Scholarly article on topic 'Perspective: Role of structure prediction in materials discovery and design'

Perspective: Role of structure prediction in materials discovery and design Academic research paper on "Materials engineering"

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Academic research paper on topic "Perspective: Role of structure prediction in materials discovery and design"

Perspective: Role of structure prediction in materials discovery and design

Richard J. Needs' and Chris J. Pickard'

Citation: APL Materials 4, 053210 (2016); doi: 10.1063/1.4949361 View online: http://dx.doi.Org/10.1063/1.4949361 View Table of Contents: http://aip.scitation.org/toc/apm/4Z5 Published by the American Institute of Physics

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Perspective: Role of structure prediction in materials discovery and design

Richard J. Needs1,a and Chris J. Pickard2,b

1Theory of Condensed Matter Group, Cavendish Laboratory, J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom

2Department of Materials Science & Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom

(Received 18 February 2016; accepted 1 May 2016; published online 13 May 2016)

Materials informatics owes much to bioinformatics and the Materials Genome Initiative has been inspired by the Human Genome Project. But there is more to bioinformatics than genomes, and the same is true for materials informatics. Here we describe the rapidly expanding role of searching for structures of materials using first-principles electronic-structure methods. Structure searching has played an important part in unraveling structures of dense hydrogen and in identifying the record-high-temperature superconducting component in hydrogen sulfide at high pressures. We suggest that first-principles structure searching has already demonstrated its ability to determine structures of a wide range of materials and that it will play a central and increasing part in materials discovery and design. © 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http:llcreativecommons.orgllicenseslbyl4.0i). [http://dx.doi.org/10.1063/L4949361]

I. INTRODUCTION

Searching for crystalline structures of materials using first-principles density-functional-theory (DFT) methods1 has motivated, aided, questioned, or corroborated many experimental studies. One of the most exciting new discoveries motivated in part by DFT studies has been the reports by Drozdov et al.2,3 of superconductivity with a transition temperature (Tc) of 203 K measured on compression of hydrogen sulfide to pressures of ~200 GPa. This exceeds the lowest temperature recorded on Earth at ground level of 184 K and smashes the previous record superconducting Tc of 164 K in HgBaCaCuO at 30 GPa.4,5 Superconductivity was inferred from the observed sharp drop in the resistivity to zero, the decrease in Tc with applied magnetic field and the presence of a strong isotope effect of the correct sign and roughly the expected magnitude.3

Compressed hydrogen sulfide has been studied experimentally over many years.614 However, the superconductivity that was observed in hydrogen sulfide was generally thought to arise from metallic sulfur formed at high pressures. The enormous Tc found by Drozdov et al.3 in hydrogen sulfide was therefore a great surprise. The number of papers published on the theory and modelling of high Tc superconductivity in hydrogen sulfide has increased rapidly since 2014, see for example Refs. 15-27.

The high-temperature superconductivity found in hydrogen sulfide was foreshadowed by theoretical work. A DFT study by Li et al.15 was the first to suggest that metallic H2S could become a high-temperature superconductor, which they predicted to have a Tc of 80 K at 160 GPa. In the same study Li et al.15 also showed that pressure-induced decomposition of H2S into its elements was thermodynamically unfavorable. This result overturned the conclusion from a DFT study28 that pressure-induced decomposition into the elements might occur, and suggested that new H/S compounds could be formed.

arn11@cam.ac.uk bcjp20 @ cam.ac.uk

2166-532X/2016/4(5)/053210/14

4, 053210-1

© Author(s) 2016.

Subsequent to the work of Li et al.,15 Duan et al.16 reported a DFT study of (H2S)2H2 at high pressures. They investigated several H/S structures including H3S-R3m which is stable at lower pressures and was estimated to have a Tc of ~160 K at 130 GPa, and the higher pressure H3S-Im3m phase that was estimated to have a Tc of around 200 K at 200 GPa. These results are in reasonable agreement with the experimental data of Drozdov et al.3 These data indicated the presence of two superconducting components, with maximum Tc's of about 150 K (R3m) and 200 K (Im3m) at pressures around 150 GPa. DFT studies by Li et al.15 and Duan et al.16 were cited in the experimental papers of Drozdov et al.,2,3 and had clearly influenced their thinking.

