New Light Harvesting Materials Using Accurate and Efficient
Bandgap Calculations - Supplementary Materials Information
Ivano E. Castelli,a Falco H¨user,a Mohnish Pandey,a Hong Li,a Kristian S. Thygesen,a Brian
Seger,b Anubhav Jain,c Kristin Persson,c Gerbrand Ceder,d and KarstenW. Jacobsena
This Supplementary Information is divided in three sections.
(i) First, we expand the comparison between the different
methods to calculate the bandgaps, looking at the signed,
mean absolute and relative errors for the investigated set of
20 materials. In addition, the band structures calculated with
GLLB-SC are compared with the eigenvalues obtained from
HSE06 and from the different levels of GW, for the two materials
ZrS2 and BaHfN2. (ii) Second, a feasibility study of all
the candidate materials for one-photon water splitting shown
in Figure 4, is reported by looking at the literature available
about these materials. In the manuscript, only the five more realistic
materials and the materials known to the community are
described. (iii) Third, the complete list of calculated bandgaps
with their id are reported. These data are also freely available
on the Materials Project database1 and on the Computational
Materials Repository.2
Comparison of Different Methods to Calculate
the Bandgaps
Figure 2 in the manuscript, shows the bandgaps for a set of
materials calculated with LDA, different levels of the GW approximation,
HSE06, and GLLB-SC. The set of materials has
been divided into small and wide bandgap semiconductors and
only the analysis of the errors of the small bandgap set has
been reported. Here, we expand the analysis also to the wide
bandgap materials.
Table 1 shows the mean absolute (signed) errors for the
wide bandgaps. GLLB-SC is the exchange-correlation functional
that approximates better the eigenvalue-self-consistent
GWwith an MAE of 1.54 eV, slightly better than G0W0 (MAE
of 1.62 eV). The performance of HSE06 versus GW is considerably
worst for the wide bandgap set compared with the
small gap ensemble. In fact, for the small bandgaps, the MAE
is 0.46 eV, worse than GLLB-SC and better than G0W0, while
for the wide gaps, the MAE is 2.38 eV. This is even more
clear from the MRE (Table 2), where the mean relative error
a Center for Atomic-scale Materials Design, Department of Physics, Technical
University of Denmark, DK 2800 Kongens Lyngby, Denmark.
b Center for Individual Nanoparticle Functionality, Department of Physics,
Technical University of Denmark, DK 2800 Kongens Lyngby, Denmark.
c Computational Research Division, Lawrence Berkeley National Laboratory,
1 Cyclotron Rd, Berkeley, CA 94720, USA.
d Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
Fig. 1 Band structure, aligned to the valence band, of ZrS2 (id
1186) calculated with GLLB-SC (blue lines), HSE06 (green
squares), G0W0 (red dots), GW0 (purple diamonds), and GW
(orange triangles).
Fig. 2 Band structure, aligned to the valence band, of BaHfN2 (id
10322) calculated with GLLB-SC, HSE06, and different GW levels.
for GLLB-SC and G0W0 with respect to GW is slightly better
for wide gap sets compared to the small set (14.7% and
15.1% for the GLLB-SC and 16.1% and 18.0% for the G0W0,
respectively), while it is much worst for the wide gaps set with
respect to the small gaps set for HSE06 (22.7% and 16.4%,
respectively). As expected for construction, GW0 gives an
improvement of the results of G0W0, and gives the best approximation
to the GW gaps. Despite this, the computational
cost required by any level of GW is at this stage to high to
be used in a high-throughput screening and cheaper methods
should be preferred. The materials thus identified can be then
studied with more accurate methods.
For both HSE06 and GW levels, the computational costs
1