1

Supplementary information

Superconductive “sodalite”-like clathrate calcium hydride at high

pressures

Hui Wang1, John S. Tse2, Kaori Tanaka2, Toshiaki Iitaka3, and Yanming Ma1★

1State Key Lab of Superhard Materials, Jilin University, Changchun 130012, P. R. China,

2Department Physics and Engineering Physics, University of Saskatchewan, Saskatoon,

Saskatchewan, S7N 5E2, Canada,

3Computational Astrophysics Laboratory, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198,

Japan.

★e-mail: mym@jlu.edu.cn

Index Page Computational details 2-3 CaH2 4-5 CaH4 6-11 CaH6 12-19 CaH8 20-22 CaH10 23-25 CaH12 26-29 References 30

2

Computational details

Our approach is based on a global minimization of free energy surfaces merging

ab initio total-energy calculations via particle swarm optimization technique as

implemented in the CALYPSO code. Structure simulations were performed at 50, 100,

150 and 200 GPa with up to four formula units in the models for CaH2n (n=1-6). The

first step of the structure simulation is to generate random structures (for the first

generation) symmetrically constrained within 230 space groups. Once a particular

space group is selected, the lattice parameters are then confined within the chosen

symmetry. The corresponding atomic coordinates are generated by the

crystallographic symmetry operations. The second step is the local optimization,

which can drive the energy of the candidate structures to the local minimum. After

that, lowest-enthalpy structures (the best 70% of previous generation), which are on

the most promising area of the configuration spaces, were selected to produce the next

generation by PSO, and random structures (30% of the population of each generation)

were also generated symmetrically constrained within 230 space groups. A symmetry

checking technique had also been applied, in which the appearance of identical

symmetric structures is strictly forbidden. This allows the generation of diverse

structures, which are crucial for the efficiency of global minimization. The local

optimizations were done with the conjugate gradients method and were stopped when

the enthalpy changes became smaller than 2 × 10-5 eV per atom. Usually, the structure

searching simulation reaches the convergence after we generated 1000 ~ 1200

structures (30 ~ 40 generations).

To analyze the results of structure simulations, we selected a number of distinct

lowest-enthalpy structures and optimized their structures as a function of pressures

using VASP code. To reduce the errors, the cut-off energy for the expansion of

wavefunctions into plane waves was set to 400 eV in all calculations, and the

Monkhorst–Pack1 grid with a maximum spacing of 0.03 Å−1 was individually adjusted

in reciprocal space to the size of each computational cell. This usually gave

well-converged total energies (within ~ 1 meV per atom).

3

Band structure, density of state, phonon dispersion and electron-phonon coupling

calculations for tI10-CaH4 and cI14-CaH6 (as well as Ca0H6 and CaH0) were

performed with Quantum-ESPRESSO package (Q-E). Troullier-Martins

norm-conserving pseudopotentials2 for H and Ca were generated by the Opium code3

with 1s1 and 3s23p64s2 as valence electrons, respectively. Based on convergence tests,

we adopted a kinetic energy cutoff of 90 Ry and 32 × 32 × 32 (48 × 48 × 48) k-points

mesh in the first BZ for tI10-CaH4 (cI14-CaH6). Phonon dynamic matrix elements of

CaH6 (Im-3m) were performed in the first BZ on a 12 × 12 × 12 q mesh. To ensure the

convergence of the electron-phonon coupling matrix elements, a large 48 × 48 × 48

k-points mesh is required in the electronic calculation.

Band structure and density of state of CaH2, CaH4, CaH6 and CaH12 were

examined by using VASP code. The k-point mesh was carefully chosen to ensure the

convergence of the results. The Fermi surfaces of cI14-CaH6 were calculated by using

VASP within 40 × 40 × 40 k-points mesh. Phonon dispersions of CaH2, CaH4, and

CaH6 were also performed by using supercell method4 with 108, 81, 135, 80 and 112

atoms in the cell for hP6-CaH2, hP3-CaH2, tI10-CaH4, oC20-CaH4 and cI14-CaH6, as

implemented in Fropho5 and Phononpy5. The difference of zero-point energy (ZPE)

for cI14-CaH6 between the calculated results through VASP and Q-E, i.e. ΔZPE =

ZPE VASP- ZPE Q-E, is found to be negligible, being less than 1 % of ZPEQ-E.

