how to obtain rotationally invariant orbitals in PDOS projection

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seungjae_kwak
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how to obtain rotationally invariant orbitals in PDOS projection

#1 Post by seungjae_kwak » Wed Apr 21, 2021 12:40 pm

Dear users.

I am using LORBIT=11 with spin polarized calculations to obtain PDOS for oxide surfaces.

While I was at it, I came upon the question of how are the x, y, z directions defined?

To find this, I have set up a toy experimented with simple molecule Co(OH6), using nsw=0, in a vacuum box, with rotating the molecules and obtained the PDOS.

I have also calculated Band centers for each orbitals, which I found to be different for each cases.

Co(OH6) complex was positioned so that each OH are aligned to the axes (case 1), and rotated so that non of the OHs are aligned to the 3 axes (case 2).

Case 1 and Case 2 led to different Band centers for each dxy, dyz, dzx, dx2-y2, dz2.

Though this too is understandable, due to this, band center of t2g orbitals (dxy, dyz, dzx) and eg orbitals (dx2-y2, dz2) are changed in the two cases, where in case 1, t2g center < eg center, but in case 2, t2g center>eg center.

Another experiment using O2 molecules gave me lower px bands if O2 are horizontal to the x-axis, and lower pz if aligned to z axis.

Thus, I have concluded the orbitals are defined with respect to the original cell.

This is problematic, as my metal oxides too, are like case 2 in that octahedrally coordinated M-O bonds are not alligned to the cell axes.

My question is, 1. how should we obtain PDOS projections that are invariant to such rotations?

2. Or, can we rotate the direction of the axis for which the PDOS projections are to be made? (So that t2g <eg can hold even in cases where OH are not aligned to the cell's axes?)

Thank you in advance.

andreas.singraber
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Re: how to obtain rotationally invariant orbitals in PDOS projection

#2 Post by andreas.singraber » Wed May 12, 2021 1:39 pm

Hello!

First of all, your investigation led you to the correct assumption that the orbitals are indeed defined with respect to the original cell in the POSCAR file.

Unfortunately, there is no feature in VASP for defining a rotated coordinate system which would only apply to the PDOS projections. One possible solution is of course to perform the rotation in a post-processing step after obtaining the results in the DOSCAR file (wiki/index.php/DOSCAR). If feasible, another approach would be to rotate the original structure in the POSCAR so that it matches the desired coordinate system for the PDOS analysis.

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Re: how to obtain rotationally invariant orbitals in PDOS projection

#3 Post by seungjae_kwak » Sun May 16, 2021 5:39 am

Thank you Andreas for the answer. But I don't really understand how rotating the DOSCAR could be done via postprocessing since in my understanding, it only holds DOS projected onto each ions. To be able to obtain wanted PDOS via some sort of postprocessing, I imagine one should obtain some sort of data in form of uniform grid to integrate. Is this possible in vasp?

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Re: how to obtain rotationally invariant orbitals in PDOS projection

#4 Post by andreas.singraber » Thu May 20, 2021 10:08 am

No, unfortunately there is no feature to export this kind of data on a grid. Thinking more carefully about it, I guess your best option is to rotate the original structure. The post-processing idea was to combine some columns in the DOSCAR file in a clever way, just like when you rotate by 90° around the z-axis the x and y components get interchanged. In a similar way there may be combinations in the d-columns that would correspond to the desired rotation. But this is certainly not trivial and I am not sure whether it is generally applicable.

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