CHEMISTRY PAPER No.13 : MODULE No.24

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CHEMISTRY

PAPER No.13 : Application of Group theory and its applications MODULE No.24 : Group theory and vibrational spectroscopy part-1

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Subject Chemistry

Paper No and Title 13 Applications of molecular symmetry and group theory

Module No and Title 24, Group theory and vibrational spectroscopy part-1

Module Tag CHE_P13_M24

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TABLE OF CONTENTS 1. Learning Outcomes 2. Introduction 3. Role of symmetry in vibrational spectral studies 3. 1Normal Modes of Vibration 4.(A)Infrared Spectroscopy (IR): 4.1 Factors increasing the number of absorption bands 4.2 Factors limiting the number of absorption bands 4.3 Block diagram for a common IR spectrometer 4.4 Detectors 5. Summary

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1. Learning Outcomes

After studying this module, you shall be able to

• Know about spectroscopy • Learn about IR spectroscopy • Define vibrational modes and normal modes of vibration • Learn basics of IR spectroscopy • Learn about the interaction of electromagnet waves with molecules • Learn about instrumentation • Learn about basic parts of instrument and source of IR radiations

2. Introduction

We have studied in earlier modules about the symmetry of the molecules. To what point group molecule belongs? What are the different types of symmetry elements present in the molecules? How many symmetry operations are generated? It is the symmetry operations that constitute a group. How to represent a group using various functions as the basis? What is reducible representation and how it can be reduced to irreducible representations? We have also learnt about character table of a point group and why these are important to a chemist? Now we will make use of all the knowledge about symmetry and group theory in dealing with the chemical applications of bonding, MO formation vibrational spectra of transitional metal complexes etc. In this module we will discuss vibrational spectroscopy in light of symmetry of the molecule. The Symmetry of the molecules and solids is very important and is very powerful tool in the hand of chemists for understanding of bonding and physical properties. Infrared spectroscopy is one of the most important analytical techniques available to scientists. One of the great advantages of infrared spectroscopy is that any sample in any state may be investigated .Liquids, solutions, pastes, powders, films, fibres, gases and surfaces can all be investigated properly and with accuracy. Infrared spectroscopy is a technique based on the vibrations of the atoms of a molecule. An infrared spectrum is commonly obtained by passing infrared radiation through a sample and determining what fraction of the incident radiation is absorbed at a particular energy. The energy at which any peak in an absorption spectrum appears corresponds to the frequency of a vibration of a part of a sample molecule. The point group theory of molecular symmetry will now be used for interpreting the vibrational spectra of the molecules.

3. Role of symmetry in vibrational spectral studies

The presence of certain symmetry in molecules greatly reduces the efforts in predicting the molecular properties of molecules. In earlier chapters we have seen that how Г3N can be obtained and reduced to irreducible representations of the point group to which the molecule belongs. In this chapter we will make

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use of these principles to have good deal of information’s about IR and Raman spectra of the molecules. A vibrational spectroscopy - IR and Raman are the most common vibrational spectroscopies for assessing molecular motion and fingerprinting species. Routine energy range of IR/Raman is 200 - 4000 cm–1. One of the practical uses of point groups and group theory for the inorganic chemist in is predicting the number of infrared and Raman bands that may be expected from a molecule. Spectroscopic techniques all work on the principle of that, under certain conditions, materials absorb or emit energy. Different spectroscopic techniques operate over different, limited frequency ranges within this broad spectrum, depending on the processes and magnitudes of the energy changes. The infrared region of the spectrum encompasses radiation with wave numbers ranging from about 12,800 to 10 cm-1 or wavelengths from 0.78 to 1000 µm. The infrared spectrum is divided into near-, mid-, and far-infrared radiation. Table -1 gives energy ranges for these regions. Table.1 IR spectral regions