Errea et al. performed extensive structure searches over 44 H/S stoichiometries,17 finding the cubic H3S-Im3m phase to be the most stable at the pressures at which the ~200 K superconductivity had been observed. Searches over a much smaller number of stoichiometries were performed by Duan et al.29 Errea et al.17 also showed that anharmonic vibrations significantly reduce the Tc of H3S-Im3m. The high-pressure cubic structure of H3S of space group Im3m in which the sulfur atoms lie on a body-centered cubic (bcc) lattice has now been confirmed by X-ray diffraction experiments,30 see Fig. 1. These results demonstrated convincingly that the very-high Tc superconducting material is not H2S, but is instead H3S.

Li et al.18 reported theoretical and experimental studies of the products of dissociation of solid H2S under strong compression. First-principles structure searches predicted new thermodynami-cally stable structures with stoichiometries H2S3, H3S2, HS2, and H4S3. H4S3 was predicted to be thermodynamically stable over the pressure range 25-113 GPa. X-ray diffraction measurements indicated the presence of H3S and H4S3.18 The experimental conditions and the kinetics of chemical reactions clearly play an important role in determining the H/S structures that are observed.

Very recently, Errea et al.19 have demonstrated that the quantum hydrogen-bond symmetriza-tion that occurs on formation of H3S-Im3m is responsible for the very high Tc. They have also shown that anharmonic vibrations stabilise this structure down to lower pressures than would be obtained within the harmonic approximation.

The above calculations were performed using the ab /ratio random structure searching method (AIRSS)31,32 and the castep code,33 and the calypso particle-swarm optimization method34,35 and the vasp code.36,37 Superconductivity was calculated using the quantum espresso code.38 The PBE density functional39 was used for all calculations reported here.

In 2013 we performed a DFT study of H2O up to terapascal (TPa) pressures in which we predicted its decomposition into H2O2 and a hydrogen-rich phase at about 5 TPa.40 We also found a H3O structure with the same Im3m structure as in H3S. We moved on to consider H2S at high pressures, which has long been considered as a proxy for H2O at pressures beyond those currently accessible to experiments. We subsequently heard about the work of Drozdov et al. on superconducting hydrogen sulfide and decided to pool our expertise with groups in Europe and China to work on it (see the list of authors of Ref. 17).

DFT methods can provide quite accurate energetics for sp-bonded materials such as H/S compounds. The increasing availability of computational resources and developments in the methods and robustness of the codes has led to the ability to perform the numerous DFT calculations on

FIG. 1. The high-pressure /m3m cubic structure (left) and the lower-pressure R3m trigonal structure (right) of H3S.

FIG. 2. Convex hull plot of the formation enthalpy of the H/S system at 200 GPa as a function of the fraction of sulfur, x, from AIRSS. The stoichiometry is H(j-x)Sx. Each red dot corresponds to a relaxed structure. The data show that H3S-/m3m (corresponding to x = 0.75) is the only thermodynamically stable compound of the H/S system at 200 GPa.

the wide range of structures required for successful searches. As an illustration we have performed additional structure searches for H/S compounds at a pressure of 200 GPa. We used the castep33 plane wave pseudopotential code with the PBE density functional,39 ultrasoft pseudopotentials,41 a k-point mesh of spacing 2n x 0.07 A-1, and a basis set energy cutoff of 230 eV. These computational parameters provide moderate accuracy, and higher accuracy calculations would be used to obtain converged results. The calculations were run for 24 h on 924 cores, and 17 887 structures from 3 to 16 atoms were relaxed. The results of these calculations are shown on a "Convex Hull" plot in Fig. 2.