Besides, the validity of the adopted pseudopotentials from VASP library and

those generated by Opium was carefully checked by comparing the calculated

electronic band structures with that obtained from the full-potential (linearized)

augmented plane-wave + local orbitals method6 (as implemented in Wien2k7) for

cI14-CaH6 at 150 GPa. We found the mutual agreement for the different

pseudopotentials. Moreover, the band structures derived from VASP/Wien2k are

nearly identical to that obtained from Q-E (Figure S17), implying that the

pseudopotentials used in this work are reliable.

4

1. CaH2

a. discussion of stability, structural transitions and metallization pressures b. enthalpy of formation as a function of pressure (Figure S1) c. electronic densities of states (DOS) at 0, 150, and 200 GPa (Figure S2)

By using CALYPSO technique on crystal structure prediction of CaH2 with four

formula units per simulation cell at pressures of 0, 5, 50, 100, 150, and 200 GPa, we

predicted the Pnma (Pearson symbol: oP12), P63/mmc (Pearson symbol: hP6), and

P6/mmm (Pearson symbol: hP3) structures at elevated pressures. Specifically, the

oP12 structure was predicted at 0 and 5 GPa, while the hP6 structure at 50, 100, and

150 GPa, and the hP3 structure at 200 GPa. As a result, the derived phase transitions

take the sequence of oP12→hP6→hP3, in excellent agreement with previous

experimental8 and theoretical9 results. The calculated transition pressures are 16 and

178 GPa for these two phase transitions, respectively. All the three phases were

demonstrated to be dynamically stable at their stable pressure ranges by direct phonon

calculations. The zero-point energies (ZPE) through the quasiharmonic model are

calculated to be 0.228 and 0.236 eV/atom at 150 GPa and 200 GPa, respectively.

The formation enthalpy of CaH2 in oP12 (0-15 GPa), hP6 (20-170 GPa), and hP3

(180-200 GPa) structures relative to Ca + H2 as a function of pressure is shown in Fig.

S1. We adopted the most stable structures for solid H2 and elemental Ca at certain

pressures, e.g. H2 in the P63/m (0-100 GPa), C2/c (110-200 GPa) structures10, and Ca

in the fcc (0-5 GPa), bcc (10-30 GPa), I41/amd (40-70 GPa), P41212 (80-110 GPa),

Cmca (120 GPa), and I4/mcm(00γ) (130-200 GPa) structures11. Current results

indicate that CaH2 is energetically stable against to the decomposition into calcium

and hydrogen in the pressure range 0-200 GPa. Therefore, the “convex hull” phase

diagram for CaH2n (n = 2-6) is constructed with respect to CaH2 and H2 in the main

text.

The calculated densities of states (DOS) of the three phases of CaH2 are shown

in Fig. S2. Our results suggest that CaH2 in both oP12 and hP6 structures are

non-metallic, characterized by the obvious band gaps of 3.05 eV (at 0 GPa) and 0.48

5

eV (at 150 GPa), respectively, however, CaH2 becomes metallic at 178 GPa when it

transforms into hP3 structure.

Figure S1 Enthalpy of formation (meV/atom) of CaH2 relative to Ca and H2 as a function of pressure.

Figure S2 Electronic DOS of CaH2 at 0, 150, and 200 GPa. The dashed lines denote the Fermi level.