Region Wavelength cm-1 Frequecies(v),Hz Near 12800 to4000 3.8x1014to1.2x1014 Middle 4000-200 1.2x1014to 6.0x1012 Far 200to10 6.0x1012 to 3.0x1011 Commonaly used 4000 to 670 1.2x1014to 2.0x1013 3.1 Normal Modes of Vibration The complex vibrations of a molecule are the superposition of relatively simple vibrations called the normal modes of vibration. Each of these vibrational motions involve displacement of the atoms or deformation of angles .These independent displacements/deformations are called normal modes of vibrations of the molecules. These are generally divided in bond stretchings and angle deformations. Each of these vibrational modes occur at characteristics energy/ frequency which is dependent on the strength of restoring force, called as restoring force constant. Each normal mode of vibration has a fixed frequency. It is easy to calculate the expected number of normal modes for a molecule made up of N atoms. For N atomic molecule the degrees of freedom are 3N. Out of these we have to take care of three translational motions along x-,y-,z- axes and three rotational degrees of freedom, Rx,Ry,Rz rotations about x,y,z axes respectively. A mode in which all atoms are moving in the same direction is equivalent to moving the molecule in that direction. A mode in which atoms move to rotate (change the orientation of) the molecule. There are 3 rotational modes for nonlinear molecules, and 2 rotational modes for linear molecules. These motions also occur when molecule absorbs IR radiations. These translational and rotational modes are shown in the figure.1

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Translational Modes

Rotational Modes

x

y

z

z

y

x

Fig.1 Translational and rotational modes of a tri atomic molecule (i) Linear molecule of N atoms has normal modes = 3N – 5 as rotation about molecule is generally forbidden (ii) Nonlinear/bent molecule/ of N atoms has normal modes = 3N - 6 The symmetries of the normal modes can be classified with the help of symmetry and group theory. Some these modes of vibrations for linear and nonlinear molecules are given in fig.2

C OOSymmetric stretch

C OO Antisymmetric stretch

CO

O

C OO

Bending

Linear molecule CO2 3N-5

O

HH

O

HH

O

HH

non linear H2O 3N- 6

Fig.2 Normal modes of vibrations for linear and non linear molecules

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Various bond stretching and bond angle deformations which can be made as basis for representations in IR spectroscopy are shown in figure.3

O

H

H O

H

HIn plane bending

Out of planbending

O

H

H

Rocking Scissoring

O

H

H

Wagging Twisting

O

HH

O

HH

Symmetric stretching

Antisymmetric stretching

Fig.3 Various bond stretching and angle deformation modes of vibration in tri atomic molecule

All these modes vibrate with different frequency and thus require different energy to occur. How the values these characteristics energy/ frequency are obtained? There two complimentary techniques available for this (A)Infrared Spectroscopy (IR)

(B)Raman spectroscopy (R) .Both these techniques when used together provide lot of information about molecular bonding. Let us mention the basic principles of these techniques. The fundamental difference between IR and Raman techniques is that in the former absorption of photons is studied in later case scattering of photons (elastic and non-elastic) is studied. Detailed discussion of these techniques is beyond the scope this manuscript. However, fundamental principles of these will be mentioned in very brief. 4. (A)Infrared Spectroscopy (IR): In infrared spectroscopy if a sample is irradiated with infrared light, then those frequencies that match the corresponding frequencies of vibrational modes will be absorbed i.e., absorbed frequency can be measured. During infrared radiation on the molecule, rotational motions of the molecule , translational motions of the molecule, vibration of bonds in the molecule and angle deformations in the molecule do occur depending of the frequency range. Rotational and translation motions complicate the investigations. So we have to account for these motions. In order the absorption of IR radiations by the molecule occur following two conditions must be satisfied (a) Dipole moment the molecule must change as a result of molecular vibration. The change in dipole moment allows the electric field component of electromagnet radiations to interact with the molecule’s electric diploe moment. The symmetric molecules which do not have dipole moment during vibrations do not interact with the electromagnet radiations. And thus these are IR inactive.

