Supplementary Materials
Supplementary Materials
to accompany
Crystal Structures, Optical Properties and Effective Mass Tensors of CH 3 NH 3 PbX 3 (X=I and Br) Phases Predicted from HSE06 by
Jing Feng1 and Bing Xiao2
1. School of Engineering and Applied Science, Harvard University, Cambridge, MA 02138, USA 2. Department of Physics, College of Science and Engineering, Temple University, Philadelphia, PA, 19122, USA.
Supporting Information Placeholder
(Dated: FEB 27, 2014)
1
1 Details and methods All first principles calculations1 were conducted using the plane wave basis in CASTEP code 2. The normalconserving type pesudopotentials (NCPPs)3 within the frozen core approximation were employed in our work, i.e., H1s, C2s2p, N2s2p, I5s5p, Br4s4p and Pb6s6p. Note that the scalar-relativistic effects have been included in the construction of standard Pb NCPP. The remaining non-relativistic effect turns on the spin-orbital coupling interaction which is beyond the capability of any plane wave code using NCPPs. Therefore, the spin-orbital coupling induced mass splitting of carriers (holes or electrons) near the band extremes was completely neglected. The Monkhorst-Pack type k-meshes used in our calculations were 10 × 8 × 10 and 8 × 8 × 10 for orthorhombic and tetragonal phases, respectively. The kinetic energy cutoff was set to 900 eV.
2 Lattice parameters and band gap of CH 3 NH 3 PbX 3 (X= I and Br) compounds In Table s1, we show the optimized structural parameters of tetragonal and orthorhombic CH 3 NH 3 PbX 3 (X= I and Br) phases. The computed values of them are also compared with experimental results. In our calculations, the dispersion interactions were computed from an empirical pair-wise corrections proposed by Grimme
4
in
terms of DFT+D2 scheme. The exchange-correlation functional of DFT part was computed by Perdew-BurkeErnzerhof generalized gradient approximation (PBE-GGA) 5. The results shown in Table.s1 indicate that for the obtained equilibrium cell volumes, PBE overestimates them significantly, compared to experimental values. Meanwhile, the PBE+D2 method shrinks the cell volume, but it is only slightly more accurate than PBE. In some cases, the optimized the cell volumes from Local-density approximation (LDA)1 are surprisingly close to experimental results, which are due to the well-known overbinding error in the local density approximation. In Ref 6, the computed lattice constants of MAPbI 3 by nonlocal van der Waals functional optB86-vdW are in excellent agreement with experiments, implying the intrinsic flaw of applying the empirical pair-wise corrections in the structural predictions for van der Waals bound solids.
2
Table s1: The optimized structural parameters and fundamental band gaps of T- and O-MAPbX 3 (X = I and Br) structures by different DFT methods. The computed values are compared to experimental results.
MAPbI 3
MAPbBr 3
MAPbI 3
MAPbBr 3
a
Ref. 11, 17;
b
Ref. 12, 19;
Tetragonal
Tetragonal
Orthorhombic
Orthorhombic
LDA
GGA
PBE+D2
HSE06
Expa.
Expb.
a
8.7312
8.887
8.8
8.8
8.8
8.855
c
12.9698
13.0204
13.0475
13.0475
12.685
12.659
V
1004.39
1028.33
1010.4
1010.4
982.33
992.6
gap
0.98
1.89
1.81
1.69
1.633
1.66
a
8.4
8.4
8.6
8.6
8.3381
8.322
c
12.3217
12.5153
12.3126
12.3126
11.8587
11.832
V
869.41
883.08
910.64
910.64
824.4632
819.4
gap
0.54
2.26
2.43
2.34
2.258
2.337
a
8.375
9.0289
8.871
8.871
8.8362
8.861
b
