Question about a measured spectra

[BillKet]

Hello! I have the spectra below measured, which shows transitions from a $^{2}\Sigma_+$ electronic level (the ground state) to an excited $\Omega=3/2$ level (there are several other level around it, so I decided that using Hund case c would be better, than Hund case a, but in Hund case a this state would be mainly $^{2}\Pi_{3/2}$). I know the molecular constants of the $^{2}\Sigma_+$ state and I would like to get some values for the excited state. The resolution is not great, so I don't expect really accurate values, but ideally I would like to fit something of the form: $$T_{3/2}+B_{3/2}J(J+1)+D_{3/2}[J(J+1)]^2$$
The molecules are quite hot, so we have several vibrational levels populated (at least the first 4-5 based on some preliminary experiments). However, I am not really able to bring the simulated spectra (I am using pgopher) close to this measured one, such that I can start the fit from a region close to the truth one. I can get a pair of left/right peaks (on the left and right of that central empty zone) for the right parameters for a given vibrational transition, but I get only 1 pair of peaks. However my spectra seems to have a lot of those (almost like the spectra is mirrored around that empty region) and adding more vibrational levels doesn't really help much. New vibrational levels are shifted to the left or to the right with respect to each other, but what I would need is something that stays at the center, in the empty region, but moves the left and right peaks further away from each other. I was not able to get this effect. Has anyone seen a spectra like this before? Can someone give me any advice on how to proceed? Thank you!

 

[Twigg]

How hot were the molecules? Temperature or Doppler linewidth is fine.

As you mentioned, adding more vibrational states doesn't add mirrored peaks like you see. Have you tried adding more rotational states to the initial distribution beyond the 4-5 you originally saw? That's what would make the most sense to me.

However, I am not really able to bring the simulated spectra (I am using pgopher) close to this measured one, such that I can start the fit from a region close to the truth one. I can get a pair of left/right peaks (on the left and right of that central empty zone) for the right parameters for a given vibrational transition, but I get only 1 pair of peaks.

You did try sweeping the value of $B_{3/2}$, right? And you still only see one peak? Even though you have 4-5 rotational levels populated initially? That doesn't make a whole lot of sense.

 

[BillKet]

How hot were the molecules? Temperature or Doppler linewidth is fine.

As you mentioned, adding more vibrational states doesn't add mirrored peaks like you see. Have you tried adding more rotational states to the initial distribution beyond the 4-5 you originally saw? That's what would make the most sense to me.You did try sweeping the value of $B_{3/2}$, right? And you still only see one peak? Even though you have 4-5 rotational levels populated initially? That doesn't make a whole lot of sense.

Thank you for your reply! By more rotational states, you mean rotational states that are populated in the ground state? Currently I didn't set a cut on that. The temperature in pgopher is set to 500K and I have all the J values between 0 and 100.

Do you mean that each of the peaks we see there is actually a rotational peak? This is what confuses me. The width of each peak is a few tens of GHz, so each peak in the plot has a few tens of rotational peaks under it. So I assumed that each pair of left-right peak is actually one vibrational transition (including all the transition from multiple rotational levels). But again, that accounts for only one pair of peaks. Changing the rotational constants makes one such pair change its shape a bit, but doesn't add new peaks.

 

[Twigg]

This is what confuses me. The width of each peak is a few tens of GHz, so each peak in the plot has a few tens of rotational peaks under it.

Right, sorry, dumb oversight on my part. I think I just got confused because you presented a formula for rotational spectra as what you wanted to fit to.

Yeah ok I see what you mean now. Weirdly, your spectrum would make sense if you somehow magically had a Franck Condon factor of 0 for the $\Delta \nu = 0$ line, but that seems unlikely to me. I'm biased though because I've only ever worked on molecules with low vibrational branching ratios (i.e., molecules that lend themselves to quantum state control, and thus have highly diagonal FCFs).

 

[BillKet]

Right, sorry, dumb oversight on my part. I think I just got confused because you presented a formula for rotational spectra as what you wanted to fit to.

Yeah ok I see what you mean now. Weirdly, your spectrum would make sense if you somehow magically had a Franck Condon factor of 0 for the $\Delta \nu = 0$ line, but that seems unlikely to me. I'm biased though because I've only ever worked on molecules with low vibrational branching ratios (i.e., molecules that lend themselves to quantum state control, and thus have highly diagonal FCFs).

I see what you mean. But from the theoretical predictions this should be highly diagonal. There will be some off-diagonal terms, but highly suppressed (not sure if we would see them at all).

Could it be that I need other terms in the Hamiltonian (although I don't they will be big enough to change anything)?

 

[Twigg]

What's your ground state vibrational constant (harmonic frequency)?

 

[BillKet]

What's your ground state vibrational constant (harmonic frequency)?

It is about 400 cm$^{-1}$.

 

[Twigg]

Yep, sorry, I'm stumped. I can't see how your vibrational spectrum would look like that (no central peak for the diagonal lines) unless you had another quantum number involved (splitting into two peaks for the diagonal lines). I didn't think an omega doublet or lambda doublet could be as big as 10's of cm^-1 though. I'm going to shut up until the real spectroscopy gurus get around to this.