I am curious about crystal field effects on a given atom by analysing $m_l$
projected DOS, the individual d-orbitals are given with respect to the Cartesian coordinates (not the lattice constants). So if you have, say an octahedrally coordinated transition metal, we may need to rotate the cell such that the octahedron is oriented along the Cartesian axes. Example, the structure looks like,
where the top layer and bottom layer octahdrals are in same alignment but centre transition metals containg layer is in different alignment. So the $d$
orbitals are not aligned with the Cartesian axis. Therefore, we need to construct a 3x3 rotational matrix that transforms to my desired frame. As I perform DFT calcuation in VASP in POSCAR format, so I am looking for a code or any package to generate the transformation matrix (for $d$ orbitals, a 5x5 matrix) from POSCAR or any format of structural information file. Thank you in advance.
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$\begingroup$ I'm a bit confused by your 5x5 matrix comment. Exactly what quantity are you trying to rotate that is a 5x5 matrix? A portion of the density matrix? Given VASP uses a planewave basis set I think this unlikely, but presumably you have projected the PW basis onto some kind of local one, and then are using that for whateveer you want (Population analysis?) and as I'm not really a planewave person I'm not sure how you use this process. $\endgroup$– Ian BushCommented May 1 at 6:28
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$\begingroup$ openmopac.net/manual/rotate_atomic_orbitals.html might provide part of an answer, depending on exactly what you are doing. sciencedirect.com/science/article/abs/pii/0166128086800525 is probably of interest as well. But until you clarify why you have a 5x5 matrix its difficult to answer this. $\endgroup$– Ian BushCommented May 3 at 6:58
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