6

2. CaH4

a. discussion of stability, structural transitions and metallization pressures b. enthalpy as a function of pressure (Figure S3) c. structural parameters (Table S1, Table S2) d. crystal structures (Figure S4 and Figure S5) e. phonon densities of states at 50, 150 and 200 GPa (Figure S6) f. densities of states at 50, 150 and 200 GPa (Figure S7) g. band structures at 50 and 150 GPa (Figure S8 and Figure 9)

By using CALYPSO technique on crystal structure prediction of CaH4 with

simulation cells containing up to four formula units at pressures of 50, 100, 150 and

200 GPa, we found that the I4/mmm (Pearson symbol: tI10, Figure S4) and Cmcm

(Pearson symbol: oC20, Figure S5) structures are the most stable modifications at low

(50 -150 GPa) and high pressures (200 GPa), respectively. The calculated tI10→oC20

transition pressure is 180.6 GPa (Figure S3). Both phases are dynamically stable at

their stable pressure ranges as suggested by the phonon calculations. As is shown in

Figure 1 of main text, CaH4 within tI10 structure is the globally most stable

stoichiometry of CaH2n (n = 1-6) at the pressure range of 50-150 GPa. We also

estimated ZPE of tI10-CaH4 at 150 and 200 GPa, which are 0.251 and 0.262 eV/atom,

respectively. For CaH2 the calculated ZPE are 0.228 and 0.236 eV/atom at 150 and

200 GPa, whereas the ZPE of H2 at 150 and 200 GPa are 0.280 and 0.296 eV/atom ,

respectively, derived from an interpolation of earlier reliable results10. The resulting

difference of the zero-point energy, i.e., ΔZPE = ZPE(CaH4) - ZPE(H2) - ZPE(CaH2)

is very small, 2.2 and 2.0 meV/atom at 150 and 200 GPa, respectively, which have

negligible effect on the phase stability of CaH4.

We also examined the stability of tI10 structure in CaH4 with respect to the

decomposition into CaH3 and CaH5. CALYPSO structure simulations with up to four

formula units per simulation cell for CaH3 and CaH5 were performed at 50, 100, 150

and 200 GPa. Though the formation enthalpies of CaH3 and CaH5 are negative with

respect to CaH2 + H2 at pressures above 100 and 50 GPa, respectively, they are

metastable compared with tI10-CaH4 (see Figure S11). More specifically, the

formation enthalpies of CaH4 with respect to CaH3 + CaH5 at 100, 150 and 200 GPa

7

are –99.1, -51.2, and -31.8 meV/atom, respectively, indicating that CaH4 is

energetically more stable than the decomposition into CaH3 + CaH5.

The calculated electronic DOS and band structures of the tI10 and oC20 phases

of CaH4 are shown in Figures S7-S9, respectively. Our band structure results suggest

that metallization of CaH4 can be achieved in tI10 phase at pressures above 50 GPa.

However, since the density-functional calculations typically underestimate energy gap

within 30% - 50%, the metallization pressure of tI10-CaH4 might be much higher than

above 50 GPa (e.g., at 150 GPa, Figure S9).

Figure S3 Calculated enthalpies of oC20-CaH4 relative to tI10-CaH4.

8

Table S1 Calculated structural parameters of tI10-CaH4 at 50 GPa.

tI10 (space group I4/mmm )

a, b, c [Å] 3.131 3.131 5.319 α, β, γ [˚] 90.000 90.000 90.000 H1 (4 d) 0.000 0.500 0.250 H2 (4 e) 0.000 0.000 0.575 Ca (2 a) 0.000 0.000 0.000

Table S2 Calculated structural parameters of oC20-CaH4 at 200 GPa.

oC20 (space group Cmcm) a, b, c [Å] 2.463 5.723 4.095 α, β, γ [˚] 90.000 90.000 90.000 H1 (8 f) 0.0000 0.125 0.915 H2 (8 f) 0.0000 0.284 0.354 Ca (4 c) 0.0000 0.585 0.250

9

Figure S4 Crystal structure of tI10-CaH4 within a 1×2×2 supercell at 50 GPa.