12.2468
13.0822
13.1254
13.1254
12.5804
8.581
c
9.0167
8.6362
8.636
8.636
8.5551
12.62
V
924.82
1020.09
1005.54
1005.54
951.01
959.5
gap
0.853
2.07
1.96
1.63
1.633
a
8.0505
8.493
8.015
8.015
7.979
b
11.3536
12.1899
12.341
12.341
11.849
c
8.3754
8.056
8.522
8.522
8.58
V
765.54
834.02
842.98
842.98
811.1804
gap
0.99
2.37
2.344
2.31
2.258
2.337
3 Electronic structures of CH 3 NH 3 PbX 3 (X= I and Br) compounds The electronic structures of T- and O-phases of MAPbX 3 were calculated using HSE06 4 in this work. Note that all calculations for hybrid functional were carried out on the top of PBE+D2 structures. The obtained band dispersions of T- and O-MAPbX 3 (X= I and Br) are illustrated in Figure s1. The highest occupied and the lowest unoccupied bands are highlighted using red and blue colors in the graph for each structure. All computed structures exhibit the direct band gap at Γ-point in the Brillouin zone. The band gaps of them are indicated in
3
Figure s1. Meanwhile, the values are given in Table.s1. We have compared the computed band gaps of T- and OMAPbX 3 (X= I and Br) to those experimental values and the results by HSE06 shows the best results for all these compounds. PBE accidently predicts the reasonable band gaps for MAPbBr 3 in tetragonal and orthorhombic phases. In other two structures of MAPbI 3 , PBE even overestimates the fundamental band gaps. Meanwhile, LDA underestimates the band gaps for all structures. One should note that in the framework of DFT, the fundamental band gap is not a ground state property of condensed phase; therefore, even within the exact exchange-correlation functional, the Kohn-Sham single particle band gap is still not exactly the same as the physical band gap, missing the derivative continuity in the exchange-correlation functional at the integer number of electrons. In other words, the observed good agreement of PBE band gaps with experimental values in some MAPbX 3 structures is merely coincidence7, 8. Band structure of O-MAPbI3
Band structure of T-MAPbI3
6
6 Violet 3.2 eV
Violet 3.2 eV
4
Energy ( eV )
Energy ( eV )
4
2
Gap = 1.627 eV
Red 1.6 eV
0
-2
(0.5,0,0)
Gap = 1.69 eV
-4
G (0,0,0)
Z
Q
X
(0,0.5,0) (0,0.5,0.5) (0.5,0.5,0.5)
U (0,0,0.5)
A
G (0,0,0)
(0.5,0,0)
G
Z
(0,0,0)
Band structure of O-MAPbBr3 Violet 3.2 eV
U (0,0,0.5)
G (0,0,0)
Violet 3.2 eV
4
Energy ( eV )
Energy ( eV )
X
6
4
2
Gap = 2.31 eV
Red 1.6 eV
0
-2
2
Gap = 2.34 eV Red 1.6 eV
0
-2
-4
A
Q
(0,0.5,0) (0,0.5,0.5) (0.5,0.5,0.5)
Band structure of T-MAPbBr3
6
(0.5,0,0)
Red 1.6 eV
0
-2
-4
A
2
-4
G (0,0,0)
Z
Q
X
(0,0.5,0) (0,0.5,0.5) (0.5,0.5,0.5)
U (0,0,0.5)
G
A
(0,0,0)
(0.5,0,0)
G (0,0,0)
Z
Q
X
(0,0.5,0) (0,0.5,0.5) (0.5,0.5,0.5)
U (0,0,0.5)
G (0,0,0)
Figure. s1: The band dispersions of T- and O-MAPbX 3 (X = I and Br) structures computed from HSE06. The fundamental band gaps of them are direct at G point.
4
The densities of states of T- and O-MAPbX 3 structures are shown in Figure s2. Besides those atoms, the bonding orbitals of C-N pair and (PbX 3 )- can be explained using the molecule orbitals of a hetero-atomic pair in the quantum chemistry 8. 60
60
O-MAPbI3
40
30
20
10
40
30
20
10
0
0 -10
-5
0
5
Energy ( eV )
-10
10
60
-5
0
Energy ( eV )
5
10
60
O-MAPbBr3
MA Br Pb
T-MAPbBr3
MA Br Pb
50
Density of States ( eV . cell-1 )
50
Density of States ( eV . cell-1 )
MA I Pb
50
Density of States ( eV . cell-1 )
50
