# Predicted High-Pressure Hot Superconductivity in Li2CaH16 and Li2CaH17
Phases that Resemble the Type-II Clathrate Structure

Morgan Redington  Department of Chemistry, State University of New York at
Buffalo, Buffalo, NY 14260-3000, USA  Eva Zurek<EMAIL_ADDRESS>Department
of Chemistry, State University of New York at Buffalo, Buffalo, NY 14260-3000,
USA

###### Abstract

High-temperature high-pressure superconducting hydrides are typically
characterized by cage-like hydrogenic lattices filled with electropositive
metal atoms. Here, density functional theory based evolutionary crystal
structure searches find two phases that possess these geometric features and
are related to the Type-II clathrate structure. In these $Fd\overline{3}m$
Li2CaH16 and $R\overline{3}m$ Li2CaH17 phases the calcium atom occupies the
larger cage and the lithium atom the smaller one. The highest superconducting
critical temperatures predicted within the isotropic Eliashberg formalism, 330
K at 350 GPa for $Fd\overline{3}m$ Li2CaH16 and 370 K at 300 GPa for
$R\overline{3}m$ Li2CaH17, suggest these structures fall in the class of high-
energy-density quantum materials known as hot superconductors. As pressure is
lowered the cage-like lattices distort with the emergence of quasimolecular
hydrogenic motifs; nonetheless Li2CaH17 is predicted to be superconducting
down to 160 GPa at 205 K.

##  1 Introduction

In 1968, Neil Ashcroft predicted that metallic hydrogen – the hypothetical
ground state of the lightest element under pressure – could behave as a high-
temperature superconductor 1. Nearly four decades later Ashcroft described how
the pressures required to metallize hydrogen could be decreased via addition
of a second element that "chemically precompressed" the system 2. As early as
2015, experimental studies supporting Ashcroft’s prediction came to the fore.
These included measurements of high superconducting critical temperatures
(Tcs) in phases with unique stoichiometries, stable only under pressure,
including H3S (Tc = 203 K, 150 GPa) 3, LaH10 (Tc = 260 K, 200 GPa) 4, 5, YH9
(Tc = 262 K, 182 GPa) 6, YH6 (Tc = 224 K, 166 GPa) 7, CaH6 (Tc = 210-215 K,
160-172 GPa) 8, 9, 10, and CeH9 11, 12, 13 (Tc = 100 K, 166 GPa). Recently,
local magnetometry experiments on CeH9, performed via nitrogen-vacancy centers
embedded within the diamond anvil, provided evidence of the Meissner effect
14.

The immense pressures required to stabilize the superconducting binary
hydrides can only be reached in diamond anvil cells and come coupled with
experimental intricacy and expense, making theoretical calculations an
appealing method to both determine systems of interest and interpret
experimental results 15, 16. Density functional theory (DFT) calculations
foster accurate predictions for superconducting properties (if properly
converged), and crystal structure prediction (CSP) techniques have been
successful in uncovering promising synthetic targets (for unit cells that are
not too complex) 17. The chemical space has been thoroughly scoured for
fruitful high-temperature superconducting binary hydrides 18, 19, 20. In
contrast, ternary hydrides present relatively unexplored possibilities,
however predictions for this class of hydrides are significantly more
challenging 21. The vast chemical space means that an increased number of
stoichiometries must be considered for each elemental combination, with a more
complex potential energy landscape that requires a greater number of
structures be optimized in the CSP runs 22. To overcome these challenges,
machine learning potentials have been used to roughly explore the phase
diagram prior to performing more costly DFT optimizations 23, and high-
throughput calculations have been employed to study elemental substitutions on
previously-discovered superconducting templates 24. The introduction of a
third element could potentially be used to lower the stabilization pressure,
such as in synthesized LaBeH8 (Tc = 110 K, 80 GPa) 25 and predicted BaSiH8 (Tc
= 71 K, 3 GPa) 24, or increase the superconducting critical temperature as in
the synthesized (La,Ce)H9 (Tc = 148-178 K, 97-172 GPa) 26 and predicted
Li2ScH20 (Tc = 242 K, 300 GPa) 27. The former strategy is usually accomplished
by using one electropositive element and one $p$-block element, whereas the
latter strategy usually requires the combination of two electropositive
elements. Recently, superconductivity in an entropy-stabilized quaternary
hydride, (La,Y,Ce)H10, has been reported with a maximum Tc of 190 K at 112 GPa
28.

The hydrogenic lattices of the binary hydride superconductors of an
electropositive element that have very high $T_{c}$s generally assume cage-
like structures within which a metal atom is encapsulated. Several
stoichiometries are well known. The MH6 sodalite-like clathrate, first
exemplified by CaH6 8, 9, 10, has a metal atom, M, centered in an H24 cage
consisting of six square and eight hexagonal faces. The MH9 structure, which
surrounds the metal atom with an H29 cage of six irregular squares, six
pentagons and six hexagons, is found in numerous rare-earth compounds
including synthesized YH9 6 and CeH9 11, 12, 14. Further increasing the
hydrogen content, MH10 stoichiometries, where the metal atom sits within
hydrogenic polyhedra of six squares and twelve hexagons, are perhaps the most
well-known owing to the synthesis of the LaH10 4, 5 superhydride. The
structure of the hydrogen lattice in these MH10 systems is known as “AST” in
the clathrate and zeolite community 29. More recently, larger hydride cages
have been predicted to encapsulate rare earth metals. These include MH18 (M=Y,
La, Ce, Ac, Th) stoichiometries with cubic ($Fmmm$ and $Fddd$) space groups,
possessing H36 cages, with a maximum predicted Tc of 329 K at 350 GPa for
CeH18 30. Can we draw inspiration from these systems and other occurring
clathrates, specifically with phases that contain two electropositive
elements?

Looking across the periodic table to other cage-forming elements we encounter
silicon, which is able to form large polyhedral structures of sp3 bonded Si
atoms that are filled with metal atoms, characterizing the silicon clathrates
(SiCL). Two of the most well studied SiCLs are the type-I M8Si24 (the Weaire-
Phelan structure), which can be interpreted as two Si20 and 6 Si24 cages
filled with a metal atom, and the type-II Mx≤24Si136 structure, which is made
of 16 Si20 and 8 Si28 cages with a variable number of metal atoms that can be
controlled by the synthesis conditions 31, 32, 33, 34, 35. Several of the
known silicon clathrates are superconductors, for example the type-I Ba8Si46
36, with an ambient pressure Tc of 8 K. Recent experiments report the
synthesis of (Ba/La/Eu)4H23 37, 38, 39 high pressure hydrides in the type-I
structure, with untested Tcs, and Lu4H23 40, with a Tc of 73 K at 218 GPa.
Furthermore, predicted Li2(La/Y)H17 27 both match the type-II structure, with
the highest Tc being 156 K at 160 GPa for Li2LaH17. These structure types have
also been explored for Li2NaH16, Li2NaH17, and LiNa3H23 41, predicting a
maximum Tc of 340 K at 300 GPa for Li2NaH17. Prior to these structural
correlations being drawn, a computational study predicted that when the MgH16
42 structure was doped with Li, an $Fd\overline{3}m$ Li2MgH16 “hot
superconductor” 43, which differs from the type-II structure by only a single
Wyckoff site, possessing a record calculated maximum Tc of 473 K at 250 GPa
could be stabilized 43.

Herein, through careful DFT calculations we investigated if a high-temperature
superconductor analogous to Li2MgH16 43, but where Mg is replaced by Ca, could
be stabilized under pressure. Because the type-I and type-II SiCL structures
each possess two cages with distinct sizes, we hypothesized they would be
particularly well suited templates for incorporating mixed metal atoms, and in
our specific case lithium would fill the smaller cages and calcium the larger
ones. Lithium is light, lending itself to strong electron-phonon coupling,
with the goal of increasing Tc. Furthermore, as several Ca hydrides are
synthesized or predicted superconductors, we intended to improve upon their
properties with the addition of Li. With these motivations, we performed CSP
searches at megabar pressures for Li2CaHn ($n=10-20$). Both stable and
metastable phases were discovered, and their electronic structures were
analyzed. Two dynamically stable metallic structures, one that is a distortion
of the type-II SiCL, and one that can be derived from it, were found, and
electron-phonon coupling calculations were performed to estimate their
isotropic Eliashberg Tcs: 330 K at 350 GPa for $Fd\overline{3}m$ Li2CaH16, and
205 K at 160 GPa or 370 K at 300 GPa for $R\overline{3}m$ Li2CaH17. This work
extends the list of predicted “hot” superconducting ternary hydrides by two.