Fig. 3 shows the electronic density of states (eDos) of cubic H3S-1m3m calculated within DFT using the OptaDOS code.42 Note the sharp peak in the electronic density of states at the Fermi energy. This peak has significant weight on the s-like electronic states of hydrogen atoms and the p states of sulfur atoms. Nevertheless, H3S at high pressures is best described as a hydrogen superconductor in which the sulfur atoms stabilise the H3S-R3m and H3S-/m3m structures, rather

FIG. 3. Calculated electronic density of states of the cubic Im3m structure of H3S at 200 GPa.

than playing a direct role in their superconductivity. The Van Hove singularities in the eDoS near the Fermi level may also have a significant influence on the superconducting properties.43

II. SUPERCONDUCTING HYDRIDES

The scientific journey that has led to the synthesis and identification of high-Tc H3S was kick-started by work published in 1968 by Ashcroft,44 see also Ref. 45. This paper laid out the case for possible high-Tc superconductivity in strongly compressed hydrogen, based on the likely strong electron-phonon coupling, high vibrational frequencies, and pressure-induced metallicity. At elevated pressures the energy scales of electron-phonon coupling and vibrational frequencies are likely to be increased, as is the density of electronic states at the Fermi energy. These characteristics suggest the possibility of high-Tc superconductivity in hydrogen at high pressures. An early first-principles calculation of superconductivity in the Cmca phase of metallic hydrogen suggested a Tc of 107 K at 347 GPa,46 while a more recent calculation gives a Tc of 250 K at about 450 GPa.47 However, this phase is now known to be thermodynamically unstable, see Ref. 48. A structure of I4]_/amd symmetry found in high-pressure searches is predicted to be stable above about 400 GPa49,50 and is the best candidate for high-Tc superconductivity in solid hydrogen found to date. Unfortunately experiments have not so far been able to test this conjecture.

The suggestion that applied pressure may enhance superconductivity is not confined to hydrogen. Ashcroft argued that hydrides might exhibit high-Tc superconductivity under sufficient pressure.51 Feng et al.52 predicted structures of silane (SiH4) at high pressures using "chemical intuition" and DFT methods. An early form of the AIRSS structure searching method was used to find more stable structures in an overnight run on a standard single processor machine.31 Structures that we had found of SiH4 with I41/a and I42d symmetries were subsequently verified by X-ray diffraction experiments,53,54 although the I41/a phase is insulating, see Fig. 4. Ashcroft's work has motivated many theoretical efforts to predict new high-temperature superconductors, and experimental studies of hydrides at high pressures.

An early application of structure searching to discovering potential high Tc superconductivity in AlH355 was followed up by other studies. It was found that anharmonic vibrations suppress electron-phonon coupling in AlH3 at high pressures which explains a significant discrepancy with earlier theoretical studies.56 Superconductivity was recently predicted in AlH3(H2) with a very large Tc of about 140 K at 250 GPa.57 However, our structure searches suggest this phase to be unstable to decomposition at high pressures. High-temperature superconductivity was also predicted in a number of metallic hydrides57-67 but most of the predicted Tc's were not realized.

FIG. 4. The 141/a structure of SiH4 (left) and the slightly less stable 142d structure (right) found by AIRSS and subsequently observed experimentally. Silicon atoms are shown in gold and hydrogen atoms in white. The high symmetry insulating 141/a structure consists entirely of equivalent Si-H-Si electron-deficient three-centre-two-electron "banana" bonds, similar to those found in diborane (B2H6).

The experimental observation in 2001 of high-temperature electron-phonon-based superconductivity in MgB2 with a Tc of 39 K aroused considerable interest.68 69 Two types of electrons were found to exist at the Fermi energy with < bonding character leading to strong superconductivity and n bonding character giving rise to much weaker superconductivity. This Tc was the highest achieved in a conventional superconductor prior to H3S. The jump in Tc by a factor of five from MgB2 to H3S is very striking.

Over the years various "rules" for guiding searches for high-temperature superconductors have been proposed, the most well-known of which are "Matthias's Rules." These rules have been modified and added to over the years as new experimental results became available. For example, the discovery of iron-based high-temperature superconductors in which magnetism plays an important role is inconsistent with Matthias's rules.70-72 Matthias's rule that transition metals are more likely to exhibit high-temperature superconductivity than simple metals has been challenged by superconducting H3S. In fact most of the "rules" for the occurrence of superconductivity have been broken by new discoveries, which makes the subject even more interesting.

