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Computational Approaches to Materials Science Modeling at

the Atomistic Scale

Invited Speaker Presentation at ICCST & CADD 2016

3th November 2016De baron Hotel Langkawi

byYoon Tiem Leong,

School of Physics, USM

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Abstract

Modelling using state-of-the-art computational approach is a convenient yet very powerful way to complement experimental studies on material systems. Materials at the atomistic level in particular can be studied using various computational approaches based on different theoretical foundations, such as Quantum Monte Carlo, Density Functional Theory, Monte Carlo, Molecular Dynamics and Density Functional Tight-Binding. A brief introduction to these computational methodologies will be presented in this talk, along with some exemplifying systems studied via these approaches to illustrate the usefulness of this methodology in studying simple materials system

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Biomolecules/Drugs Design/Proteins/ …

Quantum Chemistry

Materials Physics – Electronic Structures / Response Functions (e.g., Dielectric Response Functions/ Born effective charge/ Spontaneous polarization), Phonon modes and frequencies / Heat Properties / Charge Transport Properties / Magnetic Properties / Mechanical Properties / Electrical Conductivity / …

Differences in Systems of Interest

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Compute, study, manipulate, predict, and ultimately design physical properties at atomic level using computers

Aims of Computational Modelling of Materials

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Classical vs. Ab-initio

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Quantum Monte Carlo

Density Functional

Theory

Density Functional

Tight-Binding

Molecular Dynamics

Computational Methods

Ab initio methods Empirical

method

“Empirical” ab

initio method

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Finite vs Periodic Systems

•Bulk crystalline systems

•Thin films

•2D nanostructures

•Nano clusters

•Quantum dots

•Biomolecules

•Polymer

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Periodic Systems

•Unit cell

•Space group

•Lattice parameters

•Basis atoms

•Periodic boundary condition

•Plane-wave basis set

•k-point

Finite Systems

•No unit cell

•Point group

•No lattice parameters

•Coordinates of all atoms

•Terminated boundary condition

•Gaussian-orbital basis sets

•k-point is Irrelevant

Finite vs Periodic Systems, from Computational Point of View

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•BaTiO4 in Tetragonal phase C60

Illustration of Finite and Periodic Systems

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DFT

DFT calculates the electronic density of ground state energy of a system from first-principles by approximating the Schrodinger equation via a Nobel-Prize winning scheme, KS equations.

Everything else is derived from the ground state energy and the electron density

MD

Calculates atomic forces and system energy by approximating the atoms as classical particles. The potentials are usually calculated from semi-empirical relations fitted against empirically measured data. The fitted functions don't necessarily have clear physical meaning.

DFT vs MD

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Pros

•Electronic structures

•Ab-initio: No empirical input required

Pros

•Orders of magnitude faster than DFT.

•Can handle large system, ≳ 106

•Details of evolution and dynamics in real time can be revealed

DFT vs MD

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Cons

•Computationally expensive

•Smaller simulation size

•No real-time dynamics

•XC functions may be inaccurate, eps. for strongly correlated systems

Cons

• Strongly dependent on availability of accurate classical potentials

• Only non-quantum properties can be evaluate (e.g., thermodynamicalproperties, mechanical)

DFT vs MD

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principles, augmented with DFT pre-calculated data

Parametrized DFT – Band structure energy, charge fluctuation energy, repulsion energy

SF files

2 order faster than DFT

Contender to DFT but relatively

DFTB

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Software

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QMC, DFTB, DFT or MD?

Depends on what systems and

what you want to know from

the system, and

How rich you are

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Structural Optimisation

• Input structure has to be optimized before deriving physical properties from it.

• Assure that the structures are stable and at their lowest energy state by performing structural optimization on the initial structures.

• An incorrect ground state structure could cause a totally different thermal properties!

• Initial input structures – from existing literature/experiment/data bases

• In many cases, the ground state structures are generally unknown – global minimization search algorithm is required.