##  2 Methods

Exploratory crystal structure prediction (CSP) searches using the open-source
XTALOPT 44, 45 evolutionary algorithm (EA) 12th 46 release were performed to
identify stable and metastable phases. EA runs were performed for the
following stoichiometries: Li2CaHn ($n$=10-20) and Li2Ca at 100, 200, and 300
GPa. The initial generation consisted of random symmetric structures created
by the RANDSPG algorithm.47 Duplicate structures were identified via the
XTALCOMP algorithm for removal from the breeding pool.48 The breeding
operators employed and their relative probabilities were: (i) stripple (50%),
(ii) permustrain (35%), and (iii) crossover (15%). The minimum number of
generated structures was set to 1500. Each structure optimization consisted of
four consecutive geometry optimizations, with each increasing in precision.
The final geometry optimization step of the EA search employed a cutoff energy
of 400 eV and a $k$-grid generated using the $\Gamma$-centered Monkhorst-Pack
scheme 49, with the number of divisions along each reciprocal lattice vector
chosen such that the product of this number with the real lattice constant was
30 Å. After the EA searches concluded, the three most enthalpically favored
unique structures at each stoichiometry and pressure were used for further
analysis.

Precise geometry optimizations, electronic structure calculations, electron
localization functions (ELF), Bader charges, and first principles molecular
dynamics (FPMD) simulations were performed using DFT calculations with the PBE
functional as implemented in the Vienna Ab Initio Simulation Package (VASP).
50, 51 We employed a planewave basis set with an energy cutoff of 600 eV,
along with PAW potentials 52 where the H 1s1, Li 1s22s22p0 and Ca 3p64s23d0.01
electrons were treated explicitly in all calculations. $k$-meshes were
generated using the $\Gamma$-centered Monkhorst-Pack scheme 49, and the number
of divisions along each reciprocal lattice vector was chosen such that the
product of this number with the real lattice constant was 50 Å. All FPMD
simulations were performed with a 2 $\times$ 2 $\times$ 2 supercell, a single
$k$-point at $\Gamma$, an $NVT$ ensemble (constant number of particles,
constant volume, constant temperature), Nosé-Hoover thermostat 53, a 0.5
femtosecond timestep, and temperatures corresponding to the predicted
$T_{c}$s. The crystal orbital Hamilton populations (COHPs) and the negative of
the COHP integrated to the Fermi level (-iCOHP) were calculated using the
LOBSTER package to analyze bonding. 54, 55

To determine if the predicted structures were dynamically stable, and obtain
their zero-point energy, harmonic phonons were calculated using the supercell
approach. In the supercell approach, Hellmann-Feynman forces were calculated
from a supercell constructed by replicating the optimized structure wherein
the atoms had been displaced, and dynamical matrices were computed using the
PHONOPY code. 56 Quantum ESPRESSO (QE) was used to obtain the dynamical matrix
and electron-phonon coupling (EPC) parameters.57 H, Li, and Ca
pseudopotentials obtained from the QE pseudopotential library were generated
by the Vanderbilt ultrasoft method with a 1s1 configuration for H, a 1s22s12p0
configuration for Li, and a 3s23p64s23d04p0 configuration for Ca. The PBE
functional was employed for all QE calculations. Plane-wave basis set cutoff
energies were set to 70 Rydbergs (Ry) for all systems. The Methfessel-Paxton
Brillouin-zone smearing of 0.015 Ry was applied.58 The EPC parameter $\lambda$
was calculated using Gaussian broadenings in increments of 0.005 Ry ranging
from 0.005 to 0.050 Ry. A 15 $\times$ 15 $\times$ 15 $k$-grid with a $q$-mesh
of 5 $\times$ 5 $\times$ 5 was employed for Li2CaH17 at 300 GPa. Subsequent
calculations on Li2CaH17 utilized a $q$-mesh of 3 $\times$ 3 $\times$ 3, which
was found to be sufficiently converged for EPC properties (Table S7).
Therefore, a 15 $\times$ 15 $\times$ 15 $k$-grid with a _q_ -mesh of 3
$\times$ 3 $\times$ 3 was utilized for Li2CaH16. For Li2CaH17 the EPC appeared
to be converged with these parameters at a broadening of 0.030 Ry, and
Li2CaH16 converged at a broadening of 0.050 Ry. Critical temperature (Tc)
values were obtained by numerical solutions of the Eliashberg equation 59 with
a Coulomb repulsion parameter, $\mu^{*}$, of 0.1.

##  3 Results and Discussion

###  3.1 Hydrogenic Motifs

Let us take a closer look at the predicted Li2CaHn structures, to better
understand the peculiarities of their atomic configurations, and in particular
the hydrogenic motifs that are so important for their superconducting
properties. Based on the extensive work performed on binary high-pressure
hydrides containing electropositive elements 20, 22, it is known that the
presence of H- and H${}_{3}^{-}$ anions is detrimental for superconductivity.
When these are present, the hydrides are metallized via band induced
broadening and overlap, resulting in a low density of states (DOS) at the
Fermi level ($E_{\text{F}}$). Typically, compounds with H${}_{2}^{-}$ motifs
are predicted to possess intermediate $T_{\text{c}}$s owing to the metallicity
that stems from the partial filling of the antibonding H2 $\sigma_{u}^{*}$
orbitals, and a comparatively high DOS at $E_{\text{F}}$ ($N(E_{\text{F}})$).
However, increasing the dimensionality of the hydrogenic lattices, from 1D
chains to 2D sheets to 3D extended lattices, maintains a high
$N(E_{\text{F}})$, and increases the number of phonon modes that can be
involved in the EPC mechanism, thereby resulting in the highest predicted
$T_{\text{c}}$s. For this reason, compounds with cage-like lattices that
enclathrate electropositive atoms are among those with the highest computed
and measured superconducting critical temperatures.

Analysis of the structures found in our CSP searches reveals these same
hydrogenic motifs, and illustrates how they vary as a function of hydrogen
content and pressure (Table S8). The Li2CaHn $n=10-13$ stoichiometries were
typically characterized by H- and bent, asymmetric H${}_{3}^{-}$ units,
interspersed with H2 molecules at all pressures investigated. The most stable
$n=14-15$ phases featured these same motifs at 100 and 200 GPa, however by 300
GPa incomplete clathrate cages began to emerge, suggesting that both the metal
to hydrogen ratio and pressure are key for clathrate formation in the high-
pressure hydrides. A clathrate cage is found within Li2CaH16 at 300 GPa, but
it dissociates to an incomplete clathrate at 200 GPa and further to a
hydrogenic lattice containing discrete H${}_{3}^{-}$, H2 and H- units by 100
GPa. The global minimum Li2CaH17 phase possesses a clathrate structure at both
300 and 200 GPa, but dissociates to form H2 and H- by 100 GPa. Within Li2CaH18
and Li2CaH19 incomplete clathrates are present at 300 GPa, with H2 units
interspersed within the lattice for $n=18$. At pressures of 100 and 200 GPa,
these incomplete clathrates dissociate to form H${}_{3}^{-}$, H2 and H-.
Lastly, Li2CaH20 possesses only H2 units at 100, 200, and 300 GPa. Our
observations are in-line with a chemical pressure analysis, which illustrates
that clathrate formation in the high-pressure hydrides depends on the size-
match between the metal cation and the hydrogenic cluster encapsulating it 60.
We postulated that the Li2CaH16 and the Li2CaH17 structures could be
candidates for high-temperature, and perhaps “hot” superconductivity, given
the proclivity of clathrate-structure-types for large EPC values.

###  3.2 Ternary Phase Diagrams

The most stable structures found in the CSP searches were employed to
construct 3D convex hulls (Figures S1-S3) at 100, 200 and 300 GPa at zero-
temperature and within the clamped nuclei approximation. Because the
compositions considered all possessed a 2:1 lithium to calcium ratio while the
hydrogen content varied, 2D cuts of the generated convex hulls, corresponding
to a plane of increasing H content from Li2Ca at 100 GPa, or 2 Li + Ca at 200
and 300 GPa were also plotted (Figure S5, S6). At 300 GPa a Li2CaH17 phase was
predicted to be thermodynamically stable, while the structure closest to, but
not on, the hull, Li2CaH16, lay 7 meV/atom above it (Table S2 and Figure 1).
Notably, as discussed above, both of these possessed hydrogenic clathrate
cages.

