In the search for new functional materials, quantum mechanics is an exciting starting point. The fundamental laws that govern the behaviour of electrons have the possibility, at the other end of the scale, to predict the performance of a material for a targeted application. In some cases, this is achievable using density functional theory (DFT). In this Review, we highlight DFT studies predicting energy-related materials that were subsequently confirmed experimentally. The attributes and limitations of DFT for the computational design of materials for lithium-ion batteries, hydrogen production and storage materials, superconductors, photovoltaics and thermoelectric materials are discussed. In the future, we expect that the accuracy of DFT-based methods will continue to improve and that growth in computing power will enable millions of materials to be virtually screened for specific applications. Thus, these examples represent a first glimpse of what may become a routine and integral step in materials discovery.
In 1929, the physicist Paul Dirac wrote, “The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble” (Ref. 1). Since then, many new developments in physics, such as the creation of quantum electrodynamics (which traces back to Dirac's work), have underscored the reality that much of fundamental physics remains to be discovered. However, we expect that today's chemists and materials scientists would still largely agree with Dirac's sentiment. The physical laws governing the behaviour of a material are encapsulated in the Schrödinger equation2; however, if approached directly, this equation is intractable for realistic materials. To understand the difficulty of the problem, consider that 1 gram of any material contains on the order of 1023 electrons. Solving the Schrödinger equation for this system using a computer would require approximately 1 billion petabytes (1024 bytes) of computing space simply to represent the 3 spatial coordinates of each electron. Even if that obstacle could be circumvented and it were possible to build a computer capable of solving 1028 electron interactions per second, a period equivalent to the age of the universe would still be required to solve the ∼1046 pairwise electron interactions in the system. Thus, there is no reason to assume that applying the laws of quantum mechanics to real materials should be simple. Instead, the best and often only way to probe the properties of materials is through experimentation and measurement.
Fortunately, the situation for computational materials scientists is not as hopeless as it seems. Many materials form crystal structures that can be represented by small, repeating units, much in the same way as tilework or carpet may consist of a single tessellating pattern. A macroscopic quantity of Si, for example, can be well approximated by a unit cell containing only 2 atoms (16 electrons). The resulting perfect crystal is a very good approximation of a real Si wafer used in electronics, which may contain only one defect per billion atoms. This considerable reduction of electrons, coupled with advancements that allow chemists to explicitly simulate only valence electrons, enable techniques such as quantum Monte Carlo to be performed using today's most powerful computers to solve the fundamental laws of quantum mechanics and subsequently predict the properties of materials3. However, quantum Monte Carlo techniques are time consuming, costly and currently intractable for all but the simplest materials. A more practical theory is needed for ‘everyday use’.
Hohenberg, Kohn and Sham developed such a theory in density functional theory (DFT)4,5, which has resulted in two of the top-ten cited papers of all time6 and for which Kohn received the Nobel Prize in Chemistry in 1999. DFT reformulates ground-state solutions to the Schrödinger equation as a problem of minimizing energy as a functional of the charge density (Box 1). Although the exact energy functional has not been determined, approximate models for this functional have yielded accurate predictions for many classes of materials. Thus, many of the problems once lamented by Dirac have now been circumvented, thereby allowing the physical laws of quantum physics to be connected to the technologically relevant properties of materials. Facilitated by the exponential increase in computing power, DFT has led to a paradigm change in computational materials science, whereby theorists are not only able to help explain and interpret the properties of materials but also have an active role in predicting completely new materials with specific properties for different applications.
In this Review, we detail case studies from this new world of materials design. We concentrate only on examples where theoretical prediction has led to the experimental discovery of a new material or exposed an important technological facet of a known material. The examples chosen are restricted to materials for renewable energy applications, which are a major focus in DFT-based materials discovery. Examples from other applications, including magnetic materials and multi-ferroic materials, can be found elsewhere7,
In silico materials design
Although the outputs of a DFT computation provide important fundamental attributes of a material, the path to a technological quantity of interest is rarely direct. As phrased by Gerbrand Ceder, “there is no quantum operator for a better car” (Ref. 15). Rather, in silico design involves several stages, which progress from computation to insight (see Fig. 1 for a description of these stages). A major component of this process is translating the fundamental physical outputs from DFT into knowledge that is practically useful for an application using the principles of materials science and domain-specific expertise16. To illustrate how this procedure works in practice, we discuss in the following sections several examples for which DFT was used to target technological applications.
