Potential Energy/ dipole moment curves

[jl29488]

Hi,

I wasn't sure if this is more Physics/Astro or chemistry because its actually all 3.

i've got some conceptual issues with some tasks at hands, and was wondering if anyone could clear that up for me.

(These questions are all regarding molecules)

1) How do you create a potential energy curve? What are the core ingredients? (quantum numbers etc..?)
2) How does a potential energy curve relate to a Dipole moment curve.
3) What can you extract from these curves?

Thanks so much!

 

[DrClaude]

1) How do you create a potential energy curve? What are the core ingredients? (quantum numbers etc..?)

Theoretically, you need to do some quantum chemistry, basically solving the many-body problem (nuclei + electrons) using the time-independent Schrödinger equation. By varying the distance between the atoms, you get the variation of the energy as a function of that distance, resulting in the potential energy curve. Experimentally, you need some fitting procedure, where manipulate a potential energy curve until it produces the correct set of observed levels.

2) How does a potential energy curve relate to a Dipole moment curve.

It doesn't. You can extract the dipole moment from the same quantum chemistry calculations. I'm not sure how you get the dipole moment from experiments, but I guess it is related to line strength.

3) What can you extract from these curves?

A lot of what you want to know about the properties of the molecule.

 

[jl29488]

Thanks for the reply.

Would I not solve the Schrödinger equation for the electrons and nuclei separately (Born oppenheimer approx) ?

Also, how can I extract the rotation-vibration wave functions and energies for solving for the motion of the nuclei/electrons?

Sorry if this my questions don't sound particularly ordered. I am just trying to create a mind map of how its all interlinked.

The eventual goal is to create a Molecular line list.

 

[DrClaude]

Would I not solve the Schrödinger equation for the electrons and nuclei separately (Born oppenheimer approx) ?

The nuclei are still there, just not moving! I didn't mention the BO approx explicitly, but it is what I was referring to in saying "varying the distance between the atoms."

Also, how can I extract the rotation-vibration wave functions and energies for solving for the motion of the nuclei/electrons?

Once you have the potential energy curve, you can solve the Schrödinger equation for the motion of the nuclei, and get ro-vibrational states.

 

[DrClaude]

The eventual goal is to create a Molecular line list.

Do you mean you want to theoretically calculate a series of lines, in order the be able to identify actual spectra? If that is the case, good luck! Producing work good enough to compare to experimental values is not a trivial task.