Density of States ( eV . cell-1 )
T-MAPbI3
MA I Pb
40
30
20
10
0
40
30
20
10
0
-10
-5
0
5
Energy ( eV )
10
-10
-5
0
Energy ( eV )
5
10
Figure. s2: The computed densities of states of T- and O-MAPbX 3 (X = I and Br) structures
4 Effective mass of electrons and holes in of transport CH 3 NH 3 PbX 3 (X= I and Br) compounds Table s2: The computed effective masses of holes and electrons in three principal directions for T- and O-MAPbX 3 (X = I and Br) structures using HSE06. Hole(m h *)
Electron(m e *)
[100]
[010]
[001]
[100]
[010]
[001]
MAPbI 3
Tetragonal
0.7125
0.7125
0.361
2.65
2.65
0.76
MAPbBr 3
Tetragonal
0.3053
0.3053
0.4598
1.14
1.14
0.91
MAPbI 3
Orthorhombic
1.1844
11.979
1.048
0.56
1.38
0.82
MAPbBr 3
Orthorhombic
0.3386
0.7777
0.3561
1.11
2.13
1.02
5
5 The atomic positions of all constituting elements in T- and O- MAPbX 3 (X = I and Br) phases Table s3: The atomic coordinates of Pb, I, N, C and H elements in tetragonal-MAPbI 3 structure. x
y
z
g
Site
1
I
I1
0.1865
0.01383
0.18556
1
8d
2
H
H2
0.39555
0.31826
0.38481
1
9d
3
H
H3
0.59173
0.314
0.58186
1
10d
4
Pb
Pb4
0.5
0
0
1
4b
5
I
I5
0.48258
0.25
-0.05115
1
4c
6
C
C6
0.91185
0.25
0.04446
1
5c
7
H
H7
0.33406
0.25
0.55344
1
6c
8
H
H8
0.64777
0.25
0.42545
1
7c
9
N
N9
0.93049
0.75
0.01491
1
8c
Table s4: The atomic coordinates of Pb, Br, N, C and H elements in tetragonal-MAPbBr 3 structure. x
y
z
g
Site
1
Br
I1
0.18012
0.00585
0.18741
1
8d
2
H
H2
0.46097
0.32312
0.36075
1
9d
3
H
H3
0.54046
0.31737
0.63524
1
10d
4
Pb
Pb4
0.5
0
0
1
4b
5
Br
I5
0.48224
0.25
-0.03909
1
4c
6
C
C6
0.93886
0.25
0.06943
1
5c
7
H
H7
0.31173
0.25
0.4772
1
6c
8
H
H8
0.68417
0.25
0.52933
1
7c
9
N
N9
0.94145
0.75
0.06412
1
8c
Table s5: The atomic coordinates of Pb, I, N, C and H elements in orthorhombic-MAPbI 3 structure. x
y
z
g
1
Pb
Pb1
0
-0.00141
0
1a
2
Pb
Pb2
0.50005
0.5022
0.50039
1a
3
Pb
Pb3
-0.00147
-0.0021
0.50042
1a
4
Pb
Pb4
0.49997
0.50115
0
1a
5
I
I5
0.20442
0.29553
0
1a
6
I
I6
0.7967
0.7032
0
1a
7
I
I7
0.29668
0.20328
0.50241
1a
8
I
I8
0.70295
0.20538
-0.00302
1a
9
I
I9
0.29487
0.79736
-0.00344
1a
10
I
I10
0.79407
0.29365
0.49454
1a
11
I
I11
0.20584
0.70544
0.50153
1a
12
I
I12
0.70967
0.7903
0.49203
1a
13
I
I13
0.00321
0.00654
0.24948
1a
14
I
I14
0.50545
0.49655
0.74952
1a
6
15
I
I15
0.00239
0.00654
0.74953
1a
16
I
I16
0.50482
0.49607
0.24946
1a
17
N
N17
0.45714
0.0428
0.265
1a
18
C
C18
0.55874
-0.0588
0.20057
1a
19
C
C19
0.55648
-0.05655
0.70143
1a
20
N
N20
0.45569
0.04421
0.76657
1a
21
C
C21
0.05712
0.55727
0.2654
1a
22
C
C22
0.0586
0.5587
0.76665
1a
23
N
N23
-0.04429
0.45585
0.20106
1a
24
N
N24
-0.04231
0.45781
0.70204
1a
25
H
H25
1.12701
0.62709
0.71411
1a
26
H
H26
1.1302
0.4866
0.81477
1a
27
H
H27
0.98649
0.63022
0.81482
1a
28
H
H28
0.9776
0.3434
0.71629
1a
29
H
H29
0.97445
0.47469
0.62397
1a
30
H
H30
0.84331
0.47775
0.71633
1a
31
H
H31
0.12635
0.62644
0.21374
1a
32
H
H32
0.12923
0.48596
0.31371
1a
33
H
H33
-0.01423
0.62928
0.31376
1a
34
H
H34
-0.02299
0.34208
0.2162
1a
35
H
H35
-0.02636
0.47404
0.12333
1a
36
H
H36
-0.15801
0.47718
0.21624
1a
37
H
H37
0.3863
0.98043
0.31212
1a
38
H
H38
0.38955
1.11042
0.21902
1a
39
H
H39
0.51953
1.11361
0.31214
1a
40
H
H40
0.53585
0.96411
0.11968
1a
41
H
H41
0.53242
0.82315
0.21936
1a
42
H
H42
0.67679
0.96747
0.2194
1a
43
H
H43
0.53319
0.96676
0.62067
1a
44
H
H44
0.5312
0.82462
0.7192
1a
45
H
H45
0.67531
0.96867
0.71924
1a
46
H
H46
0.38564
0.97995
0.81359
1a
47
H
H47
