The symmetry of dielectric tensor in XAS computation using vasp.6.2.1

[zhaoru_sun1]

Dear all,

I am using Vasp.6.2.1 to compute O K-edge XAS of a Pt/O surface system.
According to the tutorials in XANES_in_Diamond, XAS_theory and F. Karsai et al., Phys. Rev. B 98, 235205 (2018)., I know the absorption spectrum is directly proportional to the imaginary part of the dielectric function, which is calculated by vasp.
At the same time, for the dielectric tensor, from D. Franta, J. Appl. Phys. 127, 223101 (2020). and C. Ambrosch-Draxl and J. O. Sofo, Comput. Phys. Commun. 175, 1 (2006)., I learn about that

For orthorhombic or higher symmetry only diagonal components exist.

In my computation, I use a orthogonal supercell, but there are non-diagonal components:

#------------------------------------------------[POSCAR]

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   11.2210973099999993    0.0000000000000000    0.0000000000000000
    0.0000000000000000    9.7177553299999992    0.0000000000000000
    0.0000000000000000    0.0000000000000000   25.1999999999999993

#------------------------------------------------[OUTCAR]

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frequency dependent IMAGINARY DIELECTRIC FUNCTION (independent particle, no local field effects) density-density
E(ev)      X         Y         Z        XY        YZ        ZX
...
523.041135689617  0.000009617600  0.000009741858  0.000005636892  0.000000000000  0.000000106472 
 0.000000000000
523.073657478992  0.000009747511  0.000009727933  0.000005659724  0.000000000000  0.000000084890 
 0.000000000000
...

I don't know what's wrong? Or maybe I misunderstand something. All the related files have been attached.

[martin.schlipf]

Thank you for reporting this to us. I have forwarded this to Ferenc and he will look into this.

[ferenc_karsai]

I've analyzed the structure via ISOTROPY - findsym package and the space group of the C 1 m 1 (number 8 ) which is monoclinic, although the point group is orthorombic. So off diagonal elements are expected.

I also checked the code on orthorombic space groups and it works fine, giving no non-diagonal elements that are greater than zero.

[zhaoru_sun1]

I've analyzed the structure via ISOTROPY - findsym package and the space group of the C 1 m 1 (number 8 ) which is monoclinic, although the point group is orthorombic. So off diagonal elements are expected.

I also checked the code on orthorombic space groups and it works fine, giving no non-diagonal elements that are greater than zero.

Thanks for your test and response.
Sorry, this is my mistake. I misunderstood the concept of cell shape and symmetry of crystal point groups. According to my understanding, my initial structure was trigonal-like crystal system (P3m1, number 156), but after structural optimization, some distortions appeared, and the symmetry was reduced to C1m1, thus some small off-diagonal elements appeared. In addition, I think that the core hole in the excited oxygen atom will also affect the symmetry?

Regarding XAS calculations, there are some other questions that confuse me:

1. About the relationship between XAS and dielectric tensor:
   In XANES_in_Diamond, it says

   Usually we are interested in the sum of all components of the dielectric matrix.

   But for the surface system I am interested in, XAS is angle dependent. Then how to use the calculated dielectric tensor to obtain the XAS of a specific electric polarization direction. (like the theta, phi direction in spherical coordinate system)
   
   I am not sure about the transformation relationship between the two.
2. Another question is about the core-level shift. I learned that DFT cannot accurately calculate the transition energy. Therefore, in order to consider atoms with inequivalent sites, it is usually necessary to calculate the XAS of atoms at different sites and shift their spectra based on the core-level shift before averaging. But in VASP, the output energy in OUTCAR (~515 eV) is already close to the 1s binding energy of oxygen. So I don’t know if the core-level shift has been completed? And can I directly do the XAS averaging of different sites?

[zhaoru_sun1]

...

1. About the relationship between XAS and dielectric tensor:
   Then how to use the calculated dielectric tensor to obtain the XAS of a specific electric polarization direction.

I think that maybe the transformation is

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e(1) = sin(theta)*cos(phi)
e(2) = sin(theta)*sin(phi)
e(3) = cos(theta)
epsilon(1,:) = (/epsilon_xx, epsilon_xy, epsilon_xz/)
epsilon(2,:) = (/epsilon_xy, epsilon_yy, epsilon_yz/)
epsilon(3,:) = (/epsilon_xz, epsilon_yz, epsilon_zz/)
do i=1,3
	do j=1,3
		sigma = e(i) * epsilon(i,j) * e(j)
	enddo
enddo

where, "e" is the polarization vector, "epsilon" is the imaginary part of the dielectric tensor, "sigma" is the absorption cross section.
This is the transformation I guess. And using this transformation, I can get a formula that is similar with equation (4.7) in C. Brouder, Journal of Physics: Condensed Matter 2, 701 (1990). But I haven't understood it.

[ferenc_karsai]

1) Very nice! I would have to search myself because I haven't calculated angle resolved spectra before.

2) The absolute values of the core level energies are of course usually wrong compared to experiment. But XAS spectra are anyway shifted to experiment. For equivalent atoms on different atomic sites (same POTCAR) we would excite from the same energy, but obtain slightly different final states if we carry out the electronic calculation with the core hole due to the different geometrical environment of these atoms. I would than average over the obtained spectra. I've done something similar in (https://journals.aps.org/prb/abstract/1 ... .98.235205) to include lattice vibrations in the spectra.