Figure 1: Distance (meV/atom) of the most stable Li2CaHn ($n$=10-20)
structures above the convex hull at (a) 100, (b) 200, and (c,d) 300 GPa. In
panel (d) the distance is calculated using the zero-temperature enthalpies and
the zero-point-energy (ZPE) corrections. The pure elemental phases of Ca61,
62, Li63, and H64, optimized to the respective pressure, were used in
constructing the convex hull. For binary phases the lithium hydrides LiH,
LiH2, and LiH665, LiH9, and LiH1066 as well as the calcium hydrides CaH,
CaH267, CaH4, CaH610, CaH968, CaH12, Ca2H, and Ca3H69 were optimized to the
respective pressure. A dynamically and thermodynamically stable Li2Ca phase
was found in 100 GPa CSP searches, and used in constructing the convex hull.
However, at and above 200 GPa only dynamically unstable structures were found,
so the elemental phases in their correct stoichiometric amounts were employed
as the enthalpy reference.

The zero-point-energy (ZPE) is often important in determining relative energy
orderings for systems containing light elements, with the greatest potential
influence on H-bearing phases, as they can have the highest frequency
vibrations. For a given pressure the ZPE is affected by symmetry, with lower
symmetry systems generally having larger ZPEs, and the nature of the
hydrogenic motifs present within the crystal, with dihydrogen molecules having
a larger ZPE than hydrogens within extended lattices such as clathrate cages.
Indeed, it has been shown that the ZPE can affect the identity of the on-hull
structures in high-pressure polyhydrides containing electropositive metal
atoms 70. Obtaining the ZPE necessitates performing phonon calculations, which
allows for confirmation of dynamic stability, indicated by a lack of imaginary
modes.

Phonon calculations, performed in the harmonic approximation, suggested that
Li2CaH17, with a hydrogenic clathrate lattice, and Li2CaHn, $n$ =
(10,12,15,18-20), which did not feature clathrate structures, were dynamically
stable at 300 GPa. Li2CaH16, on the other hand, possessed two modes with
imaginary frequencies. These imaginary frequencies are related to the acoustic
modes, with the majority of the atomic displacement being due to hydrogen.
These frequencies were found to become real and positive by 350 GPa (Figure
S22), indicating stabilization due to pressure. A first-principles molecular
dynamics simulation at 330 K, however, showed that the hydrogenic lattice
remained intact, with no molecular H units forming. This suggests one or more
of the following: the phase is dynamically stable only at finite temperature;
the system may be stabilized by the inclusion of anharmonicity or quantum
effects; or the fineness of the grid needed to obtain real phonons is
prohibitively computationally expensive. Due to the large size of the unit
cell of Li2CaH16, and the associated computational expense, further
calculations investigating this discrepancy and determining the lower boundary
of dynamic stability were not performed, and the ZPE was estimated neglecting
the imaginary modes. Figure 1 (bottom panel) illustrates that inclusion of the
ZPE lowered the enthalpy of Li2CaH16 so that it joined Li2CaH17 on the 300 GPa
hull, but the remaining non-clathrate structures became destabilized, lying at
least 40 meV/atom above the hull.

Decreasing pressure moves all of the ternary hydrides progressively further
from the hull. Li2CaH16 shifts up to be 16 and 35 meV/atom above it, while
Li2CaH17 is calculated to be 9 and 36 meV/atom shy of thermodynamic stability
at 200 and 100 GPa, respectively. However, these compounds may still be
promising at sub-300 GPa pressures, despite not laying on the hull, provided
they are dynamically and thermally stable. Analysis of the zero-temperature
DFT-computed enthalpies of the compounds contained in the Materials Project
Database led to the estimate that $\sim$50% of known inorganic crystalline
materials are metastable, with a median metastability energy of 15 meV/atom
and a 90${}^{\text{th}}$ percentile of 67 meV/atom 71. For the specific case
of high-pressure hydrides, whose synthesis at high-pressures in diamond anvil
cells is often catalyzed by non-equilibrium processes such as thousands-of-
Kelvin degree laser heating, numerous examples of synthesized DFT-metastable
compounds are known. Some examples include Ca2H567, which lays 20 meV/atom
above the hull at 25 GPa, and various PHn phases, which lay 30 meV/atom above
the hull within the pressure range $\sim$80-225 GPa 72, 73, 74, 75.

###  3.3 Hydrogen Clathrate Structures

Plots of the enthalpy versus pressure of the low lying structures found in our
CSP searches (Figures S8, S9) showed that $Fd\overline{3}m$ Li2CaH16 became
preferred (over other phases with this stoichiometry) above 270 GPa, while for
Li2CaH17 the $R\overline{3}m$ structure was the most stable above 140 GPa.
From the other candidates found in our EA searches, these had the lowest
enthalpies up to a maximum investigated pressure of 500 GPa. The propensity
for high $T_{c}$ in compounds with hydrogenic clathrate lattices, the
observation that $Fd\overline{3}m$ Li2CaH16 and $R\overline{3}m$ Li2CaH17 both
possessed such lattices with a high degree of symmetry, and the finding that
both lay on the 300 GPa convex hull upon inclusion of the ZPE prompted us to
examine them in more detail.

Figure 2: Crystal structures of predicted clathrate Li2CaHn structures. Cubic
$Fd\overline{3}m$ Li2CaH16 has Li@H18 and Ca@H28 cages, with H4 tetrahedra.
Trigonal $R\overline{3}m$ Li2CaH17 (structure shown using cubic
representation) has Li@H20 and Ca@H28 cages, with hydrogen stuffed H4
tetrahedra. Calcium atoms are colored blue, lithium atoms are colored green,
and hydrogen atoms are colored pink. Dashed lines represent unit cells, while
the solid lines between hydrogens indicate weak bonds. Solid lines displayed
for the unstuffed H4 tetrahedra serve as a visual aid, and are not indicative
of bonding.

$Fd\overline{3}m$ Li2CaH16 is isotypic with previously predicted Li2MgH16 and
Li2NaH16 41, 43. In it, each Ca atom lies in a cage surrounded by four
hexagons and twelve pentagons, made of 28 hydrogen atoms, and each Li atom is
enclathrated in an 18 atom hydrogen cage with four hexagons and five
pentagons. The size of the cages around each metal atom are commensurate with
their radii, with Ca nestled in the larger cage and lithium sitting in the
smaller cage, as illustrated in Figure 2. At 350 GPa these polygons are highly
regular, with H-H bond lengths of 1.05, 1.08, and 1.12 Å. This
$Fd\overline{3}m$ symmetry lattice is markedly similar to the type-II SiCL
structure, differing by a single Wyckoff position. While the clearest hydrogen
motifs in $Fd\overline{3}m$ Li2CaH16 are the H18 and H28 cages, we can also
view the structure as possessing eight H4 tetrahedra in the conventional cell
($Z$ = 8), corresponding to one H4 tetrahedra per formula unit. These H4
tetrahedra are centred around the missing Wyckoff position that if filled
would make them isotypic to the type-II SiCL structure.

In $R\overline{3}m$ Li2CaH17, also shown in Figure 2, each Ca atom is
surrounded by four hexagons and twelve pentagons, and each Li atom is once
again found in the smaller cage, surrounded by eleven pentagons. The
additional hydrogen atom in $R\overline{3}m$ Li2CaH17 renders the
$R\overline{3}m$ phase nearly isostructural with the type-II SiCLs. In
comparison with $Fd\overline{3}m$ Li2CaH16, $R\overline{3}m$ Li2CaH17
possesses H4 tetrahedra “stuffed” with the extra hydrogen atom, which assists
in completing the cage around the Li ions. The stuffed hydrogen atom may
stabilize this structure by balancing the chemical pressure interactions
within the lattice, as has been observed in the H-stuffed H4 tetrahedra of
LaH10 60, or by allowing the structure to distort more readily. These
distortions can be seen with the reduced symmetry of the faces comprising the
polygons that make up the clathrate; each pentagon has H-H bond lengths
between 1.08 and 1.14 Å, while each hexagon has H-H bond lengths between 1.02
and 1.14 Å at 300 GPa. Investigation of the $R\overline{3}m$ Li2CaH17 phase
shows that these bonds become less uniform as pressure decreases. The
$R\overline{3}m$ phase was determined to be dynamically stable down to 160
GPa, however the full clathrate structure does not persist to this pressure,
due to the H-H bond lengths increasing (e.g. see ELF plot in Figure S21).

