Supporting Information Prediction of Novel High-Pressure Structures of Magnesium Niobium Dihydride Chuanzhao Zhang,,, Guoliang Sun, Jingjing Wang, Cheng Lu,*,, Yuanyuan Jin, Xiaoyu Kuang,*, and Andreas Hermann*, Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China Department of Physics, Nanyang Normal University, Nanyang 473061, China Department of Physics and Optoelectronic Engineering, Yangtze University, Jingzhou 434023, China Department of Physics and High Pressure Science and Engineering Center, University of Nevada, Las Vegas, Nevada 89154, United States Centre for Science at Extreme Conditions and SUPA, School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH93JZ, United Kingdom *E-mail: lucheng@calypso.cn. *E-mail: scu_kuang@163.com. *E-mail: a.hermann@ed.ac.uk. S-1
Figure S1. Predicted structures of MgH2. S-2
Figure S2. Volume-pressure relations for MgH 2. S-3
Figure S3. Phonon dispersion curves of five considered MgH 2 phases: (a) α-mgh 2 at 1 atm, (b) γ-mgh 2 at 5 GPa, (c) δ-mgh 2 at 10 GPa, (d) ε-mgh 2 at 100 GPa, and (e) ζ-mgh 2 at 180 GPa. S-4
Figure S4. Electronic band structures and densities of states for five considered MgH 2 phases: (a) α-mgh 2 at 1 atm, (b) γ-mgh 2 at 5 GPa, (c) δ-mgh 2 at 10 GPa, (d) ε-mgh 2 at 100 GPa, and (e) ζ-mgh 2 at 180 GPa. S-5
Figure S5. Electronic localization function for five considered MgH 2 compounds: (a) (001) plane for α-mgh 2 at 1 atm, (b) (010) plane for γ-mgh 2 at 5 GPa, (c) (001) plane for δ-mgh 2 at 10 GPa, (d) (010) plane for ε-mgh 2 at 100 GPa, and (e) (001) plane for ζ-mgh 2 at 180 GPa. S-6
Figure S6. Predicted structures of NbH 2. S-7
Figure S7. Volume-pressure relations for NbH 2. S-8
Figure S8. Phonon dispersion curves of two considered NbH 2 compounds: (a) the Fm-3m phase at 1 atm and (b) Pnma phase at 100 GPa. S-9
Figure S9. Electronic band structures and densities of states for two considered NbH 2 compounds: (a) the Fm-3m phase at 1 atm and (b) Pnma phase at 100 GPa. S-10
Figure S10. Electronic localization function for two considered NbH 2 phases: (a) (110) plane for the Fm-3m phase at 1 atm and (b) (010) plane for the Pnma phase at 100 GPa. S-11
Figure S11. Predicted structures of MgNbH 2. S-12
Figure S12. Enthalpy-pressure relations for Mg with respect to the P6 3 /mmc phase. S-13
Figure S13. Enthalpy-pressure relations for Nb with respect to the Im-3m phase. S-14
Figure S14. Volume-pressure relations for MgNbH 2. S-15