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Random initial structure

Relaxation of initial structure

Stopping criteria

Relaxation of coordinate

Global optimization

Local optimization

Local optimization

Move strategies:Basin Hopping, Genetic algorithm, …

Global Minimisation Search Algorithm for Optimised Structure

Globally optimized structure

Energy calculator

(DFT, MD, DFTB, …)

Used for subsequent calculation: melting (MD), magnetic moment (DFT), etc

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Global minimum search algorithms

•PTMBHGA - Parallel Tempering Multicanonical Basin Hopping Genetic Algorithm (from NCU, Taiwan), for binary clusters

•USPEX – Genetic Algorithm for periodic ternary alloy systems

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Search for ground states of clusters

•Could be a non-trivial matter

•Especially difficult for multi-atom type clusters

•Two-stage approach vs one-stage approach to locate DFT-level ground states

•Physical properties of clusters display interesting size-dependence behaviour

Lowest-Energy Configurations of Rhodium Clusters

Lowest-Energy Configurations of Rhodium Clusters

Molecular Orbital energy of Rh dimer from unrestricted HF

Magnetic Property of Rhodium Clusters via DFT

Plot of averagemagnetic moment ofRh clusters againstcluster size, while thevalues of the isomersof Rh4, Rh6 and Rh22

are indicated by thered rhombus in theplot.

Molecular Symmetry of Rh clusters

The graph comparessymmetry order of initial(green) and optimized(red) configurations of Rhclusters, while the valuesof the isomers areindicated by orangetriangle and blue crosssymbols respectively.

Molecular Symmetry vs. magnetization

The graphs displays theaverage magnetic moment(grey) and symmetry order(blue) of optimized Rhclusters against cluster size,while the values of theisomers of are indicated bythe orange dot and redcross symbols respectively.

Melting of Hf clusters

Hf13Hf7

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“Prolonged heating”

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Global Similarity index

𝑀𝑝 𝑥1, … , 𝑥𝑛 =1

𝑛

𝑖=1

𝑛

𝑥𝑖𝑝

1𝑝

𝜉𝑖𝐶𝑂𝑅 =

1

𝑛

𝑠=1

𝑛

𝑘𝑠,𝑖𝐶𝑂𝑅 + 1

−1

𝑘𝑠,𝑖𝐶𝑂𝑅 = 𝑑𝑠,𝑖

𝐶𝑂𝑅 − 𝑑𝑠,0𝐶𝑂𝑅

ҧ𝜉𝑖 =1

3𝑛

𝐶𝑂𝑅

𝑠=1

𝑛

𝑘𝑠,𝑖𝐶𝑂𝑅 + 1

−1

𝑆𝜉𝑖 ∝ 𝜎2 𝜉𝑖

“Indicator”

• Capture the global

geometry of a cluster by

comparing it to a reference

structure

• Provide detailed

information in the change

of the geometric

configuration of cluster

throughout a MD heating

process

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Global Similarity index

Link to simulation:

hf13.vlc

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of Hf clusters

Submitted to Journal of Chemical Information and Modeling. Under review.

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Growth of graphene on SiC substrate

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Building Buckled Silicene Sheet

Finding a FF that works: COMB

Melting of Silicene

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Mechanical strength of Double-walled BN nanotube

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Structural Prediction of ternary AlxIn1-xN Alloy

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Ternary alloy AlInN

Figure 2. Unit cells and structures of (a)

Al4In2N6 (Cmc21), (b) Al3In3N6 (Cm/Am), (c)

Al2In4N6 (Cc/Aa), (d) Al6In2N8 (P21), (e)

AlIn7N8

(P3m1) and (f) Al5InN6 (P31m) at

atmospheric pressure. Large blue,

medium green and small amber spheres

represent indium, aluminium and nitride

ions.