Lithium-ion batteries. These batteries are currently the dominant technology for consumer electronics and next-generation electric vehicles. In the late 1990s, pioneering work was carried out by Ceder and co-workers17,
Similarly, frameworks for connecting DFT-computable quantities to other battery-material properties, such as ionic diffusion, phase stability and thermal safety, were developed21,
One further step was taken by Jain et al.26 in developing automation software to virtually screen very large numbers of new electrode materials in a ‘high-throughput’ mode before beginning experimental testing. Using this methodology, Ceder and co-workers screened thousands of cathode materials and identified and experimentally verified several of them, including a monoclinic form of LiMnBO3 (Ref. 27), layered Li9V3(P2O7)3(PO4)2 (Ref. 28) and Cr-doped LiVO2 (Ref. 29). One interesting case study is a new class of Li3MPO4CO3 (M = transition metal) materials, which are unconventional in that they mix two different polyanion groups (phosphate and carbonate). They were ‘invented’ by automatic element substitution algorithms30,31 applied to all the relevant crystal structures in the Inorganic Crystal Structure Database (ICSD)32, which revealed that a Na-to-Li substitution in natural sidorenkite minerals could yield potential battery cathodes. Thus, using a similar strategy to that previously described for LiMn0.5Ni0.5O2, Na-containing carbonophosphates were prepared hydrothermally followed by an ion-exchange process, which resulted in the desired Li analogues33. The Li-containing carbonophosphates, with a general formula, Li3MPO4CO3, could be synthesized with various transition metals in the M site34, and the computations indicated that the choice of transition metal greatly influences the electrochemical properties. Of particular interest was Li3MnPO4CO3, for which computations predicted a possible exchange of two Li cations per Mn cation. However, further optimization of this system is required owing to a potentially incomplete Na–Li ion-exchange process. Natural sidorenkite minerals are also candidates for cathodes in next-generation Na-ion batteries35,36, in which case no ion-exchange procedure is required.
Apart from cathodes, computations have also been used to help identify 2D anode materials. Anasori et al.37 performed DFT computations to predict the atomic ordering of 20 new 2D carbide materials, known as MXenes. One of these materials, Mo2Ti2C2Tx, where T represents a surface termination, was synthesized and tested for electrochemical activity, yielding modest performance as a potential anode material that can possibly be further tuned by exploring different compositions within the MXene family.
Hydrogen production and storage. Hydrogen fuel can reach very high energy densities38, but cost of production, storage and conversion to electricity remain obstacles that have thus far limited its application. The development of new materials holds promise for improving the economics of using hydrogen as a fuel, and computations are one pathway towards identifying such compounds.
The first step in using hydrogen as an energy storage medium is its production. Hydrogen can be generated from natural gas or other hydrocarbons through a process known as steam reforming. In a study published in 1998, Besenbacher et al.39 used DFT to predict that detrimental graphite build-up on Ni catalysts for steam reforming could be inhibited by alloying with Au and verified the result experimentally. The study was an early demonstration that new materials for catalysis could be explored with DFT. Further work in catalysis for hydrogen production was conducted by Greeley et al.40, who studied cheaper alternatives to Pt for catalysing the electrolysis of water (a second way to produce hydrogen). They screened a library of 256 candidate alloys, encompassing a matrix of substrate and solute metals, for compounds that would efficiently catalyse the hydrogen evolution reaction (2H+ + 2e− → H2). Because catalysis is difficult to model directly, the authors used the Sabatier principle to relate binding energies to catalytic behaviour41. Crucially, they also included stability metrics that screened out several materials that otherwise exhibited good calculated performance. The study resulted in the identification of Bi–Pt alloys as potentially cheaper materials that retain the high performance of pure Pt in experiments40. This study was one of the first to demonstrate that DFT could be used to screen libraries of compounds for ‘hits’, and it also helped to establish that stability (and not just calculated performance) is an important criterion to ensure that DFT predictions are relevant to experiments. A final example comes from Yan et al.42, who explored photocatalytic materials for water splitting (that is, using sunlight to convert H2O to H2 and O2). They screened hundreds of transition metal oxides and selected Mn2V2O7 as a possible candidate based on a detailed assessment of the bandgap, band edge position with respect to O2/H2O and H2/H+ levels, and stability in aqueous environments (that is, Pourbaix analysis). Experimental characterization within the same study confirmed a stable photocurrent at high pH values, which was consistent with the calculations, but also revealed that a co-catalyst was needed for efficient oxygen evolution. It is worth noting that stability was again a major criterion, and, in this case, the authors were able to use a newly developed formalism for computing Pourbaix diagrams43 to add aqueous stability to their screening criteria.
