Introduction to atomistic simulations · •T. Schlick“Molecular Modeling and Simulation”...

Introduction to atomistic simulations

Lecture 1

1/22/18

1Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky

MIT 3.320 Atomistic Modeling of Materials Boris Kozinsky 2

Computers are getting smarter


Computer are getting bigger

• Computation emerged as a new science/engineering paradigm

• Computer power up by x1,000 in last decade

• Robust computation and data science methods available

• e-Science: Data-Intensive Scientific Discovery

4

2012: 1TF = 22nm chip1997: 1TF= 72 cabinets

Harvard SEAS AP 275 Atomistic Modeling of Materials Boris Kozinsky

Atomic effects: core of future systems

• Future devices are systems of materials

• Atom-level design for component functionality

• Nano-scale coupling of components

• Complexity impedes rapid progress

• Fundamental interactions are unclear

• Slow progress without understanding

• Understand cause-effect relationships

6

Mobility

Lighting

Sensing

Heat recovery


Why simulate?

• New way of designing materials systems

• Deeper understanding of interacting active material components

• Property prediction without experiments

• Quantum mechanical accuracy

• Rapid rational screening of materials

• Enabled by rapid growth of HPC

7

Structural changes

Phase stability

Reaction energies

System properties:

Electronic conductivity

Voltage

Ionic transport

HPC

Input Parameters:

Chemical composition Atomic arrangement

t

iH

ˆ


Novel carbon bonding at high pressure (80 GPa)

Phase transformation in ferromagnesite (Mg,Fe)CO3

Experiment can be too difficult

8

E. Boulard et al, Nature Communications 2014


Need a virtual microscope / spectroscope

Fingerprinting with computational Raman spectroscopy

9

Molecular identification using a library of signatures

R. Sánchez-Carrera and B. Kozinsky, Phys. Chem. Chem. Phys., 2014,16, 24549


Need a new theory

What enables high ionic conductivity in general?

10

Tet

Undistorted Oct

Distorted Oct

Tet

Undistorted Oct

Distorted Oct

Ionic conductivity vs Li concentration

B. Kozinsky et al, PRL 116, 055901 (2016)

Optimization recipe

1. Reduce Li content

2. Avoid ordered states

Disorder is good


Theory can be too complicated

Resistivity of graphene from first principles

11

Electron-phonon self-energy

Credit: Y. Z. Zhang et al.

C.H. Park et al, Nano Lett 14, 1113 (2014)

qkqkqkq

qkqkqkqq

k qk

mnm

mnmm

mnn

TfTn

TfTngN

T

,1

,,2

,21

electron-phonon matrix element

Bose-Einstein statistics

electron energy phonon frequency


Atomistic simulations in industry

12

20

40

60

80

100

2002 2004 2006 2008 2010 2012

# atomistic groups in industry


Atomistic design in industry

Gummetal® developed at Toyota R&D

• Ab-initio models used to predict the effect of crystal structure, valence electrons density of states on material stiffness

• Super elasto-plastic Ti alloy is licensed for manufacturing and distribution

Virtual Aluminum Casting at Ford

• Predictions of microstructure and intermetallic phase morphology based on atomistic and FEM modeling

• New Al-Si-Cu alloy composition used in engine blocks

• $15M investment in methods results in $100M savings

13

Evolution of ’ precipitates in Al-Si-Cu:

Simulation Experiment

Strength vs. stiffness and applications:


Atomistic design in industry

Hard disk drives at Seagate Technology

• Material development towards enhanced magnetic anisotropy and saturation needed to increased record density of hard disk drives

• Tetragonally distorted FeCo alloys were identified using ab-initio computations

14

Magnetic anisotropy and saturation:


Materials Genome Initiative

• $100M US President’s initiative announced in 2011

• Goal: 50% reduction of cost and time to develop and commercialize new materials

• Focus on computational tools in materials engineering

• Computational materials screening

• Big data management

• Accelerate by closely coupling to experiments


Need a better candidate material

Screening for better thermoelectrics with first-principles methods

16

$350/kg 15 years

15 months

$40/kg

conventional

computational

timecost

ZT = 0.9

ZT = 1.1

performance

G.Joshi, et al, Energy and Env. Sci, 7, 4070 (2014)B. Kozinsky et al, Patent Application 2015148493A1 (2015)


Which properties are determined on atomic scale?

