CMD WORKSHOP – OSAKA
September 2 - 6, 2019

Introductory LectureonComputational Materials Design
Tamio Oguchi
ISIR, Osaka University

OUTLINE• Materials Design• Computational Materials Design: CMD®
• History of the CMD® Workshop• First-Principles Calculation• Special Features of the Present CMD® Workshop

CMD® is a registered mark by the CMD® consortium.

Materials Design• Goals-Discovery of novel materials with desired property/function-Optimization of property/function that known materials
already possess• An Inverse Problem of Realization
REALIZATIONMaterials

Direct Problem
Properties

Structure
CompositionInverse Problem
DESIGN

Functions

Computational Materials Design: CMD®
• CMD® is the theoretical design/optimization of materials withdesired property/function. Specifically, CMD® involves theefficient use of computational techniques to conduct
calculations based on the basic quantum theory.

• Key Developments of Emerging CMD®
-Quantum Theory of Electrons-Computational Techniques: Methods, Algorithms, and Codes-High-Performance Computers• The purpose of the CMD® Workshop is to provide thefundamental knowledge and techniques needed to enable
materials design by computations.

Quantum Theory of Electrons‣ Band Theory for Crystalline Solids→ Condensed Matter Theory‣ Molecular Orbital Theory for Molecules→ Quantum Chemistry

Quantum Theory of Electrons in Solids — Band Theory
Quantum Mechanics in 1920s(1920s – 1930s) Dawn period: Bloch, Brillouin, Wigner, Seitz, Wannier,Slater, Kohn, Hellmann, Feynman, …
(1940s – 1950s) Development period I: Herring, Slater-Koster, PhillipsKleinman, Korringa-Kohn-Rostoker, …
(1960s) Application period: Ashcroft, Heine, Harrison, Yamashita-WakoAsano, …

(1964-1965) DFT: Hohenberg-Kohn, Kohn-Sham(1970s) Development period II: Andersen, Koelling, Hamann-SchlüterChiang, Ihm-Zunger-Cohen, …
(1980s) Development period III: Car-Parrinello, Weinert, Vanderbilt, …
(1980s – present) First-principles calculations

The 5th Solvay Conference 1927.10“Electrons and photons”

https://en.wikipedia.org/wiki/Solvay_ConferenceQuantum Theory of Electrons in Solids — Band Theory
Quantum Mechanics in 1920s(1920s – 1930s) Dawn period: Bloch, Brillouin, Wigner, Seitz, Wannier,Slater, Kohn, Hellmann, Feynman, …
(1940s – 1950s) Development period I: Herring, Slater-Koster, PhillipsKleinman, Korringa-Kohn-Rostoker, …
(1960s) Application period: Ashcroft, Heine, Harrison, Yamashita-WakoAsano, …

(1964-1965) DFT: Hohenberg-Kohn, Kohn-Sham(1970s) Development period II: Andersen, Koelling, Hamann-SchlüterChiang, Ihm-Zunger-Cohen, …
(1980s) Development period III: Car-Parrinello, Weinert, Vanderbilt, …
(1980s – present) First-principles calculations

Quantum Theory of Electrons in Solids — Band Theory
Quantum Mechanics in 1920s(1920s – 1930s) Dawn period: Bloch, Brillouin, Wigner, Seitz, Wannier,Slater, Kohn, Hellmann, Feynman, …
(1940s – 1950s) Development period I: Herring, Slater-Koster, PhillipsKleinman, Korringa-Kohn-Rostoker, …
(1960s) Application period: Ashcroft, Heine, Harrison, Yamashita-WakoAsano, …

(1964-1965) DFT: Hohenberg-Kohn, Kohn-Sham(1970s) Development period II: Andersen, Koelling, Hamann-SchlüterChiang, Ihm-Zunger-Cohen, …
(1980s) Development period III: Car-Parrinello, Weinert, Vanderbilt, …
(1980s – present) First-principles calculations

Number of publications per year (1975–2014) on topics(“density functional” or “DFT”), according to the Web ofScience Core Collection (February 2015)
Jones (2015)

