Lecture 10. Chemical Bonding. H 2 Molecule References Engel, Ch. 12 Ratner & Schatz, Ch. 10 Molecular Quantum Mechanics, Atkins & Friedman (4th ed. 2005),

Slides:

Advertisements

Similar presentations

Introduction to Computational Chemistry NSF Computational Nanotechnology and Molecular Engineering Pan-American Advanced Studies Institutes (PASI) Workshop.

Advertisements

Potential Energy Surface. The Potential Energy Surface Captures the idea that each structure— that is, geometry—has associated with it a unique energy.

Molecular Bonding Molecular Schrödinger equation

Introduction to Molecular Orbitals

Chapter 3 Electronic Structures

Chemistry 2 Lecture 1 Quantum Mechanics in Chemistry.

Computational Chemistry

Lecture 23 Born-Oppenheimer approximation (c) So Hirata, Department of Chemistry, University of Illinois at Urbana-Champaign. This material has been developed.

Chemistry 2 Lecture 10 Vibronic Spectroscopy. Learning outcomes from lecture 9 Excitations in the visible and ultraviolet correspond to excitations of.

Week 1: Basics Reading: Jensen 1.6,1.8,1.9. Two things we focus on DFT = quick way to do QM – 200 atoms, gases and solids, hard matter, treats electrons.

1 Cold molecules Mike Tarbutt. 2 Outline Lecture 1 – The electronic, vibrational and rotational structure of molecules. Lecture 2 – Transitions in molecules.

Separating Electronic and Nuclear Motions The Born-Oppenheimer Approximation All Computational Chemistry rests on a fundamental assumption called.

Monday, Nov. 11, 2013PHYS , Fall 2013 Dr. Jaehoon Yu 1 PHYS 3313 – Section 001 Lecture #17 Monday, Nov. 11, 2013 Dr. Jaehoon Yu Alpha Particle.

Quantum Mechanics & Molecular Structure Quantum Mechanics : Quantum mechanics is the foundation of all chemistry and biology. Statistical mechanics rests.

Molecular Simulation. Molecular Simluation Introduction: Introduction: Prerequisition: Prerequisition: A powerful computer, fast graphics card, A powerful.

Chemistry 2 Lecture 1 Quantum Mechanics in Chemistry.

Potensial Energy Surface Pertemuan V. Definition Femtosecond spectroscopy experiments show that molecules vibrate in many different directions until an.

1 Molecular Hamiltonians and Molecular Spectroscopy.

Potential Energy Surfaces

MOLECULAR STRUCTURE CHAPTER 14 Experiments show O 2 is paramagnetic.

CHEMISTRY 2000 Topic #1: Bonding – What Holds Atoms Together? Spring 2008 Dr. Susan Lait.

Chem 125 Lecture 12 10/4/2005 Projected material This material is for the exclusive use of Chem 125 students at Yale and may not be copied or distributed.

Introduction to Infrared Spectrometry Chap 16. Infrared Spectral Regions Table 16-1 Most used – 15.

Organic Chemistry 4 th Edition Paula Yurkanis Bruice Chapter 1 Electronic Structure and Bonding Acids and Bases Irene Lee Case Western Reserve University.

An Introduction to Molecular Orbital Theory. Levels of Calculation Classical (Molecular) Mechanics quick, simple; accuracy depends on parameterization;

Objectives of this course

Introduction. What is Computational Chemistry?  Use of computer to help solving chemical problems Chemical Problems Computer Programs Physical.

Geometry Optimisation Modelling OH + C 2 H 4 *CH 2 -CH 2 -OH CH 3 -CH 2 -O* 3D PES.

Algorithms and Software for Large-Scale Simulation of Reactive Systems _______________________________ Ananth Grama Coordinated Systems Lab Purdue University.

Base Pairing in DNA. Red = O Grey = C White = H Purple = K Ionic Radii Li + = 0.68 Å Na + = 0.97 Å K + = 1.33 Å Rb + = 1.47 Å Cavity Size (O-O Dist.)

Lecture 25: Introduction to Molecular Orbital Theory The material in this lecture covers the following in Atkins. 14 Molecular structure Molecular Orbital.

Physical Chemistry 2 nd Edition Thomas Engel, Philip Reid Chapter 23 The Chemical Bond in Diatomic Molecules.

Lecture 6. Many-Electron Atoms. Pt.4. Physical significance of Hartree-Fock solutions: Electron correlation, Aufbau principle, Koopmans’ theorem & Periodic.

Covalent Bonding Theories Hybridization. Theories of Covalent Bonding Valence Bond (VB) Theory and Orbital Hybridization The Mode of Orbital Overlap and.

Lecture 2. Postulates in Quantum Mechanics Engel, Ch. 2-3 Ratner & Schatz, Ch. 2 Molecular Quantum Mechanics, Atkins & Friedman (4 th ed. 2005), Ch. 1.

Rate Theories of elementary reaction. 2 Transition state theory (TST) for bimolecular reactions Theory of Absolute reaction Rates Theory of activated.

Lecture 11. Quantum Mechanics

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

Molecular structure The Schrödinger Equation for molecules The Born-Oppenheimer approximation 4.1 Molecular orbital theory The hydrogen molecule-ion.

