 a " 2 (Cp) 2 2- (D 5d ) a 1g a 2u e 1g e 1u e 2g e 2u

11. Cp - a 2 " e 1 " e 2 " a 1g a 2u e 1u e 1g e 2g e 2u a 1g a 2u e 1u e 1g e 2g a 1g e 1g * e 2u a 1g e 2g * a 2u e 1u a 1g 4s 4p 3d (a 2u +e 1u ) (a 1g +e 1g +e 2g ) (Cp) 2 2- M 2+ (Cp) 2 M 

12. Asymmetry Parameters $=2 $=1 $=0 $=-1  = 90°  = 0°  = 180°  = 54.73°

13. Photoelectron Imaging 800 nm 400 nm CS 2  photoelectron images (Abel inverted)