Once produced, hydrogen can be stored in several ways: for example, as a compressed gas, as a liquid or embedded within a solid compound. This last method has been the subject of several DFT investigations44,
Superconductors. Superconductivity remains one of the most elusive materials properties to predict from theory. Not only does it originate from several different physical phenomena, but the root cause of the resistance-free flow of electricity in some classes of materials is still not completely understood52. Superconducting materials are frequently divided into ‘traditional’ superconductors, in which the crucial electron-pairing interaction stems from electron–phonon coupling, and ‘new’ superconductors (for example, copper oxides and iron oxides), in which proximity to magnetic fluctuations is essential. For traditional superconductors, theory has not only provided the means to explain the observed phenomena53,
The earliest computational prediction of a superconducting material is remarkable as it was made when DFT was in its infancy. In 1984, Chang and Cohen56 observed an anomalously high electron density at the Fermi level in pressurized Si and speculated that the material may become superconducting under such conditions. One year later, the prediction was confirmed when superconductivity was observed in Si below 8.2 K at 15 GPa (Ref. 57). Similarly, Liu and Cohen58, Neaton and Ashcroft59, and Christensen and Novikov60 predicted superconductivity for several new polymorphs of Li as a function of pressure. These predictions were also verified shortly afterwards by several independent research groups61,
One challenge highlighted by these examples is polymorphism: many materials exhibit several phase transformations as a function of pressure that are not known in advance. Accurate crystal structure prediction therefore becomes a necessary step to correctly calculate the properties of a material (Box 2). For example, high-pressure silane (SiH4) was speculated68 to exhibit superconductivity at very high pressure; however, its structure was unknown. Although the superconductivity of this system has not been fully verified69, Pickard and Needs70 successfully predicted a stable structure at 250 GPa, which was subsequently confirmed by experiments71.
Theory has made a tremendous contribution to the field of superconductivity by providing a framework with predictive capability for traditional superconductors. For Fe and Cu oxides, a comprehensive theory was presented only days after their original discovery52. Although applications of superconductors traditionally appeared only in specialized areas, such as particle colliders, superconducting materials are now being utilized for grid voltage and power stabilization (for example, dynamic volt–amp reactive (DVAR) systems). To further increase the scope of their application, an increased superconducting temperature (Tc) and lower manufacturing costs are required. Although superconductivity remains a property that may be easier to measure than to compute, we expect that as the theory for the new classes of superconductor matures, efficient computational techniques to screen for novel compounds with higher Tc will be developed.
Photovoltaics. Although the use of photovoltaics (PVs) for energy generation is increasing rapidly (with an almost 125-fold growth in the US energy capacity from 2003 to 2013)72, their contribution to total electricity generation remains small. Several classes of PV materials are being actively investigated, including single-crystal, amorphous and polycrystalline Si, III–V compounds, thin-film chalcogenides, organic photovoltaics (OPVs) and multijunction devices73. DFT methods to screen inorganic compounds have been developed74, but thus far have only been applied to known classes of compounds75. Here, we focus specifically on OPVs, which became feasible following the discovery of the first organic semiconductor, trans-polyacetylene76, and subsequent ‘second-generation’ discoveries77,78. OPVs are attractive because of their potentially low cost and light weight; however, they suffer from low power conversion efficiencies and short lifetimes79. In 2006, Mühlbacher et al.80 proposed a new idea for designing organic semiconductors using copolymers, which are considered as third-generation organic semiconductors81. Copolymers comprise two monomer units that exhibit different electronic structures and geometries. Using this principle, researchers developed various organic semiconductor materials to achieve target electronic properties, including those for OPVs. However, designing these materials from first principles is not straightforward because standard DFT does not accurately model the electron localization of π-conjugated systems82. In addition, conventional conducting polymers contain tens to hundreds of atoms in a single chain and are thus too large to apply typical post-Hartree–Fock approaches. Other theoretical models and approximations of DFT must be applied83,
In 2007, Blouin et al.89 computationally screened derivatives of poly(2,7-carbozole) as potential OPVs through assessment of the following criteria: air stability, as evaluated by the position of the highest occupied molecular orbital (HOMO) energy level relative to air, a charge-transfer energy offset of the lowest unoccupied molecular orbital (LUMO) at least 0.3 eV higher than the acceptor level, and an optical bandgap between 1.2 and 1.9 eV. They calculated the properties of nine carbazole derivatives using DFT with the hybrid B3LYP exchange-correlation functional. Of these materials, six were selected for synthesis and characterization as thin films with phenyl-C61-butyric acid methyl ester (PCBM) as the acceptor and a donor/acceptor ratio of 4:1 (Fig. 4). Measurements of the short-circuit current, open-circuit voltage and fill factor confirmed poly(N-9′-heptadecanyl-2,7-carbazole-alt-5,5(4′,7′-di-2-thienyl-2′,1′,3′-benzothiadiazole) (PCDTBT) to be the best potential donor material for OPV applications. The power conversion efficiency of the new material was measured to be 3.6%89, and further optimization of the donor/acceptor ratio and morphology may be possible. In addition to the identification of a new material, the calculations helped to explain the trends observed among the six carbazole derivatives that were tested. The HOMO levels of all the derivatives were similar and fixed by the carbazole, whereas the inserted monomer units controlled the LUMO energy levels89 (later confirmed by alternative computational methods90).
