Intracrystalline Aurophilic Interactions with Novel Electronic and Optical. School of Physics, Southeast University, Nanjing , P. R.
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1 Supporting Information: Two-Dimensional AuMX 2 (M=Al, Ga, In; X=S, Se) Monolayers Featuring Intracrystalline Aurophilic Interactions with Novel Electronic and Optical Properties Qisheng Wu,,, Wen Wu Xu,,, Liang Ma, Jinlan Wang,,, * and Xiao Cheng Zeng,ǁ * School of Physics, Southeast University, Nanjing , P. R. China Department of Chemistry, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, United States Division of Interfacial Water and Key Laboratory of Interfacial Physics and Technology, Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai , P. R. China Synergetic Innovation Center for Quantum Effects and Applications (SICQEA), Hunan Normal University Changsha, Hunan , P. R. China ǁ Department of Chemical & Biomolecular Engineering and Department of Mechanical & Materials Engineering, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, United States Δ These authors contributed equally to this work. *Correspondence should be addressed to: J. Wang (jlwang@seu.edu.cn) or X. C. Zeng (xzeng1@unl.edu) S-1
2 Figure S1. Relative energies of different phases (α, β, and γ) for AuMX 2 (M=Al, Ga, In; X=S, Se) monolayers. The energies for α phases are shifted to zero. Leaving out AuGaS 2 monolayers, there are seven low-lying structures for other AuMX 2 monolayers: α-auals 2, α- AuInS 2, γ-auins 2, α-aualse 2, α-augase 2, α-auinse 2, and γ-auinse 2. S-2
3 Figure S2. Electron localization function (ELF) line profiles connecting bonding atoms in AuAlS 2 (a), AuInS 2 (b), AuAlSe 2 (c), AuGaSe 2 (d), and AuInSe 2 (e) systems. The lengths of horizontal axis correspond to bond lengths. Black, green, and magenta lines indicate ELF values in α, β, and γ phases, respectively. Aurophilic interactions in α phases and β phases are denoted in right panels. Since there is no interaction between Au atoms in γ phases, ELF line profiles connecting them are omitted here. S-3
4 Figure S3. Phonon dispersions for other low-lying AuMX 2 (M=Al, Ga, In; X=S, Se) monolayers as indicated in the caption of Figure S1: α-auals 2 (a), α-auins 2 (b), γ-auins 2 (c), α-aualse 2 (d), α-augase 2 (e), α-auinse 2 (f), and γ-auinse 2 (g). S-4
5 Figure S4. Ab initio molecular dynamics (AIMD) snapshots of some low-lying AuMX 2 (M=Al, Ga, In; X=S, Se) monolayers as indicated in the caption of Figure S1 after annealing at 500 K for 10 ps: α-auals 2 (a), α-auins 2 (b), γ-auins 2 (c), α-aualse 2 (d), α-augase 2 (e), α-auinse 2 (f), and γ-auinse 2 (g). S-5
6 Figure S5. Band structures for β and γ phases of AuMX 2 (M=Al, Ga, In; X=S, Se) monolayers on the basis of HSE06 functional: β-auals 2 (a), β-augas 2 (b), β-auins 2 (c), β- AuAlSe 2 (d), β-augase 2 (e), β-auinse 2 (f), γ-auals 2 (g), γ-augas 2 (h), γ-auins 2 (i), γ- AuAlS 2 (j), γ-augase 2 (k), and γ-auinse 2 (l). S-6