0.38909
1.11085
0.7189
1a
48
H
H48
0.51992
1.11427
0.81358
1a
Table s6: The atomic coordinates of Pb, Br, N, C and H elements in orthorhombic-MAPbBr 3 structure. x
y
z
g
1
Pb
Pb1
0
-0.00248
0
1a
2
Pb
Pb2
0.49999
0.50325
0.50047
1a
3
Pb
Pb3
-0.00224
-0.00333
0.50051
1a
4
Pb
Pb4
0.5001
0.50156
0
1a
5
Br
I5
0.20554
0.29419
0.00114
1a
7
6
Br
I6
0.79614
0.70347
0
1a
7
Br
I7
0.29617
0.20383
0.50332
1a
8
Br
I8
0.70299
0.20746
-0.00429
1a
9
Br
I9
0.29313
0.79772
-0.00505
1a
10
Br
I10
0.79278
0.29214
0.4931
1a
11
Br
I11
0.2078
0.70724
0.50217
1a
12
Br
I12
0.71268
0.78729
0.48962
1a
13
Br
I13
0.00502
0.01044
0.24888
1a
14
Br
I14
0.50869
0.49462
0.74898
1a
15
Br
I15
0.00361
0.01048
0.74902
1a
16
Br
I16
0.50759
0.49378
0.24884
1a
17
N
N17
0.4559
0.04404
0.26608
1a
18
C
C18
0.56046
-0.06057
0.2002
1a
19
C
C19
0.55773
-0.05785
0.70119
1a
20
N
N20
0.45406
0.04579
0.7682
1a
21
C
C21
0.0578
0.55803
0.26647
1a
22
C
C22
0.05977
0.55992
0.76803
1a
23
N
N23
-0.04657
0.45367
0.20042
1a
24
N
N24
-0.04412
0.45608
0.70167
1a
25
H
H25
1.12996
0.63007
0.713
1a
26
H
H26
1.13353
0.48566
0.81758
1a
27
H
H27
0.9855
0.6336
0.81763
1a
28
H
H28
0.97657
0.3393
0.71635
1a
29
H
H29
0.97349
0.47382
0.61996
1a
30
H
H30
0.83914
0.4768
0.71643
1a
31
H
H31
0.12877
0.62892
0.2123
1a
32
H
H32
0.13218
0.48464
0.31613
1a
33
H
H33
-0.01564
0.6323
0.31618
1a
34
H
H34
-0.02441
0.33754
0.21604
1a
35
H
H35
-0.02769
0.47291
0.11909
1a
36
H
H36
-0.16263
0.47587
0.21614
1a
37
H
H37
0.38281
0.98015
0.31479
1a
38
H
H38
0.38661
1.11332
0.21792
1a
39
H
H39
0.51983
1.11711
0.31481
1a
40
H
H40
0.53649
0.96344
0.11553
1a
41
H
H41
0.53304
0.81881
0.2197
1a
42
H
H42
0.68109
0.96682
0.21974
1a
43
H
H43
0.53299
0.96692
0.61673
1a
44
H
H44
0.53121
0.82079
0.71955
1a
45
H
H45
0.6791
0.96862
0.71961
1a
46
H
H46
0.38194
0.97972
0.81679
1a
47
H
H47
0.38572
1.11413
0.71835
1a
48
H
H48
0.5201
1.11795
0.81675
1a
8
References: 1. Hohenberg, P.; Kohn, W., Inhomogeneous Electron Gas. Phys Rev 1964, 136, B864. 2. Segall, M.; Lindan, P.; Probert, M.; Pickard, C.; Hasnip, P.; Clark, S.; Payne, M., First-principles simulation: ideas, illustrations and the CASTEP code. J Phys Condens Matter 2002, 14, 2717. 3. Hamann, D. R., Generalized norm-conserving pseudopotentials. Physical Review B 1989, 40, (5), 2980-2987. 4. Grimme, S., Semiempirical GGA-type density functional constructed with a long-range dispersion correction. Journal of Computational Chemistry 2006, 27, (15), 1787-1799. 5. Perdew, J. P.; Burke, K.; Ernzerhof, M., Generalized Gradient Approximation Made Simple. Physical Review Letters 1996, 77, (18), 3865-3868. 6. Wang, Y.; Gould, T.; Dobson, J. F.; Zhang, H.; Yang, H.; Yao, X.; Zhao, H., Density functional theory analysis of structural and electronic properties of orthorhombic perovskite CH 3 NH 3 PbI 3 . Physical Chemistry Chemical Physics 2014, 16, (4), 1424-1429. 7. Mosconi, E.; Amat, A.; Nazeeruddin, M. K.; Gratzel, M.; De Angelis, F., First-Principles Modeling of Mixed Halide Organometal Perovskites for Photovoltaic Applications. JOURNAL OF PHYSICAL CHEMISTRY C 2013, 117, (27), 13902-13913. 8. Baikie, T.; Fang, Y. N.; Kadro, J. M.; Schreyer, M.; Wei, F. X.; Mhaisalkar, S. G.; Graetzel, M.; White, T. J., Synthesis and crystal chemistry of the hybrid perovskite (CH 3 NH 3 ) PbI 3 for solid-state sensitised solar cell applications. JOURNAL OF MATERIALS CHEMISTRY A 2013, 1, (18), 5628-5641.
