To check whether electronic transitions are allowed between valence band maximum (VBM) and conduction band minimum (CBM) as per Laporte's rule, the parity of VBM/CBM is needed to be known. This paper discusses this in the second paragraph of page no.5. I would like to know how one can find out the parity of VBM/CBM of the material using the data generated in DFT calculations.
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2$\begingroup$ If a particular energy eigenstate $|n,\mathbf{k}\rangle$ has definite parity, this means it is also an eigenstate of the parity operator P. Then, you can calculate the expectation value $\langle n,\mathbf{k}|P|n,\mathbf{k}\rangle$ and you'll get $+1$ for even parity and $-1$ for odd parity. But note that not all energy eigenstates need to have definite parity. $\endgroup$– ProfMCommented Oct 2, 2022 at 20:21
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$\begingroup$ @ProfM how this could be obtained for example from a CASTEP output? Thank you. $\endgroup$– ShaCommented Oct 3, 2022 at 6:19
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3$\begingroup$ You need the wavefunction $|n,\mathbf{k}\rangle$ from the DFT code. I believe that a good way to extract these from CASTEP is to use c2x: c2x.org.uk $\endgroup$– ProfMCommented Oct 4, 2022 at 19:31
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$\begingroup$ I did find this paper (@ProfM as one of its authors!) using c2x for band parity analysis: doi.org/10.1103/PhysRevB.98.161203. Thank you Professor Monserrat your comment helped me to find this great paper by you. $\endgroup$– ShaCommented Oct 5, 2022 at 18:22
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$\begingroup$ Mentioned in chat. $\endgroup$– Nike Dattani - No Free TimeCommented Feb 18, 2023 at 5:49
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