7 Figure S6. Calculated optical absorption coefficients that are polarized in x (a), y (b) and z (c) directions based on HSE06 functional for the β phases of AuMX 2 (M=Al, Ga, In; X=S, Se) monolayers. Figure S7. Calculated optical absorption coefficients that are polarized in x (a), y (b) and z (c) directions based on HSE06 functional for the γ phases of AuMX 2 (M=Al, Ga, In; X=S, Se) monolayers. S-7
8 Table S1. Bader charges (unit: e) for atoms in α-, β-, and γ-augas 2 monolayers, respectively. The valence electrons for Au, Ga and S before they bond with each other are 11.0, 3.0 and 6.0, respectively. It can be easily seen that charges are transferred from Au and Ga to S atoms. Bader charge α-augas 2 β-augas 2 γ-augas 2 Au Ga S S-8
9 Table S2. Lattice parameters (a, b, c and γ; units are Å and degree) and fractional coordinates for structures of AuMX 2 (M=Al, Ga, In; X=S, Se) monolayers. System parameter α phase β phase γ phase AuAlS 2 AuGaS 2 AuInS 2 lattice atomic positions lattice atomic positions lattice atomic positions a=5.993 Å, b=6.290 Å, c=18.00 Å, γ=90.00 Au (0.000, 0.000, 0.403) Au (0.500, 0.000, 0.403) Al (0.250, 0.500, ) Al (0.750, 0.500, 0.403) S (0.000, 0.313, 0.332) S (0.500, 0.687, 0.332) S (0.000, 0.687, 0.474) S (0.500, 0.313, 0.474) a=6.127 Å, b=6.427 Å, c=18.00 Å, γ=90.00 Au (0.000, 0.000, 0.386) Au (0.500, 0.000, 0.386) Ga (0.250, 0.500, 0.386) Ga (0.750, 0.500, 0.386) S (0.000, 0.307, 0.316) S (0.500, 0.693, 0.316) S (0.000, 0.693, 0.455) S (0.500, 0.307, 0.455) a=6.789 Å, b=6.373 Å, c=18.00 Å, γ=90.00 Au (0.000, 0.000, 0.351) Au (0.500, 0.000, 0.351) In (0.250, 0.500, 0.351) In (0.750, 0.500, 0.351) S (0.000, 0.294, 0.275) S (0.500, 0.706, 0.275) S (0.000, 0.706, 0.427) S (0.500, 0.294, 0.427) a=5.956 Å, b=7.407 Å, c=18.00 Å, γ=66.30 Au (0.250, 0.993, 0.580) Au (0.750, 0.994, 0.474) Al (0.750, 0.493, 0.527) Al (0.250, 0.494, 0.527) S (0.082, 0.329, 0.600) S (0.582, 0.330, 0.453) S (0.918, 0.658, 0.454) S (0.419, 0.656, 0.600) a=6.150 Å, b=7.430 Å, c=18.00 Å, γ=65.60 Au (0.250, 0.993, 0.565) Au (0.750, 0.994, 0.456) Ga (0.750, 0.493, 0.511) Ga (0.250, 0.493, 0.511) S (0.082, 0.329, 0.585) S (0.582, 0.329, 0.436) S (0.918, 0.658, 0.436) S (0.418, 0.657, 0.585) a=6.807 Å, b=7.595 Å, c=18.00 Å, γ=63.38 Au (0.250, 0.993, 0.499) Au (0.750, 0.993, 0.422) In (0.750, 0.493, 0.461) In (0.250, 0.493, 0.461) S (0.078, 0.336, 0.509) S (0.578, 0.336, 0.412) S (0.922, 0.650, 0.412) S (0.422, 0.650, 0.509) a=b=5.337 Å, c=18.0 Å, γ=90.00 Au (0.500, 0.000, 0.411) Au (0.000, 0.500, 0.610) Al (0.000, 0.000, 0.510) Al (0.500, 0.500, 0.510) S (0.299, 0.201, 0.586) S (0.201, 0.701, 0.434) S (0.701, 0.799, 0.586) S (0.799, 0.299, 0.434) a=b=5.384 Å, c=18.0 Å, γ=90.00 Au (0.500, 0.000, 0.399) Au (0.000, 0.500, 0.604) Ga (0.000, 0.000, 0.501) Ga (0.500, 0.500, 0.501) S (0.296, 0.204, 0.580) S (0.204, 0.704, 0.423) S (0.704, 0.796, 0.580) S (0.796, 0.296, 0.423) a=b=5.631 Å, c=18.0 Å, γ=90.00 Au (0.500, 0.000, 0.399) Au (0.000, 0.500, 0.601) In (0.000, 0.000, 0.500) In (0.500, 0.500, 0.500) S (0.289, 0.211, 0.588) S (0.711, 0.789, 0.588) S (0.211, 0.711, 0.412) S (0.789, 0.289, 0.412) S-9