Figure S5 Crystal structure of oC20-CaH4 within a 1×2×2 supercell at 200 GPa.

10

Figure S6 Calculated phonon DOS of tI10-CaH4 and oC20-CaH4 at 50/150 and 200 GPa, respectively.

Figure S7 Electronic DOS of tI10-CaH4 and oC20-CaH4 at 50/150 and 200 GPa, respectively. The dashed lines denote the Fermi level. The inset figure is plotted to zoom in the DOS of tI10-CaH4 near the Fermi level. The calculated DOS of tI10-CaH4 is 0.02234 states/eV/f.u. at the Fermi level.

11

Figure S8 Band structure of tI10-CaH4 at 50 GPa. The horizontal dashed line denotes the Fermi level.

Figure S9 Band structure of tI10-CaH4 at 150 GPa. The horizontal dashed line denotes the Fermi level.

12

3. CaH6

a. discussion of stability, structural transitions and metallization pressures b. enthalpy as a function of pressure (Figure S10) c. formation enthalpy as a function of pressure (Figure S11) d. structures parameters (Table S3, Table S4 and Table S5) e. crystal structures (Figure S12, Figure S13 and Figure S14) f. phonon densities of states at 150 and 200 GPa (Figure S15) g. partial densities of states at 150 GPa (Figure S16) h. band structures at 150 GPa and 250 GPa (Figure S17) i. Fermi surface at 150 GPa (Figure S18) j. Tc of cI14-CaH6 at 150 GPa as a function ofμ*(ωmax) (Figure S19)

By using CALYPSO technique on crystal structure prediction of CaH6 with system

sizes up to four formula units at pressures of 50, 100, 150 and 200 GPa, we found that

the C2/m (Pearson symbol: mC28, Figure S12), P21/m (Pearson symbol: mP14,

Figure S13) and Im-3m (Pearson symbol: cI14, Figure S14) structures are the most

stable forms at the pressures of 50, 100 and 150–200 GPa, respectively. Besides, a

simulation with eight formula units per cell (56 atoms/unit cell) was used to double

check the simulation result at 150 GPa, where the cI14 structure was confirmed.

Figure S10 shows the enthalpy curves as a function of pressure calculated at a higher

level of accuracy. As is shown by the ‘convex hull’ phase diagram of the main text

(Figure 1), cI14 structure of CaH6 becomes the global optimal structure of CaH2n

(n=1-6) at pressure of approximate 150 GPa, while mC28 and cP14 structures are

metastable. Therefore, we mainly focus our discussions on the cI14 structure.

The cI14 structure is dynamically stable at 150 and 200 GPa as suggested by the

phonon calculations (Figure S15). The calculated ZPE are 0.208 eV/atom and 0.230

eV/atom at 150 GPa and 200 GPa, respectively. The ΔZPE, i.e. ZPE(CaH6) -

2*ZPE(H2) - ZPE(CaH2), are very large, -49.7 and -40.3 meV/atom at 150 and 200

GPa, respectively. It is noted that ZPE only has a negligible effect on the phase

stability of tI10-CaH4 (being less than 3 meV), but it can significantly revise the

stability of cI14-CaH6 structure. We found that with the inclusion of zero-point

motion, the formation enthalpies (ΔH′ = ΔH + ΔZPE) of cI14-CaH6 (-213.1

meV/atom) becomes 48.3 meV/atom lower than that of tI10-CaH4 (-164.8 meV/atom)

13

at 150 GPa. As a result, the cI14-CaH6 becomes the globally most stable structure of

CaH2n (n=1-6) at 150 GPa. Moreover, it should be noted that the large ΔZPE of cI14

structure might also influence the relative stability between cI14 and mP14 structure

(Figure S10). However, we found severe imaginary phonons of cI14-CaH6 at 100 GPa,

eliminating its existence at such a pressure. Therefore, we mainly focus our

discussions on cI14-CaH6 at pressures at and above 150 GPa. Notably, the

significantly lower ZPE of cI14 structure is originated from its atomic “H4” structural

nature.