Another type of material applicable to PVs is transparent conducting films. Such materials are unique in that they simultaneously possess large bandgaps (required for transparency) and high electrical conductivity. Transparent conductive films are used in electronic devices (for example, touchscreen displays) and can be used as an alternative to wire-mesh current collectors in PV devices. One outstanding challenge in the development of transparent conductors is the discovery of suitable p-type conductors (that is, conductors that transport positively charged holes while remaining optically transparent). Two recent studies have tackled this problem using a high-throughput screening approach91,92.
An initial study by Hautier et al.91 screened over 3,000 compounds — focusing only on known oxides — for materials with a large bandgap and a low p-type effective mass. For selected candidates, more detailed computational assessments of dopability were also performed. One of the materials identified from the screening was Ba2BiTaO6, a rhombohedral double perovskite that possesses an atypical energy alignment between the Bi 6s and O 2p orbitals, resulting in higher mobilities through hybridization. This material was synthesized using solid-state techniques by Bhatia et al.92, who confirmed the presence of high transparency (>90%) in the visible region and a high hole mobility (>30 cm2 V−1 s−1), but reported a very low carrier concentration (5 × 1013 cm−3).
Another recent study by Yan et al.93 focused on the high-throughput screening of both known and hypothetical half-Heusler ABX alloys. This study uncovered some general principles for the design of half-Heusler-based materials; for example, materials with a single transition metal are generally metallic, whereas those with two transition metals tend to be non-metals. These principles led to the identification of TaIrGe, which was synthesized and tested within the same study93. Similar to the previous case of Ba2BiTaO6, TaIrGe exhibits high visible light transparency (in the range of 85−92%) as well as very high Hall mobilities (2,730 cm2 V−1 s−1). However, its low carrier concentration (8 × 1014 cm−3) and the high cost of Ir are potential limiting factors that necessitate further optimization.
Thermoelectrics. Thermoelectric materials exploit temperature differences to drive electrical currents and vice versa. Potential applications of thermoelectric materials include waste heat recovery (from power generation plants and transportation vehicles) and refrigeration; however, commercialization has been minimal because of the relatively high cost and low efficiency of these devices.
To assess the intrinsic performance of thermoelectric materials, researchers typically employ a ‘figure of merit’ (or ZT), which is proportional to the temperature, electronic conductivity and Seebeck coefficient (the voltage generated per degree of temperature difference), and is inversely proportional to the thermal conductivity. Thermoelectric materials are challenging to design because there is an inherent trade-off between these quantities in almost all materials, which limits the ZT that can be attained. The use of phonon-glass electron-crystals and band alignment represent routes that circumvent the typical trade-offs94,95; however, these are applicable to only a small subset of materials.
Because it is difficult to estimate the quantities that determine the thermoelectric performance of a material, it would be useful to be able to compute such properties from first principles. Unfortunately, the computation of thermoelectric properties is often limited by theoretical shortcomings or computational expense. For example, estimations of the Seebeck coefficient and electronic conductivity are impeded by the difficulty of using DFT to produce accurate bandgaps and carrier lifetimes (that is, relaxation times). Furthermore, accurate treatment of the thermal conductivity is expensive and time consuming. The effects of high temperature on these properties can also be difficult to ascertain. Although almost all of these limitations can be overcome for simple materials and with careful and detailed study96, it is not currently possible to perform such detailed calculations on a large scale or for highly complex materials.