10 Continuing for Table S2 System parameter α phase β phase γ phase AuAlSe 2 AuGaSe 2 AuInSe 2 lattice atomic positions lattice atomic positions lattice atomic positions a=5.161 Å, b=6.492 Å, c=18.00 Å, γ=90.00 Au (0.000, 0.000, 0.380) Au (0.500, 0.000, 0.380) Al (0.250, 0.500, 0.380) Al (0.750, 0.500, 0.380) Se (0.000, 0.309, 0.300) Se (0.500, 0.691, 0.300) Se (0.000, 0.691, 0.459) Se (0.500, 0.309, 0.459) a=6.283 Å, b=6.639 Å, c=18.00 Å, γ=90.00 Au (0.000, 0.000, 0.364) Au (0.500, 0.000, 0.364) Ga (0.250, 0.500, 0.364) Ga (0.750, 0.500, 0.364) Se (0.000, 0.304, 0.287) Se (0.500, 0.696, 0.287) Se (0.000, 0.696, 0.441) Se (0.500, 0.304, 0.441) a=6.909 Å, b=6.522 Å, c=18.00 Å, γ=90.00 Au (0.000, 0.000, 0.448) Au (0.500, 0.000, 0.448) In (0.250, 0.500, 0.448) In (0.750, 0.500, 0.448) Se (0.000, 0.293, 0.363) Se (0.500, 0.707, 0.363) Se (0.000, 0.707, 0.532) Se (0.500, 0.293, 0.532) a=6.140 Å, b=7.757 Å, c=18.00 Å, γ=66.69 Au (0.250, 0.993, 0.536) Au (0.750, 0.994, 0.438) Al (0.750, 0.493, 0.487) Al (0.250, 0.493, 0.487) Se (0.084, 0.326, 0.567) Se (0.583, 0.327, 0.407) Se (0.917, 0.661, 0.407) Se (0.417, 0.660, 0.568) a=6.315 Å, b=7.787 Å, c=18.00 Å, γ=66.09 Au (0.250, 0.994, 0.526) Au (0.750, 0.993, 0.422) Ga (0.750, 0.493, 0.474) Ga (0.250, 0.493, 0.474) Se (0.083, 0.327, 0.555) Se (0.584, 0.326, 0.393) Se (0.917, 0.660, 0.393) Se (0.417, 0.660, 0.555) a=6.976 Å, b=7.904 Å, c=18.00 Å, γ=63.83 Au (0.250, 0.993, 0.495) Au (0.750, 0.993, 0.365) In (0.750, 0.493, 0.430) In (0.250, 0.493, 0.430) Se (0.083, 0.328, 0.520) Se (0.583, 0.328, 0.340) Se (0.918, 0.658, 0.340) Se (0.418, 0.658, 0.520) a=b=5.604 Å, c=18.0 Å, γ=90.00 Au (0.500, 0.000, 0.361) Au (0.000, 0.500, 0.565) Al (0.000, 0.000, 0.463) Al (0.500, 0.500, 0.463) Se (0.301, 0.199, 0.545) Se (0.199, 0.699, 0.381) Se (0.699, 0.801, 0.545) Se (0.801, 0.301, 0.381) a=b=5.636 Å, c=18.0 Å, γ=90.00 Au (0.500, 0.000, 0.352) Au (0.000, 0.500, 0.563) Ga (0.000, 0.000, 0.458) Ga (0.500, 0.500, 0.458) Se (0.298, 0.202, 0.541) Se (0.202, 0.702, 0.374) Se (0.702, 0.798, 0.541) Se (0.798, 0.298, 0.374) a=b=5.836 Å, c=18.0 Å, γ=90.00 Au (0.500, 0.000, 0.322) Au (0.000, 0.500, 0.532) In (0.000, 0.000, 0.427) In (0.500, 0.500, 0.427) Se (0.294, 0.206, 0.520) Se (0.206, 0.706, 0.333) Se (0.706, 0.794, 0.520) Se (0.794, 0.294, 0.333) S-10
11 Table S3. Bond lengths and angles for AuMX 2 (M=Al, Ga, In; X=S, Se) monolayers. System Phase Au-Au (Å) Au-X (Å) M-X (Å) X-Au-X ( ) AuAlS 2 β α AuGaS 2 AuInS 2 AuAlSe 2 AuGaSe 2 AuInSe 2 γ α β γ α β γ α β γ α β γ α β γ S-11
12 Table S4. Calculated 2D elastic modulus (C 2D ) and absolute values of deformation potentials (E 1 ) for the α phases of AuMX 2 monolayers. System electron hole (ev) (J/ ) (ev) (J/ ) (ev) (J/ ) (ev) (J/ ) α-auals α-augas α-auins α-aualse α-augase α-auinse S-12
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