1. Quantum Chemistry (Computational Chemistry) Instructor: Yun Hee Jang (yhjang@gist.ac.kr, MSE 302, 2323) Web: http://mse.gist.ac.kr/~modeling/lecture.html Reference: - Quantum Chemistry & Spectroscopy, Engel - Introduction to Quantum Mechanics in Chemistry, Ratner & Schatz - Molecular Quantum Mechanics, Atkins & Friedman - Modern Quantum Chemistry, Ostlund & Szabo - Essential of Computational Chemistry, Cramer - Exploring chemistry with electronic structure methods, Foresman Grading: - Exam or Term report & presentation - Hands-on-computer-lab report & presentation - Presence & Participation (questions, answers, comments, etc.)

2. I. 2013 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. 2013 Fall: Quantum Chemistry (Computational Chemistry) - Quantum-mechanical description of chemical systems One-electron & many-electron atoms Di-atomic & poly-atomic molecules III. 2014 Spring: Classical Monte Carlo (MC) Simulations of Materials - Large-scale simulation of chemical systems (or any collection of particles) IV. 2014 Fall: Classical Molecular Dynamics (MD) Simulation of Materials - Application of a combination of the above methods to understand structures, electronic structures, properties, and functions of various materials “Molecular Modeling of Materials” Lecture Series

3. Quantum Chemistry: Our Agenda (along with Engel) Postulates in quantum mechanics (Ch. 3) Schrödinger equation (Ch. 2) Simple examples of V(r) Particle in a box (translation, etc.) (Ch. 4-5) Harmonic oscillator (vibration) (Ch. 7-8) Particle on a ring or a sphere (rotation) (Ch. 7-8) Extension to chemical systems (electronic structure) Hydrogen(-like) atom (one-electron atom) (Ch. 9) Many-electron atoms (Ch. 10-11) Diatomic molecules (Ch. 12-13) Polyatomic molecules (Ch. 14) Computational chemistry (Ch. 16) A B vib rot trans statistical mechanics (N  ) - molecular partition function thermodynamics (macroscopic) microscopic

4. Rotational energy levels are more closely-spaced than vibrational energy levels. Vibrational energy levels are more closely-spaced than electronic energy levels. Classical approach: OK Quantum approach: a must!

5. -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 < 10 2 ), @ 0 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 Molecular Modeling of Materials: Quantum or Classical?

6. 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

7. I. 2013 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. 2013 Fall: Quantum Chemistry (Computational Chemistry) - Quantum-mechanical description of chemical systems One-electron & many-electron atoms Di-atomic & poly-atomic molecules III. 2014 Spring: Classical Monte Carlo (MC) Simulations of Materials - Large-scale simulation of chemical systems (or any collection of particles) IV. 2014 Fall: Classical Molecular Dynamics (MD) Simulation of Materials - Application of a combination of the above methods to understand structures, electronic structures, properties, and functions of various materials “Molecular Modeling of Materials” Lecture Series

8. What are we going to calculate (using computers)? - Energy E or U at 0 K (Gibbs free energy G or Enthalpy H) - Potential energy curve (or potential energy surface; PES) - Geometry or (Equilibrium) Structure (diffraction, NMR spectroscopy) - Vibrational frequency (IR, Raman, EELS, IETS spectroscopy) & ZPE - Thermodynamic property (T-dependent H, S, G) – statistical mechanics - Reaction energy (enthalpy) (exothermic or endothermic?) - Reaction rate (fast or slow?) - Energy barrier (activation free energy) - Protonation-deprotonation  acid-base property (pK a ) - Oxidation-reduction  Electrochemical property (reduction potential) - Optical property (band gap or HOMO-LUMO gap, UV-visible absorption) - Electrical property (Dipole moment, (hyper)polarizability, current)

9. Born-Oppenheimer approximation & Potential energy curve/surface Potential energy surface A B R E = E(R)  RR E = E(R,θ)

10. Stationary points in PES (Geometry optimization, Transition state search)

11. Intrinsic reaction coordinate (IRC) * Minimum (isomer, confomer, reactant, product) Transition state (linking two minima) for all q for other q’s for only one q (reaction coordinate) Stationary point. Transition State

12. Stationary point. Minimum Energy minimization Geometry optimization Energy minimum (Equilibrium structure) for all q A stone will roll down. A stone will stay.

13. Potential Energy Curve (1-Dimensional) A B R Simplest form: Harmonic Oscillator E = E(R) Simplified

14. Potential Energy Surface (2-Dimensional)  RR E = E(R,θ) (R fixed or optimized)(θ fixed or optimized) Sliced to make 1D curve Sliced to make 1D curve  Potential Energy Hypersurface (N-Dimensional)

15. 1D Slice of Potential Energy Hypersurface Example: Torsional Energy Curve Torsion: dihedral angle (for A-B-C-D bond) fixed or optimized

17. What quantum chemistry can bring to you. Examples. Reduction-oxidation potential, acidity-basicity (pK a ), geometry, UV/vis absorption spectrum 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. C (2011; 2015)

18. Quantum chemistry, Example No. 3: Pd-catalyzed reaction, UV/vis spectrum, organic solar cell efficiency TS1 I1 TS2I2 TS3 I3 Pd+ 22BI 0 8.9 -32.4 -18.4 -34.7 -29.1 -51.3 -26.5 Pd+ +2BI gone! PCE 3.1% PCE 0.4% -3.26 -5.22 -1.96 EX2 3.26 EX1 1.96 -2.12 -5.11 EX1 2.99

19. Free Translation (V = 0) with Boundaries: Particle in a Box (Infinite Square Wall Potential) m A particle of mass m is confined between two walls but free inside.   The same solution as the free particle but with different boundary condition.

20. zero-point energy node Final solution: energy & wave function quantized 2 Rapidly changing  Higher E

21. HOMO LUMO        375 nm A glimpse of electronic structure: PIB model of  electrons in conjugated molecules

22. HOMO LUMO 375 nm 1,3,5-hexatriene

23. Coloring of  -carotene