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Course10410109468 lectures

Symmetry and Group Theory

Prof. Anindya Datta · IIT Bombay

Start with lecture 1 At NPTEL

About

This course provides a quantitative treatment of symmetry in chemistry, using group theory. We start with determination of point group, discuss transformation matrices, abstract group theory, unitary transformations, derivation of Great Orthogonality Theorem and its consequences leading to character tables. Then, various applications in Chemistry are discussed. It is equivalent to CH 801 of IIT Bombay. The lectures are already recorded by CDEEP, IIT Bombay.

Intended audience: Chemistry.

Lectures

Week 1

  1. Lecture 1 : Symmetry point group: Introduction YouTube
  2. Lecture 2 : Symmetry point group: Examples Part I YouTube
  3. Lecture 3 : Symmetry point group: Examples Part II YouTube
  4. Lecture 4 : Symmetry point group: Examples Part III YouTube
  5. Lecture 5 : Symmetry point group: Examples Part IV YouTube

Week 2

  1. Lecture 6 : Transformation matrices and Matrix representation YouTube
  2. Lecture 7 : More on Matrix representation: Cartesian coordinates in C2v point group YouTube
  3. Lecture 8 : Matrix representation: the way ahead YouTube
  4. Lecture 9 : Introduction to Group Theory YouTube
  5. Lecture 10 : Group Multiplication Tables YouTube
  6. Lecture 11 : Groups and subgroups YouTube

Week 3

  1. Lecture 12 : Classes, Similarity transformations YouTube
  2. Lecture 13 : Introduction to Matrices YouTube
  3. Lecture 14 : Application of matrices in solution of simultaneous equations YouTube
  4. Lecture 15 : Matrix eigenvalue equation YouTube
  5. Lecture 16 : Matrix eigenvalue equation: an example YouTube

Week 4

  1. Lecture 17 : Similarity Transformations YouTube
  2. Lecture 18 : Back to transformation matrices YouTube
  3. Lecture 19 : Matrix representation revisited YouTube
  4. Lecture 20 : Function space and Transformation Operators YouTube
  5. Lecture 21 : Transformation Operators form the same group as transformation matrices YouTube
  6. Lecture 22 : Transformation Operators form a unitary representation for orthonormal basis YouTube

Week 5

  1. Lecture 23 : Transformation Operators: Switching Bases YouTube
  2. Lecture 24 : Equivalent representations YouTube
  3. Lecture 25 : Unitary Transformation YouTube
  4. Lecture 26 : Unitary Transformations-Continued YouTube
  5. Lecture 27 : Reducible and Irreducible Representations YouTube

Week 6

  1. Lecture 28 : Irreducible Representations and Great Orthogonality Theorem YouTube
  2. Lecture 29 : Character Tables: C2v YouTube
  3. Lecture 30 : Character Tables: C2v and C3v YouTube
  4. Lecture 31 : Practice Session: Review of Some Questions and Solutions YouTube
  5. Lecture 32 : Reducible to Irreducible Representations YouTube
  6. Lecture 33 : Character Tables of Cyclic Groups YouTube

Week 7

  1. Lecture 34 : Symmetry of Normal Modes: D3h YouTube
  2. Lecture 35 : Symmetry of Normal Modes: D3h : Continued YouTube
  3. Lecture 36 : Symmetry of Normal Modes: a shortcut YouTube
  4. Lecture 37 : Recap: Reducible Representation for Normal Modes YouTube
  5. Lecture 38 : Contribution of internal motion to normal modes YouTube
  6. Lecture 39 : Normal mode analysis: some examples YouTube

Week 8

  1. Lecture 40 : Infrared and Raman spectroscopy YouTube
  2. Lecture 41 : IR and Raman activity YouTube
  3. Lecture 42 : IR and Raman activity: examples YouTube
  4. Lecture 43 : Symmetry Adapted Linear Combinations (SALC) YouTube
  5. Lecture 44 : SALC:BeH2 YouTube
  6. Lecture 45 : SALC:CH4 Introduction YouTube

Week 9

  1. Lecture 46 : SALC:CH4 YouTube
  2. Lecture 47 : Projection Operators YouTube
  3. Lecture 48 : Projection Operators – Continued YouTube
  4. Lecture 49 : Generating SALC’s using Projection Operators YouTube
  5. Lecture 50 : Generating SALC’s using Projection Operators - Continued YouTube
  6. Lecture 51 : Oh complex and Group-subgroup relation YouTube

Week 10

  1. Lecture 52 : Group-Subgroup Relation YouTube
  2. Lecture 53 : SALCs as Pi-MO andCyclopropenyl group YouTube
  3. Lecture 54 : SALCs as Pi-MO, Cyclopropenyl group YouTube
  4. Lecture 55 : SALCs as Pi-MO, Benzene YouTube
  5. Lecture 56 : LCAO Huckel approximation YouTube
  6. Lecture 57 : Huckel approximation: Naphthalene YouTube

Week 11

  1. Lecture 58 : Stationary states, Multiplicity, Ethylene YouTube
  2. Lecture 59 : Napthalene -I YouTube
  3. Lecture 60 : Napthalene -II YouTube
  4. Lecture 61 : Napthalene -III YouTube
  5. Lecture 62 : Transition Metal Complexes: CFT and LFT YouTube
  6. Lecture 63 : Jahn-Teller Theorem, Tetragonal Distortion MOT:ML6, Sigma and Pi Bonds YouTube

Week 12

  1. Lecture 64 : MOT approach of bonding,H2O,Ferrocene YouTube
  2. Lecture 65 : MOT approach of bonding,H2O,Ferrocene YouTube
  3. Lecture 66 : Derivation: Great Orthogonality Theorem – I (Schurrs Lemma 1) YouTube
  4. Lecture 67 : Derivation: Great Orthogonality Theorem – II (Schurrs Lemma 2) YouTube
  5. Lecture 68 : Derivation: Great Orthogonality Theorem –III YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Bombay
Department
Chemistry and Biochemistry
Teacher
Prof. Anindya Datta
Level
Undergraduate
Language
English
Subjects
Chemistry
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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