An important idea for electron-phonon-based superconductivity that curiously was not part of Matthias's rules is that light atoms may promote superconductivity because their high phonon frequencies and large vibrational amplitudes can lead to large electron-phonon coupling. Recently we predicted that molecular water ice would show enormous electron-phonon coupling leading to a reduction in the band gap of nearly 2 eV.73 The strong electron-phonon coupling arises from both low frequency modes and high frequency O-H stretching modes. Water ice is, of course, an insulator, but the predicted band gap renormalization illustrates that very large electron-phonon coupling can be found in materials with light atoms.

III. IMPORTANCE OF FINDING THE CORRECT STRUCTURE

The most basic and important property of a material is its structure, which determines the observed behaviour. The properties of a material normally depend very sensitively on its structure. It is therefore crucial to determine the correct structures of materials. In particular, we normally seek the thermodynamically most stable structure at a given temperature and pressure, although low-energy metastable structures are also of interest. It is often necessary to search over structures with many different stoichiometries to determine the most stable ones. In practise only a finite number of stoichiometries can be searched and only a finite number of structures with a particular stoichiometry can be calculated, whereas both the number of stoichiometries and number of structures are infinite.

It has been suggested that bias in a structure search should be avoided at all costs. However, this ignores the fact that all useful structure searches depend for their success on biases. One extremely useful type of bias is to reduce the number of possible configurations. For example, we normally choose the average densities of the initial structures to be within a factor of two or so of our best estimate. This massively reduces the structure space that needs to be searched, and is what we call a "clear bias." In the following we refer to the set of all possible structures as the "structure space." In all our searches we embrace clear and easily understood biases or constraints. However, having selected these biases we insist on a uniform, random and uncorrelated, sampling of configuration space, and abhor the potentially deleterious effects of hidden bias.

A number of different approaches to structure searching using first-principles methods have been developed, such as basin hopping,74 evolutionary/genetic algorithms,75-77 minima hopping,78 ab initio random structure searching (AIRSS),32 and swarm intelligence.34 The various searching methods exhibit many similar features, and successes have been achieved using each of them.

A complete structure search on, for example, the binary hydrogen/oxygen (H/O) system would have to consider all possible H/O stoichiometries and all possible structures for each stoichiometry. The number of locally stable structures increases roughly exponentially with the number of atoms in the unit cell79 and the cost of determining the lowest energy structure increases very rapidly with system size. However, for small numbers of atoms the number of locally stable structures may increase less rapidly. Given the enormity of the searching problem, how is it possible that searches for structures containing several tens of atoms could be successful?

In fact searching for low energy structures is often not as difficult as the above discussion might imply. Choosing a suitable set of initial structures for a search is very important. If we know that H and O react to form water (H2O) then it is unhelpful to start a search with all the H atoms at one end of the cell and all the O atoms at the other end. It is also unhelpful to start a search with atoms almost on top of one another. Taking the latter point further, we can choose different minimum initial separations for H-H, H-O, and O-O nearest neighbours. We may allow nearest neighbour distances to be somewhat smaller than the physical bond lengths, so as not to impede structural relaxation. This approach is useful because it eliminates the structure space in regions where low-lying minima are highly unlikely to be found. Note that only two atomic types are present in H/O, and the presence of additional atomic types would make the searching considerably more costly.

Low-energy structures tend to have large "basins of attraction" so that they occupy a large part of the structure space80 and are therefore relatively easy to find in searches. Monte Carlo methods have been developed for measuring volumes of basins of attraction associated with minima in the potential energy surface.81 Wide and deep basins of attraction tend to be found near other low-energy basins, and the barriers between such basins tend to be relatively low. Empirically, we find that the difficulty in discovering the most stable structure tends to decrease with pressure, which suggests that the structure space becomes simpler under pressure. Also, we find that some empirical potentials have many more minima than those obtained from first-principles calculations.

High-symmetry structures are expected to have unit cells containing rather few atoms, and therefore they may be readily found in inexpensive searches. Pauling's principle that low-energy structures tend to possess symmetry is relevant here.82 These ideas suggest that constraining searches to conform to high-symmetry space groups could be a useful strategy, although clearly it makes it impossible to find very low symmetry structures which are sometimes the most stable. The use of symmetry constraints can lead to enormous reductions in the size of the structure space to be searched, although such constraints break up the structure space into disconnected regions that prevent some structures from relaxing fully. Imposing symmetry constraints can be a very efficient strategy for finding some very-low-energy structures.

