TowardComputational Materials Design ...€¦ · A theory that relates computable quan-tities to macroscopic engineering behavior is a prerequisite in order for DFT calcula-tions

IntroductionDuring the past decade, computer sim-

ulations based on a quantum-mechanicaldescription of the interactions between elec-trons and atomic nuclei have had an in-creasingly important impact on materialsscience, not only in fundamental under-standing but also with a strong emphasistoward materials design for future tech-nologies. The simulations are performedwith atomistic detail by solving theSchrödinger equation to obtain energiesand forces, require only the atomic num-bers of the constituents as input, andshould describe the bonding between theatoms with high accuracy. The Schrödinger

equation for the complex many-atom,many-electron system is not analyticallysolvable, and numerical approaches havebecome invaluable for physics, chemistry,and materials science. A breakthrough inthese computational efforts was realizedin 1964 when Walter Kohn and co-workers developed the density functionaltheory (DFT), a theory based on electrondensity, which is a function of only threespatial coordinates.1 The Kohn–Shamequations of DFT cast the intractable com-plexity of the electron–electron interactionsinto an effective single-particle potentialdetermined by the exchange-correlation

functional. This functional (i.e., a functionwhose argument is another function) de-scribes the complex kinetic and energeticinteractions of an electron with other elec-trons. Although the form of this functionalthat would make the reformulation of themany-body Schrödinger equation exact isunknown, approximate functionals haveproven highly successful in describingmany material properties.

Efficient algorithms devised for solvingthe Kohn–Sham equations have been imple-mented in increasingly sophisticated codes,tremendously boosting the application ofDFT methods. New doors are opening to in-novative research on materials across phys-ics, chemistry, materials science, surfacescience, and nanotechnology, and extend-ing even to earth sciences and molecularbiology. The impact of this fascinating de-velopment has not been restricted to aca-demia, as DFT techniques also findapplication in many different areas of in-dustrial research. The development is sofast that many current applications couldnot have been realized three years ago andwere hardly dreamed of five years ago.

The articles collected in this issue ofMRS Bulletin present a few of these suc-cess stories. However, even if the compu-tational tools necessary for performingcomplex quantum-mechanical calcula-tions relevant to real materials problemsare now readily available, designing aseries of simulations that meaningfullyrepresent a physical or chemical propertyor model a process (e.g., a chemical reac-tion or phase transformation in a mate-rial), remains a challenging task, requiringa judicious choice of approximations andan expert handling of these tools.

Designing DFT Calculations forMaterials Science

The successful application of DFT to amaterials problem involves three distinctsteps: (1) translation of the engineeringproblem to a computable atomistic model,(2) computation of the required physico-chemical properties, and (3) validation ofthe simulation results by confrontationwith laboratory experiments.

TranslationA theory that relates computable quan-

tities to macroscopic engineering behavioris a prerequisite in order for DFT calcula-tions to be relevant. Before any computa-tion can be started, significant effort oftenmust be expended to translate an engi-neering problem into questions and chal-lenges that can be addressed with DFT.This initial step requires considerable in-sight into the materials science and engi-neering aspects of the problem.

MRS BULLETIN • VOLUME 31 • SEPTEMBER 2006 659

TowardComputationalMaterials Design:The Impact ofDensity FunctionalTheory on MaterialsResearch

Jürgen Hafner, Christopher Wolverton, and Gerbrand Ceder, Guest Editors

AbstractThe development of modern materials science has led to a growing need to

understand the phenomena determining the properties of materials and processes onan atomistic level. The interactions between atoms and electrons are governed by thelaws of quantum mechanics; hence, accurate and efficient techniques for solving thebasic quantum-mechanical equations for complex many-atom, many-electron systemsmust be developed. Density functional theory (DFT) marks a decisive breakthrough inthese efforts, and in the past decade DFT has had a rapidly growing impact not only onfundamental but also industrial research. This article discusses the fundamentalprinciples of DFT and the highly efficient computational tools that have been developedfor its application to complex problems in materials science. Also highlighted are state-of-the-art applications in many areas of materials research, such as structural materials,catalysis and surface science, nanomaterials, and biomaterials and geophysics.

Keywords: computation, density functional theory, modeling, nanoscale, simulation.

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The translation step may be illustrated bythe application of DFT to the design ofbetter materials for rechargeable lithiumbatteries. Some properties, such as theelectrode potential for a new material, canbe directly related to total energy differ-ences2 and are therefore easy to compute.But another critical property, such as cyclelife (the loss of capacity after repeatedcharge and discharge), is more difficult topredict with DFT, because it can be causedby a variety of poorly identified phenom-ena, such as reaction of the material withthe electrolyte to form an insulating layer,mechanical degradation with resultingloss of electrical contact, and phase trans-formations in the material. Each of thesefactors requires a different computation.

ComputationIn many cases, solving the Schrödinger

equation is not enough. The length andtime scales accessible by DFT calculationsare defined by the maximal system size(typically a few hundred atoms; up to afew thousand in special cases) and by themaximum time span that can be coveredby ab initio molecular dynamics (MD) sim-ulations (several tens of picoseconds). Astrategy of multiscale simulations must beused to translate the results of atomisticDFT simulations to real-world scales. Asan example, the elementary steps in thecatalytic oxidation of CO on a metallic sur-face (adsorption/desorption/diffusion ofCO and O2, surface oxidation, dissociationof oxygen, reaction CO + O → CO2, des-orption of CO2, etc.) at fixed chemicalpotentials of the reactants may be treatedby DFT calculations, and the results mustbe fed into kinetic Monte Carlo simula-tions to develop a comprehensive pictureof the reaction under realistic pressure con-ditions and at real time scales (see alsothe article by Nørskov et al. on catalysis inthis issue).

