Addition/Correction pubs.acs.org/JPCL
Correction to “Crystal Structures, Optical Properties, and Effective Mass Tensors of CH3NH3PbX3 (X = I and Br) Phases Predicted from HSE06” Jing Feng and Bing Xiao* J. Phys. Chem. Lett. 2014, 5 (7), 1278−1282. DOI: 10.1021/jz500480m S Supporting Information *
n our recent publication entitled “Crystal Structures, Optical Properties, and Effective Mass Tensors of CH3NH3PbX3 (X = I and Br) Phases Predicted from HSE06” in the Journal of Physical Chemistry Letters,1 we have discussed the structural, electronic, and optical properties of new hybrid organic− inorganic solar energy harvesters with pervoskite-type crystal structures in CH3NH3PbX3 compounds by employing the firstprinciples calculations. In the original paper, we did not mention other two important theoretical calculations published recently using density functional theory (DFT) or other manybody perturbation theory (GW) for the same system. By the meantime, we also found several obvious mistakes in our Supporting Information for the structural details of CH3NH3PbX3 (X = I and Br). Here, we would like to apologize to the readers and try to address those issues. Our main results and conclusions in the paper are intact.
I
pseudopotential. Any ab initio code using those two types of pesudopotential is unable to describe the SOC. This problem can be successfully addressed by using either full-electron method or simply employing the more accurate pseudopential approximation such as PAW method. The effects of SOC on the band dispersions and effective masses of CH3NH3PbX3 (X = I and Br) have been discussed by Even2 et al. using PBE + SOC method and Umari3 et al. with GW + SOC. The results obtained by those calculations indicate that PBE underestimates the band gaps of CH3NH3PbX3 compounds. PBE + SOC reduces the band gaps of them further. Meanwhile, many-body perturbation method (GW) tends to overestimate the quasiparticle band gaps of CH3NH3PbX3 structures slightly. After including the SOC correction to GW, the band gaps are in good agreement with experimental values. Therefore, GW + SOC is more accurate than PBE + SOC for the electronic band dispersions. In our paper, we employed the HSE06 to compute the band gaps of CH3NH3PbX3 structures. HSE06 itself gives the accurate band gaps for the computed structures. We expect that the HSE06 + SOC method will slightly underestimate the band gaps. Another significant effect of SOC is the change of effective masses of electron at the bottom of conduction band. This has been discussed in detail by Even and co-workers.2 There is no significant change of band dispersions near the top of valence band. Therefore, the computed effective masses of holes in our paper are not affected and remain correct. However, due to the strong splitting of p1/2 and p3/2 states at the bottom of conduction band, the effective masses of electrons reported in our paper are no longer valid. From refs 2 and 3, we can see the SOC will reduce the electron effective mass abruptly. As a result, the mobility of electron in CH3NH3PbX3 compounds could be much higher than that predicted by DFT without SOC correction.
1. SPIN ORBITAL COUPLING EFFECTS In our calculations, the scalar relativistic effects were included properly in terms of pseudopotentials. The nonscalar relativistic effect was completely omitted. In the DFT calculation, the nonscalar relativistic effect or spin orbital coupling (SOC) is usually treated as a perturbation term, which can be expressed as Ĥ = Ĥ 0 + Ĥ SOC
(1)
where Ĥ 0 is the Hamiltonian of Kohn−Sham noninteracting system and spin−orbital coupling is given by Ĥ SOC = ζ(r)L̂ ·S .̂ L̂ and Ŝ are the total orbital angular momentum and total spin momentum, respectively. The radial dependent function ζ(r) is given by ζ (r ) ∝
d V (r ) dr
(2)
Here, V(r) is the one-center Coulomb potential between a valence electron and nucleus. From eq 2, we can see that the SOC is strong when the V(r) changes rapidly with r. It is also known that V(r) indeed varies quickly in the space near the nucleus. Thus, the core region of an atom plays the significant role in SOC correction. For the pseudoatom with frozen core approximation, V(r) is simply the pseudopotential of any valence orbital. Because, in our study, the normal conserving pseudopotentials were used in the DFT calculations, V(r) is smooth both in valence and core regions. Therefore, the SOC is almost completely missing due to the poor construction of V(r) in the core region for normal conserving or ultrasoft © 2014 American Chemical Society
2. NEW UPDATES FOR SUPPORTING INFORMATION We made some corrections in the Supporting Information. The original one has some confusions and mistakes in the captions of the Tables and Figures. Here, we would like to mention some of them. In Table s1, we explained why the HSE06 lattice constants are exactly the same as PBE+D2 method. Published: May 2, 2014 1719
dx.doi.org/10.1021/jz500831m | J. Phys. Chem. Lett. 2014, 5, 1719−1720
The Journal of Physical Chemistry Letters
Addition/Correction
In Tables s3−s6, the captions of them are written, and we also corrected some errors in the last two columns in each Table. For the convenience, the structural files of tetragonal and orthorhombic CH3NH3PbI3 phases are prepared in .cif format. This allows the readers to visualize and modify the CH3NH3PbI3 structures very easily.
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ASSOCIATED CONTENT
S Supporting Information *
This material is available free of charge via the Internet at http://pubs.acs.org.
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REFERENCES
(1) Feng, J.; Xiao, B. Crystal Structures, Optical Properties, and Effective Mass Tensors of CH3NH3PbX3 (X = I and Br) Phases Predicted from HSE06. J. Phys. Chem. Lett. 2014, 1278−1282. (2) Even, J.; Pedesseau, L.; Jancu, J.; Katan, C. Importance of Spin− Orbit Coupling in Hybrid Organic/Inorganic Perovskites for Photovoltaic Applications. J. Phys. Chem. Lett. 2013, 4 (17), 2999−3005. (3) Umari, P.; Mosconi, E.; Filippo, D. Relativistic GW calculations on CH3NH3PbI3 and CH3NH3SnI3 Perovskites for Solar Cell Applications. Sci. Rep. 2014, 4, 4467.
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