Symmetry Properties of Molecules

Slides:

Advertisements

Similar presentations

Symmetry Translation Rotation Reflection Slide rotation (S n )

Advertisements

Group Theory II.

Watkins/Fronczek - Rotational Symmetry 1 Symmetry Rotational Symmetry and its Graphic Representation.

Group Theory in Chemistry

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

A Science of Aesthetics Transformations You Cannot See.

Symmetry and Group Theory

Molecular Symmetry Symmetry Elements Group Theory

Lecture 28 Point-group symmetry I

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

Today in Inorganic…. Uses of Symmetry in Chemistry Symmetry elements and operations Properties of Groups Symmetry Groups, i.e., Point Groups Previously:

Perturbation Theory H 0 is the Hamiltonian of for a known system for which we have the solutions: the energies, e 0, and the wavefunctions, f 0. H 0 f.

Vibrational Spectroscopy CHE 626 Alex Nazarenko

Symmetry operations are movements or actions that leave the molecule apparently unchanged. Symmetry elements are the points, lines, or planes in space.

Lecture # 8 Molecular Symmetry

Lecture 9 THE SYMMETRY POINT GROUPS

Part 2.5: Character Tables

Chapter 4 Molecular Symmetry

PH0101 UNIT 4 LECTURE 3 CRYSTAL SYMMETRY CENTRE OF SYMMETRY

3-D figures. Reflectional Symmetry For 2D figure: If a plane figure can be divided by a line into two identical parts and these parts are mirror images.

Lecture 37: Symmetry Orbitals

Symmetry Motif: the fundamental part of a symmetric design that, when repeated, creates the whole pattern Operation: some act that reproduces the.

The determination of point groups of molecules

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

Symmetry and Group Theory

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

1 Physical Chemistry III (728342) Chapter 5: Molecular Symmetry Piti Treesukol Kasetsart University Kamphaeng Saen Campus.

CH4 – four-fold improper rotation

Symmetry and Introduction to Group Theory

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

Symmetry Tomáš Suk.

1 Internal Order and Symmetry GLY 4200 Fall, 2015.

EEE539 Solid State Electronics 1. Crystal Structure Issues that are addressed in this chapter include:  Periodic array of atoms  Fundamental types of.

Bonding in polyatomic molecules

Symmetry Edward A. Mottel Department of Chemistry Rose-Hulman Institute of Technology.

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.

Ch 4 Lecture 1 Symmetry and Point Groups I.Introduction A.Symmetry is present in nature and in human culture.

Group Theory and Spectroscopy

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

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

Chapter 4. Molecular Symmetry

Point Groups (section 3.4, p. 66) Point group: a set of symmetry operations that completely describe the symmetry of an object/molecule. Going back to.

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

Bonding in polyatomic molecules

Molecular Symmetry Symmetry Elements and Operations Using Symmetry in Chemistry Understand what orbitals are used in bonding Predict.

Dr. Said M. El-Kurdi1 Chapter 4 An introduction to molecular symmetry.

Symmetry and Introduction to Group Theory

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

Done by Shobana.N.S 1 BY SHOBANA.N.S QUEEN MARY’S COLLEGE.

Ligand Group Orbitals Created by Chip Nataro (Lafayette College and posted on VIPEr ( on March 27, Copyright.

Lecture 34: Symmetry Elements The material in this lecture covers the following in Atkins. 15 Molecular Symmetry The symmetry elements of objects 15.1.

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

Point & Space Group Notations

Symmetry Rotation Translation Reflection. A line on which a figure can be folded so that both sides match.

Chem 222 Spring How to determine point group symmetry H&S Example: BF 3 Is the molecule linear? NO Does the molecule have T d, O h or I.

Chapter 1 Point Group Symmetry.

Reflectional Symmetry (Bilateral Symmetry) The mirror line runs from the tip of the head to the toes. The human body does not have perfect symmetry ( internal.

Chem IV - Symmetry and Group Theory

Symmetry and Group heory

A Science of Aesthetics

Ch 9 – Covalent Bonding: Orbitals

Character Tables for Point Groups

Ch 9 – Covalent Bonding: Orbitals

Symmetry “the correspondence in size, form and

Symmetry and Introduction to Group Theory

Properties of point groups:

Symmetry operations: Transformations mapping the nuclear frame of a molecule onto an indistinguishable version of itself  symmetry elements: symmetry.

Presentation transcript:

Symmetry Properties of Molecules Chemistry 330 Symmetry Properties of Molecules

Symmetry Elements Some of the symmetry elements of a cube. The twofold, threefold, and fourfold axes are labelled with the conventional symbols.

Proper Rotations An NH3 molecule has a threefold (C3) axis An H2O molecule has a twofold (C2) axis.

Mirror Planes An H2O molecule has two mirror planes. They are both vertical (that is, contain the principal axis) and so are denoted v and ‘v.

Dihedral mirror planes Dihedral mirror planes (d) bisect the C2 axes perpendicular to the principal axis.

The Inversion Centre A regular octahedron has a centre of inversion (i).

Improper Rotation Axes A CH4 molecule has a fourfold improper rotation axis (S4) The staggered form of ethane has an S6 axis composed of a 60 rotation followed by a reflection.

The Inversion Centre The presence of a twofold axis and a horizontal mirror plane jointly imply the presence of a centre of inversion in the molecule.

The Dn Point Group A molecule with n twofold rotation axes perpendicular to an n-fold rotation axis belongs to the group Dn.

The Dnh Point Group A molecule with a mirror plane perpendicular to a Cn axis, and with n twofold axes in the plane, belongs to the group Dnh.

Cubic Point Groups Tetrahedral and octahedral molecules are drawn in a way that shows their relation to a cube: they belong to the cubic groups Td and Oh, respectively.

The Point Group Flow Diagram A flow diagram for determining the point group of a molecule. Start at the top and answer the question posed in each diamond (Y = yes, N = no).

Molecules and Point Groups A summary of the shapes corresponding to different point groups.

Equivalent Elements Some symmetry elements are implied by the other symmetry elements in a group Presence of an inversion means at least an S2 element Hence, i and S2 are equivalent

Characters of Rotations A rotation through 180 about the internuclear axis leaves the sign of a  orbital unchanged but the sign of a  orbital is changed. The characters of the C2 rotation are +1 and -1 for the  and  orbitals, respectively.

Classes and Groups Symmetry operations in the same class are related to one another by the symmetry operations of the group.

The px Orbitals and Symmetry A px orbital on the central atom of a C2v molecule and the symmetry elements of the group.

Reflections The two orbitals shown here have different properties under reflection through the mirror plane: one changes sign (character -1), the other does not (character +1).

SALC’s Two symmetry-adapted linear combinations Each span a one-dimensional irreducible representation, and their symmetry species are different.

More SALC’s Typical symmetry-adapted linear combinations of orbitals in a C3v molecule.

Symmetry Species and Orbital Overlap Orbitals of the same symmetry species may have non-vanishing overlap The a1 and the two components of the doubly degenerate e orbitals