Table S1. Structural information of the predicted structures for MgH 2 at ambient pressure. Phase P4 2 /mnm (136) P2 1 /m (11) P4/nmm (129) P-62m (189) P6 3 /mmc (194) Pbc2 1 (29) Pnma (62) Pbcn (60) Pbca (61) Lattice parameters (Å, ) a=4.5058 b=4.5058 c=3.0069 a=9.4698 b=3.1711 c=5.3441 β=99.6073 a=3.2548 b=3.2548 c=4.8475 a=5.2354 b=5.2354 c=3.0973 γ=120 a=3.2396 b=3.2396 c=5.6525 γ=120 a=4.8926 b=4.6437 c=4.7747 a=5.2875 b=3.1159 c=6.0056 a=4.4889 b=5.4326 c=4.9214 a=9.3077 b=4.8906 Atom coordinates (fractional) Atom x y z Mg1(2a) 0.00000 0.00000 0.00000 H1(4f) 0.30426 0.30426 0.00000 Mg1(2e) 0.86594 0.75000 0.33696 Mg2(2e) 0.44191 0.75000 0.73647 Mg3(2e) 0.76684 0.25000 0.81853 H1(2e) 0.44524 0.75000 0.34736 H2(2e) 0.86881 0.75000 0.96651 H3(2e) 0.92556 0.25000 0.59940 H4(2e) 0.76347 0.25000 0.20841 H5(2e) 0.39522 0.25000 0.01913 H6(2e) 0.28532 0.25000 0.46129 Mg1(2c) 0.00000 0.50000 0.23446 H1(2a) 0.00000 0.00000 0.00000 H2(2c) 0.50000 0.00000 0.37334 Mg1(2d) 0.33333 0.66667 0.50000 Mg2(1a) 0.00000 0.00000 0.00000 H1(3g) 0.25902 0.00000 0.50000 H2(3f) 0.40336 0.40336 0.00000 Mg1(2d) 0.33333 0.66667 0.75000 H1(2c) 0.33333 0.66667 0.25000 H2(2a) 0.00000 0.00000 0.00000 Mg1(4a) 0.03070 0.26536 0.25049 H1(4a) 0.38205 0.09660 0.14154 H2(4a) 0.25787 0.55697 0.96957 Mg1(4c) 0.75129 0.25000 0.60218 H1(4c) 0.52030 0.25000 0.33471 H2(4c) 0.36142 0.75000 0.07575 Mg1(4c) 0.00000 0.33352 0.75000 H1(8d) 0.27177 0.10971 0.58064 Mg1(8c) 0.38288 0.02988 0.77489 H1(8c) 0.29827 0.38137 0.66944 S-16
c=4.7624 H2(8c) 0.47353 0.74246 1.01345 P6 3 (173) Pa-3 (205) Fm-3m (225) I4 1 /amd (141) Pnnm (58) a=3.1937 b=3.1937 c=6.1236 γ=120 a=4.8039 b=4.8039 c=4.8039 a=4.7451 b=4.7451 c=4.7451 a=3.8434 b=3.8434 c=9.0603 a=4.5145 b=4.4960 c=3.0096 Mg1(2c) 0.33333 0.66667 0.25000 H1(2d) 0.33333 0.66667 0.75000 H2(2a) 0.00000 0.00000 0.00000 Mg1(4a) 0.00000 0.00000 0.00000 H1(8c) 0.34673 0.34673 0.34673 Mg1(4a) 0.00000 0.00000 0.00000 H1(8c) 0.25000 0.25000 0.25000 Mg1(4b) 0.50000 0.50000 0.00000 H1(8e) 0.50000 0.50000 0.21514 Mg1(2b) 0.00000 0.00000 0.50000 H1(4g) 0.30826 0.30042 0.50000 S-17
Table S2. Structural information of five considered MgH 2 phases. Phase Pressure Lattice parameters (Ǻ, ) α-mgh 2 1 atm a=4.506, b=4.506, c=3.007 γ-mgh 2 5 GPa a=4.372, b=5.245, c=4.784 δ-mgh 2 10 GPa a=4.705, b=4.434, c=4.451 ε-mgh 2 100 GPa a=4.259, b=2.626, c=5.009 ζ-mgh 2 180 GPa a=2.734, b=2.734, c=3.529, γ=120 Atom coordinates (fractional) Atom x y z Mg1(2b) 0.000 0.000 0.500 H1(4g) 0.304 0.304 0.500 Mg1(4c) 0.000 0.327 0.750 H1(8d) 0.267 0.102 0.576 Mg1(4a) 0.030 0.267 0.229 H1(4a) 0.402 0.118 0.168 H2(4a) 0.254 0.556 0.965 Mg1(4c) 0.250 0.250 0.608 H1(4c) 0.026 0.250 0.311 H2(4c) 0.147 0.750 0.073 Mg1(2d) 0.333 0.667 0.750 H1(2c) 0.333 0.667 0. 250 H2(2a) 0.000 0.000 0.000 S-18
Table S3. The calculated Bader charges of Mg and H atoms in five considered MgH 2 crystals. Phase Pressure Atom Charge value (e) ω (e) α-mgh 2 1 atm Mg 0.01 1.99 H 1.99 0.99 γ-mgh 2 5 GPa Mg 0.41 1.59 H 1.80 0.80 δ-mgh 2 10 GPa Mg 0.39 1.61 H 1.80 0.80 ε-mgh 2 100 GPa Mg 0.45 1.55 H 1.78 0.78 ζ-mgh 2 180 GPa Mg 0.49 1.51 H 1.76 0.76 ω is the charge transfer from Mg to a H atom. S-19