9
to accompany
Crystal Structures, Optical Properties and Effective Mass Tensors of CH 3 NH 3 PbX 3 (X=I and Br) Phases Predicted from HSE06 by
Jing Feng1 and Bing Xiao2
1. School of Engineering and Applied Science, Harvard University, Cambridge, MA 02138, USA 2. Department of Physics, College of Science and Engineering, Temple University, Philadelphia, PA, 19122, USA.
Supporting Information Placeholder
(Dated: FEB 27, 2014)
1
1 Details and methods All first principles calculations1 were conducted using the plane wave basis in CASTEP code 2. The normalconserving type pesudopotentials (NCPPs)3 within the frozen core approximation were employed in our work, i.e., H1s, C2s2p, N2s2p, I5s5p, Br4s4p and Pb6s6p. Note that the scalar-relativistic effects have been included in the construction of standard Pb NCPP. The remaining non-relativistic effect turns on the spin-orbital coupling interaction which is beyond the capability of any plane wave code using NCPPs. Therefore, the spin-orbital coupling induced mass splitting of carriers (holes or electrons) near the band extremes was completely neglected. The Monkhorst-Pack type k-meshes used in our calculations were 10 × 8 × 10 and 8 × 8 × 10 for orthorhombic and tetragonal phases, respectively. The kinetic energy cutoff was set to 900 eV.
2 Lattice parameters and band gap of CH 3 NH 3 PbX 3 (X= I and Br) compounds In Table s1, we show the optimized structural parameters of tetragonal and orthorhombic CH 3 NH 3 PbX 3 (X= I and Br) phases. The computed values of them are also compared with experimental results. In our calculations, the dispersion interactions were computed from an empirical pair-wise corrections proposed by Grimme
4
in
terms of DFT+D2 scheme. The exchange-correlation functional of DFT part was computed by Perdew-BurkeErnzerhof generalized gradient approximation (PBE-GGA) 5. The results shown in Table.s1 indicate that for the obtained equilibrium cell volumes, PBE overestimates them significantly, compared to experimental values. Meanwhile, the PBE+D2 method shrinks the cell volume, but it is only slightly more accurate than PBE. In some cases, the optimized the cell volumes from Local-density approximation (LDA)1 are surprisingly close to experimental results, which are due to the well-known overbinding error in the local density approximation. In Ref 6, the computed lattice constants of MAPbI 3 by nonlocal van der Waals functional optB86-vdW are in excellent agreement with experiments, implying the intrinsic flaw of applying the empirical pair-wise corrections in the structural predictions for van der Waals bound solids.
2
Table s1: The optimized structural parameters and fundamental band gaps of T- and O-MAPbX 3 (X = I and Br) structures by different DFT methods. The computed values are compared to experimental results.
MAPbI 3
MAPbBr 3
MAPbI 3
MAPbBr 3
a
Ref. 11, 17;
b
Ref. 12, 19;
Tetragonal
Tetragonal
Orthorhombic
Orthorhombic
LDA
GGA
PBE+D2
HSE06
Expa.
Expb.
a
8.7312
8.887
8.8
8.8
8.8
8.855
c
12.9698
13.0204
13.0475
13.0475
12.685
12.659
V
1004.39
1028.33
1010.4
1010.4
982.33
992.6
gap
0.98
1.89
1.81
1.69
1.633
1.66
a
8.4
8.4
8.6
8.6
8.3381
8.322
c
12.3217
12.5153
12.3126
12.3126
11.8587
11.832
V
869.41
883.08
910.64
910.64
824.4632
819.4
gap
0.54
2.26
2.43
2.34
2.258
2.337
a
8.375
9.0289
8.871
8.871
8.8362
8.861
b
12.2468
13.0822
13.1254
13.1254
12.5804
8.581
c
