[DFTB-Plus-User] : Simulating Silicon Crystal : Does DFTB estimate the phase of the wavefunction accurately?

[Mohiyaddin, Fahd A.]

?Hello,

I am trying to simulate a silicon crystal with DFTB invoking the periodic boundary condition. With the Siband parameters (https://www.dftb.org/parameters/download/siband/siband-1-1-cc/), I am able to obtain the band-structure (band.out file) successfully, and get the experimental band gap (~1.13 eV) for silicon. In the band structure, silicon also has 6 conduction band minima (located 1.13 eV above the valence band) located in k-space at the following k-points :

kx = (2*pi/a0)*(0.844, 0, 0),
k-x = (2*pi/a0)*(-0.844, 0, 0)?,
ky = (2*pi/a0)*(0, 0.844, 0),
k-y = (2*pi/a0)*(0, -0.844, 0)??
kz = (2*pi/a0)*(0, 0, 0.844),
k-z = (2*pi/a0)*(0, 0, -0.844).

, where a0= 0.543nm is the lattice constant of silicon. This is all as expected.

I now calculate the charge density (e.g. file  wp-1-184-5-abs2.cube) for the conduction band minima at each of the above k-points, with DFTB and WAVEPLOT. The charge density at these k-points looks correct, where I can see the periodicity of the crystal and sharp peaks in the charge density at each silicon lattice site. This is also expected and no-problem there.

To obtain the wavefunction at the conduction band minima for the above k-points, I combine the data obtained from the real and imaginary .cube files, provided by WAVEPLOT. For my case, these files are named wp-1-184-5-real.cube and wp-1-184-5-imag.cube.  So, I treat the total wavefunction as:

(data from wp-1-184-5-real.cube) + 1i* (data from wp-1-184-5-imag.cube).

Is the above combination a correct way for estimating the wave function, and will the relative phase between real and imaginary parts be treated correctly at all coordinates in space?

Ultimately, I am interested in the Fourier transform of the wave-function. I don't see the expected results from previous literature that were obtained with VASP (see Table 1 in the paper : https://journals.aps.org/prb/pdf/10.1103/PhysRevB.84.155320). There are additional several frequency components in the Fourier domain which I note from DFTB, compared to the above paper.

I have also tried playing with different unit cells (primitive and cubic) for silicon in DFTB. The results from different unit cells give me the same charge densities, but the Fourier transforms of the wave functions are different. Hence, I was wondering whether I am combining the wave functions correctly, and does DFTB take into account the phase of the wave function accurately.

Has anybody encountered such problems with the DFTB wave-function and its phase in any material?
In case anybody is interested, I can also share my input files.

Regards,
Fahd Mohiyaddin
Postdoctoral Research Associate
Computational Sciences & Engineering Division
Oak Ridge National Laboratory (USA)
Phone: +1-865-237-7242<tel:(865)%20237-7242>
Website: https://www.ornl.gov/staff-profile/fahd-mohiyaddin
Skype: fahd.a.m






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