The Nobel Prize in Chemistry 1998Walter Kohn

John A. Pople

The Nobel Prize in Chemistry 1998 was divided equally between
Walter Kohn "for his development of the density-functional theory"
and John A. Pople "for his development of computational methods
in quantum chemistry".
http://www.nobelprize.org/nobel_prizes/chemistry/laureates/1998/

Quantum Theory of Electrons in Solids — Band Theory
Quantum Mechanics in 1920s(1920s – 1930s) Dawn period: Bloch, Brillouin, Wigner, Seitz, Wannier,Slater, Kohn, Hellmann, Feynman, …
(1940s – 1950s) Development period I: Herring, Slater-Koster, PhillipsKleinman, Korringa-Kohn-Rostoker, …
(1960s) Application period: Ashcroft, Heine, Harrison, Yamashita-WakoAsano, …

(1964-1965) DFT: Hohenberg-Kohn, Kohn-Sham(1970s) Development period II: Andersen, Koelling, Hamann-SchlüterChiang, Ihm-Zunger-Cohen, …
(1980s) Development period III: Car-Parrinello, Weinert, Vanderbilt, …
(1980s – present) First-principles calculations

Growing Power of Supercomputers
Peak Performance (FLOPS)K Computer

Earth SimulatorYearComputational Materials Design Workshop• Background-In 2001-2002, a Specialist Training Project was held at theInternational Institute for Advanced Studies (IIAS) in Kyoto, inthe field of Information Biology. — An active effort to not
merely ensure that the students acquired the target
knowledge but rather to create opportunities for bilateralinterchange with the instructors, with the aim of using thesynergy to train a group of specialists who would become thefuture leaders in these areas.

-Osaka University had many researchers specializing in firstprinciples calculations: Profs. H. Akai, H. Katayama-Yoshida,
H. Kasai, and so on. They launched the “Development ofmethods for computational nano-materials design” computerbased project involving some other researchers in Japanunder the support of JST in 2001.

-Through the receipt of assistance from the JST project, theCMD® Workshop was born in September 2002 as the second
IIAS specialist training project.

1st CMD Workshop at IIAS in September 2002⇧
Morikawa⇧
Yoshida⇧⇧Akai Kasai⇧
Kanamori⇧
Hamada⇧Terakura⇧
NakanishiComputational Materials Design Workshop• Since 2002 the 5-day Workshops have been held twice a year

(spring and autumn) and the 35th Workshop is being witnessed
here.

-Total number of participants (till 34th WS): 1547

‣ Grad. & Undergrad. Students: 906‣ University/College Staffs (incl. National Labs): 261‣ Researchers from campanies: 380

http://phoenix.mp.es.osaka-u.ac.jp/CMD/

Asian CMD® Workshop• Since around 2007, the number of foreigners attending theWorkshop from Southeast Asia has increased. Most of these are
graduate students studying abroad at Osaka University. This
made it difficult to conduct the lectures and hands-on training inJapanese only, and not only the explanatory slides but the oral
explanations came to be presented in both Japanese andEnglish. This style of instruction has continued to these days,
but it has produced problems as well.

• Interchange with people from the Southeast Asian region

through the CMD® Workshop became the inspiration in 2008 forthe start of Asian CMD® Workshop in Southeast Asia. In August
2008, the first Asian CMD® Workshop was held at Institut
Teknologi Bandung in Indonesia. In September 2008, an AsianCMD® Workshop was held at De La Salle University in thePhilippines. In the following year, Asian CMD® Workshops wereheld again in Indonesia and the Philippines, and in Vietnam aswell. In 2010, the number of countries was expanded to four withthe addition of Thailand. It has continued to be held till thesedays.

Asia CMD Workshop @ UKM in 2016

First-Principles Calculations• Provide a way for solving a direct problem by prediction.

PREDICTION
Materials

Direct Problem
Properties

Structure
Composition

Inverse Problem
DESIGN

FunctionsFirst-Principles Calculations★ Starting from first principles, equations are derived under someapproximations and solved for a realistic system.