9.0167
8.6362
8.636
8.636
8.5551
12.62
V
924.82
1020.09
1005.54
1005.54
951.01
959.5
gap
0.853
2.07
1.96
1.63
1.633
a
8.0505
8.493
8.015
8.015
7.979
b
11.3536
12.1899
12.341
12.341
11.849
c
8.3754
8.056
8.522
8.522
8.58
V
765.54
834.02
842.98
842.98
811.1804
gap
0.99
2.37
2.344
2.31
2.258
2.337
3 Electronic structures of CH 3 NH 3 PbX 3 (X= I and Br) compounds The electronic structures of T- and O-phases of MAPbX 3 were calculated using HSE06 4 in this work. Note that all calculations for hybrid functional were carried out on the top of PBE+D2 structures. The obtained band dispersions of T- and O-MAPbX 3 (X= I and Br) are illustrated in Figure s1. The highest occupied and the lowest unoccupied bands are highlighted using red and blue colors in the graph for each structure. All computed structures exhibit the direct band gap at Γ-point in the Brillouin zone. The band gaps of them are indicated in
3
Figure s1. Meanwhile, the values are given in Table.s1. We have compared the computed band gaps of T- and OMAPbX 3 (X= I and Br) to those experimental values and the results by HSE06 shows the best results for all these compounds. PBE accidently predicts the reasonable band gaps for MAPbBr 3 in tetragonal and orthorhombic phases. In other two structures of MAPbI 3 , PBE even overestimates the fundamental band gaps. Meanwhile, LDA underestimates the band gaps for all structures. One should note that in the framework of DFT, the fundamental band gap is not a ground state property of condensed phase; therefore, even within the exact exchange-correlation functional, the Kohn-Sham single particle band gap is still not exactly the same as the physical band gap, missing the derivative continuity in the exchange-correlation functional at the integer number of electrons. In other words, the observed good agreement of PBE band gaps with experimental values in some MAPbX 3 structures is merely coincidence7, 8. Band structure of O-MAPbI3
Band structure of T-MAPbI3
6
6 Violet 3.2 eV
Violet 3.2 eV
4
Energy ( eV )
Energy ( eV )
4
2
Gap = 1.627 eV
Red 1.6 eV
0
-2
(0.5,0,0)
Gap = 1.69 eV
-4
G (0,0,0)
Z
Q
X
(0,0.5,0) (0,0.5,0.5) (0.5,0.5,0.5)
U (0,0,0.5)
A
G (0,0,0)
(0.5,0,0)
G
Z
(0,0,0)
Band structure of O-MAPbBr3 Violet 3.2 eV
U (0,0,0.5)
G (0,0,0)
Violet 3.2 eV
4
Energy ( eV )
Energy ( eV )
X
6
4
2
Gap = 2.31 eV
Red 1.6 eV
0
-2
2
Gap = 2.34 eV Red 1.6 eV
0
-2
-4
A
Q
(0,0.5,0) (0,0.5,0.5) (0.5,0.5,0.5)
Band structure of T-MAPbBr3
6
(0.5,0,0)
Red 1.6 eV
0
-2
-4
A
2
-4
G (0,0,0)
Z
Q
X
(0,0.5,0) (0,0.5,0.5) (0.5,0.5,0.5)
U (0,0,0.5)
G
A
(0,0,0)
(0.5,0,0)
G (0,0,0)
Z
Q
X
(0,0.5,0) (0,0.5,0.5) (0.5,0.5,0.5)
U (0,0,0.5)
G (0,0,0)
Figure. s1: The band dispersions of T- and O-MAPbX 3 (X = I and Br) structures computed from HSE06. The fundamental band gaps of them are direct at G point.
4
The densities of states of T- and O-MAPbX 3 structures are shown in Figure s2. Besides those atoms, the bonding orbitals of C-N pair and (PbX 3 )- can be explained using the molecule orbitals of a hetero-atomic pair in the quantum chemistry 8. 60
60
O-MAPbI3
40
30
20
10
40
30
20
10
0
0 -10
-5
0
5
Energy ( eV )
-10
10
60
-5
0
Energy ( eV )
5
10
60
O-MAPbBr3
MA Br Pb
T-MAPbBr3
MA Br Pb
50
Density of States ( eV . cell-1 )
50
Density of States ( eV . cell-1 )
MA I Pb
50
Density of States ( eV . cell-1 )
50
Density of States ( eV . cell-1 )
T-MAPbI3
MA I Pb
40
30
20
10
0
