Electronic-structure theory for data-driven materials discovery
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1 Monday, July 31: Tuesday, August 1: Wednesday, August 2: Thursday, August 3: Friday, August 4: Electronic-structure theory for data-driven materials discovery Implementing DFT Periodic systems Benchmark data and sampling Time and length scales Monday, July 31: Tuesday, August 1: Wednesday, August 2: Thursday, August 3: Friday, August 4: Monday, August 7: Tuesday, August 8: Wednesday, August 9: Thursday, August 10: Friday, August 11: Electronic-structure theory for data-driven materials discovery Implementing DFT Periodic systems Benchmark data and sampling Time and length scales Multiscale and machine learning Wavelets, statistical mechanics, and cluster expansion Beyond LDA and GGA (2): Quasiparticle approaches Transport and Reactions The Next Frontiers 1
2 7/31/2017 Berlin at The End of The 19th Century Since 1969 Excursion (Teufelsberg) Since 1793 Dahlem Berlin 1896 Adlershof 5 km Introduction of New Paradigms to Materials Science Knowledge in Basic Science and Engineering 1st paradigm: Empirical Science 3rd paradigm: Computational Science (Simulations) 2nd paradigm: Theoretical Science (Laws and Models) 4th paradigm: Big-DataDriven Science ΔU = Q W add figures add figures Materials Discovery from Electronic Structure Change in Heat Work internal added done energy to system by system Laws of clasdetection of sical mechadensity-funcpatterns and nics, electrodymatthias Scheffler tional theory anomalies in namics, ther- der Max-Planck-Gesellschaft Fritz-Haber-Institut and beyond, Big Data; modynamics, Berlin, Germany molecular machine learquantum Experiments dynamics ning, etc. mechanics year 2
3 Introduction of New Paradigms to Materials Science 1 st paradigm: Empirical Science Experiments Knowledge in Basic Science and Engineering 2 nd paradigm: 3 rd paradigm: Theoretical Computational Science (Laws Science and Models) (Simulations) ΔU = Q W Change in internal energy Heat added to system Work done by system Laws of classical mechanics, electrodynamics, thermodynamics, quantum mechanics add figures Density-functional theory and beyond, molecular dynamics 4 th paradigm: Big-Data- Driven Science add figures Detection of patterns and anomalies in Big Data; machine learning, etc year The Novel Materials Discovery (NOMAD) Laboratory maintains the largest Repository for input and output files of all important computational materials science codes. From its open-access data it builds several Big-Data Services helping to advance materials science and engineering. Watch a 3-minute summary on the NOMAD Laboratory CoE NOMAD Scope and Overview Data is a crucial raw material of the 21st century. Surprisingly, extreme-scale aspects of Big-Data are very much under-explored in materials science and engineering, one reason being that towards 3
4 The NOMAD CoE Scope, Structure, Content The NOMAD Repository accepts /requests in- and output files of all important codes. Currently, the NOMAD Repository contains > 39 million total-energy calculations. Code-Independent Archive Encyclopedia Repository HPC Big-Data Analytics Visualization 4
5 Log 10 # Total-Energy Calculations ASAP ATK CASTEP CP2K CRYSTAL dl-poly dmol-3 exciting FHI-aims Gaussian GPAW libatoms Molcas NWChem ORCA Q-E qbox turbomole VASP WIEN2k 7/31/2017 Visualization Two examples: CO 2 activation Exciton in LiF 1) Prepare your VR glasses 2) Get your smart phone Outreach Videos You may also try the true VR VIVE SYSTEM here at the HU. The NOMAD CoE Scope, Structure, Content Repository Code-Independent Archive Visualization HPC Encyclopedia Big-Data Analytics The NOMAD Archive 90% of the VASP files are from AFLOWlib S. Curtarolo and OQMD 2 0 C. Wolverton. Codes with more than 100 uploads 5
6 The Big-Data Challenge Volume (amount of data), Variety (heterogeneity of form and meaning of data), Velocity at which data may change or new data arrive, Veracity (uncertainty of quality). (Big) Data of materials does not only provide direct information but the data is structured. until recently Volume (amount of data), Query and read out what was stored; highthroughput screening. The Big-Data Challenge Variety (heterogeneity of form and meaning of data), Velocity at which data may change or new data arrive, Veracity (uncertainty of quality). 6