ValidationAfter DFT computations are performed,

validation is an important step. This re-quires going beyond the computation ofenergies, band structures, and atomic con-figurations to the calculation of experi-mentally accessible properties such asmechanical or thermodynamic propertiesand electronic or vibrational spectra.

Discrepancies between computationand experimental observation can be attributable to inaccuracies in the DFT ap-proach, but more often point to discrep-ancies between the experimental andcomputational situations. An experimen-tal result may be influenced by impuritiesnot accounted for in the computation, itmay be kinetically constrained, or it may

differ from the computed result because ofother factors that are not characterizedwell in the problem translation. However,it should be emphasized that one of themost important roles of computationalmodeling is to provide information that isnot accessible (or accessible only with greatdifficulty) by laboratory experiments.

Hierarchy of Exchange-CorrelationFunctionals for DFT

DFT reformulates the many-bodySchrödinger equation in the form of a setof coupled one-electron equations (theKohn–Sham equations), where all of themany-body interactions are contained inthe exchange-correlation functional

Exc [n(r�)], (1)

where n(r�) is the electron density distribu-tion in the crystal. (For a modern intro-duction into DFT, see, for example,Dreizler and Gross3 or the recent book byMartin,4 which also provides a thoroughintroduction to the theory and practice ofelectronic structure calculations.) However,the exact form of this functional for whichthe Kohn–Sham equations would give ex-actly the same ground-state answer as themany-body Schrödinger equation is notknown, and approximations must be used.Perdew5 has referred to the hierarchy ofapproximations developed during the lasttwo decades as the “Jacob’s ladder of DFT.”� In the local density approximation(LDA), the local exchange-correlation en-ergy density is taken to be the same as in auniform electron gas of the same density.Modern forms of the LDA are based onthe total energy of the homogeneous elec-tron gas derived from quantum MonteCarlo calculations.� The generalized gradient approxima-tion (GGA) introduces a dependence ofExc on the local gradient of the electrondensity, �∇n(r�)�. Many different forms ofGGA functionals are available in the liter-ature, but for materials simulations, it isgood practice to use parameter-free func-tionals derived from known expansion coefficients and sum rules of many-bodytheory6,7 and to avoid empirical parame-terizations popular in molecular quantumchemistry.� Meta-GGA functionals use the kineticenergy density (or the Laplacian of theelectron density) as an additional variable.8� Hyper-GGA uses Kohn–Sham one-electron wavefunctions (instead of themany-body wavefunctions) to evaluatethe Hartree–Fock exchange formula; thisis commonly called “exact” exchange.� Hybrid functionals9,10 mix exact (i.e.,Hartree–Fock) and DFT exchange.

LDA and GGA are by far the most com-monly used functionals today. All func-tionals exist in spin-degenerate andspin-polarized versions. Quite generally,GGA calculations represent a systematicimprovement, compared with the LDA,although for heavy elements, a certaintendency of the GGA to overcorrect theLDA error is observed. In certain cases(prominent examples are the structuraland magnetic ground state of iron and thepotential-energy landscape for moleculardissociation on a metal surface) the differ-ence is not merely a quantitative one: onlyGGA calculations11 predict iron to be bccand magnetic, whereas the LDA predictsthe ground state to be hexagonal and non-magnetic. Only GGA calculations lead tothe correct height and location of the dis-sociation barrier for a diatomic moleculein contact with the surface of a metal.12

Climbing the density functional ladderfurther to the meta-GGA or hyper-GGAleads to only moderate progress, com-pared with the GGA.13 Hybrid functionalsenjoy enormous popularity in molecularchemistry, but in materials science theyare merely at the test stage. Preliminary re-sults show great promise for insulatingand semiconducting systems, but alsoshow a need to develop new hybrid func-tionals better suited to describing metals.14

Basis SetsPractically, the effective one-electron

Kohn–Sham equations are nonlinear partial differential equations that are itera-tively solved by representing the electronicwave functions by a linear combination ofa set of basis functions. Basis sets fall intotwo classes: plane-wave basis sets andlocal basis sets. Basis-set convergence iscrucial for the accuracy of the calcula-tions—in particular, for the prediction ofpressure, stresses, and forces.

Plane-Wave Basis Sets: CalculatingAccurate Forces and Stresses

Basis-set convergence is easily con-trolled in calculations using plane-wavebasis sets; it is sufficient to monitor theevolution of the results with the cut-off en-ergy, the highest kinetic energy associatedwith a plane wave. However, to achieveconvergence at a tractable computationaleffort, the plane-wave basis set must be ei-ther augmented by solutions of the radialSchrödinger equation in a region sur-rounding the nucleus (a modern approachfollowing this line is the full-potential lin-earized augmented plane-wave method,LAPW) or by using pseudopotentials todescribe the electron–ion interaction. Aparticular advantage of plane-wave calcula-tions is that the calculation of forces acting

660 MRS BULLETIN • VOLUME 31 • SEPTEMBER 2006

The Impact of Density Functional Theory on Materials Research





on the atoms and stresses on the unit cellis straightforward with the Hellmann–Feynman theorem. This opens the route toquantum ab initio MD simulations study-ing the time development of a system.

Local Basis Sets: Toward LinearScaling

Basis-set convergence is much more dif-ficult to control if local basis functions (forexample, atom-centered orbitals in a lin-ear combination of atomic orbitals, orLCAO) are used. These approaches havebeen actively pursued as, in principle, amuch smaller basis set; typically 10 to 20basis functions per atom should be suffi-cient to achieve the same accuracy asplane-wave calculations using hundredsof plane waves per atom. However, veryrecent extended tests have questioned thatadvantage, indicating that to match the ac-curacy of fully converged plane-wave cal-culations, very large local basis sets arerequired.14 A specific advantage of localbasis sets is that they enable the imple-mentation of linear-scaling DFT methods(i.e., algorithms for which the computa-tional effort increases linearly with thenumber of atoms).15–17 These techniquesrely on the fact that the wave functionmay be localized and have an exponentialdecay leading to a sparse Hamiltonian.