We also examined the stability of cI14 structure of CaH6 with respect to the

decomposition into CaH5 and CaH7. CALYPSO structure simulations with up to four

formula units in the models for CaH5 and CaH7 were also performed at 150 and 200

GPa. Though the formation enthalpies of CaH5 and CaH7 are negative with respect to

CaH2 and solid H2 at pressures above 150 GPa, they are metastable with respect to

cI14-CaH6 (see Figure S11). More specifically, the formation enthalpy of CaH6 with

respect to CaH5 + CaH7 at 150 and 200 GPa are –39.6 and -48.6 meV/atom,

respectively, indicating that CaH6 is energetically more stable than the decomposition

into CaH5 + CaH7.

At 150 GPa, the Fermi level (EF) cuts the band structure of cI14-CaH6 in a

region where H 1s and Ca 3d contribute mostly to DOS (Figure S16). The bands cross

the Fermi level steeply (Figure S17), but some of them show minima at Г lying just

0.24 eV below the Fermi level, and therefore, simultaneously provide two kinds of

conduction electrons: highly mobile and confined. Similar electronic structure has

previously been found in niobium, the metal with the highest Tc (e.g. 9.3 K) of all

element superconductors at ambient pressure, and been proposed to favor the electron

pairing and superconducting behavior12.

14

Figure S10 Calculated enthalpies of mP14 and cI14 structures relative to mC28 in CaH6.

Figure S11 Enthalpies of formation (ΔH, with respect to CaH2 + H2) of CaHn (n=3-8 and 12). The abscissa x is the fraction of H2 in the structures. The open, solid and half-filled symbols indicate the structures are composed of monatomic H, molecular H2, and a coexistence of H2 and H, respectively. The metastable structures are shown by circles, while stable structures are denoted by other symbols. The estimated stability pressure ranges were determined with static enthalpies and may shift upon inclusion of the zero-point motion of the nuclei. The tI10′ and cI14′ correspond to formation enthalpies of tI10 and cI14 with the inclusion of zero-point energy at 150 GPa. Evidently, CaH6 become the globally optimal structure at 150 GPa if we include the zero-point energy.

15

Table S3 Calculated structural parameters of mC28-CaH6 at 50 GPa.

mC28 (space group C2/m)

a, b, c [Å] 6.294 3.066 9.276 α, β, γ [˚] 90.000 135.150 90.000 H1 (4 i) 0.401 0.000 0.130 H2 (4 i) 0.773 0.000 0.947 H3 (4 i) 0.288 0.000 0.601 H4 (4 i) 0.588 0.000 0.534 H5 (4 i) 0.107 0.000 0.184 H6 (4 g) 0.000 0.626 0.000 Ca (4 i) 0.916 0.000 0.295

Table S4 Calculated structural parameters of mP14-CaH6 at 100 GPa.

mP14 (space group P21/m) a, b, c [Å] 5.266 3.114 3.258 α, β, γ [˚] 90.000 104.468 90.000 H1 (2 e) 0.419 0.750 0.567 H2 (2 e) 0.594 0.750 0.064 H3 (2 e) 0.994 0.750 0.232 H4 (2 e) 0.193 0.750 0.925 H5 (2 e) 0.293 0.750 0.735 H6 (2 e) 0.486 0.750 0.190 Ca (2 e) 0.801 0.750 0.657

Table S5 Calculated structural parameters of cI14-CaH6 at 150 GPa.

cI14 (space group Im-3m) a, b, c [Å] 3.501 3.501 3.501 α, β, γ [˚] 90.000 90.000 90.000 H (12 d) 0.250 0.000 0.500 Ca (2 a) 0.000 0.000 0.000

16

Figure S12 A 2×1×1 supercell of mC28-CaH6 at 50 GPa.