$R\overline{3}m$ Li2CaH17 was not anticipated to be the most stable spacegroup
for this stoichiometry. Previous studies have predicted an $Fd\overline{3}m$
M3H17 phase, where M is a metal atom, in compounds such as Li2(Sc/La/Y/Na)H17
27, 41. These $Fd\overline{3}m$ symmetry M3H17 phases are isostructural with
the type-II SiCL, while the $R\overline{3}m$ Li2CaH17 phase can be seen as a
distortion of this structure. The external pressure, internal (or chemical
pressure) and the number of valence electrons that are transferred from the
metal atoms to the hydrogen cage, and potential metal-hydrogen interactions
may be important factors driving this distortion. The external pressure most
directly affects the $pV$ (pressure-volume) term to the enthalpy, often
favoring the formation of closed packed structures at higher pressures. The
chemical pressure is related to the ionic radius of the metal atom and how it
fits into the cage, with ions that are too-small or too-large resulting in
distorted lattices 60. The number of valence electrons that are donated from
the electropositive element to the hydrogenic lattice can influence the types
of hydrogenic motifs that are present 10, and the resulting H-H distances,
which are also influenced by interactions such as Ca d $\rightarrow$ H2
$\sigma^{*}$ backbonding 67. To confirm that the $R\overline{3}m$ phase is
indeed favored over $Fd\overline{3}m$, the cubic structure was built and
optimized. Comparison of the 300 GPa enthalpies revealed that the
$R\overline{3}m$ phase possessed a lower internal energy, $U$, but a higher
$pV$ term. The bonds in the $R\overline{3}m$ phase are more distorted than the
highly ordered $Fd\overline{3}m$ phase, and these distortions likely
contribute to the enthalpic favorability of the $R\overline{3}m$ structure for
the metal atoms studied here. Furthermore, the $Fd\overline{3}m$ phase of
Li2CaH17 was determined to be both dynamically unstable at 300 GPa, and
enthalpically disfavored over the pressure range of 100-500 GPa, so it was
therefore not considered for additional calculations.

Compared to molecular H-H bonds at the same pressure, the H-H bond lengths in
both $R\overline{3}m$ Li2CaH17 and $Fd\overline{3}m$ Li2CaH16 are longer
(Table 1). Bader analysis showed that the caged Li and Ca atoms donate charge
to the nearby hydrogen atoms, which may covalently bond with one another. For
$R\overline{3}m$ Li2CaH17 at 160 GPa, each H atom gains on average
0.16$e^{-}$, with Ca losing 1.05$e^{-}$ and Li donating a smaller amount of
charge, 0.84$e^{-}$. When the pressure is increased to 300 GPa, each H atom in
$R\overline{3}m$ Li2CaH17 gains on average 0.15$e^{-}$, while Ca loses
0.89$e^{-}$ and Li donates 0.80$e^{-}$. Thus, increasing pressure appears to
even out the amount of charge transferred from both the formally divalent and
monovalent metal atoms, perhaps because a shorter distance between the
hydrogen atom and calcium can enhance the amount of backdonation between the
occupied antibonding hydrogen-lattice states and the Ca d orbitals, as
previously found within compressed CaH4 67 and Ca-S-H ternary hydrides 76. The
Bader charges calculated for $Fd\overline{3}m$ Li2CaH16 at 350 GPa are
similar, with H gaining 0.15$e^{-}$ on average, and Ca and Li donating
0.90$e^{-}$ and 0.78$e^{-}$, respectively.

Table 1: Distances and -iCOHPs for select H-H atom pairs in $Fd\overline{3}m$
Li2CaH16, $R\overline{3}m$ Li2CaH17, $C2/c$ H2, and $Im\overline{3}m$ CaH6.
The edges column specifies how many bonds of that length make up the edges of
hexagons and pentagons that comprise the clathrate faces.

System | Pressure (GPa) |  r${}_{\text{H-H}}$ (Å) | -iCOHP (eV/bond)† | Edges
---|---|---|---|---
$Fd\overline{3}m$ Li2CaH16 | 350 | 1.05 | 2.12 (2.04) | 2x $\pentago$
|  | 1.08 | 1.67 (1.98) | 6x $\hexagon$, 2x $\pentago$
|  | 1.12 | 1.44 (1.60) | 1x $\pentago$
$C2/c$ H2 | 350 | 0.75 | 6.37 |
|  | 1.14 | 1.16 |
$R\overline{3}m$ Li2CaH17 | 300 | 1.00 | 2.60 (2.45) | 1x $\pentago$
|  | 1.03 | 2.09 (2.46) | 2x $\hexagon$, 1x $\pentago$
|  | 1.08 | 2.32 (2.00) | 2x $\pentago$
|  | 1.09 | 1.85 (1.83) | 2x $\pentago$
|  | 1.13 | 1.23 (1.65) | 6x $\hexagon$
|  | 1.14 | 1.46 (1.54) | 4x $\hexagon$, 2x $\pentago$
$C2/c$ H2 | 300 | 0.75 | 6.35 |
|  | 1.14 | 1.13 |
$Im\overline{3}m$ CaH6 | 300 | 1.15 | 1.33 | 6x $\hexagon$, 4x $\Box$

† The -iCOHP values for a hypothetical lattice of hydrogen where no Li or Ca
is present, but the H positions are unchanged are provided in parentheses.

To further investigate the bonding within the hydrogenic lattice, the negative
of the crystal overlap Hamiltonian population, integrated to the Fermi level
(-iCOHP), was calculated for $Fd\overline{3}m$ Li2CaH16 and $R\overline{3}m$
Li2CaH17 at 350 and 300 GPa, respectively, and compared to the -iCOHP for the
$C$2/$c$ phase of molecular hydrogen at the same pressure (Table 1).
Unsurprisingly, the intermolecular -iCOHP for $C$2/$c$ H2 was significantly
stronger than that obtained for the shortest distance in the ternary hydrides
(6.37 vs. 2.12 eV/bond, and 6.35 vs. 2.60 eV/bond, respectively).
Interestingly, though the shortest intramolecular distances within $C$2/$c$ H2
were nearly identical to the longest H-H bonds in $Fd\overline{3}m$ Li2CaH16
and $R\overline{3}m$ Li2CaH17, the -iCOHPs calculated for these atom pairs in
the clathrate cages were somewhat stronger (1.16 vs. 1.44 eV/bond, and 1.13
vs. 1.46 eV/bond, respectively). We can compare the -iCOHPs of the Li2CaH16/17
phases with those computed for the compressed calcium polyhydrides, in
particular $Im\overline{3}m$ CaH6, a sodalite-like structure with a hydrogen
cage. At 300 GPa, the bond measuring 1.15 Å in $Im\overline{3}m$ CaH6 has an
-iCOHP value of 1.33 eV/bond, making it slightly weaker than the 1.14 Å H-H
bond in $R\overline{3}m$ Li2CaH17 at 300 GPa (1.46 eV/bond). Removing the
alkali and alkaline earth metal atoms from the lattice, but without any
further relaxation, yields a different set of -iCOHP values, illustrating how
these electropositive elements affect the bonding in the hydrogen lattice.
Though in some cases the interactions are strengthened and in other times they
are weakened by the presence of the metal atoms, overall the -iCOHPs computed
for the empty cages become more equalized with a somewhat smaller spread.

###  3.4 Electronic Structure and Superconductivity

$Fd\overline{3}m$ Li2CaH16 and $R\overline{3}m$ Li2CaH17 are calculated to
have a high $N(E_{\text{F}})$ (Figure 3), primarily of hydrogen $s$ character,
boding well for superconductivity. The contribution of the calcium states to
$N(E_{\text{F}})$ is intermediate, while the contribution of the lithium
states is minimal. Therefore, the DOS plots are consistent with a Li+ cation,
and a not-fully-ionised calcium, resulting from the backdonation of charge
from the hydrogenic lattice to the Ca d orbitals, as supported by the large
amount of Ca d states at $E_{\text{F}}$. In $Fd\overline{3}m$ Li2CaH16 at 350
GPa and $R\overline{3}m$ Li2CaH17 at 300 GPa $E_{\text{F}}$ lies just below a
peak in the DOS, suggesting that further electron doping (e.g. by replacing Li
via a divalent metal atom with a similar ionic radius, or Ca by a trivalent
metal atom) could potentially enhance $T_{\text{c}}$. Such peaks in the DOS
have previously been reported in $Fd\overline{3}m$ symmetry Li2NaH17 (just
above $E_{\text{F}}$) and Li2YH17 (just below $E_{\text{F}}$) at 300 GPa 27,
41. Assuming a full transfer of electrons from the electropositive element to
the hydrogenic lattice yields three-donated-electrons in Li2NaH17 and four-
donated-electrons in Li2CaH17. In both of these systems $E_{\text{F}}$ sits
below the peak in the DOS, so more electrons must be added. However, in
Li2YH17, with five-donated-electrons, $E_{\text{F}}$ lies just above the peak.
Thus, the optimal number of electron required to maximize $T_{\text{c}}$ is
between four and five. We find that adding an additional 0.38 $e^{-}$ per FU
(formula unit) ($\sim$4 $e^{-}$/10 FU) to Li2CaH16 at 350 GPa and an
additional 0.40 $e^{-}$ per FU (4 $e^{-}$/ 10 FU) to Li2CaH17 at 300 GPa would
place $E_{\text{F}}$ on that peak. Therefore, a quaternary compound with an
approximate Li2Ca0.6M0.4H16/17 stoichiometry, where M is a trivalent metal ion
such as Sc, Y, or La may potentially result in a higher $T_{\text{c}}$ than
those calculated here, provided the structure is dynamically stable.

