Regarding the issue of calculating the J value for orbital coupling

[cr N]

Dear  HeXu , 

          This is part of the numerical values for the J value coupling of the sub-orbitals calculated using TB2J and wannier90. Now it is the coupling matrix between the five d sub-orbitals of V1 and V2. I would like to ask, is this matrix necessarily a symmetric matrix? If it has to be a symmetric matrix, is this asymmetry now occurring because the quality of the wannier functions is insufficient? I will attach my calculation results along with the fitted wannier functions. Thank you for taking the time to answer my questions. I wish you good health and success in your work!

Best regards, 

Chaoran Niu

[Xu He]

Hello, 

The matrix does not have to be symmetric. 

For Jij, J_{23}  means the interaction of the 2nd orbital of the atom i and the 3rd orbital of the atom j.

            J_{32}  means the interaction of the 3rd orbital of the atom i and the 2nd orbital of the atom j.

This is not guaranteed to be the equivalent. 

It is the Jij_{23} = Jji_{32}, not Jij_{23}=Jij_{32}.

 

Sometimes you can find the matrix symmetric, but that depends on additional symmetry. 

Best regards, 

HeXu

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