17

MicroscopicAtomic Componentscale

Ab-initio Meso-scale Continuum

strength, reliability

battery energy

electronic conductivity

Ionic conductivity

magnetic energy

surface reactivity


Scales of materials simulation

18

Atomistic dynamics

Batteries

Domain phase fields

Electrochemistry

Micro-mechanics

Fuel Cells

Magnets

Photovoltaics

Thermoelectrics

Piezoelectrics

Films, Coatings

Alloys

Plastics

Inter-grain transport

Nanostructures

MicroscopicAtomic Componentscale

Mo

de

ling

app

roac

he

s

Discovery, design Optimization


Atomistic materials design applications

19

Photovoltaics Piezoelectrics

High-k ceramicsLi batteriesCoatings

Thermoelectrics

Atom-driven systems

Sensors

Steel

NanostructuresMotors


Atomistic modeling zoo

20

Accuracy, transferability

Co

mp

uta

tio

n s

pe

ed

Classical pair potentials

Reactive force fields

GW

Correlated wavefunction

DFT

Quantum Monte Carlo

Large systems

Small systems

Hartree-FockTD-DFT

“first-principles, ab-initio”

102-103 atoms

105-108 atoms

10 atoms

“empirical, classical”

Many-body potentials


Computable properties

21

Crystal structure of solids, bulk modulus

Reaction energies, electrochemical voltages

Thermodynamic phase stability

Dielectric properties, piezoelectric coefficients

Vibrational spectra

Thermo-mechanical properties, heat capacity, expansion

Ionic transport, molecular dynamics

Raman spectra, NMR spectra

Electronic conductivity, electron-phonon coupling

Thermal conductivity, phonon-phonon scattering

Optical excitations, photoelectricity

Co

mp

uta

tio

n c

om

ple

xity

1 hour

1 day

1 week

1 month


22

Understand

Compute

Simplify

Automate

Validate

Design


Course Information

Objective: The class is aimed at beginning graduate students and will introduce a variety of atomistic simulation methods used in different fields of materials science

Instructor: Boris Kozinsky (MD 347, [email protected] )

Organization: 90 minute lectures with some lectures replaced by an in-class lab

Time/place: Mon and Wed, 10am-11.30pm, Room MD 323

Teaching Assistants: TBD

Web site: https://canvas.harvard.edu/courses/36431

Grade: ≈ 5 lab assignments + final project, NO EXAMS

Registration: All students are required to register for credit


Course Objectives

• Teach the tools of modern computational materials science at the atomistic level

• Evaluate common methods and their applicability to diverse materials problems

• Review materials theory, physics and chemistry as is required to understand the basis for a particular method

• Provide overview of algorithms with broad applicability

• Teach hands-on practical skills for computational materials science (Linux, Python)

• Establish basis for independent research in materials computations


Schedule


1 M 1/22/18 Introduction to Atomistic simulation

2 W 1/24/18 Potentials, Supercells, Relaxation

M 1/29/18 No class

3 W 1/31/18 Numerical aspects. Periodicity.

4 F 2/2/18 Lab 1: Energetics and structure with empirical potentials

5 M 2/5/18 QM review

6 W 2/7/18 First principles Energy Methods: Hartree-Fock, SCF

7 M 2/12/18 Beyond HF, Intro to DFT

8 W 2/14/18 Crystals, plane wave basis

M 2/19/18 President's day

9 W 2/21/18 Lab 2: Density Functional Theory I

10 M 2/26/18 Case studies of DFT. Properties and accuracy

11 W 2/28/18 Advanced DFT. New developments and alternative algorithms

12 M 3/5/18 Lab 3: Density Functional Theory II

13 W 3/7/18 DFT continued

Schedule


M 3/12/18 spring break

W 3/14/18 spring break

14 M 3/19/18 Finite temperature: Review of Stat Mech and Excitations

15 W 3/21/18 Molecular Dynamics formalism

16 M 3/26/18 Molecular Dynamics: technical aspects

17 W 3/28/18 MD applications, transport phenomena

18 M 4/2/18 Lab 4: Molecular Dynamics II

19 W 4/4/18 Transitions, energy landscapes, free energy

20 M 4/9/18 Monte Carlo

21 W 4/11/18 Lab 5: Monte Carlo

22 M 4/16/18 Lattice models

23 W 4/18/18 Cluster expansions and KMC

24 M 4/23/18 Case studies, materials design

25 W 4/25/17 Project presentations

Survey

https://www.surveymonkey.com/r/5NP28K8


Lab logistics

• Install Oracle VirtualBox on your laptop• https://www.virtualbox.org/wiki/Downloads• Linux Mint 18.1 Xfce (preconfigured VM image will be provided)• https://www.linuxmint.com/edition.php?id=230

• Google Cloud computing resources will be provided

• Remember basic Linux commands• http://linuxcommand.org/

• Learn Python• https://www.programiz.com/python-programming• http://hetland.org/writing/instant-python.html

• Detailed setup instructions will be posted on website


General Literature

• F. Jensen, " Introduction to Computational Chemistry", Wiley.