For molecular, insulating, and semicon-ducting systems, linear-scaling, or O(N),techniques enable the performance ofatomistic studies for systems containingthousands of atoms. However, this doesnot hold if the gap between occupied andempty states vanishes, as in metals, forwhich it has turned out to be difficult toreconcile linear scaling and high accuracy.

Potentials and PseudopotentialsMethods using local basis sets or aug-

mented plane waves may be constructedas all-electron methods in the sense thatthe effective one-electron potential is cal-culated using the full set of relaxed coreand valence orbitals. In plane-wave calcu-lations, the electron–ion interactions mustbe described by a pseudopotential, elimi-nating the need for an explicit treatment ofthe strongly bound and chemically inertcore electrons. Pseudopotentials may alsobe used in local orbital methods to reducethe computational effort. The theory ofpseudopotentials is mature, but the prac-tice of constructing transferable and effi-cient pseudopotentials is far fromstraightforward. Methods for generatingpseudopotentials include the pseudopo-tentials by Troullier and Martins18 (conserv-ing the norm of the wave function) andthe ultrasoft pseudopotentials introduced

by Vanderbilt19 (which have the merit ofmaking calculations for d- and f-electronmetals feasible at an acceptable computa-tion cost). The criterion for the quality of apseudopotential is not how well the calcu-lation matches experiment, but how wellit reproduces the result of accurate all-electron calculations. Mature codes (seeTable I) provide extensive databases ofwell-tested pseudopotentials. A certaindrawback of pseudopotential calculationsis that because of the nonlinearity of theexchange interaction between valenceand core electrons, elaborate nonlinearcore corrections are required in all sys-tems where the overlap between thevalence- and core-electron densities is notcompletely negligible. The projector-augmented wave (PAW) method pro-posed by Blöchl20 and adapted by Kresseand Joubert21 avoids the necessity of corecorrections and combines the efficiencyof pesudopotentials with the accuracy offull-potential, all-electron calculations.

CodesA variety of mature DFT codes are

nowadays available to the materials sci-ence community. Some of them are acces-sible through general public licenses,whereas others are proprietary. Thecodes are based on different choices of



Table I: Commercially or Freely Available Density Functional Theory Codes.

Code Name Basis Set Potentials Web Site

Plane Wave

Pseudopotential Codes

ABINIT Plane wave Pseudo, PAWa www.abinit.orgCASTEP Plane wave Pseudo www.tcm.phy.cam.ac.uk/castep/CPMD Plane wave Pseudo www.cpmd.org/Dacapo Plane wave Pseudo dcwww.camp.dtu.dk/campos/Dacapo/FHImd Plane wave Pseudo www.fhi-berlin.mpg.de/th/fhimd/PWscf Plane wave Pseudo www.pwscf.org/VASP Plane wave Pseudo, PAW cms.mpi.univie.ac.at/vasp

Pseudopotential Codes with

Other Basis Sets

Quickstep Gaussian + plane wave Pseudo cp2k.berlios.de/quickstep.htmlSIESTA Local/numerical Pseudo www.uam.es/departamentos/ciencias/fismateriac/siesta/

All-Electron Codes

CRYSTAL Local all-electron www.crystal.unit.itFPLO Local all-electron www.ifw-dresden.de/agtheo/FPLO/Gaussian 03 Local all-electron www.gaussian.comADF Local all-electron www.scm.comDMol3 Local/numerical all-electron people.web.psi.ch/delley/dmol3.htmlFLAIR LAPWb all-electron www.uwm.edu/~weinert/flair.htmlQMD-FLAPW LAPW all-electron flapw.comWIEN2K LAPW all-electron www.wien2k.at

aPAW � projector-augmented wave method.bLAPW � linearized augmented plane-wave method.





basis sets, potentials, exchange-correlationfunctionals, and algorithms for solving theSchrödinger equation. A summary ofmany existing codes is given in Table I.There are currently a large number ofpseudopotential codes, all of which haveLDA and GGA functionals and enable the performance of static electronic struc-ture and total energy calculations as wellas ab initio MD simulations, using eitherBorn–Oppenheimer or Car–Parrinello dy-namics. The all-electron PAW method isimplemented in VASP and ABINIT codes.Exact exchange and hybrid functionals areimplemented in the newest releases ofCPMD and VASP. For the pseudopotentialcodes, an important point is the availabil-ity of thoroughly tested, accurate, and effi-cient pseudopotentials for all elements.Many of these codes come with suites ofpseudopotentials developed and recom-mended by the code developer.

All-electron codes exist using local oraugmented plane-wave basis sets. BothGaussian 03 and CRYSTAL can performDFT, exact exchange, and hybrid calcula-tions, and FPLO is a fully relativistic codefor solving the Dirac equation. DMol3 usesa numerical basis set working either in anall-electron mode or using semilocalpseudopotentials. WIEN2K, FLAIR, andQMD-FLAPW are all-electron codes usingthe full-potential LAPW method. WIEN2Koffers the ability to add local orbitals to thebasis set to speed up convergence. All-electron codes are important for providingbenchmarks for pseudopotential codes;this applies in particular to the full-potential LAPW method in which theaugmented plane-wave basis provides anefficient control of basis-set convergence.

Today, calculations with tens of atomsare extremely fast, with pseudopotentialas well as all-electron codes. Calculationsfor unit cells containing a few hundredatoms are routine with pseudopotentialand PAW codes, but are very demandingor even out of reach for most all-electroncodes. Using the most efficient codes, veryaccurate calculations involving a thou-sand or more atoms are possible (it shouldbe pointed out that the real figure of meritis the number of valence electrons—thecurrent limit is somewhere close to 104

electrons). Linear-scaling calculations maybe extended to several thousands of atoms.