40
30
20
10
0
-10
-5
0
5
Energy ( eV )
10
-10
-5
0
Energy ( eV )
5
10
Figure. s2: The computed densities of states of T- and O-MAPbX 3 (X = I and Br) structures
4 Effective mass of electrons and holes in of transport CH 3 NH 3 PbX 3 (X= I and Br) compounds Table s2: The computed effective masses of holes and electrons in three principal directions for T- and O-MAPbX 3 (X = I and Br) structures using HSE06. Hole(m h *)
Electron(m e *)
[100]
[010]
[001]
[100]
[010]
[001]
MAPbI 3
Tetragonal
0.7125
0.7125
0.361
2.65
2.65
0.76
MAPbBr 3
Tetragonal
0.3053
0.3053
0.4598
1.14
1.14
0.91
MAPbI 3
Orthorhombic
1.1844
11.979
1.048
0.56
1.38
0.82
MAPbBr 3
Orthorhombic
0.3386
0.7777
0.3561
1.11
2.13
1.02
5
5 The atomic positions of all constituting elements in T- and O- MAPbX 3 (X = I and Br) phases Table s3: The atomic coordinates of Pb, I, N, C and H elements in tetragonal-MAPbI 3 structure. x
y
z
g
Site
1
I
I1
0.1865
0.01383
0.18556
1
8d
2
H
H2
0.39555
0.31826
0.38481
1
9d
3
H
H3
0.59173
0.314
0.58186
1
10d
4
Pb
Pb4
0.5
0
0
1
4b
5
I
I5
0.48258
0.25
-0.05115
1
4c
6
C
C6
0.91185
0.25
0.04446
1
5c
7
H
H7
0.33406
0.25
0.55344
1
6c
8
H
H8
0.64777
0.25
0.42545
1
7c
9
N
N9
0.93049
0.75
0.01491
1
8c
Table s4: The atomic coordinates of Pb, Br, N, C and H elements in tetragonal-MAPbBr 3 structure. x
y
z
g
Site
1
Br
I1
0.18012
0.00585
0.18741
1
8d
2
H
H2
0.46097
0.32312
0.36075
1
9d
3
H
H3
0.54046
0.31737
0.63524
1
10d
4
Pb
Pb4
0.5
0
0
1
4b
5
Br
I5
0.48224
0.25
-0.03909
1
4c
6
C
C6
0.93886
0.25
0.06943
1
5c
7
H
H7
0.31173
0.25
0.4772
1
6c
8
H
H8
0.68417
0.25
0.52933
1
7c
9
N
N9
0.94145
0.75
0.06412
1
8c
Table s5: The atomic coordinates of Pb, I, N, C and H elements in orthorhombic-MAPbI 3 structure. x
y
z
g
1
Pb
Pb1
0
-0.00141
0
1a
2
Pb
Pb2
0.50005
0.5022
0.50039
1a
3
Pb
Pb3
-0.00147
-0.0021
0.50042
1a
4
Pb
Pb4
0.49997
0.50115
0
1a
5
I
I5
0.20442
0.29553
0
1a
6
I
I6
0.7967
0.7032
0
1a
7
I
I7
0.29668
0.20328
0.50241
1a
8
I
I8
0.70295
0.20538
-0.00302
1a
9
I
I9
0.29487
0.79736
-0.00344
1a
10
I
I10
0.79407
0.29365
0.49454
1a
11
I
I11
0.20584
0.70544
0.50153
1a
12
I
I12
0.70967
0.7903
0.49203
1a
13
I
I13
0.00321
0.00654
0.24948
1a
14
I
I14
0.50545
0.49655
0.74952
1a
6
15
I
I15
0.00239
0.00654
0.74953
1a
16
I
I16
0.50482
0.49607
0.24946
1a
17
N
N17
0.45714
0.0428
0.265
1a
18
C
C18
0.55874
-0.0588
0.20057
1a
19
C
C19
0.55648
-0.05655
0.70143
1a
20
N
N20
0.45569
0.04421
0.76657
1a
21
C
C21
0.05712
0.55727
0.2654
1a
22
C
C22
0.0586
0.5587
0.76665
1a
23
N
N23
-0.04429
0.45585
0.20106
1a
24
N
N24
-0.04231
0.45781
0.70204
1a
25
H
H25
1.12701
0.62709
0.71411
1a
26
H
H26
1.1302
0.4866
0.81477
1a
27
H
H27
0.98649
0.63022
0.81482
1a
28
H
H28
0.9776
0.3434
0.71629
1a
29
H
H29
0.97445
0.47469
0.62397
1a
30
H
H30
0.84331
0.47775
0.71633
1a
31
H
H31
0.12635
0.62644
0.21374
1a
32
H
H32
0.12923
0.48596
0.31371
1a
33
H
H33
-0.01423
0.62928
0.31376
1a
34
H
H34
-0.02299
0.34208
0.2162
1a
35
H
H35
-0.02636
0.47404
0.12333
1a
36
H
H36
-0.15801
0.47718
0.21624
1a
37
H
H37
0.3863
0.98043
0.31212
1a
38
H
H38
0.38955
1.11042
0.21902
1a
39
H
H39
0.51953
1.11361
0.31214
1a
40
H
H40
0.53585
0.96411
0.11968
1a
41
H
H41
0.53242
0.82315
0.21936
1a
42
H
H42
0.67679
0.96747
0.2194
1a
43
H
H43
0.53319
0.96676
0.62067
1a
44
H
H44
0.5312
0.82462
0.7192
1a
45
H
H45
0.67531
0.96867
0.71924
1a
46
H
H46
0.38564
0.97995
0.81359
1a
47
H
H47
0.38909
1.11085
0.7189
1a
48
H
H48
0.51992
1.11427