Nevertheless, these challenges have not deterred computational searches for new thermoelectric materials. Rather, researchers frequently approximate many quantities in an effort to yield qualitative (but nevertheless predictive) trends that can be used to compare different materials with a relatively high degree of confidence. In 2006, Madsen97 pioneered the use of computational search techniques for thermoelectric materials. The approximation had severe limitations: thermal conductivity was not modelled, the functionals used underestimated the bandgaps, and a constant and arbitrary relaxation time was used for electronic transport. Despite these known limitations, Madsen was able to recover known thermoelectric materials (such as skutterudites) in his screening and, crucially, also predicted new materials. One of the most promising materials predicted was an anisotropic n-type LiZnSb, which was calculated to have ZT in the range of 1.4–2.4 (depending on the approximations used). The LiZnSb material was subsequently synthesized by Toberer et al.98 but could not be formed with n-type doping. Instead, the experiments indicated that LiZnSb was intrinsically p-type and possessed a much lower ZT of less than 0.1.
Despite the approximations used and not arriving at the desired material, the measured Seebeck coefficients showed remarkable agreement with those calculated for the p-type material (Fig. 5). Rather, the problem seemed only to be that the desired material could not be synthesized with the correct carrier type. Indeed, Toberer et al.98 noted the propensity of many materials similar to LiZnSb to form p-type compounds in the experimental literature. Thus, the limitation of the study97 was not the overt and known approximations made during the screening process, but the implicit assumptions about dopability and carrier type, which were not considered at all. Nevertheless, Madsen's study triggered several other computational investigations into new thermoelectric materials99,100. For example, Zhu et al.101 recently reported a TmAgTe2 thermoelectric material discovered using high-throughput DFT with an experimentally measured ZT reaching 0.35. Furthermore, new formalisms for estimating thermoelectric properties42 suggest that more computational predictions may be made in the near future.
Capacitors. A capacitor stores electrostatic energy through the polarization of an electric field within a material. There are many classes of capacitors corresponding to different mechanisms of polarization, including traditional dielectric capacitors, ferroelectrics, carbon-based supercapacitors and pseudocapacitors.
Taking dielectric capacitors as an example, the primary desirable properties include a high dielectric constant, high breakdown strength and excellent cycling stability. Sharma et al.102 conducted an exhaustive search for novel dielectric polymeric materials by screening 1D repeat units for high dielectric constants (both ionic and electronic) using density functional perturbation theory and an effective medium theory103,104. Although the electronic component of the dielectric constant depended almost linearly on the bandgap, the ionic contribution showed no such dependence; this behaviour was exploited to maximize the dielectric capacity. Within the same study, three of the most promising candidates (none of which had been previously considered as a dielectric) were synthesized, with favourable agreement between the predicted and measured properties. This agreement was particularly good for polyurea [–NH–CO–NH–C6H4−]n, which exhibited a dielectric constant of 5.4–5.8 and a dielectric loss at 1 kHz of 1%. However, one of the top materials identified, polythiourea, was experimentally observed to exhibit limited solubility and sensitivity to processing conditions. Hence, subsequent computational work explored chain derivatives and substitutions; this information was used in experimental investigations105 towards improvement of the material. This work elegantly showcases the efficiency of combining computational and experimental techniques by leveraging the strengths of each domain. Although solubility and processing remain difficult to calculate accurately, the dielectric constant can be reliably estimated as a function of structural and chemical properties. Thus, rather than trying to perform the entire design in silico, the goal is almost always to focus the experimental efforts within a specific chemical and structural space.