Another very useful approach is to use "chemical units." In the H/O system we are justified in searching only the H2O stoichiometry because chemistry tells us that only structures of this stoichiometry are thermodynamically stable (unless the pressure is extremely high, see Ref. 40). For example, we could place H2O "units" randomly within the cell, instead of placing the atoms randomly, in conjunction with minimum distance constraints.

Many other ideas can readily be incorporated in the searches. For example, one can concentrate searches on particular space groups that have been found by experiment or previous searches to be common in certain types of structure, such as in inorganic or organic crystals.83 Structure searching is also very flexible and can readily be adapted for discovering point defect structures,84,85 surface and interface structures,86-88 etc. The most important aspects of searching are illustrated in Fig. 5.

IV. STRUCTURES OF SOLID HYDROGEN AT HIGH PRESSURES

Experimental determination of high-pressure structures of solid hydrogen is extremely challenging because of its low X-ray scattering and the small sample sizes obtained at the pressures of interest of up to above 350 GPa.89 X-ray diffraction experiments have provided useful data,90 but most of the experimental data has been provided by infra-red and particularly Raman vibrational spectroscopy. Unfortunately it has not proved possible to determine high pressure structures of hydrogen from the available experimental information alone, apart from that of the low pressure phase I whose hexagonal structure was solved over two decades ago. The structure of phase II is unknown, but the lowest energy candidate from structure searching91 is in plausible agreement with the experimental vibrational data. The high pressure phase III represents a triumph for structure searching in that the lowest energy structure from the AIRSS searches of C2/c symmetry gives a good account of the experimental vibrational data,49 see Fig. 6.

Energetically competitive "mixed structures" of I bam and Pbcn symmetries consisting of alternate layers of molecules with short bonds and considerably longer bonds were reported in the

FIG. 5. The AIRSS wheel of good fortune for finding new low-energy structures. The main elements of successful searching are presented. Elements from the wheel can be combined in different ways in a particular search. For example, in searching for superconductors we might consider only high-symmetry structures. We could also choose that the initial structures be composed of chemically relevant units. Experimental constraints can also be applied. The use of minimum initial separations reduces the size of the structure space to be studied and speeds up the relaxation procedure. Although we consider structures from databases for comparison, our most interesting and important results have arisen from AIRSS calculations.

AIRSS study of Ref. 49. In 2011 Eremets et al.92 reported the experimental discovery of a new phase IV of hydrogen, see also Ref. 93. We immediately saw that the Ibam and Pbcn structures might explain features of the new phase IV. Additional AIRSS calculations identified a structure of Pc symmetry that was similar to Ibam and Pbcn, but more energetically stable.94 It seems very unlikely that such a strange structure-type would have been conceived without the aid of first-principles structure searches. It is clear that structure searching has played a crucial role in determining the structures of high-pressure phases of hydrogen. The Pc structure that we use to model phase IV is shown in Fig. 6.

An experimental paper has recently appeared on a new high-pressure phase V of solid hydrogen.95 This could be a step on the route to finding metallic solid hydrogen, with implications for potential high temperature superconductivity. A very recent preprint96 questions some of the conclusions of Ref. 95. Studying solid hydrogen at high pressures remains a very active field.

V. A GLIMPSE OF THE FUTURE

Developments in diamond-anvil-cell (DAC) techniques are making it possible to compress materials to ever higher pressures. The record high pressure for hydrogen in a "standard" DAC is currently about 350 GPa. Two-stage DACs have recently reached pressures of up to 750 GPa with an osmium sample,97 although the stress showed significant anisotropy. This breakthrough will open new vistas in high-pressure experimental research that will stimulate further structure searches. "Ramped compression" techniques are being developed in which the precise control of strong laser pulses generates enormous pressures far beyond those accessible in static diamond anvil cells, but at much lower temperatures than in shock wave studies. Compression of diamond to 5 terapascals (TPa) was recently achieved at the National Ignition Facility (NIF) in the USA, which is 14 times the pressure at the centre of the Earth,98 see also Refs. 99 and 100. It is therefore now possible to investigate experimentally the conditions found deep within giant planets. One of the great challenges will be to retrieve high-quality experimental data gathered under extreme conditions from X-ray diffraction experiments, and extended X-ray absorption fine structure (EXAFS) measurements for probing local quantities. This will allow identification of structures and measurement of

