I Molecular Hamiltonian - Ammonia

87
1
Hello everybody,

The general expression of molecular Hamiltonian operator for any molecule is:
$$\hat{H} = \hat{T}_n+\hat{T}_e+\hat{V}_{ee}+\hat{V}_{nn}+\hat{V}_{en}+\hat{f}_{spin-orbit} $$
where:
##\hat{T}## correspond to kinetic energy operator
##\hat{V}## correspond to potential energy operator
##e## and ##n## subscripts correspond to electrons and nucleus which compose the molecule.
My question is : when I try to apply this to the ammonia molecule case, it seems like incomplete for me because the famous "bi-stable" potential energy operator of ammonia is missing. How to introduce it?

Thank you everybody.

Konte.
 

DrClaude

Mentor
6,971
3,144
My question is : when I try to apply this to the ammonia molecule case, it seems like incomplete for me because the famous "bi-stable" potential energy operator of ammonia is missing. How to introduce it?
What operator is that???

The double-well potential of ammonia comes about simply from solving the electronic problem with the Hamiltonian you gave, in the Born-Oppenheimer approximation. What you get then is a multidimensional surface, and there is a particular "cut" in that surface that corresponds to the "inversion coordinate," which is a double well.
 
87
1
What operator is that???
I mean to say : the double-well potential of ammonia.
You answered my question, I think.
Thanks.

Konte
 

Want to reply to this thread?

"Molecular Hamiltonian - Ammonia" You must log in or register to reply here.

Related Threads for: Molecular Hamiltonian - Ammonia

  • Posted
Replies
3
Views
1K
  • Posted
Replies
4
Views
276
  • Posted
Replies
3
Views
515
  • Posted
Replies
2
Views
440
  • Posted
Replies
17
Views
527
  • Posted
Replies
6
Views
5K
  • Posted
Replies
1
Views
624
  • Posted
Replies
4
Views
5K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads

Top