Tools and CapabilitiesFor many applications in materials sci-

ence, the availability of a basic code forsolving the Schrödinger equation is notsufficient; the resulting energies, wavefunctions, and electron and spin densi-ties are merely the starting point for thecalculations of many different materials

properties. Much current code develop-ment is focused on the development ofroutines for the post-processing of DFT re-sults (“tools“) to yield a comprehensivedescription of materials and dynamicmodeling of time-dependent processes inmaterials. Examples of such capabilitiesinclude1. Crystal structure, phase stability, andphase diagrams. Whereas the calculationof structural free-energy differences forpolytypes of ordered crystalline materialsis a standard task within DFT, the combi-nation of ab initio total energy calculationswith genetic algorithms22,23 is leading tothe development of a truly predictivecomputational crystallography.2. Mechanical properties. Symmetry-general techniques have been developedfor the calculation of elastic constants.24

Intense efforts are being made to calculatetensile and shear strength and to simulatefracture behavior.25

3. Vibrational spectroscopy. The vibra-tional eigenstates of molecular and crys-talline systems can now be calculatedeither via direct force-constant methods26

or a linear response route,27 includingquantitative predictions of infrared,Raman, and inelastic neutron scatteringintensities.4. Surfaces and interfaces. Accurate calcu-lation of surface and interface energies enables the prediction of the morphologyof nanoclusters and precipitate shapes. Ab initio MD has made it possible to resolveeven very complex surface reconstructions.28

5. Adsorption, reactions, and catalysis.Whereas theoretical studies previouslyhave been restricted to ideal low-indexsurfaces, recent advances permit the in-vestigation of molecular adsorption andreactions at stepped, kinked, and de-fective surfaces29 and the simulation ofcatalytic reactions under realistic condi-tions of temperature and pressure. Acid-catalyzed reactions at the internal surfacesof functionalized microporous and meso-porous materials have been studied usinga variety of DFT techniques.30

6. Spectroscopy and dielectric properties.The possibility of calculating the polariz-ability of a material via a Berry phaseapproach has led to a new quality of calcu-lated optical spectra31 and has opened theway toward an ab initio treatment of ferro-electricity32 and piezoelectricity.33 Tools forcalculating nuclear magnetic resonancespectra34 and for scanning tunneling spec-troscopy35 have been developed.7. Magnetic properties. A fully relativistictreatment is required to tackle problemsrelated to magnetic anisotropy; a vector-field treatment of magnetization density isnecessary for the description of the complex

non-collinear structure of frustrated anti-ferromagnets where exchange interac-tions and lattice topology are in conflict.36

8. Electronic transport. The developmentof tools for the calculation of electronictransport processes in nanostructured materials is a very active field. Particularattention has been paid to transport in sys-tems showing giant magnetoresistance37

and in molecular devices.38

9. Liquids and glasses. Although diffrac-tion experiments yield the full three-dimensional structure for crystallinematerials, these techniques yield only one-dimensional projections of the structure ofliquids and glasses. Ab initio MD leads tohighly accurate structural prediction forliquids and glasses without the use of em-pirical force fields.39

Only a few references are given in this sec-tion for lack of space; the reader is referredto the Internet home pages of the most im-portant ab initio codes (see Table I).

Multiscale Modeling: Bridging theGaps in Time and Length Scales

It is clear that substantial gaps exist be-tween the dimensions of even the largestsystems accessible to DFT simulations andbetween the maximum time span of ab ini-tio MD simulations and the time andlength scales of laboratory experiments.To bridge these gaps, strategies for multi-scale simulations are being developed.This task is tackled from different sides.Configurational free energies of extendedsystems, including substitutional disorderin multicomponent systems, can be ob-tained from cluster-expansion methods,which extract representative lattice mod-els from DFT that can then be used inMonte Carlo simulations to obtain suchquantities as temperature–compositionphase diagrams, short-range order of dis-ordered phases, interfacial free energies,and precipitate shapes.40,41 The specialquasi-random structure approach42 makespossible the direct calculation of electronicand energetic properties of disorderedsystems using small-unit-cell structuresamenable to DFT. These models have beenimplemented with significant success andlead to true structure predictions, laterverified by experiments.43 In a similarspirit, DFT computations of the formationenergy of intermetallic compounds havebeen used as input in the CALPHADmodels for the thermodynamics of mate-rials.44 One new area that holds consider-able promise is the integration of DFTwith phase-field models to study the evo-lution of microstructures.45 DFT can beused to compute such quantities as freeenergies, diffusion constants, and interfa-cial energies. These first-principles-predicted







quantities can then serve as the thermody-namic and kinetic driving forces for thephase-field models of microstructuralevolution.

Another strategy for solving the lengthscale problem is embedding. For a smallreactive center where atomistic resolutionand high accuracy are important, a calcu-lation at a high level of sophistication isperformed. The boundary conditions forthis calculation are determined by a treat-ment of the area surrounding the center ata lower level. Examples for this approachare the quantum-mechanical/molecularmodeling approach used in heteroge-neous catalysis;46 the description of crackpropagation using DFT to simulate thecrack tip, embedded in an atomistic force-field description of the strain field at in-termediate distances; and a continuumapproach on a macroscopic scale. A partic-ularly attractive version of this embed-ding scheme is the “learn-on-the-fly”strategy,47 where local quantum computa-tions are used to continually tune the pa-rameters of the force field used for theclassical part of the simulations.