FIG. 6. Top: The C2/c layered structure of solid hydrogen shown at 300 GPa provides a good model of the observed phase III. Note that in fact a B2/n space group setting was used to produce a more orthorhombic cell. Bottom: The Pc layered structure of solid hydrogen at 250 GPa which models phase IV of hydrogen. Light pink dashed lines indicate close contacts between molecules and light grey solid lines indicate molecules in lower layers. Molecules in the Pc structure with short bonds have dark shading. The C2/c and Pc structures are the most stable found by AIRSS at high pressures, and they provide good accounts of the experimental vibrational signals of phases III and IV. The C2/c structure reproduces the large infrared vibronic response observed in phase III, which accords with the fact that the two ends of the molecules have different environments. Phase IV exhibits a vibronic mode with an almost constant high frequency and a second vibronic mode whose frequency declines rapidly with pressure. AIRSS finds structures in this pressure regime consisting of alternate layers of strong and weakly bonded molecules which can account for the experimentally observed vibrational data for phase IV.

properties.101 These experimental developments will further stimulate first-principles DFT calculations of solids at extreme pressures and temperatures. For example, there has been much interest in predicting the stability of "electride" structures at high pressures in which some of the higher energy electrons occupy interstitial regions within the crystal and behave as anions,40,100,102-105 see Fig. 7. However, very different results might be obtained if the effects of (anharmonic) vibrations were included at the high pressures and temperatures that occur within giant planets.

DFT calculations are relatively cheap, and the cost of a particular calculation falls rapidly, year-on-year. This leads to a dynamic field in which improvements in accuracy and breadth of applicability occur rapidly, motivating even more ambitious studies. Many of the most limiting aspects of experimental studies do not exist in calculations, for example, in DFT studies the stoichiometry is known precisely, the system is pure so there are no unwanted materials that can induce chemical

FIG. 7. Two views of face centered cubic carbon at a pressure of 50 TPa. An electride structure is formed in which the valence electrons (green) are spatially separated from the 1 s core electrons of the carbon atoms (grey). There is competition between the attraction of the valence electrons to the positively charged core and the reduction in the kinetic energy achieved by the valence electrons moving away from the 1s cores so that they are not subject to Pauli repulsion from the 1s electrons.

reactions, the presence of large kinetic barriers does not hinder most structure searches, calculations can identify both stable and metastable phases, and signals are not blocked by the diamonds used in high-pressure studies as of course no diamonds are present (and therefore none are broken), etc. Hooking up experiments directly to DFT calculations should accelerate progress. There is practically no limit to the range of pressures that can be explored in DFT structure searching (individual calculations and searches generally get easier as the pressure is increased), and therefore it should be possible to make fundamental progress in materials under extreme pressures.

The agreement between the calculated structures and superconducting properties of H3S and the experimental data is very good. This strongly suggests that superconducting H3S has indeed been synthesized, and engenders confidence in both theory and experiment. It would be very interesting to return to experimental and theoretical studies of metallic hydrides to try and determine why theory gave values of Tc that were much larger than those found experimentally. One likely reason for these discrepancies could be the substantial difficulties involved in such experimental studies, particularly in sample preparation. Another problem was that some early structure searches were poor and tended to produce rather unstable structures with substantial eDoS at the Fermi energy (Ef). A structure with a low eDoS at EF normally corresponds to complete or nearly complete filling of the bonding orbitals, which leads to greater thermodynamic stability than in strongly metallic structures. The true ground state structure tended to have a lower eDoS at EF, and therefore

a lower propensity for superconductivity. It is worth mentioning that our recent structure searches for hydrogen sulfide at high pressures involved relaxing around one million structures, see Refs. 17 and 18. The use of approximate density functionals is also a significant issue. The neglect of an-harmonicity in earlier calculations could also have been problematic in some cases. However, here there is much room for optimism because methods for performing accurate vibrational calculations within DFT are being actively developed.106,107

We conclude that experiments on hydrogen sulfide vindicate Ashcroft's ideas on superconducting hydrides. It is, however, still unclear whether high-Tc superconductivity will be observed in pure hydrogen.