In this Review, we surveyed many successful examples of predicting materials for renewable energy using computations. Although not all case studies could be highlighted (see Table 1 for a more comprehensive list), the works discussed embody many of the overall principles for modern computational materials design. As demonstrated, many types of DFT prediction can provide guidance for experimental synthesis. In some cases, such as the high-throughput screening of battery cathodes resulting in sidorenkites, standard DFT can be used to predict many of the important properties of a material before it is selected for synthesis. This type of analysis is closest to a ‘virtual screening’ model, for which DFT calculations act as a cheap and scalable proxy for experimentation. However, in other cases, such as for thermoelectric LiZnSb, assumptions are inherent in the DFT analysis. In these cases, it is important to emphasize how the assumptions bias the results and at what level of accuracy the predictions should be trusted. For such cases, one can still use DFT in a qualitative way to guide experiments to yield useful results. For example, the predictions of superconductivity were based largely on the examination of the computed density of states (DOS) and qualitatively searching for features thought to correlate with the target metrics. Such cases are common in the DFT literature; for example, Bentien et al.106,107 realized that FeSb2 should form a very-high-Seebeck-coefficient material based largely on correlating features of the computed DOS with known high-Seebeck-coefficient materials. Thus, the aim is not always comprehensive screening or the development of fully predictive models, but rather to accelerate the discovery process past the ability of experimentation alone. Sometimes, limitations of standard DFT that prevent a comprehensive virtual screening approach can be overcome through careful application of more exact methods. However, it is important to emphasize that attention to accuracy is never a substitute for relevance. For example, Madsen could have computed more accurate bandgaps for the predicted n-type LiZnSb material; however, such an effort would have been irrelevant as the subsequent experiment revealed LiZnSb to be p-type. Thus, it is often not the known approximations that derail a DFT prediction, but rather that some properties of the experimentally attainable material were not considered at all. It should also be noted that theoretical prediction is not always the most efficient route to obtain complete information about a material; often, calculations can be more time consuming and less straightforward than experiments. Interestingly, there seems to be little correlation between the difficulty of a measurement and a calculation. For example, the superconducting temperature (Tc) is still challenging to calculate despite being fairly straightforward to measure. By contrast, calculating single-crystal bulk ionic mobility is efficient compared with the experiments required. Therefore, it can be extremely beneficial to combine experimental and computational techniques, leveraging the best of both worlds as was demonstrated by the research groups of Ramprasad102 and Sotzing105 in the discovery and optimization of dielectric polymers.
A characteristic of the DFT approach that is both a strength and a limitation is its potential to compute scenarios outside the realm of nature. Even though this capability was detrimental to the thermoelectrics study conducted by Madsen, it enabled the more speculative study of the lattice-spacing effect on Li-ion mobilities pursued by Kang and colleagues24. Although the initial calculations for LiMn0.5Ni0.5O2 with greater layer spacing were purely hypothetical, the calculations were nevertheless able to demonstrate the potential of such a material if it could be synthesized. Being able to easily control thermodynamic conditions without knowing the specifics of how they can be achieved experimentally is a tremendously important and often-neglected advantage of computations. The ability to answer ‘what if’ questions such as what if I can increase the layer spacing away from equilibrium, make the material defect free, reach 200 GPa, stabilize a metastable structure — and how these changes would affect the properties — can guide the experiments and pave the way towards rational design and optimization. Conversely, it can be difficult to distinguish when a computationally derived material and its associated properties are outside the realm of what is physically possible. It is all too easy for theorists to posit new materials that are impossible for experimentalists to make. Today, one can evaluate the decomposition energy of new compounds into known phases (an indicator of thermodynamic stability) and also assess the dynamical stability with respect to phonons. However, there remains a great need in the field to emphasize stability and to develop better methods to bridge the gap between computational prediction and successful synthesis.
Finally, it is important to point out that even with a high-throughput computational approach, the possible outcomes are bounded by the initial decision with respect to the chemical and structural space. For example, a major recent development in the PVs community is the hybrid organic–inorganic halide perovskite system108,109. Such materials were completely off the radar of computational studies, which had focused separately on inorganic or organic systems. Thus, even large-scale computational screening is certainly not exhaustive, and calculations will continue to be guided by experiments. Although the present method of using DFT to screen for new materials has strengths and limitations, it is important to point out that the capabilities of DFT continue to expand. For example, in the 10-year span from 2005 to 2015, the total computing capability of the top 500 computing systems has expanded by a factor of 200, from 1.7 to 363 PFlop s−1 (see Top500 website). This improvement, combined with more efficient and stable numerical algorithms for solving the equations, means that studies that were considered too computationally expensive just a decade ago are now being run routinely. Similarly, new methods for treating the limitations of DFT are being developed and packaged into stable and easy-to-use software libraries. Thus, it is an exciting time for theorists and experimentalists alike to leverage the new capabilities that DFT-based materials design has to offer.
This work was intellectually led by the Materials Project supported by the US Department of Energy Office of Science, Office of Basic Energy Sciences Department under Contract No. DE-AC02-05CH11231. Y.S. thanks the Battery Materials Research Program under the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Vehicle Technologies of the US Department of Energy.