Chapter 4 Symmetry and its Applications Symmetry = do something to a molecule and have it look the same.

Slides:

Advertisements

Similar presentations

Symmetry Translation Rotation Reflection Slide rotation (S n )

Advertisements

Group Theory II.

Chapter 6-1 Chemistry 481, Spring 2014, LA Tech Instructor: Dr. Upali Siriwardane Office: CTH 311 Phone Office Hours:

Application of group theory- Infrared and Raman Activity

Symmetry and Group Theory

Molecular Symmetry Symmetry Elements Group Theory

Lecture 13 APPLICATIONS OF GROUP THEORY 1) IR and Raman spectroscopy. Normal modes of H 2 O Three normal vibrations of H 2 O transform as 2 A 1 and 1 B.

Lecture 4. Point group Symmetry operations Characters +1 symmetric behavior -1 antisymmetric Mülliken symbols Each row is an irreducible representation.

CHEM 515 Spectroscopy Vibrational Spectroscopy II.

CHEM 515 Spectroscopy Vibrational Spectroscopy III.

Lecture 11 REPRESENTATIONS OF SYMMETRY POINT GROUPS 1) Mulliken labels

CHEM 515 Spectroscopy Vibrational Spectroscopy IV.

Vibrations of polyatomic molecules

Frequency Calculation. *A nonlinear molecule with n atoms has 3n — 6 normal modes: the motion of each atom can be described by 3 vectors, along the x,

Lecture 7. Reducible representation: How the basis objects transform. By adding and subtracting the basis objects the reducible representation can be.

The Irreducible reps are orthogonal. Hence for the reducible rep and a particular irreducible rep j  (character of Reducible Rep)(character of Irreducible.

Spectroscopy 1: Rotational and Vibrational Spectra CHAPTER 13.

How Chemists Use Group Theory Created by Anne K. Bentley, Lewis & Clark College and posted on VIPEr ( on March.

Part 2.5: Character Tables

Part 2.6: Using Character Tables

Chapter 4 Molecular Symmetry

Lecture 12 APPLICATIONS OF GROUP THEORY 1) Chirality

Lecture 37: Symmetry Orbitals

Lecture 10 REPRESENTATIONS OF SYMMETRY POINT GROUPS 1) Basis functions, characters and representations Each symmetry operation in a group can be represented.

Vibrational Spectroscopy

Vibrational Spectroscopy

Review: Applications of Symmetry, cont.

Group theory 101 Suggested reading: Landau & Lifshits, Quantum Mechanics, Ch. 12 Tinkham, Group Theory and Quantum Mechanics Dresselhaus, Dresselhaus,

Symmetry and Group Theory

Infrared Spectroscopy

Symmetry operation motion of molecule which leaves it indistinguishable from before. Symmetry element plane, line (axis) or point (centre) about which.

Immediate Consequences of Symmetry I. Optical Activity (Chirality) If a mirror image of a molecule cannot be superimposed on the original the molecule.

Ch121 X - Symmetry Symmetry is important in quantum mechanics for determining molecular structure and for interpreting spectroscopic information. In addition.

Today in Inorganic…. Symmetry elements and operations Properties of Groups Symmetry Groups, i.e., Point Groups Classes of Point Groups How to Assign Point.

Physical Chemistry 2 nd Edition Thomas Engel, Philip Reid Chapter 27 Molecular Symmetry.

Group Theory and Spectroscopy

1 CH6. Symmetry Symmetry elements and operations Point groups Character tables Some applications.

Ch 4 Lecture2 Applications of Symmetry

Transformations Day 1: Graphing. Vocabulary Transformations – mapping of a figure on the coordinate plane. 1) Reflection: Mirror image x-axis (x,y) →(x,-y)

Lecture 28 Point-group symmetry I. Molecular symmetry A typical conversation between chemists … Symmetry is the “language” all chemists use every day.