Figure S13 A 2×1×2 supercell of mP14-CaH6 at 100 GPa.

17

Figure S14 A 1×2×2 supercell of cI14-CaH6 at 150 GPa.

Figure S15 Calculated phonon DOS of cI14-CaH6 at 150 and 200 GPa.

18

Figure S16 The upper panel shows the calculated partial DOS of cI14-CaH6 at 150 GPa . The vertical black dashed line denotes the Fermi level.

Figure S17 Calculated band structures of cI14-CaH6 at 150 GPa (black dot line) and 250 GPa (red solid line).

19

Figure S18 Calculated Fermi surfaces of cI14-CaH6 at 150 GPa.

Figure S19 Calculated Tc of cI14-CaH6 at 150 GPa as a function of μ*(ωmax) from Eliashberg and McMilan equations, respectively.

20

4. CaH8

a. discussion of stability b. enthalpy as a function of pressure (Figure S20) c. structures parameters (Table S6, and Table S7) d. crystal structures (Figure S21 and Figure S22)

By using CALYPSO technique on crystal structure prediction of CaH8 with

simulation cells containing up to four formula units at pressures of 50, 100, 150 and

200 GPa, we found that the P-1 (Pearson symbol: aP18, Figure S21) and C2/m

(Pearson symbol mC36, Figure S22) structures are most stable modifications of CaH8

at low (50-100 GPa) and high pressures (150-200 GPa). The calculated aP18→mC36

transition pressure is 113.3 GPa (Fig. S19). As is shown in Figure 1 of main text,

CaH8 is only a metastable stoichiometry of CaH2n (n = 1-6), and therefore, only the

structure information is given here.

Figure S20 Calculated enthalpies of mC36-CaH8 relative to aP18-CaH8.

21

Table S6 Calculated structural parameters of aP18-CaH8 at 50 GPa.

Table S7 Calculated structural parameters of mC36-CaH8 at 150 GPa.

mC36 (space group C2/m) a, b, c [Å] 4.531 5.104 5.766 α, β, γ [˚] 90.000 129.881 90.000 H1 (8 j) 0.573 0.367 0.776 H2 (8 j) 0.780 0.156 0.655 H3 (8 j) 0.315 0.805 0.916 H4 (4 g) 0.500 0.758 0.500 H4 (4 g) 0.000 0.074 0.000 Ca (4 i) 0.434 0.000 0.714

aP18 (Space group P-1) a, b, c [Å] 3.067 3.482 7.976 α, β, γ [˚] 79.613 79.314 64.175 H1 (2 i) 0.716 0.876 0.421 H2 (2 i) 0.470 0.799 0.266 H3 (2 i) 0.191 0.268 0.357 H4 (2 i) 0.087 0.064 0.566 H5 (2 i) 0.891 0.504 0.689 H6 (2 i) 0.515 0.452 0.546 H7 (2 i) 0.844 0.388 0.917 H8 (2 i) 0.541 -0.116 0.026 Ca (2 i) 0.812 0.209 0.174

22

Figure S21 A 1×3×1 supercell of aP18-CaH8 at 50 GPa.

Figure S22 A 1×2×2 supercell of mC36-CaH8 at 150 GPa.

23

5. CaH10

a. discussion of stability b. enthalpy as a function of pressure (Figure S23) c. structures parameters (Table S8 and S9) d. crystal structures (Figure S24 and Figure S25)

By using CALYPSO technique on crystal structure prediction of CaH10 with

simulation cells containing up to four formula units at pressures of 50, 100, 150 and

200 GPa, we found that the P21/m (Pearson symbol: mP22, Figure S24) and C2/m

(Pearson symbol: mC22, Figure S25) structure are most stable forms of CaH10 at low

(50-150 GPa) and high pressures (200 GPa). The calculated mP22→mC22 transition

pressure is 163.1 GPa (Figure S23). As is shown in Figure 1 of main text, CaH10 is

only a metastable stoichiometry of CaH2n (n = 1-6), and therefore, only the structure

information is given here.

