[QE-developers] issues regarding handling the psp in XSpectra

Wed Feb 23 18:45:24 CET 2022

Dear QE developers,

I am a postdoc researcher working at the Brookhaven National Lab under the supervision of Dr. Deyu Lu. My current research project involves benchmark calculations of Ti K-edge XANES using the XSpectra code (QE 6.5 and 6.6), which was compiled on our local cluster using intel/psxe suite, mvapich2 and intel mkl library. This project is in collaboration with Dr. John Vinson from NIST and Exciting developers, including Dr. Christian Vorwerk from U. Chicago, Benedikt Maurer and Fabian Peschel from Humboldt-Universität zu Berlin<https://scholar.google.com/citations?view_op=view_org&hl=en&org=15466593082447993016>.

I noticed the default of the XSpectra parameter r_paw(1:...) was set to 1.5*rc, where rc is the cutoff radius for the pseudo-potential. XSpectra performs a pretreatment of the pseudopotential in two steps in subroutine init_gipaw_1.f90: First, it normalizes the all electron partial wave functions. Second, it calculates the projectors using the normalized partial waves according to the dual orthonormality. This pretreatment is done with the default paw cutoff radius at 1.5 times the cutoff stored in the paw pseudopotential file (r_paw(1:...) = 1.5*rc).

To understand the effects of the cutoff radius scaling, we did several tests for Ti K-edge XANES. We considered two Ti core hole PAW pseudopotentials (see attachment). The first one is generated in our group that has two 4p projectors, with cutoff radius at 1.75 and 1.79 Bohr and reference energy at 7.06 and 0.78 Ryd, respectively. This potential was used previously for the XANES simulations published in Nano Letters 19 (6), 3457-3463, 2019. In the second potential, we only kept one 4p projector with reference energy at 0.78 Ryd and cutoff radius at 1.79 Bohr.

To understand the effects of normalization of the all-electron partial wave and projector generation, we consider two cases. In the first case referred to as original, we modified the source code (init_gipaw_1.f90 and paw_gipaw.f90; attached) to disable the partial wave normalization and projector generation and take the partial waves and projectors as those in the pseudopotential file. In the second case referred to as regenerated, we follow the standard XSpectra pretreatment of the partial wave and projector. In the regenerated mode, we denote r_paw = 1.0*rc as hard cutoff and r_paw = 1.5*rc as soft cutoff by specifying r_paw in the input file using standard XSpectra code.

[Chart, line chart  Description automatically generated]

Figure 1 Comparison of projectors (a and c) and the partial waves (b and d) stored in the pseudopotential file with one 4p projector (labelled as original) with those regenerated in Xspectra (labelled as regenerated). (a) and (b): hard cutoff; (c) and (d): soft cutoff.

[Diagram  Description automatically generated]

Figure 2 Comparison of projectors (a and c) and the partial waves (b and d) stored in the pseudopotential file for the Ti core hole pseudopotential with two projectors.

Next we compare partial waves and projectors obtained for anatase TiO2 (mp-390) in Figure 1 (with one 4p projector) and Figure 2 (with two 4p projectors). We note that the results shouldn't depend on the system we choose, as it only concerns the PAW pseudopotential. We can see that the shape of partial waves has a trivial dependence on r_paw and the PSP pretreatment, and the differences only come from a scaling factor. However, the shape of the projector shows much stronger dependence on these two factors, due to the enforced orthogonality condition applied onto matrix S in subroutine init_gipaw_1.f90. As shown in Fig. 1a with hard cutoff, regenerated projector has a sharp drop to 0 at rc, while the tail in the original projector is smooth. The same trend is also found in Fig. 2a. With the soft cutoff in Figs. 1c and 2c, one can see that the generated projectors are extended to 1.5 rc. While the original projectors are mostly out-of-phase in Fig. 2c, the regenerated projectors become mostly in-phase below 2 Bohr.

These subtle changes in partial waves and projectors can have a non-trivial impact on calculated XANES spectra. We performed three calculations for anatase TiO2 (mp-390): i) original, ii) regenerated hard cutoff and iii) regenerated and soft cutoff. The calculated XANES spectra are shown in Figure 3.

[Chart, line chart, histogram  Description automatically generated]

Figure 3 The Ti K-edge XANES spectra of anatase TiO2 (mp-390) calculated using (a) one and (b) two 4p projectors.

We consider the reference spectrum as those calculated from the original mode, in which rc is always the same as in the PSP file and the projector from the PSP file goes to zero at 1.0*rc. However, after the pretreatment, we can see differences in intensities compared with the original spectrum. In Fig 3a, both regenerated hard cutoff and soft cutoff will lead to noticeable differences compared to the reference spectra throughout the full energy range. When using two 4p projectors, however only the spectra calculated soft cutoff deviates from the original spectrum, while the spectra calculated with hard cutoff is identical compared with the reference as shown in Fig 3b. The reason why the PSP pretreatment behaves differently with 1 or 2 4p projectors has not been fully understood.

In addition, we compared the XANES spectra for anatase TiO2 (mp-390), rutile TiO2  (mp-2657) and brookite TiO2 (mp-1840) obtained with XSpectra and with OCEAN and EXCITING, which are two codes widely used to calculate the XANES spectra by solving BSE. In this test, we only used the pseudopotential with two 4p projectors. Since XSpectra outputs the cross-section while OCEAN and EXCITING output the imaginary part of the dielectric constant, the XSpectra data are rescaled in order to compare the results directly with the other two codes as shown in Fig 4. Overall, OCEAN and EXCITING match very well as expected since they are both BSE codes. It is also clear that XANES spectra obtained from XSpectra with hard cutoff agree better than with soft cutoff, especially in terms of peak intensities.

[Chart  Description automatically generated]

Figure 4 Comparison of XANES spectra obtained with XSpectra, OCEAN and EXCITING. (a) Anatase TiO2, (b) Rutile TiO2 and (c) Brookite TiO2.

Based on our tests results, we found that the XSpectra results are more consistent without the reconstruction of the all-electron partial waves and the projectors in the core-hole potential. Therefore, we believe that the default r_paw=1.5*rc together with PSP pretreatment are likely introduce some artifact in the XANES spectra such that the main edge intensity is weakened, as compared to the original spectra from XSpectra and reference spectra from other codes. We appreciate your feedback on this matter.

Thanks,

Fanchen

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