0.81358
1a
Table s6: The atomic coordinates of Pb, Br, N, C and H elements in orthorhombic-MAPbBr 3 structure. x
y
z
g
1
Pb
Pb1
0
-0.00248
0
1a
2
Pb
Pb2
0.49999
0.50325
0.50047
1a
3
Pb
Pb3
-0.00224
-0.00333
0.50051
1a
4
Pb
Pb4
0.5001
0.50156
0
1a
5
Br
I5
0.20554
0.29419
0.00114
1a
7
6
Br
I6
0.79614
0.70347
0
1a
7
Br
I7
0.29617
0.20383
0.50332
1a
8
Br
I8
0.70299
0.20746
-0.00429
1a
9
Br
I9
0.29313
0.79772
-0.00505
1a
10
Br
I10
0.79278
0.29214
0.4931
1a
11
Br
I11
0.2078
0.70724
0.50217
1a
12
Br
I12
0.71268
0.78729
0.48962
1a
13
Br
I13
0.00502
0.01044
0.24888
1a
14
Br
I14
0.50869
0.49462
0.74898
1a
15
Br
I15
0.00361
0.01048
0.74902
1a
16
Br
I16
0.50759
0.49378
0.24884
1a
17
N
N17
0.4559
0.04404
0.26608
1a
18
C
C18
0.56046
-0.06057
0.2002
1a
19
C
C19
0.55773
-0.05785
0.70119
1a
20
N
N20
0.45406
0.04579
0.7682
1a
21
C
C21
0.0578
0.55803
0.26647
1a
22
C
C22
0.05977
0.55992
0.76803
1a
23
N
N23
-0.04657
0.45367
0.20042
1a
24
N
N24
-0.04412
0.45608
0.70167
1a
25
H
H25
1.12996
0.63007
0.713
1a
26
H
H26
1.13353
0.48566
0.81758
1a
27
H
H27
0.9855
0.6336
0.81763
1a
28
H
H28
0.97657
0.3393
0.71635
1a
29
H
H29
0.97349
0.47382
0.61996
1a
30
H
H30
0.83914
0.4768
0.71643
1a
31
H
H31
0.12877
0.62892
0.2123
1a
32
H
H32
0.13218
0.48464
0.31613
1a
33
H
H33
-0.01564
0.6323
0.31618
1a
34
H
H34
-0.02441
0.33754
0.21604
1a
35
H
H35
-0.02769
0.47291
0.11909
1a
36
H
H36
-0.16263
0.47587
0.21614
1a
37
H
H37
0.38281
0.98015
0.31479
1a
38
H
H38
0.38661
1.11332
0.21792
1a
39
H
H39
0.51983
1.11711
0.31481
1a
40
H
H40
0.53649
0.96344
0.11553
1a
41
H
H41
0.53304
0.81881
0.2197
1a
42
H
H42
0.68109
0.96682
0.21974
1a
43
H
H43
0.53299
0.96692
0.61673
1a
44
H
H44
0.53121
0.82079
0.71955
1a
45
H
H45
0.6791
0.96862
0.71961
1a
46
H
H46
0.38194
0.97972
0.81679
1a
47
H
H47
0.38572
1.11413
0.71835
1a
48
H
H48
0.5201
1.11795
0.81675
1a
8
References: 1. Hohenberg, P.; Kohn, W., Inhomogeneous Electron Gas. Phys Rev 1964, 136, B864. 2. Segall, M.; Lindan, P.; Probert, M.; Pickard, C.; Hasnip, P.; Clark, S.; Payne, M., First-principles simulation: ideas, illustrations and the CASTEP code. J Phys Condens Matter 2002, 14, 2717. 3. Hamann, D. R., Generalized norm-conserving pseudopotentials. Physical Review B 1989, 40, (5), 2980-2987. 4. Grimme, S., Semiempirical GGA-type density functional constructed with a long-range dispersion correction. Journal of Computational Chemistry 2006, 27, (15), 1787-1799. 5. Perdew, J. P.; Burke, K.; Ernzerhof, M., Generalized Gradient Approximation Made Simple. Physical Review Letters 1996, 77, (18), 3865-3868. 6. Wang, Y.; Gould, T.; Dobson, J. F.; Zhang, H.; Yang, H.; Yao, X.; Zhao, H., Density functional theory analysis of structural and electronic properties of orthorhombic perovskite CH 3 NH 3 PbI 3 . Physical Chemistry Chemical Physics 2014, 16, (4), 1424-1429. 7. Mosconi, E.; Amat, A.; Nazeeruddin, M. K.; Gratzel, M.; De Angelis, F., First-Principles Modeling of Mixed Halide Organometal Perovskites for Photovoltaic Applications. JOURNAL OF PHYSICAL CHEMISTRY C 2013, 117, (27), 13902-13913. 8. Baikie, T.; Fang, Y. N.; Kadro, J. M.; Schreyer, M.; Wei, F. X.; Mhaisalkar, S. G.; Graetzel, M.; White, T. J., Synthesis and crystal chemistry of the hybrid perovskite (CH 3 NH 3 ) PbI 3 for solid-state sensitised solar cell applications. JOURNAL OF MATERIALS CHEMISTRY A 2013, 1, (18), 5628-5641.
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