MOLECULAR STRUCTURE CHAPTER 14 Experiments show O 2 is paramagnetic.

Lecture 10. Chemical Bonding. Generalization & Matrix Representation References Engel Ch.12, Ratner & Schatz, Ch.11 Quantum Chemistry, McQuarrie, Ch.9.

Molecular simulation methods Ab-initio methods (Few approximations but slow) DFT CPMD Electron and nuclei treated explicitly. Classical atomistic methods.

Quantum Chemistry: Our Agenda (along with Engel)

Why do bonds form? Energy of two separate H atoms Lennard-Jones potential energy diagram for the hydrogen molecule. Forces involved: We understand that.

Chemistry 700 Lectures. Resources Grant and Richards, Foresman and Frisch, Exploring Chemistry with Electronic Structure Methods (Gaussian Inc., 1996)

Lecture 13. Geometry Optimization References Computational chemistry: Introduction to the theory and applications of molecular and quantum mechanics, E.

Lecture 7. Many-Electron Atoms. Pt.5. Good quantum numbers (Terms & Levels) & the Zeeman effect References Ratner Ch , , Engel Ch.11, Pilar.

Lecture 11. Hydrogen Atom References Engel, Ch. 9

CHEMISTRY 2000 Topic #1: Bonding – What Holds Atoms Together? Spring 2008 Dr. Susan Lait.

Ch 12. Chemical Bond in Diatomic Molecules MS310 Quantum Physical Chemistry The chemical bond is at the heart of chemistry. A qualitative molecular orbital.

Lecture 5. Many-Electron Atoms. Pt

Developing a Force Field Molecular Mechanics. Experimental One Dimensional PES Quantum mechanics tells us that vibrational energy levels are quantized,

Quantum Chemistry: Our Agenda Postulates in quantum mechanics (Ch. 3) Schrödinger equation (Ch. 2) Simple examples of V(r) Particle in a box (Ch. 4-5)

Lecture 8. Chemical Bonding

1 Tentative content material to be covered for Exam 2 (Wednesday, November 2, 2005) Chapter 16Quantum Mechanics and the Hydrogen Atom 16.1Waves and Light.

Last hour: Total WF: In the BOA, the electronic WF uses R only as a parameter  separation of variables, treating degrees of freedom for nuclear and electronic.

Lecture 9. Many-Electron Atoms

Molecular Orbital Theory Bonding Models: Lewis Structures and VSEPR Valence Bond (VB) or Localized Electron (LE) Theory Molecular Orbital (MO) Theory Bonding.

Quantum Mechanical Description of Molecules Glenn V. Lo Department of Physical Sciences Nicholls State University.

Ch.1. Elementary Quantum Chemistry

Lecture 12. Potential Energy Surface

Chemistry 120 Molecular Structure Both atoms and molecules are quantum systems We need a method of describing molecules in a quantum mechanical way so.

Molecular Bonding Molecular Schrödinger equation

Molecular Orbital Theory

Chapter 7 Lecture presentation

Chemical Bonding Mr. Sonaji V. Gayakwad Asst. professor

Tightbinding (LCAO) Approach to Bandstructure Theory

Rules for Predicting Molecular Geometry 1. Sketch the Lewis structure of the molecule or ion 2. Count the electron pairs and arrange them in.

18.1 Electron Waves and Chemical Bonds

DEPARTMENT OF CHEMISTRY

Presentation transcript:

Lecture 10. Chemical Bonding. H 2 Molecule References Engel, Ch. 12 Ratner & Schatz, Ch. 10 Molecular Quantum Mechanics, Atkins & Friedman (4th ed. 2005), Ch.8 Computational Chemistry, Lewars (2003), Ch.4 A Brief Review of Elementary Quantum Chemistry

fixed Born-Oppenheimer approximation Constant

Born-Oppenheimer Approximation Simplifies further the Schrödinger equation (separation of variables) Difference in the time scales of nuclear and electronic motions Nuclei are much heavier (~1800 times) and slower than electrons. Electrons can be treated as moving in the field of fixed nuclei. A full Schrödinger equation for a molecule can be solved in two steps: 1) Motion of electron around the nuclei at fixed positions 2) Energy curve of the molecule as a function of nuclei position Focus on the electronic Schrödinger equation

Born-Oppenheimer Approximation & Potential Energy Surface (Curve) Potential energy surface A B R

Potential Energy Curve (1D = diatomic molecule) A B R E = E(R) Potential Energy Surface (2D = constrained triatomic)  RR E = E(R,θ) For molecules, in general, Potential Energy “Hypersurface” (N-Dimensional) – We cannot draw it! (R fixed or optimized)(θ fixed or optimized) Sliced to make 1D curve Sliced to make 1D curve

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

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

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

\\ \home\your_id

Molecular Orbitals (MO) Near the equilibrium distance, an electron delocalized over the whole molecule.

Overlap integral

MO energy diagram: E(R) as a function of R unbound state: antibonding bound state: bonding

Buildup of electron charge around protons & between protons Decrease of charge outside of bonding region Decrease of electron charge around protons & between protons Increase of charge outside of bonding region

Molecular Orbital (MO) Model – LCAO-MO

LCAO-MO model gives wrong dissociation limit. MO wave function = VB wave function + ionic terms