Figure S23 Calculated enthalpies of mC22-CaH10 relative to mP22-CaH10.

24

Table S8 Calculated structural parameters of mP22-CaH10 at 50 GPa.

Table S9 Calculated structural parameters of mC22-CaH10 at 200 GPa.

mC22 (space group C2/m)

a, b, c [Å] 5.855 3.111 4.708 α, β, γ [˚] 90.000 142.239 90.000 H1 (8 j) 0.489 0.741 0.079 H2 (4 i) 0.762 0.000 0.612 H3 (4 i) 0.480 0.000 0.686 H4 (4 i) 0.255 0.000 0.095 Ca (2 c) 0.000 0.000 0.500

mP22 (space group P21/m) a, b, c [Å] 3.578 3.695 6.574 α, β, γ [˚] 90.000 78.769 90.000 H1 (4 f) 0.075 0.983 0.033 H2 (4 f) 0.103 0.999 0.462 H3 (2 e) 0.462 0.250 0.148 H4 (2 e) 0.447 0.250 0.397 H5 (2 e) 0.054 0.250 0.235 H6 (2 e) 0.140 0.750 0.691 H7 (2 e) 0.458 0.750 0.971 H8 (2 e) 0.226 0.750 0.177 Ca (2 e) 0.315 0.250 0.712

25

Figure S24 A 3×1×1 supercell of mP22-CaH10 at 50 GPa.

Figure S25 Crystal structure of mC22-CaH10 at 200 GPa.

26

6. CaH12

a. discussion of stability, structural transitions and metallization pressures b. enthalpy as a function of pressure (Figure S26) c. structures parameters (Table S10 and Table S11) d. crystal structures (Figure S27 and Figure S28) e. densities of states at of 100 and 200 GPa (Figure S29)

By using CALYPSO technique on crystal structure prediction of CaH12 with

simulation cells containing up to four formula units at pressures of 50, 100, 150 and

200 GPa, we found that the R-3 (Pearson symbol: hR13, Figure S27) and C2/c

(Pearson symbol: mC52, Figure S28) structure are most stable forms of CaH12 at low

(50-150 GPa) and high pressures (200 GPa). The calculated hR13→mC52 transition

pressure is 176.5 GPa (Figure S26). The electronic DOSs (Figure S29) of hR13 and

mC52 structures suggest that both the two structures are metallic.

Figure S26 Calculated enthalpies of mC52-CaH12 relative to hR13-CaH12.

27

Table S10 Calculated structural parameters of hR13-CaH12 at 150 GPa.

hR13 (space group R-3)

a, b, c [Å] 3.238 3.238 3.238 α, β, γ [˚] 89.750 89.750 89.750 H1 (18 f) 0.176 0.212 0.710 H2 (18 f) 0.990 0.219 0.429 Ca (3 a) 0.000 0.000 0.000

Table S11 Calculated structural parameters of mC52-CaH12 at 200 GPa.

mC52 (space group C2/c) a, b, c [Å] 4.868 4.377 6.392 α, β, γ [˚] 90.000 119.365 90.000 H1 (8 f) -0.074 0.490 0.341 H2 (8 f) 0.784 0.710 0.414 H3 (8 f) 0.643 0.205 0.784 H4 (8 f) 0.466 0.230 0.944 H5 (8 f) 0.310 0.584 0.421 H6 (8 f) 0.876 0.474 0.551 Ca (4 e) 0.000 0.880 0.250

28

Figure S27 Crystal structure of hR13-CaH12 at 100 GPa.

Figure S28 Crystal structure of mC52-CaH12 at 200 GPa.

29

Figure S29 DOS of hR13 and mC52-CaH12 at 100 and 200 GPa, respectively. The dashed lines denote the Fermi levels.

30

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