Quantum Chemistry (Computational Chemistry) Instructor: Yun Hee Jang MSE 302, 2323) Web: 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.)

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 (Computational Chemistry) - Quantum-mechanical description of chemical systems One-electron & many-electron atoms Di-atomic & poly-atomic molecules III Spring: Classical Monte Carlo (MC) Simulations of Materials - Large-scale simulation of chemical systems (or any collection of particles) IV 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

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 ) Diatomic molecules (Ch ) Polyatomic molecules (Ch. 14) Computational chemistry (Ch. 16) A B vib rot trans statistical mechanics (N  ) - molecular partition function thermodynamics (macroscopic) microscopic

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!

-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 Molecular Modeling of Materials: Quantum or Classical?

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

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 (Computational Chemistry) - Quantum-mechanical description of chemical systems One-electron & many-electron atoms Di-atomic & poly-atomic molecules III Spring: Classical Monte Carlo (MC) Simulations of Materials - Large-scale simulation of chemical systems (or any collection of particles) IV 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

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)

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

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

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

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

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

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)

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

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)

Quantum chemistry, Example No. 3: Pd-catalyzed reaction, UV/vis spectrum, organic solar cell efficiency TS1 I1 TS2I2 TS3 I3 Pd+ 22BI Pd+ +2BI gone! PCE 3.1% PCE 0.4% EX EX EX1 2.99

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.

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

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

HOMO LUMO 375 nm 1,3,5-hexatriene

Coloring of  -carotene