Figure 3: The electronic band structure and projected density of states, with
the Fermi energy set to 0 eV for (a) $Fd\overline{3}m$ Li2CaH16 at 350 GPa and
(b) $R\overline{3}m$ Li2CaH17 at 300 GPa.

The descriptors for high-$T_{\text{c}}$ superconductivity – $\lambda$ and the
logarithmic average phonon frequency, $\omega_{\text{log}}$ – were computed
for these two phases at pressures where they were dynamically stable (Table
2). For $Fd\overline{3}m$ Li2CaH16, imaginary modes were absent only at 350
GPa, where this phase possessed the largest $N(E_{\text{F}})$ that we
computed. The large $\lambda$ of 2.58 necessitated that the Eliashberg
equations be solved numerically, and using a value of 0.1 for the Coulomb
shielding parameter, $\mu^{*}$, we obtained a $T_{\text{c}}$ of 330 K for
$Fd\overline{3}m$ Li2CaH16 at this pressure. Though this predicted
$T_{\text{c}}$ is over 100 K lower than that computed for the isotypic
Li2MgH16 at 250 GPa 43, it surpasses room temperature, rendering Li2CaH16 a
“hot” superconductor. Its phonon band structure, phonon projected densities of
states and Eliashberg spectral function are shown in Figure 4(a). Because of
the mass differences between the three atom types, the phonons can be well
separated into regions where the contributions from a particular atom are
dominant. Therefore, the total EPC could be partitioned into contributions
originating from vibrations in the low-frequency regime, projected mostly onto
the calcium atoms (15%), followed by a lithium-dominant region (9%), then by
the mainly hydrogenic modes above 750 cm-1 (76%). No high-frequency modes
indicative of the presence of molecular hydrogen units were observed, with the
highest vibrational frequency being 2385 cm-1, in-line with the previously
computed value of 2400 cm-1 for Li2MgH16 at 300 GPa 43. The much higher
$\lambda$ of Li2MgH16 at 300 GPa compared to that of Li2CaH16 at 350 GPa (3.35
vs. 2.58) is likely in part due to the lower pressure at which it could be
stabilized, as $\lambda$ was shown to decrease with increasing pressure.43 The
larger $\lambda$ and lighter mass of Mg as compared to Ca are both factors
that result in the higher $T_{\text{c}}$ of Li2MgH16. Another compound that
resembled $Fd\overline{3}m$ Li2CaH16, $Pm\overline{3}n$ LiNa3H23with a type-I
SiCL structure, possessed a very similar $N(E_{\text{F}})$, $\lambda$ and
therefore a very similar $T_{\text{c}}$ of 310 K at 350 GPa was predicted 41.

Table 2: Superconducting parameters for $Fd\overline{3}m$ Li2CaH16 and $R\overline{3}m$ Li2CaH17. $T_{\text{c}}$ was calculated with $\mu^{*}$ = 0.1, numerically solving the Eliashberg equations. The density of states at the Fermi level, $N$(EF), is provided in units of states/eV/formula unit, and $S$ is the superconducting figure of merit 77. System | Pressure (GPa) | $\lambda$ |  $\omega_{\text{log}}$(K) |  $N$($E_{\text{F}}$) |  $T_{\text{c}}$ (K) | $S$
---|---|---|---|---|---|---
$Fd\overline{3}m$ Li2CaH16 | 350 | 2.58 | 1123 | 1.23 | 330 | 0.94
$R\overline{3}m$ Li2CaH17 | 300 | 2.56 | 1312 | 0.99 | 370 | 1.22
$R\overline{3}m$ Li2CaH17 | 220 | 3.42 | 922 | 0.84 | 317 | 1.42
$R\overline{3}m$ Li2CaH17 | 160 | 1.72 | 1205 | 0.74 | 205 | 1.24

Figure 4: Phonon dispersion curves, projected phonon density of states
(PHDOS), Eliashberg spectral function scaled by the frequency
($2\alpha^{2}F/\omega$), and the integrated electron-phonon coupling constant
($\lambda$). (a) Properties for $Fd\overline{3}m$ Li2CaH16 at 350 GPa. (b)
Properties for $R\overline{3}m$ Li2CaH17 at 300 GPa.

Let us now turn to $R\overline{3}m$ Li2CaH17, whose EPC was well above the
threshold requiring the use of the Eliashberg formalism in the studied
pressure range: 2.56 at 300 GPa and 1.72 at 160 GPa. At 300 GPa the predicted
$T_{\text{c}}$, 370 K, was near the boiling point of water on Earth’s surface,
rendering this another example of a “hot” superconductor. This critical
temperature, while lower than that predicted for $Fd\overline{3}m$ Li2MgH16,
has greatly improved upon the $T_{\text{c}}$ of CaH6. At this pressure
vibrations that fell in the primarily Ca-based low frequency region
contributed 15% to the total EPC, whereas Li-dominant vibrations contributed
4%, and primarily H vibrations contributed 81%. The superconducting properties
of $R\overline{3}m$ Li2CaH17 can be compared directly to Li2ScH17, Li2YH17,
Li2LaH17, and Li2NaH17, hydride superconductors with similar structures 27, 41
(Table S8). Li2CaH17 and Li2NaH17 not only stand out as being better metals
than Li2ScH17, Li2YH17, and Li2LaH17, but also have much larger EPCs, leading
to much higher predicted $T_{\text{c}}$s.

Both the $N(E_{\text{F}})$ and the $T_{\text{c}}$ decreased with decreasing
pressure for Li2CaH17, although $\lambda$ was highest at 220 GPa, where
$\omega_{\text{log}}$ was lowest. Analysis of the structure and the ELF
(Figure S7) revealed that the hydrogen clathrate is beginning to break apart
into molecular units at this pressure, leading to the large increase in
$\lambda$ caused by the structural instability. However, these molecular units
reduce $T_{\text{c}}$ in-line with previously observed trends 22. The
formation of molecular units becomes more pronounced as pressure decreases,
and by 160 GPa 50% of the hydrogen atoms constitute H2 or H${}_{3}^{-}$
molecules, with the other half of the hydrogens forming 9-membered rings,
decreasing $\lambda$ and the calculated $T_{\text{c}}$ even further. The
$T_{\text{c}}$ for $R\overline{3}m$ Li2CaH17 at 160 GPa is calculated to be
205 K, surprisingly similar to that of CaH6 ($T_{\text{c}}$ = 210-215 K,
160-172 GPa) 8, 9, 10. At 160 GPa, the limit of dynamical stability for
$R\overline{3}m$ Li2CaH17 (Figure S14), its superconducting figure of merit
77, $S=$ 1.24, is markedly similar to that of $Im\overline{3}m$ H3S at 150
GPa, 1.31, and somewhat larger than that of $Fd\overline{3}m$ Li2LaH17 at 160
GPa, 0.95.3, 27 The highest phonon modes for $R\overline{3}m$ Li2CaH17 are
2275 cm-1 at 300 GPa and 2190 cm-1 at 160 GPa. These modes can be compared to
the highest phonon modes for atomic metallic hydrogen at 500 GPa being
approximately 2600 cm-1 78, with those of LaH10 being 2300 cm-1 at 300 GPa 4,
5 and for CaH6 being near 2000 cm-1 at 150 GPa10.