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ε(ω) = ε1 (ω) + iε2(ω)

Dielectric response function of AlxIn1-xN Alloy

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Computational Physics subgroupSchool of Physics, USM

Group Leader: Yoon Tiem Leong

Main collaborators: Prof. S. K. Lai (National Central University, Taiwan).

Dr. Lim Thong Leng (Multimedia University, Melaka Campus)

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Computational Physics subgroupSchool of Physics, USM

Graduate students:

1. Min Tjun Kit

2. Soon Yee Yeen

3. Ong Yee Ping

4. Goh Eong Sheng

5. Puvanesvari Rajan

6. Robin Chang Yee Hui

7. Lee Thong Yan

8. Siti Harwani bt Md Yusoff

9. Koh Pin Wai

10. Lian Ming Huei

11. Yusuf Zuntu

12. Ng Wei Chun

13. Pauline Yew*

14. Baharak Mehrdel*

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Research topics Computational Physics subgroup

1. Extended Hubbard Model for High Tc

Superconducting Cuprates (QMC)

2. Ferroelectric oxide (DFT)

3. III-Nitride Ternary Alloy (DFT)

4. Rhodium clusters (DFT)

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Research topics Computational Physics subgroup

5. Hf clusters (DFT cum MD)

6. Ternary nanoclusters (DFT cum MD)

7. Atomistic simulation of silicon- and carbon-

based clusters (DFTB)

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Research topics Computational Physics subgroup

8. MD simulation of epitaxial graphene

formation on SiC substrate (MD)

9. Melting and breaking of nanostructures

10.Nano wetting of LJ particles (MD)

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We acknowledge Prof. S. K. Lai of National Central University, Taiwan, for his kind courtesy to provide and allow us to use the PTMBHGA code his group developed.

Universiti Sains Malaysia RU grant (No. 1001/PFIZIK/811240) is acknowledged

Acknowledgement

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•Yusuf Zuntu Abdullahi, Yoon Tiem Leong, Mohd Mahadi Halim, Md. Roslan Hashim, Mohd. Zubir Mat Jafri, Lim Thong Leng, Mechanical and electronic properties of graphitic carbon nitride sheet: First-principles calculations, Solid State Communications 248 (2016) 144–150

•E. S. Goh and L.H. Ong and T.L. Yoon and K.H. Chew, Structural relaxation of BaTiO3 slab with tetragonal (100) surface: Ab-initio comparison of different thickness, Current Applied Physics 16 (2016) 1491 – 1497

List of publications

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• Y.H. Robin Chang, T.L. Yoon, T.L. Lim, Ab initio computations of the linear and nonlinear optical properties of stable compounds in Al-In-N system, Current Applied Physics 16 (2016), 1491–1497

•Yee Hui Robin Chang, Tiem Leong Yoon, Thong Leng Lim and Maksim Rakitin, Thorough investigations of the structural and electronic properties of AlxIn1-xN ternary compound via ab initio computations, Journal of Alloys and Compounds 682 (2016) 338 - 344

List of publications

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•Yusuf Zuntu Abdullahi, Yoon Tiem Leong, Mohd Mahadi Halim, Md. Roslan Hashim, Mohd. Zubir Mat Jafri, Lim Thong Leng, Geometric and electric properties of graphitic carbon nitride sheet with embedded single manganese atom under bi-axial tensile strain, Current Applied Physics, 16 (2016) 809–815

•E.S. Goh, L.H. Ong, T.L. Yoon and K.H. Chew, Structural and response properties of all BaTiO3 phases from density functional theory using the projector-augmented-wave methods, Computational Materials Science, 117 (2016) 306 - 314

List of publications

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•T. L. Yoon, T. L. Lim, T. K. Min, S. H. Hung, N. Jakse, Yoon, Epitaxial growth of graphene on 6H-silicon carbide substrate by simulated annealing method, The Journal of Chemical Physics 139 (2013) 204702

List of publications

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Thank you

Presented byYoon Tiem Leong | School of Physics