Photoelectron Spectroscopy

1
Photoelectron Spectroscopy

• Lecture 4 Deconvolution of complex ionization
  structure
• Band shapes with non-resolved vibrational
  structure
• Other complications
• Deriving chemical meaningful information

2
This is the model weve defined
Lowest energy transition Adiabatic transition
(?0 ? ?0) Most probable (tallest) transition
Vertical transition
Ground state vibrational population follows a
Boltzmann distribution e-E/kT kT at room
temperature is 0.035 eV (300 cm-1)
3
But things arent typically that simple!
2T2g Ionization of M(CO)6
This lump contains seven ionizations!
4
Factors we have to consider for inorganic/organic
molecules of the type involved in your research

• Complicated vibrational structure
• Multiple interdigitated modes
• Vibronic coupling between final states
• Additional final state effects
• Jahn-Teller splitting
• Spin-orbit splitting
• Congested spectra
• Inability to individually observe all ionizations
  of interest
• And we have to figure this all out in a way that
  gives chemically meaningful information

5
Data Analysis of Spectroscopic Results

• The Bible
• Data Reduction and Error Analysis for the
  Physical Sciences, Philip R. Bevington and D.
  Keith Robinson, 2nd Edition, McGraw-Hill, 1992

We often wish to determine one characteristic y
of an experiment as a function of some other
quantity x. That iswe make a series of N
measurements of the pair (xi,yi), one for each of
several values of the index i, which runs from 1
to N. Our object is to find a function that
describes the relation between these two measured
variables.
6
Fitting Data using WinFP

• Use a series of functions, each defined with some
  number of degrees of freedom, to represent an
  arbitrary function, the spectrum.
• Define an initial fit using your chemical
  intuition and knowledge about the molecule.
• Have the computer perform a least-squares
  analysis to arrive at a fit that then best
  matches the experimental variables.
• The specific method we are using to search
  parameter space, define conditions of
  convergence, and find a local minima is the
  Marquardt Method. See Chapter 8 of Bevington for
  details.

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What function is appropriate?

• Poisson distribution
• Analytical form appropriate to measurements that
  describe a probability distribution in terms of a
  variable x and a mean value of x.
• Appropriate for describing experiments in which
  the possible values of data are strictly bounded
  on one side but not on the other.
• Non-continuous only defined at 0 and positive
  integral values of the variable x
• Guassian distribution
• more convenient to calculate that the Poisson
  distribution
• Continuous function defined at all values of x
• Limiting case for the Poisson distribution as the
  number of x variables becomes large
• Lorentzian distribution
• appropriate for describing data corresponding to
  resonant behavior (NMR, Mossbauer)
• Voigt Function Combination of Lorentzian and
  Gaussian functions
• Used to describe Lorentzian data with Gaussian
  broadening.

8
Modeling a potential energy surface with a
symmetric Gaussian
9
Modeling a potential energy surface with an
asymmetric Gaussian
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How do we fit data in a chemically meaningful way?

• Think about the expected electronic structure
  first!
• Consider how many valence ionizations are likely
  to be clearly observed before the overlapping
  sigma bond region (lower than about 12 eV
  ionization energy).
• Luckily, these are usually the ionizations
  related to the interesting orbitals of a
  molecule.

11
LCAO Model The energies of the atomic orbitals
are the starting point for the energies of the
molecular orbitals
 Numbers with three decimal places are actual
atomic ionization energies.Numbers with two
decimal places are interpolated.Energies of
unfilled p orbitals determined by excitation
energy from the ground state.Transition metal d
orbital energies interpolated between ionization
of d1 configuration of group I element and d10
configuration of group VIII element.Lanthanides
and actinides list ionization energies only.
Adapted by Dennis Lichtenberger from Craig
Counterman
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What Influences MO Ionization Energies?

• Ionization energies of atomic orbitals
• Oxidation state, formal charge, charge potential
• Bonding or anti-bonding interactions
• See MO Theory presentation by Dennis
  Lichtenberger on the website for a detailed
  discussion of how to estimate MO ionization
  energies.

13
Some rough rules of thumb on the kinds of
ionizations clearly observed for larger molecules

• Transition metal d ionizations, 6-10 eV.
• Aryl HOMO ionizations
• Benzene 9.25 eV, doubly degenerate
• Main group p lone pair ionizations
• For halides, F 14 eV, Cl 11 eV, Br 9 eV, I 8
  eV (SO splitting large for Br, I)
• Metal-ligand dative bonds

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Decide how many valence ionizations should be
clearly observed

• If band shapes ionizations
• Begin fitting using that number of Gaussians
• If band shapes gt ionizations
• Consider possible causes vibrational structure,
  spin-orbit splitting, etc.
• Decide how this information should be chemically
  modeled.
• If band shapes lt ionizations
• Fit using the minimum number of Guassians needed
  to define shape of the spectrum
• Fit the spectra of a series of related molecules
  in a similar way so that comparisons can be made.
• Least-squares analysis
• Look at results, possibly iterate through the
  steps again until achieving a good fit that can
  be defended as giving chemically meaningful
  information.

15
Conclusions

• Photoelectron band shapes can be modeled with
  asymmetric Gaussians functions.
• Might not be able to analytically represent all
  data content, but do want to represent data in a
  consistent, chemically meaningful way.
• When analyzing data, think, then fit.