Hi From the core spectra has anyone manage to work out the S so that we can find delta r. We dont know whether to iust use intensity or do something with the area. Also for the valence spectra, have u plotted individual peaks or just made one voight peak cover each group of peaks ie the different states?

I have a problem with fitting the voigt function to the peaks. The parameters I use is x0 and Gamma, but these are apparently not sufficient. Any suggestions for parameters?

//Felix

Hey, I just want to check some reasoning for question 4.

So to find (delta)r, im hoping that it is safe to say, that from a spectra which plots intensity against the energy difference between the ground and ionised state, we can work out S when n(ionised state)=0. From this we get delta and if we know mu and omega we can work out (delta r).But do we definitely take it that we know omega, from the fact that it is said we know the vibration frequency of the molecule in the gound state? ie do we assume that omega corresponds to the ground state frequency. And also what do people think on the question about whether or not you can determine if it is positive or negative? My thinking was that if delta is squared and if S is always positive ( because of the position of the potentials along the x axis) then it wouldn't be possible to have a negative value?

Lleah

I never defined the alpha used in the vibrational wavefunctions. It is not the same as the alpha (for the Morse potential) you have in the project instructions.

• For the harmonic oscillator alpha was simple a convenient short-hand for sqrt( reduced_mass * omega / hbar), not an independent parameter.
• For the Morse potential, I would say alpha and x_e are two ways to express the anharmonicity, related via equation (6).
• In both cases alpha has the dimension 1/length, but there is an extra factor in the Morse-alpha that makes it much smaller.

Near the end of the physics part of the lecture I mentioned some confusion about notation S or I for the Franck-Condon factor. There is some naming confusion also in the litterature, where S can have different meanings:

• On the lecture I used it (as P. Atkins does) for the overlap integral <final vibration n|initial vibration 0>=<n|0>, which should be squared to get a relative transition intensity I(n<-0) = |<n|0>|^2.
  We used the vibrational wavefunctions for specific vibrational quantum number n and the change Delta r in bond length to express I (which was some 80% for n=0 in N2 valence photoemission)
• In the project instructions (and most litterature, e.g. Cederbaum,Smedh,Mishima,Karabunarliev,Pullerits) S has a different meaning, more closely related to the change in bond length Delta r, given by equations (9)-(10) in the instructions. This S is not dependent on vibrational quantum number, instead the relation (eq. 7) I(n<-0)= S^n exp(-S) / n! is used to get the relative intensity. The benefit of this approximation is that it works for any final vibrational quantum number, n, and is much simpler than evaluating overlap between vibrational wavefunctions. This S is called the Huang-Rhys factor or sometimes poissonian parameter.

All sources except Atkins agree that it is I (the relative intensity) that should be called the Franck-Condon factor, so for the future I will update the project instructions (that used the name for S). You are still supposed to find a value for S in Exercise 3 and later, but it would be more correct to use the name "Huang-Rhys-factor" for it. Just to repeat, The Huang-Rhys factor then allows us to easily calculate any Franck-Condon factor I(n<-0) using equation (7). You will be excused if this naming confusion slips into your reports too