• D. Frenkel and B. Smit, "Understanding Molecular Simulation", Academic Press.

• M.P. Allen and Tildesley, "Computer Simulation of Liquids", Oxford Science Publishers

• R. Phillips, "Crystals, Defects and Microstructures", Cambridge University Press.

• J.M. Thijsen, "Computational Physics", Cambridge University Press.

• T. Schlick “Molecular Modeling and Simulation” Springer

• Leach, “Molecular Modelling: Principles and Applications”, Prentice Hall

• Haile, “Molecular Dynamics Simulation: Elementary Methods”, Wiley Professional

• Tuckerman, “Statistical Mechanics: Theory and Molecular Simulation”, Oxford University Press

• Specific references will be provided per topic


Can we decouple ions from electrons?

Separation of time scales

Born Oppenheimer (adiabatic) approximation:For a System characterized by wavefunction and atomic configuration

every atomic configuration electrons are in their ground state

When is adiabatic approximation not valid?

Temperature (OK if excitations are fast on nuclear motion time scale)

Long lived excitations (two BO surfaces in semiconductors)

Coupling of nuclear and electron degrees of freedom

30

E(R i) min E(

R i , )

iR

410/ Mme


Example of Born-Oppenheimer violation

• Strong coupling between electron and nuclear coordinates for phonons with q ~ 2kF (Kohn anomaly)

31

Shift of Raman frequency with doping of a single graphene layer

Non-adiabatic modelAdiabatic (BO) DFT


What is the simplest atomistic model

32

One type of atom

Hard core repulsion

Can describe nanoparticle colloids

Exhibits solid-liquid phase transitionB. J. Alder and T. E. Wainwright, J. Chem. Phys. 27, 1208 (1957)

First ever MD publication

Not so good for atoms


• Bonding and anti-bonding states form in locally overlapping electron orbitals

• Inert shells can still interact via dipole-dipole interactions

Atomic interaction is often local

33

H H

H H

He He


Pair potentials forms

• Pairwise energy summation

• Attractive at long range

• Repulsive at short range (caution at high speed)

• Usually requires a cutoff• Watch out for discontinuous forces

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)(2

10 j

jii RRVEE


Lennard-Jones: a simple two-parameter form

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V(r) A

r12

B

r6

V(r)

r

12

2

r

6

When expressing Temperature, Pressure and Density in renormalized units all LJ systems are identical

is unit of energy scale is unit of length

3

3

1:Density

:Pressure

:eΤemperatur

Bk


First MD simulation with a continuous potential

500-atom simulation was performed on an IBM 704


Other potential forms

Morse potential

Born-Mayer/Buckingham

Many other potential forms are used

37

201)( rreDrV

86)(

r

D

r

CAerV Br

C-H stretch energy in methane

Figure from Jensen


Applications

Applications of potentials to oxides, metals, organics

Applicability of pair potentials Embedded Atom Method (EAM)

Many-body potentials for Si

Electrostatic interaction, ionic crystals

Force fields for organic compounds

Recent developments


Pair potential forms

Morse potential

Born-Mayer/Buckingham

Potentials can be wrong because of parameters or functional form (physics)

OK for noble gases (Ar, He)

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201)( rreDrV

86)(

r

D

r

CAerV Br

Pauli repulsion

dipole-dipole interactions


Numerical aspects

Computational speed 104-106 faster than DFT

Short-range potentials can be cut off (and shifted)

Keep fixed or updated neighbor lists

Reduce computation cost scaling from N2 to N

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Total energy

Force


Potentials enable large simulations

https://www.youtube.com/watch?v=Wr7WbKODM2Q

9 Billion atoms

200,000 cpus (IBM BlueGene at LLNL)

2 ns of time (1M steps)

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https://arxiv.org/abs/0810.3037


Which of these green atoms has the highest bonding energy?

Which of these molecules has the lowest energy/atom?

Tendency to form close-packed structuresPrefer high coordination number (many bonds)

Energy depends on the number of bonds

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No angular dependenceproblem for localized covalently bonded materials

)(2

10 j

jii RRVEE


Crystal issues

Pair Potentials cannot predict crystal structures in metals or covalent solids

fcc - bcc energy difference can be shown to be “fourth moment” effect (i.e. it needs four-body interactions)

No stability against shear. Lack of Cauchy Pressure

Shear elastic constants C12 = C44 for any pair potential


Introduction to atomistic simulations · •T. Schlick“Molecular Modeling and Simulation”...

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Transcript of Introduction to atomistic simulations · •T. Schlick“Molecular Modeling and Simulation”...