★ Two main characteristics:- General-purpose: the methods do not depend on material
systems and properties to be studied-Non-empirical: the methods do not require any experimental
parameters and knowledges as input except for fundamental
physical quantities (m, e, h)‣ We may possibly:➡ Predict properties to be compared with experiments➡ Understand underlying microscopic mechanisms➡ Design new materials with desired property/function

First-Principles Calculations• Basic Approximations-Born-Oppenheimer Approx. → Interacting N-electron problem
under external field (nuclear position: structure)-One-electron Approx. → Non-interacting problem‣ Local Density Approximation to Density Functional Theory➡ Kohn-Sham equations to be solved• Band Theory for Crystalline Systems• Real-Space Methods for Nanostructure Systems

Band Theory• Crystal Systems with Periodic Boundary Condition- Bloch Theorem‣ A one-electron quantum-mechanical state in aperiodic potential can be specified with a wave
vector k. → quantum number~r2 + ve↵ (r)2m2Felix Blochkkj (r) = "j1952 Nobel prize

kj (r)

dispersion relation: band structure• Brilloiun Zone: a volume in the k space that includes
all the independent electronic stateskz
2.0kyENERGY(Ry)1.5

1.0.5kx.0

Brillouin zone of fccWLΓXU

band structure of fcc AlΓHow to Solve Kohn-Sham Eq.
• Bloch Theory → Plane Wave Representation- Rigorous but practically intractable• Coulomb Singularity in Potential Terms- Pseudopotential method with plane waves‣ Contributions from core (nucleus and core electron

potentials, and orthogonality to core electron states) arereplaced by a soft (easily Fourier transformed) potential.

-Augmentation method‣ Plane wave basis functions are augmented inside muffintin spheres with localized atomic-like spherical-wavefunctions.

-Green's function method‣ Formulated as a multiple scattering problem andmathematically equivalent to the idea of augmentation
without invoking explicit basis functions

What We Get• Many kinds of physical quantities that can be directly comparedwith experimental observables-Structural properties‣ heat of formation, phonon, elastic constants, thermalexpansion, ...

-Electric properties‣ electric polarization, piezoelectric constants, Born
charges, ...

-Magnetic properties‣ magnetic moments (spin and orbital), magnetic coupling,magnetoanisotropy energy, hyperfine constants, ...

-Optical properties‣ optical constants, absorption spectra, ...
-.....

Structural Properties• Born-Oppenheimer Potential = Total EnergyE({Rn }) = +X

Z n Z n0 e 2+ Ee ({Rn })0|RR|nn
0n>n• Atomic Forces → structural optimization, molecular dynamics
Fn ({Rn }) =rn E({Rn })• Force Constants → phonon, structural stability@2kn↵,n0 ({Rn }) =E({Rn })@Rn↵ @Rn0

Total Energy for a Given Structure and Composition

diamondAl

simple cubicbcc

SifccP

First-Principles Molecular-Dynamics Simulation• Si(111) 7x7 Surface

I. Stich et al. 2002

What We Get• Spin Magnetic Moments- Slater-Pauling CurveExper.

Extension to spin-density functional
E = E [n(r), m(r)]spin density
Spin Moment
Mspin = 2µB

Calc.
= µB

Dederichs et al. JMMM100, 241(1991).

XZjh j |sz | j i

dr m(r)35th CMD® Workshop• Common Lectures- CMD Introductory- Short Talks, Case Study Talks, Special Lecture• Beginners Course- Machikaneyama, STATE-Senri, HiLAPW• Advanced Course- A: Naniwa, ABCAP, RSPACE, Salmon- B: Machikaneyama, ecalj, ES-OPT• Supercomputer Course- STATE-Senri• Spintronics Course- Lectures and Hands-on/Machikaneyama, ecalj, ES-OPT• Materials Informatics Course- CrySPY, LIDG

Hope you enjoy the Workshop
http://phoenix.mp.es.osaka-u.ac.jp/CMD/