##  4 Conclusions

Previous theoretical calculations have predicted that “hot superconductors”,
compounds that are superconducting at room temperature and above, may be
stabilized under extreme pressures 41, 30, 43. Interest in these high-energy-
density quantum materials stems from the fact that quantum behavior at
atmospheric pressures is typically only observed at low temperatures. Herein,
crystal structure prediction searches combined with density functional theory
calculations predict two new hot superconductors, with critical temperatures,
$T_{\text{c}}$s, as high as 330 K at 350 GPa for $Fd\overline{3}m$ Li2CaH16
and 370 K at 300 GPa for $R\overline{3}m$ Li2CaH17. These ternary hydride
phases are predicted to lie on the 300 GPa convex hull (when zero-point-energy
effects are included). Li2CaH17 was found to be dynamically stable down to 160
GPa in the harmonic approximation, where its $T_{\text{c}}$ was predicted to
be similar to previously-synthesized H3S 3 and CaH68, 9, 10.

The structures of $Fd\overline{3}m$ Li2CaH16 and $R\overline{3}m$ Li2CaH17 can
both be described as clathrate-like hydrogenic lattices where the heavier
calcium cation occupies the larger H28 cages, and the smaller lithium atom is
situated within H18 or H20 encapsulations. Both of these phases are related to
the Type-II clathrate structure with Li2CaH17 being a rhombohedral distortion
of the $Fd\bar{3}m$ symmetry lattices found in the silicon variants, and
$Fd\overline{3}m$ Li2CaH16 being derived from the ideal Type-II clathrate
structure via removal of a single hydrogen atom. We postulate that the
$T_{\text{c}}$ in these ternary hydrides could be enhanced by tuning the
average valence of the enclathrated electropositive metal atoms so that the
Fermi level sits on the peak in the densities of states, resulting in
compositions such as Li2Ca0.6M0.4H16/17, where M is a trivalent metal ion.

##  5 Acknowledgements

Funding for this research was provided by the NSF award DMR-2136038 and the
U.S. Department of Energy, National Nuclear Security Administration, through
the Capital-DOE Alliance Center under Cooperative Agreement DE-NA0003975. EZ
acknowledges the U.S. Department of Energy, Office of Science, Fusion Energy
Sciences funding the award entitled High Energy Density Quantum Matter under
Award No. DE-SC0020340. Calculations were performed at the Center for
Computational Research at SUNY Buffalo (https://hdl.handle.net/10477/79221).

## Notes

The authors declare no competing financial interest.