Is H3S the highest-Tc material that will be found? We see no reason why this must be the case. The eDoS of H3S has a sharp peak at EF that is similar in height to that of a homogeneous electron gas of the same density, and the highest vibrational frequencies are much lower than in solid hydrogen. The superconductivity in H3S therefore arises in circumstances that could occur in other metallic hydrides. Only a fraction of potential superconducting compounds have been studied under ambient conditions, and an even smaller fraction at high pressures. For example, the number of structure searches and experimental studies for ternary hydrides performed with the aim of finding high temperature superconductors is small. Further experimental and theoretical studies will undoubtedly uncover new high-Tc superconductors. For example, Drozdov et al. have recently reported superconductivity at high pressures in PH3 above 100 k.108,109 There is every reason to be optimistic about finding new metallic hydrides with even higher superconducting Tc's than H3S.

It should be noted that the structure prototypes predicted for phases III and IV of solid hydrogen do not appear in databases such as the Inorganic Crystal Structure Database (ICSD) of experimental structures.110 In fact databases of experimental structures are currently very small. The various efforts currently underway to construct databases of DFT structures will help to provide much larger amounts of structural data.

Structure searching can be combined successfully with X-ray or neutron diffraction data, and other techniques such as X-ray absorption spectroscopy. This is particularly synergetic in the case of diffraction because, even if the structure cannot be solved directly from the experimental data, the cell vectors may often be deduced from experiment, which makes searching for the correct structure enormously easier. (Space group or other structural data might also be available to further reduce the searching task.) A few successful calculations of this type have already been performed,111,112 and we look forward to them becoming a routine part of structure determination.

Some structures may be stabilized by anharmonic nuclear vibrations at saddle points of the Born-Oppenheimer surface. For example, at low temperatures elemental lithium adopts a rhom-bohedral structure, but upon heating above ~100 K it adopts the high-symmetry bcc structure.113 As mentioned above, the cubic Im3m structure of H3S responsible for the very high Tc in H3S is stabilized down to considerably lower pressures when anharmonic quantum nuclear zero-point motion is included.19 Both lithium at low pressures and H3S-Im3m at high pressures are close to structural instabilities. Matthias emphasised the importance of structural symmetry in determining superconducting Tc's,114 and empirical observations suggest that cubic symmetry is particularly efficacious. It is well-known that superconductivity can arise in the vicinity of soft vibrational modes, charge transfer instabilities, quantum critical points, etc. We are currently developing an approach based on first-principles structure searching that should enable the discovery of structures stabilised by anharmonic nuclear motion. Such searches might lead us to new superconducting hydrides and other structures of interest.115

We have emphasised the overriding importance of determining the correct structure of a material, which arises from the very strong dependence of properties on structure. Structures may be discovered by experiment and/or structure searching using first-principles or empirical methods, backed up by the available databases. At the moment the human directing the structure searching plays a very important role, but we expect that this can be reduced and eventually eliminated using expert systems and machine learning that can emulate the decision making of a trained human. Structure prediction should benefit from these developments. The success of first-principles structure searching will promote the prediction of new materials, interpretation of experimental data, identification of stable and metastable structures, and the design of materials.

ACKNOWLEDGMENTS

R.J.N. and C.J.P. gratefully acknowledge financial support from the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant Nos. EP/J017639/1 and EP/G007489/2. C.J.P. is also supported by a Royal Society Wolfson Research Merit award. Calculations were performed on the Cambridge High Performance Computing Service facility and the HECToR and Archer facilities of the U.K.'s national high-performance computing service (for which access was obtained via the UKCP consortium under Grant Nos. EP/K013688/1 and EP/K014560/1.

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102 M.-S. Miao and R. Hoffmann, "High pressure electrides: A predictive chemical and physical theory," Acc. Chem. Res. 47, 1311 (2014).

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115 B. Monserrat, C. J. Pickard, and R. J. Needs (unpublished).