7 Request by colleagues form industry Give guidelines about Date for special issues missing Analyzing and estimating error bars from high-accuracy references m mm μm nm the base space densityfunctional theory (and beyond) ab initio Molecular Electronic Dynamics Structure Theory Predictive modeling and simulations must address all time and space scales Master Equation (ab initio kinetic Monte Carlo) Continuum Equations, Rate Equations and Finite Element Modeling this is what we want (need) time fs ps ns μs ms s hours years We need robust, error-controlled links with knowledge of uncertainty between the various simulation methodologies 7
8 Modeling Materials Properties and Functions: The Many-Body Schrödinger Equation With: 1, Modeling Materials Properties and Functions: The Many-Body Schrödinger Equation With: 1, 8
9 Modeling Materials Properties and Functions: The Many-Body Schrödinger Equation With: 1, Dirac: 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. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation. Proceedings of the Royal Society of London. Ser. A, Vol. 123, No. 792 (6 April 1929) Modeling Materials Properties and Functions: The Many-Body Schrödinger Equation With: 1,??? 9
10 Born-Oppenheimer Approximation Where Φ ν are solutions of the electronic Hamiltonian : ({r k }) ({r k }) = ({r k }) frequently (commonly) applied approximations: neglect non-adiabatic coupling (terms of order m/m I ) keep only Λ 0 the dynamics of electrons and nuclei decouple The BO Approximation does not account for correlated dynamics of ions and electrons. For example: polaron-induced superconductivity dynamical Jahn-Teller effect at defects in crystals some phenomena of diffusion in solids temperature dependence of band gaps non-adiabaticity in molecule-surface scattering and chemical reactions relaxation and transport of charge carriers (e or h) etc. Some Limits of the Born-Oppenheimer Approximation 10
11 Some Limits of the Born-Oppenheimer Approximation The BO Approximation does not account for correlated dynamics of ions and electrons. For example: polaron-induced superconductivity dynamical Jahn-Teller effect at defects in crystals some phenomena of diffusion in solids temperature dependence of band gaps non-adiabaticity in molecule-surface scattering and chemical reactions relaxation and transport of charge carriers (e or h) etc. The Total Energy e.g. from DFT (see later) a classical term <Λ 0 T ion Λ 0 > E tot NM zero point energy cohesive energy a 0 + a The total energy per atom without zero-point vibrations as a function of the inter-atomic distance: the Born-Oppenheimer surface. The measured inter-atomic distance is the average over the positions of vibrating atoms. a 0 lattice parameter 11
12 H e Φ = E Φ Density-Functional Theory The Hohenberg-Kohn Theorem (1964) n(r) = n[φ] = Φ (r r i ) Φ i Set of non-degenerate groundstate wave functions Φ of arbitrary N-electron Hamiltonians. The dashed arrow is not possible. Thus, here is a one-to-one correspondence between Φ N and n(r). E = Min E v [n(r)] Set of particle densities n(r) belonging to non-degenerate N-electron ground states. Comparison Density-Functional of Wave-Function Theory and The Hohenberg-Kohn Density-Functional Theorem Theory (1964) 12
13 Comparison Density-Functional of Wave-Function Theory and The Hohenberg-Kohn Density-Functional Theorem Theory (1964) The Hohenberg-Kohn-Sham Ansatz of Density-Functional Theory Kohn-Sham (1965): Replace the original many-body problem by an independent electron problem that can be solved! E v [n] = T s [n] + v(r) n(r) d3 r + E Hartree [n] + E xc [n] With T s [n] the kinetic energy functional of independent electrons, and E xc [n] the unknown functional. The challenge is to find useful, approximate xc functionals. The existence of a one-to-one relationship does not imply that the xc functional can be written down Walter as Kohn a closed mathematical expression. In fact, it is just an algorithm: n(r) H e E e, Φ N 13
14 Walter Kohn passed away April 19, 2016 at the age of 93 I started with DFT Nobel Prize 1980 Number of articles and patents in materials science including the term density functional theory published per year during the past 25 years. Walter Kohn at West Beach Santa Barbara at age years before DFT invention 34 years after DFT invention 14
