Should Birge–Sponer plots always have a negative gradient?

I have a set of data I would like to use the Birge–Sponer extrapolation with, but the data is the wavenumbers of the bands in the vibrational-electronic spectrum of a diatomic molecule for $$v' = 0, 1, 2, 3, 4, 5, 6.$$

I thought the $$y$$ axis should have the wavenumber values given as they are (in $$\pu{cm^-1}),$$ but the values given increase with $$v'$$ giving a positive gradient of the graph.

Every plot I have seen has had a negative gradient. Have I interpreted what should go on the $$y$$-axis wrongly?

• Yes, they should have a negative gradient. The energy gap between each level decreases as the vibrational quantum number increases. Maybe your data is for the energy difference between $v=0$ and $v$ as opposed to the difference between the levels? – H.Linkhorn Apr 3 at 19:52
• Yes! I apologise if this seems a basic question. I am finding this field quite tricky- how should I think about converting this to the energy gap between the levels? – Marina Calder Apr 3 at 19:55
• Don't apologies, we're all here to learn!!! To get the energy gaps between each of the levels you will need to subtract the values to leave you the difference. I would recommended drawing a diagram. If you need more help I can write a longer answer explaining how to get each value. – H.Linkhorn Apr 3 at 20:00
• Let me know when you've got your full plot all looking good :) – H.Linkhorn Apr 3 at 20:17
• Yay! I think I have it. It certainly looks nice and gives sensible values. Thank you again for your help, I wouldn't have understood this properly at all without you. – Marina Calder Apr 3 at 20:39