Symmetry groups of molecule - Hamiltonian

  • #1
87
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Main Question or Discussion Point

Hello everybody,

As I mentioned in the title, it is about molecular symmetry and its Hamiltonian.
My question is simple:
For any molecule that belong to a precise point symmetry group. Is the Hamiltonian of this molecule commute with all the symmetry element of its point symmetry group?

Thanks.
Konte
 

Answers and Replies

  • #3
87
1
Yes.
Thank you for your answer.
Could you please indicate how to demonstrate this (any link or book?)
 
  • #4
A. Neumaier
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Thank you for your answer.
Could you please indicate how to demonstrate this (any link or book?)
I don't know of a reference. This is more or less by definition, because atoms with the same number of protons and neutrons are indistinguishable. If you use a second-quantized formulation, you cannot create Hamiltonians where this fails.

In practice one uses first-quantized formulations only and enforces this through how the molecular force field is set up - by imposing identical coefficients on terms that differ only by a permutation.
 
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  • #5
87
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I don't know of a reference. This is more or less by definition, because atoms with the same number of protons and neutrons are indistinguishable. If you use a second-quantized formulation, you cannot create Hamiltonians where this fails.

In practice one uses first-quantized formulations only and enforces this through how the molecular force field is set up.
Many thanks anyway. In fact, I suspect that the answer is "yes" , so you reassure me largely.
I turn to somebody who can indicate any demonstration if possible please.

Thanks
 

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