Time-scale gaps are caused by energybarriers for chemical reactions and first-order structural phase transitions. Rareevents such as activated chemical reactionscan be treated within transition-statesampling methods;48 temperature-accelerated MD methods49,50 or meta-dynamic techniques.51 This allows one toidentify novel phases under extreme ther-modynamic conditions and to trace outtransformation pathways for structuralphase transitions. Kinetic Monte Carlosimulations can be used to simulategrowth processes or chemical reactions onregular lattices under realistic conditionsof temperature.

HardwareDFT simulations of materials do not re-

quire supercomputer resources. A typicalhardware base for such simulations consists of a PC cluster with fast proc-essors equipped with sufficient memory(�1 Gbyte) and a fast interconnect. Mod-ern DFT codes offer efficient simulationof medium-sized systems on clusters ofabout 32 CPUs.

Applications of DFT in MaterialsResearch

This issue of MRS Bulletin collects a di-versity of DFT success stories from suchwide-ranging materials research topics assurface science and catalysis, earth sci-ences, nanotechnology, and structuralmetals. Of course, any such list of ex-amples will necessarily be incomplete, butit should give the reader a sense of the

types of capabilities and opportunitiespresently at hand.

Mechanical Properties andStructural Materials

The article by Ikehata et al. from theToyota research group of Takashi Saito de-scribes a specific example of the use ofDFT in an alloy design problem, namely,the search for a low-modulus, high-strength titanium alloy. This article pro-vides an excellent illustration of the powerof a combined theoretical and experimen-tal approach directed toward the searchfor a material with specified properties.

Applications of DFT to structural mate-rials also exist in steels, notably, the workof Olson and co-workers,52 who use vari-ous computational materials techniques toaccelerate the design process of new high-strength steels. The Virtual AluminumCastings program at Ford Motor Com-pany involves the use of DFT and its con-nection to higher-length-scale modelingtools44,45 directed toward improvedprocessing and enhanced properties ofaluminum cast alloys.

A novel MD approach combiningquantum-mechanical embedding withclassical force-field models has been usedby Csanyi et al.47 to model crack propaga-tion in silicon using a model containingabout 200,000 atoms (see Figure 1). About300 atoms near the crack tip are treatedquantum-mechanically, and this is essen-tial for a correct description of the (2 × 1)periodicity of the reconstruction of thecrack surface. Although this method hascurrently been applied to Si, future exten-sions of this method to structural materi-als could produce useful insight on crackpropagation in a variety of materials types.

Catalysis and Surface ScienceElectronic-structure calculations have

been used extensively in the fields of sur-face science and catalysis. Nørskov et al.review how DFT is being used to eluci-date atomic-scale mechanisms forchemical reactions on surfaces and toquantitatively describe the rates of hetero-geneous catalysis reactions. These authorsalso provide an intriguing discussion ofthe future prospects of the calculations topredict new catalysts and, hence, providea rational guide for catalyst development.DFT techniques are also applied to the in-vestigation of acid-based catalysis by mi-croporous materials such as zeolites. Aninteresting innovation is the production of ε-caprolactam (a precursor molecule tothe polymer nylon-6) by conversion of cyclohexanone (the so-called Beckmannrearrangement) in a zeolite or a struc-turally related aluminophosphate,53,54 a re-action that is environmentally much morebenign than the conventional routethrough homogeneous catalysis in sulfu-ric acid. Figure 2 shows the final step inthe formation of ε-caprolactam, the hy-drolysis of an intermediate carbiminiumion in the pore of a zeolite.

Magnetism and Magnetic MaterialsThe enormous increase in the recording

density of hard disk drives by eight ordersof magnitude during the past 50 years (seethe May 2006 issue of MRS Bulletin on“Materials for Magnetic Data Storage”)has been achieved by downsizing the bitsrecorded in the magnetic storage layer.This approach is, however, limited by theonset of superparamagnetism, which oc-curs when the grain size in the recordingmedium is reduced to an extent that themagnetic energy stored in a grain be-comes comparable to the thermal energy.Recently, based on DFT calculations,tetragonal iron cobalt alloys were pro-posed as promising materials with the de-sired high uniaxial magnetic anisotropyand high saturation magnetization.55 Sta-bility of the tetragonal FeCo phase can beachieved in FeCo/Pt superlattices (seeFigure 3); again, DFT calculations turnedout to be essential.56 This is a good exampleof a real computer-aided materials design.

Oxides and MineralsDFT works quite well on oxides of al-

kali, alkaline-earth, and main group ele-ments. In their article, Brodholt andVocadlo describe the uses of DFT in geol-ogy and the earth sciences. Calculationshave the ability to simulate conditions inthe Earth’s interior that would otherwisebe quite problematic to reproduce in thelaboratory. Applications of DFT have



Figure 1. Propagation of a (111)[110]crack in silicon, modeled using the“learn-on-the-fly” scheme mixingquantum and classical simulations. Note the (2 × 1) periodicity of thereconstruction appearing on the upperopening surface. After Csanyi et al.47





predicted such fundamental properties asthe properties of iron and (Mg,Fe)SiO3under the extreme pressures and temper-atures of the Earth’s interior. DFT calcula-tions have also recently been shown to putbounds on the possible composition of theEarth’s core and have identified a newphase of (Mg,Fe)SiO3 just above the core.The application of DFT in transition-metaloxides requires considerably more care, asthe spurious self-interaction in DFT overlydelocalizes electrons, leading to excessivemetallic behavior and the washing out ofmixed-valence states in doped oxides, affecting local spin magnetism, conduc-tivity, and even phase stability. Despitethese limitations, DFT and enhanced DFTmethods can be used to assist in the ra-tional design of new materials. A good ex-ample can be found in the search for a

lithium-battery electrode material withhigher energy and power density.43 In thisfield, DFT computations are now com-monplace in industry and academic labs.

