Computer-Aided Molecular Modeling of Materials Instructor: Yun Hee Jang MSE 302, 2323) TA: Eunhwan Jung MSE 301, 2364) Web: Reference: - D. Frenkel & B. Smit, Understanding molecular simulations, 2nd ed. (2002) - M. P. Allen & D. J. Tildesley, Computer simulation of liquids (1986) - A. R. Leach, Molecular modeling: principles and applications, 2nd ed. (2001) - and more Grading: - Homework: reading page summary - Exam or Term report: Mid-term & Final - Hands-on computer labs (report & presentation) - Presence & Participation (questions, answers, comments, etc.)

Why do we need a molecular modeling (i.e. computer simulation at a molecular level) in materials science? N (number of atoms) or L (size) of a system of interest) Difficulty (cost, time, manpower, inaccuracy) Molecular simulation in virtual space Experiment in real space Traditional (Past) Materials science N~10 23, L~10 cm Experiment didn’t need simulation. too hard easy Emerging (future) Materials science N~10 2, L~10 nm Simulation will lead. easy hard

1918 – Physics – Max Planck – Quantum theory of blackbody radiation 1921 – Physics – Albert Einstein– Quantum theory of photoelectric effect 1922 – Physics – Niels Bohr – Quantum theory of hydrogen spectra 1929 – Physics – Louis de Broglie – Matter waves 1932 – Physics – Werner Heisenberg – Uncertainty principle 1933 – Physics – Erwin Schrodinger & Paul Dirac – Wave equation 1945 – Physics – Wolfgang Pauli – Exclusion principle 1954 – Physics – Max Born – Interpretation of wave function 1998 – Chemisty – Walter Kohn & John Pople 2013 – Chemisty – Martin Karplus, Michael Levitt, Arieh Warshel Nobel Prize History of Molecular Modeling Quantum Mechanics Quantum Chemistry Classical Molecular Simulation

Review of Nobel Information 2013 Chemistry -Simulation or Modeling of molecules (in materials) on computers -Classical (Newtonian) physics vs. Quantum (Schrodinger) physics -Quantum description of atoms and molecules: electrons & nuclei -Strength: applicable to describe electronic (photo)excitation -Strength: interatomic interactions described “naturally” -Strength: chemical reactions (bond formation/breaking) -Weakness: slow, expensive, small-scale (N < K -Classical description of atoms and molecules: balls & springs -Strength: fast, applicable to large-scale (large N) systems -Strength: close to our conventional picture of molecules -Strength: easy to code, free codes available, finite T -Weakness: interatomic interactions from us (force field) -Weakness: no chemical reactions, no electronic excitation -Application: structural, mechanical, dynamic properties

Quantum vs. Classical description of materials With reasonable amount of resources, larger-scale (larger-N) systems can be described with classical simulations than with quantum simulations. Quantum simulation in virtual space N (number of atoms) or L (size) of a system of interest) Difficulty (cost, time, manpower, inaccuracy) Experiment in real space easy hard Classical simulation in virtual space

First-principles Quantum Mechanics QM MD Large-scale Molecular Dynamics - Validation: DFT + continuum solvation - Reaction: solvent molecule + CO 2 complex - Validation: Interatomic potential (Force Field) - Viscosity, diffusivity distribution: bulk solvent Monte Carlo Process Simulation MC - Grand Canonical (GCMC) or Kinetic (KMC) - Flue gas diffusion & Selective CO 2 capture Example of multi-scale molecular modeling: CO 2 capture project

solvent (PzH 2 ) PzH 2 + -CO 2 - PzH-CO 2 H PzH 2 (regener) PzH 2 + CO 2 - PzH 3 + PzHCO 2 - +CO 2 +PzH 2 PzH 3 + Pz(CO 2 ) 2 2- PzH 3 + -CO 2 PzH + -2CO 2 - +CO 2 Piperazine PzH 3 + HCO kcal/mol (MEA) 7.8 O H N C 7 Step 1: Quantum: Reaction

Quantum simulation Example No. 2: Pd 촉매 반응, UV/vis spectrum 재현, 유기태양전지 효율 저하 설명 TS1 I1 TS2I2 TS3 I3 Pd+ 22BI Pd+ +2BI gone! PCE 3.1% PCE 0.4% EX EX EX1 2.99

