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Project: Photoemission using synchrotron radiation at MAX Lab. A virtual lab project. Goals. Learn about photoelectron spectra Extract the bond distance for different states of CO+ from PES (Franck-Condon analysis) Extract the life time of valence and core electronic states

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Presentation Transcript
goals
Goals
  • Learn about photoelectron spectra
  • Extract the bond distance for different states of CO+ from PES (Franck-Condon analysis)
  • Extract the life time of valence and core electronic states
  • Learn about fitting in MATLAB
  • Learn about convolution
photoelectron spectroscopy
Photoelectron spectroscopy
  • Ionization
  • Electron kinetic energy is measured
  • Data presented on a binding-energy scale
  • Electronic states
  • Vibrational states
vibrational progressions
Vibrational progressions
  • Real-life spectra: anharmonic model

Harmonic term

Anharmonic term

Adiabatic binding energy

line shapes
Line shapes
  • Lorentzian
  • The quantum mechanical result using Fermi’s Golden Rule for photoionization produces a similar equation, also described using a Lorentzian distribution about the nominal energy, 0. The width of the peak at half of the peak maximum (FWHM) is defined as 
slide6
Gaussian
  • Photon BW
  • Electron analyzer resol
  • Doppler broadening
  • Widths sum in quadrature
  • The half width of the ‘Gaussian’ function at a value of 1/e is standard deviation), the FWHM is then 2.354 
data treatment
Data treatment
  • Fit the data to a function

Peak energies (vibrational progression)

Line shapes:

    • Lorentzian natural line shape
    • Gaussian profile ‘measurement’
  • Mathematically speaking
    • Measurement: convolution of Gauss + Lorentz
pre lab exercise
Pre-lab exercise
  • Plot Lorentzian
  • Plot Gaussian profiles
  • Convolute these profiles
  • Study the result…
analysis
Analysis
  • Develop a model function for fit profile
  • Line shape: convolution
  • Peak energies: vibrational progression
  • Least-squares fit: minimize difference between model and measurement, adjust model parameters
  • Use peak intensities in Franck-Condon analysis to get bond-distance change
least squares fit
Least-squares fit
  • Funct(E,,exe,n,,I1..In)
    • N,  are known
    • E, ,I1..In we can guess (initial)
  • MATLAB

optimization = fminsearch('difpart1',initial,options);

fitdata2 = ourfit(modelfunct,datax,datay);

d=conv(gaussian,spectrum1);

initial = [14.34,0.27,12500,680,0.010,0.02];

additional information
Additional information
  • Data files: http://www.sljus.lu.se/fys224/project2/uppgift/data_files.html
  • Files for exercise:http://www.sljus.lu.se/fys224/project2/uppgift/ar_3p.html
  • CO ground state:The ground state internuclear distance for carbon monoxide (X 1+ state) is 1.1283 Å (Huber & Herzberg, Molecular spectra and molecular structure IV, van Nostrand Reinhold, New York, 1979). Calculate the change in internuclear distance for the transitiion to the final A state (about 16.5 eV binding energy) using the Franck-Condon principle. Assume a harmonic potential for this calculation and use the corrected linear-coupling model. The ground state vibrational energy, gr, is 2170.2 cm-1.