15 The xc Functional T s, E Hartree, and E xc are all universal functionals in n(r), i.e., they are independent of the special system studied. (general theory: see the work by Levy and Lieb) ϵ xc-jellium (n) Ceperley and Alder (1980) n E xc-lda = ϵ xc-jellium (n) n(r) d 3 r neglecting is the localdensity approximation The xc Functional T s, E Hartree, and E xc are all universal functionals in n(r), i.e., they are independent of the special system studied. (general theory: see the work by Levy and Lieb) ϵ xc-jellium (n) Ceperley and Alder (1980) n E xc-lda = ϵ xc-jellium (n) n(r) d 3 r neglecting is the localdensity approximation 15
16 accuracy accuracy 7/31/2017 Perdew s Dream: Jacob s Ladder in Density-Functional Theory The exchange-correlation functional our favorite 5 unoccupied ψ i (r), EX + crpa, as given by ACFD 4 occupied ψ i (r), hybrids (B3LYP, PBE0, HSE, ) 3 τ (r), meta-gga (e.g., SCAN) 2 n(r), Generalized Gradient Approximation 1 n(r), Local-Density Approximation τ(r) : Kohn-Sham kinetic-energy density EX: exact exchange: crpa : random-phase approximation for correlation ACFD : adiabatic connection fluctuation dissipation theorem Bohm, Pines (1953); Gell-Mann, Brueckner (1957); Gunnarsson, Lundqvist (1975, 1976); Langreth, Perdew (1977); X. Ren, P. Rinke, C. Joas, and M. S., Invited Review, Mater. Sci. 47, 21 (2012) Perdew s Dream: Jacob s Ladder in Density-Functional Theory The exchange-correlation functional our favorite 5 unoccupied ψ i (r), EX + crpa, as given by ACFD 4 occupied ψ i (r), hybrids (B3LYP, PBE0, HSE, ) 3 τ (r), meta-gga (e.g., SCAN) 2 n(r), Generalized Gradient Approximation 1 n(r), Local-Density Approximation τ(r) : Kohn-Sham kinetic-energy density EX: exact exchange: crpa : random-phase approximation for correlation ACFD : adiabatic connection fluctuation dissipation theorem Bohm, Pines (1953); Gell-Mann, Brueckner (1957); Gunnarsson, Lundqvist (1975, 1976); Langreth, Perdew (1977); X. Ren, P. Rinke, C. Joas, and M. S., Invited Review, Mater. Sci. 47, 21 (2012) 16
17 7/31/2017 The First (Convincing) DFT Calculations Stability of crystals and crystal phase transitions Total energy (Ryd./atom) silicon M. T. Yin and M. L. Cohen PRB 26 (1982) < and PRL 1980 > tin Approximations: LDA, pseudopotentials, diamond neglect of relati-7.92 vistic effects see also: V.L. Moruzzi, J.F. Janak, and A.R. Williams Calculated Electronic Properties of Metals; Pergamon (1978) Volume Valence-Electron Density of Semiconductors a) Ge (top), b) GaAs (middle), and c) ZnSe (lower) in electrons per unit-cell volume. Ga 17
18 7/31/2017 V. L. Moruzzi, J. F. Janak, and A. R. Williams Calculated Electronic Properties of Metals Pergamon Press (1978) Approximations: LDA, muffin-tin approximation, neglect of relativistic effects. Ab Initio Atomistic Thermodynamics Free-Energy Calculations by DFT Exploit thermodynamic equilibria and the concept of thermal reservoirs (atomic chemical potentials). Concentration of defects at finite T Surface structure and composition in realistic environments Order-order and order-disorder phase transitions Equilibrium shape of (nano) crystals Limitations: The accuracy of the xc functional (with respect to kbt) only thermodynamic equilibrium 18
19 Au 13 at Room Temperature visiting many metastable structures Ab initio molecular dynamics Ab Initio Melting Curve of Fe as Function of Pressure 19
20 Significant Progress But Our Knowledge Is Still Close to Zero About 240,000 inorganic compounds have been synthesized so far. Many more are possible. And what do we know? Elastic constants: about 200 compounds Dielectric constant Heat conductance 200 Superconductors 1,000 Topological insulators 3D: 42, 2D: 7 For almost every property we are well below 1% in coverage. Introduction of New Paradigms to Materials Science 1 st paradigm: Empirical Science Knowledge in Basic Science and Engineering 2 nd paradigm: 3 rd paradigm: Theoretical Computational Science (Laws Science and Models) (Simulations) ΔU = Q W The future is already here. Change in Heat Work It is just unevenly distributed. internal added done energy to system by system add figures Laws of classical mechanics, electrody- (*1948), William F. Gibson namics, thermodynamics, Canadian American and fiction writer and quantum essayist Experiments mechanics Density-functional theory and beyond, molecular dynamics 4 th paradigm: Big-Data- Driven Science add figures Detection of patterns and anomalies in Big Data; machine learning, etc year 20
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