What quantum/classical molecular modeling can bring to you: Examples. Reduction-oxidation potential, acibity/basicity (pK a ), UV-vis spectrum, density profile, etc. J. Phys. Chem. B (2006) J. Phys. Chem. A (2009, 2001), J. Phys. Chem. B (2003), Chem. Res. Toxicol. (2003, 2002, 2000), Chem. Lett. (2007) cm -1 J. Phys. Chem. B (2011), J. Am. Chem. Soc. (2005, 2005, 2005)

Step 2: Classical: 2-species (AMP and PZ) distribution in water Which one (among AMP and PZ) is less soluble in water? Which one is preferentially positioned at the gas-liquid interface? Which one will meet gaseous CO 2 first? Hopefully PZ to capture CO2 faster, but is it really like that? Let’s see with the MD simulation on a model of their mixture solution!

제일원리 다단계 분자모델링 ► 물질구조 분자수준 이해 ► 선험적 특성 예측 ► 신물질 설계 ► 물질특성 향상 2. 고전역학 분자동력학 모사 ( 컴퓨터 구축 10 2 ~10 7 개 원자계의 뉴턴방정식 풀기 ) - 전자 무시, ball ( 원자 ) & spring ( 결합 ) 모델로 분자 / 물질 표현 ( 힘장 ) - Cheap ► 대규모 시스템에 적용, 시간 / 온도에 따른 구조 / 형상 변화 모사 1. 양자역학 전자구조 계산 ( 컴퓨터 구축 10 1 ~10 3 개 원자계 슈레딩거방정식 풀기 ) - 정확, 경험적 패러미터 불필요, 제일원리계산, but expensive ► 소규모 시스템 MULTI SCALE MODELING MD atomistic molecular QM electronic structure KMC charge- transport CGMD coarse- grained FF snapshot CG-FF nanoscale morphology transport parameter understanding new design prediction test validation EXPERIMENT synthesis fabrication characterization First-principles multi-scale molecular modeling

I Spring: Elements of Quantum Mechanics (QM) - Birth of quantum mechanics, its postulates & simple examples Particle in a box (translation) Harmonic oscillator (vibration) Particle on a ring or a sphere (rotation) II Fall: Quantum Chemistry - Quantum-mechanical description of chemical systems One-electron & many-electron atoms Di-atomic & poly-atomic molecules III Spring: Classical Molecular Simulations of materials - Large-scale simulation of chemical systems (or any collection of particles) Monte Carlo (MC) & Molecular Dynamics (MD) IV Fall: Molecular Modeling of Materials (Project-oriented class) - Application of a combination of the above methods to understand structures, electronic structures, properties, and functions of various materials Lecture series I-IV: Molecular Modeling of Materials

P T A typical experiment in a real (not virtual) space 1.Some material is put in a container at fixed T & P. 2.The material is in a thermal fluctuation, producing lots of different configurations (a set of microscopic states) for a given amount of time. It is the Mother Nature who generates all the microstates. 3.An apparatus is plugged to measure an observable (a macroscopic quantity) as an average over all the microstates produced from thermal fluctuation. P T How do we mimic the Mother Nature in a virtual space to realize lots of microstates, all of which correspond to a given macroscopic state? How do we mimic the apparatus in a virtual space to obtain a macroscopic quantity (or property or observable) as an average over all the microstates? P T

microscopic states (microstates) or microscopic configurations under external constraints (N or , V or P, T or E, etc.)  Ensemble (micro-canonical, canonical, grand canonical, etc.) Average over a collection of microstates Macroscopic quantities (properties, observables) thermodynamic –  or N, E or T, P or V, C v, C p, H,  S,  G, etc. structural – pair correlation function g(r), etc. dynamical – diffusion, etc. These are what are measured in true experiments. they’re generated naturally from thermal fluctuation In a real-space experimentIn a virtual-space simulation How do we mimic the Mother Nature in a virtual space to realize lots of microstates, all of which correspond to a given macroscopic state? By MC & MD methods! it is us who needs to generate them by QM/MC/MD methods.