Semiconductors andNanotechnology

Semiconductors probably form the classof materials that has seen the most widespread use of DFT. Calculations ofelectronic properties for known semicon-ductors, such as bandgaps and defectstates, are now commonplace and havebeen performed for virtually all unary andbinary semiconductor systems as well asfor a wealth of higher-order compounds,ordered and disordered alloys, dopanttypes, and surface structures. In his contri-bution to this issue, Marzari reviews theapplications of DFT to semiconductornanotechnology, concentrating on Si-Hnanostructures, single-walled carbon nano-tubes, and self-assembled monolayers.The combined investigation, based on ex-periment and DFT calculations, of the ad-sorption of large organic molecules onmetallic and semiconducting surfaces, theformation of ordered structures through aself-assembly process,57 and the electronictransport process in these molecular de-vices38 is an essential contribution towardthe development of molecular electronics.

BiomaterialsDFT calculations play an increasingly

important role for understanding complexprocesses in biological materials. For ex-ample, the protonation of the retinal chro-mophore is of crucial importance forthe visual process. Protonation leads to theformation of a highly polarizable π-systemrequired for long-wavelength adsorbanceand wavelength regulation by the proteinenvironment, and deprotonation is re-quired for the protein to reach the activat-ing state after light adsorption. Sugiharaet al.58 and Röhrig et al.59 have appliedDFT techniques to investigate the structure

and dynamics of the retinal chromophoreof rhodopsin in different environments.Figure 4 shows the DFT-optimized struc-ture of the chromophore binding site. Oneof the exploratory studies based on alinear-scaling code presents a total energycalculation of a piece of DNA consisting ofmore than 2500 atoms.17

High-Throughput Ab InitioCalculations

High-throughput (combinatorial) ex-perimentation has played an increasinglyimportant role in materials science. Bystudying large numbers of systems, onecan screen combinatorial spaces for newsystems with desired properties. ModernDFT codes have now become very robust,enabling many tasks to be performed au-tomatically. Combined with the increasingspeed of computers, this opens the waytoward high-throughput computation.60

Pioneering applications have been de-voted to crystal structure predictions61 andthe search for stable quaternary alloys.62

Summary and OutlookDFT is the most detailed “microscope”

currently available to glance into theatomic and electronic details of matter. Assuch, it has catalyzed a renewed interestinto the fundamental science, chemistry,and physics of materials. Its impact islikely to continue to grow through the fur-ther development of tools that build uponDFT to model higher-level properties notdirectly accessible to DFT because of time-scale, length-scale, or complexity issues.Much of this application-driven modelingis likely to be performed by people withfield-specific knowledge in cooperationwith the DFT practitioners and code devel-opers; therefore, educating the materials



Figure 3. Schematic of the tetragonal“3/7” superlattice of an Fe0.36Co0.64 alloyand Pt, showing a huge perpendicularmagnetic anisotropy energy (the latticeparameters are CFeCo �0.317 nm and CPt �0.417 nm). This superlattice hasbeen proposed on the basis of DFTcalculations and experimentally realized by sputter deposition. AfterAndersson et al.55

Figure 4. Schematic of the DFTenergy-optimized structure of thechromophore binding site in rhodopsinof a protonated 11-cis-retinal Schiffbase (Lys296) in contact with aglutamate ion (Glu113), an amino acid(Thr94), and a water molecule (Wat2b).HI, HIII, and HVII are regions inmitochondrial DNA. After Sugihara et al.58

Figure 2. (a) Initial, (b) transition, and (c) final states of the hydrolysis of a carbiminium ion toform N-protonated ε-caprolactam, catalyzed by an acid zeolite. After Bucko et al.54





scientists of the future through new text-books, online courses, and tutorials isa crucial aspect of increasing the impactof DFT.

Despite all of its successes, DFT is notaccurate for all problems. We have alreadymentioned the continuing effort to con-struct exchange-correlation functionalsleading to improved accuracy. AlthoughDFT does an excellent job on the ground-state properties of metals and semicon-ductors, the “bandgap” problem (i.e., thedifficulty of achieving a quantitatively ac-curate prediction of the gap between thehighest occupied and the lowest emptyeigenstates) and the inability to describethe physics of van der Waals interactionsare notorious. Also, the properties ofstrongly correlated systems such astransition-metal oxides are not well repro-duced by common exchange-correlationfunctionals. Evidently, explorations of themany-body aspects of electron correlationbeyond current DFT methods are needed,and this is currently a very active field ofresearch. Many-body perturbation theory(the GW method) corrects most of thebandgap problem in DFT, even for diffi-cult cases such as narrow-gap semicon-ductors.63 LDA+U approaches combine aDFT description of extended states with aHartree–Fock-like treatment of theCoulomb repulsion U between states innarrow d- and f-bands, and lead to a sig-nificant improvement in the structural,electronic, magnetic, and optical proper-ties of transition-metal oxides64 and othersystems where electron localization isstrong. Dynamic mean-field theory(DMFT) may be considered as a many-body extension of DFT that attempts tocapture the true many-body physics of theelectron–electron interaction. For stronglycorrelated systems, LDA+DMFT agreeswith LDA+U, but it subsumes the LDA forweakly correlated metals and achieves acorrect description at arbitrary strength ofthe onsite Coulomb repulsion.65 At thispoint, no unified “post-DFT” theory ex-ists, and practitioners will need to decidewith care which improvement strategy isbest suited for a property that cannot beaccurately computed at the DFT level. Fi-nally, the recent development of a highlyefficient quantum Monte Carlo approach66

could open the way toward materials sim-ulations with an unprecedented level ofaccuracy and sophistication.

