The volume of literature on the use of infrared spectroscopy for determination of molecular structure and bonding has grown with an ever-increasing speed in the second half of the twentieth century. Possibly, this pedagogical knowledge of normal vibration could be linked with group-frequency concept which merits more attention than it gets. This short monograph is an attempt to fulfill our desire in this direction.
After defining spectrum and spectroscopies in chapter I, chapter 11 deals withthe concepts associated with vibrational spectroscopy of molecules in general.No assumption has been made for students to have any detailed knowledge of mathematics. The presentation style is intentionally kept very concise in order that the reader may not be lost in the larger view of details. This would, possibly bridge the gap between mathematics and biology students for an effortless reading. The chapters would best be regarded as maps. It will show the beginner where he can go and to a theoretician where he has been! In fact, symmetry and group theory are closely related to the field of spectroscopy. The same knowledge with regard to manipulation in spectral data analysis is extremely essential as described in chapter II*. In chapter III, frequencies which are basically associated with functional groups are discussed. Chapter IV deals with the experimental techniques used to record i.r. spectra. It also gives tips for interpretation of the data thus obtained.Calculated attempts have been made to show its relationship to the concepts discussed in earlier chapters in order to remove the empiricism in the variation of band positions in the related i.r. spectra.
Our belief in Chinese proverb "I hear and I forget; I see and I remember;I do and I understand" is unshakable. Chapter V is written to fulfill this purpose.Working out the problems given would give the readers an idea of how much they have assimilated the concepts. It is not our expectation from the students that they will be able to evaluate frequencies obtained by using "normal coordinate analysis" but we do expect them to be able to interpret these intelligently. A special feature of our presentation of the subject relates to chapter V where nearly 300 problems have been given with solution. It might provide readers a confidence in analyzing situation and solving the problem. It is our earnest suggestion to them that they should try their utmost prior to looking at the solution.
It is not possible to be exhaustive in a small monograph like the present one.We hope the readers will appreciate the synopsis of the encyclopedic matter. The authors would be grateful if the readers care to point out mistakes, errors and omissions to help us redress the same in the next revised edition.
Our appreciation and thanks are due to, (a) our spouses for their patience and tolerance ofboredom during the period of writing the manuscript, (b) Our children whose company we missed, and, (c) Our typist and graphicist who completed the manuscript, without any grudge.
Also, our special thanks are due to Shri Mohan Goyal & Mabnijee for their constant encouragement throughout preparation of the manuscript.
Our thanks are also due to Sumedha Agrawal, Kshitij Gupta and Pankaj Chauhan for their assistance in preparing the manuscript.

1 Introduction 1-6

1.1 Definition of Spectroscopy and Their Various Types 1

1.2 I.R.and Raman Spectra 5

1.3 Classical Concept of Vibrational and Rotational Motions 5

2 Theoretical Concepts of Vibrational Spectroscopy A Brief Overview 7-70

2.1 Classification of Motions 7

2.2 Motion in Liquid and Solid State 9

2.3 Basic Concepts of Study of Vibrational Spectra 10

2.4 Vibrating System of Point Masses. General Qualitative Description of Vibrational Calculation 12

2.5 Internal Coordinates 23

2.6 Calculation of Vibrational Frequencies using Internal Coordinates 24

2.7 Relationship between Cartesian and Internal Coordinates [F and G Matrices] 28

2.8 G. Matrix 30

2.9 Exploitation of Symmetry in the Calculation of Either Force Constants or Molecular Frequencies 32

2.1O Classes 42

2.11 Group Multiplication Table 43

2.12 Representations of Groups 44

2.13 Properties of lrreducible Representations 52

2.14 Representation Spanned by Internal Coordinates 60

2.15 Quantitative Applications of Symmetry Coordinates and their Quantitative Applications 63

2.16 Potential and Kinetic Energy, Symmetry Factoring of G and F Matrices and Secular Determinant using Symmetry Coordinates 66

2.17 Selection Rules 67

2.18 Summary 68

3 Group Frequency Concept and Its Applications-General Review of Organic and Inorganic Compounds 71-110

3.1 Definition of Group Frequency 73

3.2 Group Frequencies of AXn Type of Molecules 75

3.3 Factors Responsible for the Shifts of the Characteristic Band Positions 81

3.4 Limitations of Group Frequency Concept 88

3.5 Group Frequency Tables 90

3.6 Some Miscellaneous Topics Related to Group Frequency of l.R. Bands 90

3.7 Infrared Spectra of Organic and Inorganic Compounds 94

3.8 Examples 1O1

4. Experimental Methods and Interpretation of IR Spectra of Some Molecules 111-144

4.1 Sampling of Materials 112

4.2 Instrumentation 120

4.3 Fourier Transform Instruments 130

5 Problems with Solutions 145-258

Appendix 259-286

Index 287-288

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