## References

  * Ashcroft 1968 Ashcroft, N. W. Metallic Hydrogen: A High-Temperature Superconductor? _Phys. Rev. Lett._ 1968, _21_ , 1748–1748
  * Ashcroft 2004 Ashcroft, N. W. Hydrogen Dominant Metallic Alloys: High Temperature Superconductors? _Phys. Rev. Lett._ 2004, _92_ , 187002
  * Drozdov et al. 2015 Drozdov, A. P.; Eremets, M. I.; Troyan, I. A.; Ksenofontov, V.; Shylin, S. I. Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system. _Nature_ 2015, _525_ , 73–76
  * Somayazulu et al. 2019 Somayazulu, M.; Ahart, M.; Mishra, A. K.; Geballe, Z. M.; Baldini, M.; Meng, Y.; Struzhkin, V. V.; Hemley, R. J. Evidence for Superconductivity above 260 K in Lanthanum Superhydride at Megabar Pressures. _Phys. Rev. Lett._ 2019, _122_ , 027001
  * Drozdov et al. 2019 Drozdov, A. P.; Kong, P. P.; Minkov, V. S.; Besedin, S. P.; Kuzovnikov, M. A.; Mozaffari, S.; Balicas, L.; Balakirev, F. F.; Graf, D. E.; Prakapenka, V. B.; Greenberg, E.; Knyazev, D. A.; Tkacz, M.; Eremets, M. I. Superconductivity at 250 K in lanthanum hydride under high pressures. _Nature_ 2019, _569_ , 528–531
  * Kong et al. 2021 Kong, P. P.; Minkov, V. S.; Kuzovnikov, M. A.; Drozdov, A. P.; Besedin, S. P.; Mozaffari, S.; Balicas, L.; Balakirev, F. F.; Prakapenka, V. B.; Chariton, S.; Knyazev, D. A.; Greenberg, E.; Eremets, M. I. Superconductivity up to 243 K in the yttrium-hydrogen system under high pressure. _Nat. Commun._ 2021, _12_ , 5075
  * Troyan et al. 2021 Troyan, I. A. et al. Anomalous High-Temperature Superconductivity in YH6. _Adv. Mater._ 2021, _33_ , 2006832
  * Ma et al. 2022 Ma, L.; Wang, K.; Xie, Y.; Yang, X.; Wang, Y.; Zhou, M.; Liu, H.; Yu, X.; Zhao, Y.; Wang, H.; Liu, G.; Ma, Y. High-Temperature Superconducting Phase in Clathrate Calcium Hydride ${\mathrm{CaH}}_{6}$ up to 215 K at a Pressure of 172 GPa. _Phys. Rev. Lett._ 2022, _128_ , 167001
  * Li et al. 2022 Li, Z. W. et al. Superconductivity above 200 K discovered in superhydrides of calcium. _Nat. Commun._ 2022, _13_ , 2863
  * Wang et al. 2012 Wang, H.; Tse, J. S.; Tanaka, K.; Iitaka, T.; Ma, Y. Superconductive Sodalite-like Clathrate Calcium Hydride at High pressures. _Proc. Natl. Acad. Sci. U.S.A._ 2012, _109_ , 6463–6466
  * Salke et al. 2019 Salke, N. P.; Mahdi Davari Esfahani, M.; Zhang, Y.; Kruglov, I. A.; Zhou, J.; Wang, Y.; Greenberg, E.; Prakapenka, V. B.; Liu, J.; Oganov, A. R.; Lin, J.-F. Synthesis of Clathrate Cerium Superhydride CeH9 at 80-100 GPa with Atomic Hydrogen Sublattice. _Nat. Commun._ 2019, _10_ , 4453–4453
  * Li et al. 2019 Li, X.; Huang, X.; Duan, D.; Pickard, C. J.; Zhou, D.; Xie, H.; Zhuang, Q.; Huang, Y.; Zhou, Q.; Liu, B.; Cui, T. Polyhydride CeH9 with an Atomic-Like Hydrogen Clathrate Structure. _Nat. Commun._ 2019, _10_ , 3461–3461
  * Peng et al. 2017 Peng, F.; Sun, Y.; Pickard, C. J.; Needs, R. J.; Wu, Q.; Ma, Y. Hydrogen Clathrate Structures in Rare Earth Hydrides at High Pressures: Possible Route to Room-Temperature Superconductivity. _Phys. Rev. Lett._ 2017, _119_ , 107001–107001
  * Bhattacharyya et al. 2024 Bhattacharyya, P. et al. Imaging the Meissner effect in hydride superconductors using quantum sensors. _Nature_ 2024, _627_ , 73–79
  * Zurek and Grochala 2015 Zurek, E.; Grochala, W. Predicting Crystal Structures and Properties of Matter Under Extreme Conditions via Quantum Mechanics: the Pressure is On. _Phys. Chem. Chem. Phys._ 2015, _17_ , 2917–2934
  * Miao et al. 2020 Miao, M.; Sun, Y.; Zurek, E.; Lin, H. Chemistry under high pressure. _Nat. Rev. Chem._ 2020, _4_ , 508–527
  * Flores-Livas et al. 2020 Flores-Livas, J. A.; Boeri, L.; Sanna, A.; Profeta, G.; Arita, R.; Eremets, M. A perspective on conventional high-temperature superconductors at high pressure: Methods and materials. _Phys. Rep._ 2020, _856_ , 1–78
  * Bi et al. 2019 Bi, T.; Zarifi, N.; Terpstra, T.; Zurek, E. _Reference Module in Chemistry, Molecular Sciences and Chemical Engineering_ ; Elsevier, 2019; pp 1–36
  * Wang et al. 2017 Wang, H.; Li, X.; Gao, G.; Li, Y.; Ma, Y. Hydrogen-Rich Superconductors at High Pressures. _Wiley Interdiscip. Rev. Comput. Mol. Sci._ 2017, _8_ , 1–13
  * Zurek and Bi 2019 Zurek, E.; Bi, T. High-Temperature Superconductivity in Alkaline and Rare Earth Polyhydrides at High Pressure: A Theoretical Perspective. _J. Chem. Phys._ 2019, _150_ , 050901–050901
  * Lilia et al. 2022 Lilia, B. et al. The 2021 room-temperature superconductivity roadmap. _J. Phys. Condens. Matter_ 2022, _34_ , 183002
  * Hilleke and Zurek 2022 Hilleke, K. P.; Zurek, E. Tuning chemical precompression: Theoretical design and crystal chemistry of novel hydrides in the quest for warm and light superconductivity at ambient pressures. _J. Appl. Phys._ 2022, _131_
  * Ferreira et al. 2023 Ferreira, P. P.; Conway, L. J.; Cucciari, A.; Di Cataldo, S.; Giannessi, F.; Kogler, E.; Eleno, L. T. F.; Pickard, C. J.; Heil, C.; Boeri, L. Search for ambient superconductivity in the Lu-N-H system. _Nat. Commun._ 2023, _14_ , 5367
  * Lucrezi et al. 2022 Lucrezi, R.; Di Cataldo, S.; von der Linden, W.; Boeri, L.; Heil, C. In-silico synthesis of lowest-pressure high-Tc ternary superhydrides. _Npj Comput. Mater._ 2022, _8_ , 119
  * Song et al. 2023 Song, Y.; Bi, J.; Nakamoto, Y.; Shimizu, K.; Liu, H.; Zou, B.; Liu, G.; Wang, H.; Ma, Y. Stoichiometric Ternary Superhydride ${\mathrm{LaBeH}}_{8}$ as a New Template for High-Temperature Superconductivity at 110 K under 80 GPa. _Phys. Rev. Lett._ 2023, _130_ , 266001
  * Bi et al. 2022 Bi, J.; Nakamoto, Y.; Zhang, P.; Shimizu, K.; Zou, B.; Liu, H.; Zhou, M.; Liu, G.; Wang, H.; Ma, Y. Giant enhancement of superconducting critical temperature in substitutional alloy (La,Ce)H9. _Nat. Commun._ 2022, _13_ , 5952
  * Sun et al. 2022 Sun, Y.; Wang, Y.; Zhong, X.; Xie, Y.; Liu, H. High-temperature superconducting ternary $\mathrm{Li}\text{$-$}R\text{$-$}\mathrm{H}$ superhydrides at high pressures $(R=\mathrm{Sc},\mathrm{Y},\mathrm{La})$. _Phys. Rev. B_ 2022, _106_ , 024519
  * Chen et al. 2024 Chen, S.; Wang, Y.; Bai, F.; Wu, X.; Wu, X.; Pakhomova, A.; Guo, J.; Huang, X.; Cui, T. Superior Superconducting Properties Realized in Quaternary La-Y-Ce Hydrides at Moderate Pressures. _J. Am. Chem. Soc._ 2024, _146_ , 14105–14113
  * Amri et al. 2010 Amri, M.; Clarkson, G. J.; Walton, R. I. Anisotropic Thermal Expansion of SiO2 and AlPO4 Clathrasils with the AST-Type Structure. _J. Phys. Chem. C_ 2010, _114_ , 6726–6733
  * Zhong et al. 2022 Zhong, X.; Sun, Y.; Iitaka, T.; Xu, M.; Liu, H.; Hemley, R. J.; Chen, C.; Ma, Y. Prediction of Above-Room-Temperature Superconductivity in Lanthanide/Actinide Extreme Superhydrides. _J. Am. Chem. Soc._ 2022, _144_ , 13394–13400
  * Beekman and Nolas 2006 Beekman, M.; Nolas, G. Synthesis and thermal conductivity of type II silicon clathrates. _Physica B_ 2006, _383_ , 111–114
  * Vollondat et al. 2022 Vollondat, R.; Roques, S.; Chevalier, C.; Bartringer, J.; Rehspringer, J.-L.; Slaoui, A.; Fix, T. Synthesis and characterization of silicon clathrates of type I Na8Si46 and type II NaxSi136 by thermal decomposition. _J. Alloys Compd._ 2022, _903_ , 163967
  * Ammar et al. 2004 Ammar, A.; Cros, C.; Pouchard, M.; Jaussaud, N.; Bassat, J.-M.; Villeneuve, G.; Duttine, M.; Manatrier, M.; Reny, E. On the clathrate form of elemental silicon, Si136: preparation and characterisation of NaxSi136(x–>0). _Solid State Sci._ 2004, _6_ , 393–400
  * Liu et al. 2023 Liu, Y.; Briggs, J. P.; Majid, A. A. A.; Furtak, T. E.; Walker, M.; Singh, M.; Koh, C. A.; Taylor, P. C.; Collins, R. T. Formation of Type II Silicon Clathrate with Lithium Guests through Thermal Diffusion. _Inorg. Chem._ 2023, _62_ , 6882–6892
  * Yamanaka et al. 2014 Yamanaka, S.; Komatsu, M.; Tanaka, M.; Sawa, H.; Inumaru, K. High-Pressure Synthesis and Structural Characterization of the Type II Clathrate Compound Na30.5Si136 Encapsulating Two Sodium Atoms in the Same Silicon Polyhedral Cages. _J. Am. Chem. Soc._ 2014, _136_ , 7717–7725
  * Yamanaka et al. 2000 Yamanaka, S.; Enishi, E.; Fukuoka, H.; Yasukawa, M. High-Pressure Synthesis of a New Silicon Clathrate Superconductor, Ba8Si46. _Inorg. Chem._ 2000, _39_ , 56–58