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Jürgen Hafner,Guest Editor for thisissue of MRS Bulletin, is a professor of Solid-State Sciences at theUniversity of Viennaand director of theGraduate College forComputational Materials Science. Hegraduated in 1973 fromVienna Technical University, where healso was appointed professor of theoreticalphysics in 1982 afterserving for several yearsas a research associate atthe Max Planck Institutefor Solid-State Sciences.In 1998, he accepted achair at the Faculty of Physics of the University of Vienna.

Hafner’s researchconcentrates on the application of densityfunctional methods to awide range of problemsin materials science,from magnetism at thenanoscale to surface science and catalysis. Hehas received the LudwigBoltzmann Prize fromthe Austrian PhysicalSociety and the ErwinSchrödinger Award ofthe Austrian Academyof Sciences. Also, Hafnerhas authored more than500 publications in refereed internationaljournals.

Hafner can bereached at UniversitätWien, Institut für Materialphysik andCenter for Computational

Materials Science,Sensengasse 8/12,A-1090 Wien, Austria;tel. 43-4277-51400 (di-rect) and 43-4277-51401(secretary), fax 43-4277-9514, and e-mail [email protected].

Christopher Wolverton,Guest Editor for thisissue of MRS Bulletin, isa technical leader atFord Research and Innovation Center,where he leads the Hydrogen Storage andNanoscale ModelingGroup. He received hisPhD degree in physicsfrom the University ofCalifornia at Berkeley.After completing hisPhD degree, Wolvertonperformed postdoctoralwork at the National Renewable Energy Laboratory (NREL).

His research interestsinclude computationalstudies of a variety ofautomotive and environmentallyfriendly materials viafirst-principles atomistic calculations andmethodologies for linking atomistic andmicrostructural scales.Current topics of inter-est include the discov-ery of novel hydrogenstorage reactions, phasetransformations inmetallic and oxide alloys, microstructuralevolution during heattreatment, and the theo-retical prediction of newmaterials. Wolverton

has co-authored morethan 60 peer-reviewedpublications and holdstwo patents, with several others pending.

Wolverton can bereached at Ford MotorCompany, MD3083/SRL, PO Box 2053,Dearborn, MI 48121,USA; tel. 313-390-9552,fax 313-323-1129, and e-mail [email protected].

Gerbrand Ceder,Guest Editor for thisissue of MRS Bulletin, isthe R.P. Simmons Professor of MaterialsScience and Engineeringat the Massachusetts Institute of Technology.He holds an engineeringdegree from the Univer-sity of Leuven, Belgium,and a PhD degree inmaterials science fromthe University of California at Berkeley.

Ceder’s research interests include first-principles predictions ofmaterials properties andstructure, with a focuson materials for energygeneration and storage.He has received the Battery Research Awardfrom the Electrochemi-cal Society, the CareerAward from the National Science Foun-dation, and the RobertLansing Hardy Awardfrom TMS.

Ceder can be reached atthe Department of Ma-terials Science and Engi-neering, Massachusetts

Institute of Technology,Room 13-5056, 77 Mass-achusetts Ave., Cam-bridge, MA 02139, USA;tel. 617-253-1581, fax617-258-6534, and e-mail [email protected].

John P. Brodholt is aprofessor of mineralphysics in the Depart-ment of Earth Sciencesat University CollegeLondon. The focus ofhis research is computa-tional mineral physicsapplied to the Earth’sinterior. Brodholt wasawarded the EuropeanMineralogical UnionMedal for Research Excellence in 2002 andwas elected as a fellowof the Mineralogical So-ciety of America in 2005.He has published morethan 90 papers inhis field.

Brodholt can bereached at UniversityCollege London, De-partment of Earth Sci-ences, Gower Street,London, WC1E 6BT,United Kingdom; tel.44-0-20-7679-2622, fax44-0-20-7388-7614, and e-mail [email protected].

Hideaki Ikehata is a re-searcher in the ToyotaCentral R&D Labs Inc.(TCRDL). He receivedhis MS degree fromKyoto University andsubsequently joinedTCRDL in 1998. His research interests include strengthening of

metallic materials andtheoretical predictionsof the physical proper-ties of metals by first-principles calculations.

Ikehata can bereached at Toyota Central R&D Labs Inc.,41-1 Yokomichi, Na-gakute, Aichi 480-1192,Japan; tel. 81-561-63-4660, fax 81-561-63-6156,and e-mail [email protected].

Shigeru Kuramoto is aresearcher in the ToyotaCentral R&D Labs Inc.(TCRDL). He received aDEng degree from theUniversity of Tokyo(UT) in 1994, focusingon deformation andfracture of aluminum al-loys at low tempera-tures. Prior to joiningTCRDL in 2002, Kuramoto worked as aresearcher in FurukawaElectric Co. Ltd. and asa research associate atUT. His research interests are deforma-tion and fracture inmetallic materials.



Jürgen Hafner Christopher Wolverton Gerbrand Ceder John P. Brodholt Hideaki Ikehata

Matthias Scheffler







Kuramoto can bereached at Toyota Cen-tral R&D Labs Inc., 41-1Yokomichi, Nagakute,Aichi 480-1192, Japan;tel. 81-561-63-4660, fax81-561-63-6156, and e-mail [email protected].

Nicola Marzari isassociate professor ofcomputational materialsscience in the Depart-ment of Materials Science and Engineeringat the Massachusetts In-stitute of Technology.He holds a Laureadegree in physics fromthe University of Triestein Italy and a PhD de-gree in physics from theUniversity of Cambridge. Before join-ing MIT, he was an NSFpostdoctoral fellow atRutgers University anda research scientist withthe Naval Research Laboratory and withPrinceton University.

Marzari’s research isdedicated to the devel-opment and application

of novel electronic-structure approaches tocharacterize and designadvanced materials anddevices. In 2005, he wasthe subject editor forelectronic structure inthe Handbook of MaterialsModeling (Springer).

