Project: Photoemission using synchrotron radiation at MAX Lab

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 • Learn about fitting in MATLAB • Learn about convolution

Photoelectron spectroscopy • Ionization • Electron kinetic energy is measured • Data presented on a binding-energy scale • Electronic states • Vibrational states

Vibrational progressions • Real-life spectra: anharmonic model Harmonic term Anharmonic term Adiabatic binding energy

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 

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 • 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 • Plot Lorentzian • Plot Gaussian profiles • Convolute these profiles • Study the result…

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

Franck-Condon…

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 • 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.

Project: Photoemission using synchrotron radiation at MAX Lab