Table S4. Structural information of the predicted structures for NbH 2 at ambient pressure. Phase Pnma (62) Fm-3m (225) P6 3 mc (186) P4/nmm (129) P-3m1 (164) Lattice parameters (Å, ) a=5.2531 b=3.2015 c=5.5609 a=4.5773 b=4.5773 c=4.5773 a=3.2461 b=3.2461 c=5.2112 γ=120 a=3.1246 b=3.1246 c=4.7347 a=3.2146 b=3.2146 c=5.0819 γ=120 Atom coordinates (fractional) Atom x y z Nb1(4c) 0.23817 0.25000 0.42514 H1(4c) 0.11526 0.75000 0.91449 H2(4c) 0.46703 0.75000 0.17059 Nb1(4b) 0.00000 0.00000 0.50000 H1(8c) 0.25000 0.75000 0.75000 Nb1(2b) 0.66667 0.33333 0.82180 H1(2b) 0.66667 0.33333 0.18961 H2(2a) 0.00000 0.00000 0.42546 Nb1(2c) 0.50000 0.00000 0.73493 H1(2c) 0.50000 0.00000 0.32978 H2(2a) 0.50000 0.50000 0.00000 Nb1(2d) 0.66667 0.33333 0.24308 H1(2d) 0.66667 0.33333 0.63617 H2(1b) 0.00000 0.00000 0.50000 H3(1a) 0.00000 0.00000 0.00000 S-20
Table S5. Structural information of two considered NbH 2 phases. Phase Fm-3m (225) Pnma (62) Pressure Lattice parameters (Ǻ, ) 1 atm a=4.577, b=4.577, c=4.577 100 GPa a=4.696, b=2.862, c=5.092 Atom coordinates (fractional) Atom x y z Nb1(4b) 0.000 0.000 0.500 H1(8c) 0.250 0.750 0.750 Nb1(4c) 0.736 0.250 0.410 H1(4c) 0.382 0.250 0.924 H2(4c) 0.000 0.750 0.218 S-21
Table S6. The calculated Bader charges of Nb and H atoms in two considered NbH 2 crystals. Phase Pressure Atom Charge value (e) ω (e) Fm-3m 1 atm Nb 9.77 1.33 H 1.61 0.61 Pnma 100 GPa Nb 10.02 0.98 H 1.49 0.49 ω is the charge transfer from Nb to a H atom. S-22
Table S7. Structural information of the predicted structures for MgNbH 2 at ambient pressure. Phase Pmmn (59) P-6m2 (187) Cmcm (63) P4/mmm (123) Pmma (51) Lattice parameters (Å, ) a=3.7082 b=3.3246 c=7.2781 a=3.1147 b=3.1147 c=4.9538 γ=120 a=3.1236 b=11.0181 c=4.7017 a=3.0436 b=3.0436 c=4.3633 a=4.9747 b=3.0406 c=5.4033 Atom coordinates (fractional) Atom x y z Mg1(2b) 0.00000 0.50000 0.86688 Nb1(2b) 0.00000 0.50000 0.38019 H1(2a) 0.00000 0.00000 0.23820 H2(2a) 0.00000 0.00000 0.53170 Mg1(1d) 0.33333 0.66667 0.50000 Nb1(1a) 0.00000 0.00000 0.00000 H1(2i) 0.66667 0.33333 0.78867 Mg1(4c) 0.50000 0.93481 0.75000 Nb1(4c) 0.00000 0.17798 0.75000 H1(4c) 0.00000 0.79449 0.75000 H2(4a) 0.00000 0.00000 0.50000 Mg1(1d) 0.50000 0.50000 0.50000 Nb1(1a) 0.00000 0.00000 0.00000 H1(1b) 0.00000 0.00000 0.50000 H2(1c) 0.50000 0.50000 0.00000 Mg1(2f) 0.25000 0.50000 0.65423 Nb1(2e) 0.25000 0.00000 0.15227 H1(2c) 0.50000 0.00000 0.50000 H2(2b) 0.00000 0.50000 0.00000 S-23
Table S8. Calculated elastic constants C ij (GPa), bulk modulus B (GPa), shear modulus G (GPa), Young s modulus E (GPa), B/G and Poisson s ratio ν for two stable MgNbH 2 compounds: (a) the P-6m2 phase at 100 GPa and (b) the Cmcm phase at 160 GPa. Phase C 11 C 12 C 13 C 22 C 23 C 33 C 44 C 55 C 66 B G E B/G ν P-6m2 656 310 367 664 220 173 451 182 481 2.48 0.32 Cmcm 719 563 535 939 546 709 191 215 45 621 119 336 5.22 0.41 S-24