  * Pena-Alvarez et al. 2021 Pena-Alvarez, M.; Binns, J.; Martinez-Canales, M.; Monserrat, B.; Ackland, G. J.; Dalladay-Simpson, P.; Howie, R. T.; Pickard, C. J.; Gregoryanz, E. Synthesis of Weaire-Phelan Barium Polyhydride. _J. Phys. Chem. Lett._ 2021, _12_ , 4910–4916
  * Laniel et al. 2022 Laniel, D.; Trybel, F.; Winkler, B.; Knoop, F.; Fedotenko, T.; Khandarkhaeva, S.; Aslandukova, A.; Meier, T.; Chariton, S.; Glazyrin, K.; Milman, V.; Prakapenka, V.; Abrikosov, I. A.; Dubrovinsky, L.; Dubrovinskaia, N. High-pressure synthesis of seven lanthanum hydrides with a significant variability of hydrogen content. _Nat. Commun._ 2022, _13_ , 6987
  * Semenok et al. 2021 Semenok, D. V.; Zhou, D.; Kvashnin, A. G.; Huang, X.; Galasso, M.; Kruglov, I. A.; Ivanova, A. G.; Gavriliuk, A. G.; Chen, W.; Tkachenko, N. V.; Boldyrev, A. I.; Troyan, I.; Oganov, A. R.; Cui, T. Novel Strongly Correlated Europium Superhydrides. _J. Phys. Chem. Lett._ 2021, _12_ , 32–40
  * Li et al. 2023 Li, Z. et al. Superconductivity above 70 K observed in lutetium polyhydrides. _Sci. China: Phys. Mech. Astron._ 2023, _66_
  * An et al. 2023 An, D.; Duan, D.; Zhang, Z.; Jiang, Q.; Song, H.; Cui, T. Thermodynamically stable room-temperature superconductors in Li-Na hydrides under high pressures. _arXiv_ 2023, arXiv 2303.09805
  * Vacanti et al. 2013 Vacanti, A.; Hooper, J.; Altintas, B.; Zurek, E. Metallization of Magnesium Polyhydrides Under Pressure. _Phys. Rev. B_ 2013, _87_ , 054107–054107
  * Sun et al. 2019 Sun, Y.; Lv, J.; Xie, Y.; Liu, H.; Ma, Y. Route to a Superconducting Phase above Room Temperature in Electron-Doped Hydride Compounds under High Pressure. _Phys. Rev. Lett._ 2019, _123_ , 097001
  * Lonie and Zurek 2011 Lonie, D. C.; Zurek, E. XtalOpt: an Open-source Evolutionary Algorithm for Crystal Structure prediction. _Comput. Phys. Commun._ 2011, _182_ , 372–387
  * Falls et al. 2021 Falls, Z.; Avery, P.; Wang, X.; Hilleke, K. P.; Zurek, E. The XtalOpt Evolutionary Algorithm for Crystal Structure Prediction. _J. Phys. Chem. C_ 2021, _125_ , 1601–1620
  * Avery et al. 2019 Avery, P.; Toher, C.; Curtarolo, S.; Zurek, E. XtalOpt Version r12: An open-source evolutionary algorithm for crystal structure prediction. _Comput. Phys. Commun._ 2019, _237_ , 274–275
  * Avery and Zurek 2017 Avery, P.; Zurek, E. RandSpg: An open-source program for generating atomistic crystal structures with specific spacegroups. _Comput. Phys. Commun._ 2017, _213_ , 208–216
  * Lonie and Zurek 2012 Lonie, D. C.; Zurek, E. Identifying Duplicate Crystal Structures: XtalComp, an Open-Source Solution. _Comput. Phys. Commun._ 2012, _183_ , 690–697
  * Monkhorst and Pack 1976 Monkhorst, H. J.; Pack, J. D. Special points for Brillouin-zone integrations. _Phys. Rev. B_ 1976, _13_ , 5188–5192
  * Kresse and Furthmiller 1996 Kresse, G.; Furthmiller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. _Phys. Rev. B_ 1996, _54_ , 11169–11186
  * Perdew et al. 1996 Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. _Phys. Rev. Lett._ 1996, _77_ , 3865–3868
  * Blochl 1994 Blochl, P. E. Projector augmented-wave method. _Phys. Rev. B_ 1994, _50_ , 17953–17979
  * Hoover 1985 Hoover, W. G. Canonical dynamics: Equilibrium phase-space distributions. _Phys. Rev. A_ 1985, _31_ , 1695–1697
  * Dronskowski and Blochl 1993 Dronskowski, R.; Blochl, P. E. Crystal Orbital Hamilton Populations (COHP): Energy-Resolved Visualization of Chemical Bonding in Solids Based on Density-Functional Calculations. _J. Phys. Chem._ 1993, _97_ , 8617–8624
  * Maintz et al. 2016 Maintz, S.; Deringer, V. L.; Tchougreeff, A. L.; Dronskowski, R. LOBSTER: A tool to extract chemical bonding from plane-wave based DFT. _J. Comput. Chem._ 2016, _37_ , 1030–1035
  * Togo and Tanaka 2015 Togo, A.; Tanaka, I. First Principles Phonon Calculations in Materials Science. _Scr. Mater._ 2015, _108_ , 1–5
  * Giannozzi et al. 2009 Giannozzi, P. et al. QUANTUM ESPRESSO: a Modular and Open-Source Software Project for Quantum Simulations of Materials. _J. Phys.: Condens. Matter_ 2009, _21_ , 395502–395502
  * Methfessel and Paxton 1989 Methfessel, M.; Paxton, A. T. High-Precision Sampling for Brillouin-Zone Integration in Metals. _Phys. Rev. B_ 1989, _40_ , 3616–3621
  * Eliashberg 1960 Eliashberg, G. M. Interactions between Electrons and Lattice Vibrations in a Superconductor. _Sov. Phys. JETP_ 1960, _11_ , 696–702
  * Hilleke and Zurek 2022 Hilleke, K. P.; Zurek, E. Rational Design of Superconducting Metal Hydrides via Chemical Pressure Tuning. _Angew. Chem. Int. Ed._ 2022, _61_ , e202207589
  * Nakamoto et al. 2010 Nakamoto, Y.; Sakata, M.; Shimizu, K.; Fujihisa, H.; Matsuoka, T.; Ohishi, Y.; Kikegawa, T. Ca-VI: A high-pressure phase of calcium above 158 GPa. _Phys. Rev. B_ 2010, _81_ , 140106
  * Anzellini et al. 2018 Anzellini, S.; Errandonea, D.; MacLeod, S. G.; Botella, P.; Daisenberger, D.; De’Ath, J. M.; Gonzalez-Platas, J.; Ibáñez, J.; McMahon, M. I.; Munro, K. A.; Popescu, C.; Ruiz-Fuertes, J.; Wilson, C. W. Phase diagram of calcium at high pressure and high temperature. _Phys. Rev. Mater._ 2018, _2_ , 083608
  * Lv et al. 2011 Lv, J.; Wang, Y.; Zhu, L.; Ma, Y. Predicted Novel High-Pressure Phases of Lithium. _Phys. Rev. Lett._ 2011, _106_ , 015503
  * Pickard and Needs 2007 Pickard, C. J.; Needs, R. J. Structure of Phase III of Solid Hydrogen. _Nat. Phys._ 2007, _3_ , 473–476
  * Zurek et al. 2009 Zurek, E.; Hoffmann, R.; Ashcroft, N. W.; Oganov, A. R.; Lyakhov, A. O. A Little Bit of Lithium Does a Lot for Hydrogen. _Proc. Natl. Acad. Sci. U.S.A._ 2009, _106_ , 17640–17643
  * Chen et al. 2017 Chen, Y.; Geng, H. Y.; Yan, X.; Sun, Y.; Wu, Q.; Chen, X. Prediction of Stable Ground-State Lithium Polyhydrides under High Pressures. _Inorg. Chem._ 2017, _56_ , 3867–3874
  * Mishra et al. 2018 Mishra, A. K.; Muramatsu, T.; Liu, H.; Geballe, Z. M.; Somayazulu, M.; Ahart, M.; Baldini, M.; Meng, Y.; Zurek, E.; Hemley, R. J. New Calcium Hydrides with Mixed Atomic and Molecular Hydrogen. _J. Phys. Chem. C_ 2018, _122_ , 19370–19378
  * Shao et al. 2019 Shao, Z.; Duan, D.; Ma, Y.; Yu, H.; Song, H.; Xie, H.; Li, D.; Tian, F.; Liu, B.; Cui, T. Unique Phase Diagram and Superconductivity of Calcium Hydrides at High Pressures. _Inorg. Chem._ 2019, _58_ , 2558–2564
  * Mishra et al. 2018 Mishra, A. K.; Muramatsu, T.; Liu, H.; Geballe, Z. M.; Somayazulu, M.; Ahart, M.; Baldini, M.; Meng, Y.; Zurek, E.; Hemley, R. J. New Calcium Hydrides with Mixed Atomic and Molecular Hydrogen. _J. Phys. Chem. C_ 2018, _122_ , 19370–19378
  * Ye et al. 2018 Ye, X.; Zarifi, N.; Zurek, E.; Hoffmann, R.; Ashcroft, N. W. High Hydrides of Scandium Under Pressure: Potential Superconductors. _J. Phys. Chem. C_ 2018, _122_ , 6298–6309
  * Sun et al. 2016 Sun, W.; Dacek, S. T.; Ong, S. P.; Hautier, G.; Jain, A.; Richards, W. D.; Gamst, A. C.; Persson, K. A.; Ceder, G. The thermodynamic scale of inorganic crystalline metastability. _Sci Adv_ 2016, _2_ , e1600225
  * Shamp et al. 2016 Shamp, A.; Terpstra, T.; Bi, T.; Falls, Z.; Avery, P.; Zurek, E. Decomposition Products of Phosphine Under Pressure: PH2 Stable and Superconducting? _J. Am. Chem. Soc._ 2016, _138_ , 1884–1892
  * Drozdov et al. 2015 Drozdov, A. P.; Eremets, M. I.; Troyan, I. A. Superconductivity Above 100 K in PH3 at High Pressures. _arXiv_ 2015, arXiv:1508.06224
  * Bi et al. 2017 Bi, T.; Miller, D. P.; Shamp, A.; Zurek, E. Superconducting Phases of Phosphorus Hydride Under Pressure: Stabilization by Mobile Molecular Hydrogen. _Angew. Chem. Int. Ed._ 2017, _56_ , 10192–10195
  * Fu et al. 2016 Fu, Y.; Du, X.; Zhang, L.; Peng, F.; Zhang, M.; Pickard, C. J.; Needs, R. J.; Singh, D. J.; Zheng, W.; Ma, Y. High-Pressure Phase Stability and Superconductivity of Pnictogen Hydrides and Chemical Trends for Compressed Hydrides. _Chem. Mater._ 2016, _28_ , 1746–1755
  * Yan et al. 2020 Yan, Y.; Bi, T.; Geng, N.; Wang, X.; Zurek, E. A Metastable CaSH3 Phase Composed of HS Honeycomb Sheets that is Superconducting Under Pressure. _J. Phys. Chem. Lett._ 2020, _11_ , 9629–9636
  * Pickard et al. 2020 Pickard, C. J.; Errea, I.; Eremets, M. I. Superconducting Hydrides Under Pressure. _Annu. Rev. Condens. Matter Phys._ 2020, _11_ , 57–76
  * McMahon and Ceperley 2011 McMahon, J. M.; Ceperley, D. M. Ground-State Structures of Atomic Metallic Hydrogen. _Phys. Rev. Lett._ 2011, _106_ , 165302