Marzari can bereached at the Massa-chusetts Institute ofTechnology, Departmentof Materials Science andEngineering, Room 13-5066, 77 MassachusettsAve., Cambridge, MA02139-4307, USA; tel.617-452-2758, fax 617-258-6534, and [email protected].

Naoyuki Nagasako is aresearcher in the ToyotaCentral R&D Labs Inc.(TCRDL). He joinedTCRDL after his receiv-ing his MS degree fromHiroshima University in1997. His research inter-ests include theoreticalstudies on the physicalproperties of materialsby first-principles calculations and their

application to materialsdesign.

Nagasako can bereached at Toyota Cen-tral R&D Labs Inc., 41-1Yokomichi, Nagakute,Aichi 480-1192, Japan;tel. 81-561-63-4537, fax81-561-63-5426, and e-mail [email protected].

Jens K. Nørskov is aprofessor of physics inthe Department ofPhysics at the TechnicalUniversity of Denmark(DTU). Also, he is direc-tor of the Center forAtomic-Scale MaterialsPhysics, the director ofNanoDTU, and thechair of the Danish Cen-ter for Scientific Com-puting. Nørskovreceived his PhD degreein physics in 1979 fromthe University of Aarhusin Denmark. Before hisappointment at DTU in1987, he held researchpositions at the Univer-sity of Aarhus, IBM inYorktown Heights, theNordic Institute for Theoretical Physics inCopenhagen, and Hal-dor Topsoe. In 1993, heco-founded DTU’s Center for Atomic-ScaleMaterials Physics.

Nørskov’s researchinterests include theoret-ical surface physics, heterogeneous catalysis,nanostructures and ma-terials properties,biomolecules, electro-chemistry, and hydro-gen storage. He is a

member of the RoyalDanish Academy of Science and Letters, andhis recent honors in-clude the 2005 Innova-tion Prize from DTUand an honorary doctor-ate from the Technical University of Eindhovenin 2006.

Nørskov can bereached at CAMP, De-partment of Physics, B. 307, Technical Univer-sity of Denmark, DK-2800 Lyngby, Den-mark; tel. 45-4525-3175,fax 45-4593-2399, and e-mail [email protected].

Takashi Saito is a direc-tor at the Toyota CentralR&D Labs Inc. (TCRDL).He earned a DEng de-gree from Tohoku Uni-versity in 1979, focusingon the calculation ofphase diagrams andphase transformations.After receiving his de-gree, he joined TCRDLin 1980.

His research interestsinclude mechanical andphysical properties ofhigh-performancemetallic materials.

Saito can be reachedat Toyota Central R&DLabs Inc., 41-1Yokomichi, Nagakute,Aichi 480-1192, Japan;tel. 81-561-63-3090, fax81-561-63-5441, and e-mail [email protected].

Matthias Scheffler hasbeen director of the Fritz

Haber Institute of theMax Planck Society inBerlin since 1988, and aDistinguished VisitingProfessor at the University of Californiain Santa Barbara since2005. His research areasinclude ab initio theoriesof electronic structure,in particular, densityfunctional theory, quantum Monte Carloand self-energy methods, atomistic thermodynamics, andstatistical mechanics.Various hybridmethods have beendeveloped thatallow the study ofmesoscopic systems andtime scales from pi-coseconds to seconds.Also, Scheffler has investigated semicon-ductors, metals,transition-metal oxides,carbon nanostructures,transition-metalclusters, andbiomolecules.

He was named a fellow of the AmericanPhysical Society in 1998and was honored withthe Medard W. WelchMedal and Prize in2003 and the Max BornMedal and Prizein 2004.

Scheffler can bereached at Fritz-Haber-Institut der Max-Planck-Gesellschaft,Faradayweg 4-6, D-14195 Berlin-Dahlem,Germany; tel. 49-30-8413-4711 and fax 49-30-8413-4701.

Shigeru Kuramoto Nicola Marzari Naoyuki Nagasako Jens K. Nørskov Takashi Saito

Hervé Toulhoat Lidunka Voc̀́adlo





reader in mineralphysics in the Department of EarthSciences at UniversityCollege London.

Her research interestsinclude the Earth’s coreand planetary ices. Shewas awarded theDoornbos Prize for Research Excellence in1998 and the 2004 MaxHey Medal of the Mineralogical Society of

Hervé Toulhoat isdeputy scientific direc-tor of the InstitutFrançais du Pétrole (IFP)and the director of doc-toral studies at IFPSchool in Rueil-Malmaison, France. Heearned a PhD degree inchemical engineeringfrom the Paris School ofMines in 1980, and anMSc degree from EcoleNationale Supérieure de

Chimie de Paris in 1976.Toulhoat is a member ofthe Editorial Board ofthe Journal of Catalysisand an associate member of the IUPAPCommission onComputational Physics.He has authored morethan 100 papers andholds 20 patents, mostlydealing with catalysisand processes inoil refining.

Toulhoat can bereached at InstitutFrançais du Pétrole, 1–4 avenue de Bois-Préau, 92852 Rueil-Malmaison Cedex,France; tel. 33-1-47-52-73-50, fax 33-1-47-52-70-22, and [email protected].

Lidunka Voc̀́adlo is aRoyal Society UniversityResearch Fellow and



Great Britain and Ireland.

Voc̀́adlo can bereached at UniversityCollege London, Department of Earth Sci-ences, Gower Street,London, WC1E 6BT,United Kingdom; tel. 44-20-7679-7919, fax 44-20-7679-2685, and e-mail [email protected]. �

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TowardComputational Materials Design ...€¦ · A theory that relates computable quan-tities to macroscopic engineering behavior is a prerequisite in order for DFT calcula-tions