Important concepts in IR spectroscopy

Structural Methods in Molecular Inorganic Chemistry, First Edition. David W. H. Rankin, Norbert W. Mitzel and Carole A John Wiley & Sons,

Chapter 2 Section 2.7 Graphing Techniques. Multiplying the Function or the Independent Variable by a Number.

Normal modes of vibration of a XY 3 pyramidal molecule by Dr.D.UTHRA Head Department of Physics DG Vaishnav College Chennai-106.

Partition functions of ideal gases. We showed that if the # of available quantum states is >> N The condition is valid when Examples gases at low densities.

C We have to solve the time independent problem H o  o = E o  o Harry Kroto 2004.

11-1 Infrared Spectrometry Wavelengths  0.78  m to 1000  m §3 regions àNear-, mid-, and far Theory Sources Instrumentation.

Laser Molecular Spectroscopy CHE466 Fall 2009 David L. Cedeño, Ph.D. Illinois State University Department of Chemistry Elements of Symmetry.

EXAMPLE THE SPECTRUM OF HCl SHOWS A VERY INTENSE ABSORPTION BAND AT 2886 cm -1 AND A WEAKER BAND AT 5668 cm -1. CALCULATE x e, ṽ o, THE FORCE CONSTANT.

From Point Groups to Space Groups

Molecular Orbital Theory 1.MO theory suggests that atomic orbitals of different atoms combine to create MOLECULAR ORBITALS 2. Electrons in these MOLECULAR.

1 The next two parts of the course are closely related, though at first it may not seem so.

Chem IV - Symmetry and Group Theory

Symmetry and Group heory

Geometric Transformations

Chemistry 481(01) Spring 2016 Instructor: Dr. Upali Siriwardane

Examples of point groups and their characters – more details

Normal modes of vibration of a molecule – An Exercise

Chapter 4 Symmetry and its Applications

Character Tables for Point Groups

Honors Chemistry.

Quantal rotation Molecules

Examples of point groups and their characters

Computation of Harmonic and Anharmonic Vibrational Spectra

Topics 5 & 15 Chemical Thermodynamics

PROBLEM SET 2 Do problem 1 of “section 3.11: Exercises” in page 50 of text. Do problem 5 of “section 3.11: Exercises” in page 51 of text. Do problem 10.

Quantal rotation Molecules

Presentation transcript:

Chapter 4 Symmetry and its Applications Symmetry = do something to a molecule and have it look the same

Representations of Groups: Example: effect of operations on x, y, z axes together

Reducible vs. Irreducible Representations of Groups: Example: effect of operations on x, y, z axes alone

Character Tables

Order = # symmetry operations = 6 Classes = grouping of similar operations = 3 Dimensions = # under E operation Order of group =  (characters under E) 2 Definitions by Example:

Symmetry Applications: Vibrations Examine x, y, z changes for each atom. An atom that moves gets zeros for each. Those not moving get 1 or -1 for each. Add them up to get reducible representation for atomic motions. Break reducible representation up to get list of irreducible representation. # irrrep= 1/order  (#operations in class)(character of redrep)(character of irrerep) All motions = degrees of freedom = 3n Translations = 3 and go by x, y, z functions. Rotations = 3 and go by Rx. Ry, and Rz functions. Vibrations are what’s left over. IR active translate as x, y, z functions. Raman active translate as xy, xz, yz, z 2, etc. functions.

Vibrational Analysis for Water

Vibrational Analysis of NH 3

Vibrational Analysis of XeF 4

Vibrational Analysis of Selected Vibrational Modes: CO stretches: Consider only the C-O axis. If it moves, = 0 ; if it stays, =1 Can an IR spectrum distinguish between these two isomers?

cis-ML 2 (CO) 2

trans-ML 2 (CO) 2

Chapter 4 Homework 1, 2, 3, 5, 13, 16 a-e, 21, 23 (using items from problems 4 and 5 only), 24, 25, 26, 27, 28