Is the Isotope Shift the Same for Different Vibrational Levels in Molecules?

In summary: The field shift is just the change in the volume of the nucleus for different isotopes. In short, adding more neutrons has an influence on the distribution of the protons in the nucleus, and the electrons whose orbits have a non-zero probability of being inside the nucleus get affected by this (this change in volume effect is actually significantly higher than the change in mass for higher A nuclei). Here is a nice introduction to that (page 236). But as I said before, I would like some readings where this effect is analyzed in the molecules, not just atoms i.e. how does the field effect of isotope shift affects the vibrational and rotational levels of a molecule. Thank you!
  • #1
kelly0303
563
33
Hello! Is the isotope shift between 2 (low lying) vibrational levels of the lowest 2 electronic levels (of a diatomic molecule) the same, no matter what the 2 levels are? For example, is the isotope shift associated to the ##0 \to 0## vibrational transition of 2 molecular isotopes (here I mean the lowest vibrational level of the electronic ground state and the lowest vibrational level of the first excited electronic state) the same as the ##1 \to 1## isotope shift (here I mean the first excited vibrational level of the electronic ground state and the first excited vibrational level of the first excited electronic state)? And if they are not the same, how big (order of magnitude) is the difference? Any insight or suggested reading would be greatly appreciated. Thank you!
 
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  • #2
As far as I remember the two energy spectra should be roughly independent. In other words:
E_total = E_electronic + E_vibration where both components have their own isotope shift. If you consider the isotope effect on a transition only then E_transition_isotope = E_electronic_transition_isotope + E_vibration_transition_isotope. As long as you don't change the vibrational state I don't expect the isotope shift to depend on that state.
 
  • #3
I think the principle is that the energies are separable, i.e. E_total = E_electronic + (n+1/2)hν (ignoring anharmonicity). But ν may, and generally does, vary from one electronic state to another, as the different electronic distribution affects the stiffness of bonds. Then
E(0→0) = ΔEe + 1/2 hΔν
E(1→1) = ΔEe + 3/2 hΔν
So E(0→0) is different from E(1→1) for the same isotopomer.
The isotope shift for E(0→0) will be 1/2 h(Δν1 - Δν2) = 1/2 hΔν1(1-μ12)
where the subscript 1 denotes the lighter isotopomer, and μ is the reduced mass, and for E(1→1) will be
3/2 hΔν1(1-μ12)
 
  • #4
mjc123 said:
as the different electronic distribution affects the stiffness of bonds
Then there is a difference, but that sounds like a tiny higher order effect.
 
  • #5
mfb said:
Then there is a difference, but that sounds like a tiny higher order effect.
Certainly not!

Here is an example for Cs2
1583757958401.png

and this one for O2
1583758117096.png

These curves definitely correspond to very different bond stiffness, and thus different ##\nu##.
 
  • Informative
Likes mfb
  • #6
mjc123 said:
I think the principle is that the energies are separable, i.e. E_total = E_electronic + (n+1/2)hν (ignoring anharmonicity). But ν may, and generally does, vary from one electronic state to another, as the different electronic distribution affects the stiffness of bonds. Then
E(0→0) = ΔEe + 1/2 hΔν
E(1→1) = ΔEe + 3/2 hΔν
So E(0→0) is different from E(1→1) for the same isotopomer.
The isotope shift for E(0→0) will be 1/2 h(Δν1 - Δν2) = 1/2 hΔν1(1-μ12)
where the subscript 1 denotes the lighter isotopomer, and μ is the reduced mass, and for E(1→1) will be
3/2 hΔν1(1-μ12)
Thank you for this! Actually I should have been more clear in my question (sorry for that). I am interested in high mass isotopes, where the mass shift is basically negligible i.e. ##\mu1/\mu2## is basically 1. What I am interested in is the field (volume) effect of isotope shift. I didn't find much online so any suggested reading would be really welcome.
 
  • #7
I haven't heard of the field (volume) effect of isotope shift. Can you enlighten me?
 
  • #8
mjc123 said:
I haven't heard of the field (volume) effect of isotope shift. Can you enlighten me?
The field shift is just the change in the volume of the nucleus for different isotopes. In short, adding more neutrons has an influence on the distribution of the protons in the nucleus, and the electrons whose orbits have a non-zero probability of being inside the nucleus get affected by this (this change in volume effect is actually significantly higher than the change in mass for higher A nuclei). Here is a nice introduction to that (page 236). But as I said before, I would like some readings where this effect is analyzed in the molecules, not just atoms i.e. how does the field effect of isotope shift affects the vibrational and rotational levels of a molecule. Thank you!
 

Related to Is the Isotope Shift the Same for Different Vibrational Levels in Molecules?

1. What is an isotope shift in molecules?

An isotope shift in molecules refers to the change in the relative positions of spectral lines in the emission or absorption spectrum of a molecule due to the presence of different isotopes of the same element. This shift occurs because the different isotopes have slightly different masses, leading to differences in their energies and thus their spectral lines.

2. How does isotope shift affect molecular spectroscopy?

Isotope shift can affect molecular spectroscopy by providing information about the molecular structure and dynamics. It can also affect the accuracy of spectroscopic measurements, as the presence of different isotopes can cause shifts in the spectral lines and alter the calculated values.

3. What causes isotope shift in molecules?

The main cause of isotope shift in molecules is the difference in mass between isotopes of the same element. This leads to differences in the vibrational and rotational energies of the molecule, resulting in shifts in the spectral lines.

4. How is isotope shift used in scientific research?

Isotope shift is used in scientific research to study the structure and dynamics of molecules, as well as to make accurate measurements in spectroscopy. It can also be used in fields such as geochemistry and environmental science to track the origins and movements of different isotopes in natural systems.

5. Can isotope shift be observed in all molecules?

Yes, isotope shift can be observed in all molecules that contain different isotopes of the same element. However, the magnitude of the shift may vary depending on the specific molecule and the isotopes present.

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