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(b) The frequency of IR radiations must match the natural frequency of vibrations of the molecule. If there is mismatch in frequencies there will be absorption of IR radiations. The three types of molecular transitions may occur during IR radiations. (i)When a molecule rotates about its centre of mass about any one of the axes, the electric field component fluctuates. Due to these fluctuation interactions between external electric field and internal natural electric field absorption of IR radiations may be occur. The transition energy range is of the order υ <100cm-1. Due to this vibrational peak in IR spectrum is further divided and thus complicates the investigations (ii) Vibrational-rotational transitions. This type of transition may arise due to molecular electric dipole moment caused by the combination of bond vibration and molecular rotation. (iii) In mid-IR region most of the important vibrational transitions occur. This frequency range is of the

order υ =13000 -675 cm-1. In IR spectroscopy quanta of radiation in IR region have energy comparable to those required for vibrational transitions in molecules. The energy of a molecule is the sum of energies of types E =Eele +Evib+Erot +Etra +Enuc Eele: is the electronic energy of all the electrons of the molecule Evib: is the vibrational energy of the molecule, i.e., the sum of the vibrations of the atoms in the molecule Erot: is the rotational energy of the molecule, which can rotate about the three axes, x,y,z Etra: is the translational energy of the molecule, which is due to the movement of the molecule as a whole along the three cartesian axes, x, y, z Enuc: is the nuclear energy. This technique is based on two fundamental principles/laws: (i) Hookes law and (ii) Franck-Condon principle. According to Hooke’s law a diatomic system may be assumed to be equivalent to a system of two masses A and B joined by a spring or a spring hooked to a wall fig.4

A B A B

A

unstretchedstretched

A

wall

Fig .4 Masses A and B held together with spring and a spring hooked to wall

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If the spring is stretched and then let it go. It will start vibrating about an equilibrium position. Hooke’s law is F = -kx F is the restoring force acting on the system to bring back it to original position where x is the distance

from equilibrium position, k= force constant which describes stiffness of the spring. Negative sign means restoring force. Diatomic system A-B may be treated in similar manner. The restoring force that acts on two atomic masses is related as

∆E=h/2п√ (k/µ) Where ∆E is the energy difference between ground vibrational quantum state and first excited

vibrational quantum state ie Eυ0→ Eυ+1; υ represents vibrational quantum state, k is force constant and µ is the reduced mass; µ= mAmB/ (mA+mB) where mA and mB are masses of atoms A and B respectively. Since most molecules are in υ0 vibrational quantum state at room temperature, and thus most transition will occur from

Eυ0→ Eυ+1 Frequency corresponding to this transition energy is called fundamental frequency as shown in figure .5.

υ0

υ2υ1υ1

υ0

υ3υ2

υ3

123

interatomic distances

Fig .5 Vibrational states corresponding to normal vibraional modes in Harminic Oscillator

potential energy

Therefore, first selection rule in IR spectroscopy is that the absorption of radiations will occur for transition for which ∆υ=±1only and second rule says that electric field component of electromagnetic radiations in IR region will interact with electric field component of oscillating electric dipole moment in the molecule as it vibrates. Any change in dipole moment or change in its direction will give different oscillating field components of dipole moment which can interact with electric field component of electromagnetic radiations and absorption of radiations can occur. The transition (1) is fundamental frequency corresponding to a normal mode of vibration. Transitions (2) and (3) are not fundamentals and these are first and second overtone’s frequencies. The intensities of overtones are generally less that of fundamental frequency. Though at molecular level it is not so simple and this model does not hold good and there are deviations from this model.

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(ii) According to Franck Condon principle transitions tend to take place between two vibrational states in which nuclear configurations remain same in both the states and these tend to occur when nuclear kinetic energies are very small. Most common energy sources in IR are (i) Nernst glower (ii) Globar (iii) Incandescent wire 4.1 Factors increasing the number of absorption bands (i) Overtone absorption bands occur at frequencies which are multiples of the fundamental frequencies. (ii) Combination bands are observed when two fundamental vibrations interact due to symmetry equivalence with each other and are influenced by radiation at the combined frequency. (iii) Vibrational-Rotational bands are found with single vibration mode and occur at low and high frequencies. Complex gas IR spectra are due to these Vibrational-Rotational bands (iv)Harmonic coupling bands are observed due to coupling of adjacent groups of nearly identical oscillation. 4.2 Factors limiting the number of absorption bands (i) No change in dipole moment due to symmetry of the molecule. (ii) Degeneracy: Vibrational frequencies located too closely. (iii) Weak absorptions. Detailed discussion of these factors is beyond the scope of this module. 4.3 Block diagram for a common IR spectrometer The block diagram is given in figure.6. The main parts of an IR spectrometer are: (i) IR radiation source (ii) Dispersing element and Diffraction grating (iii) Optical mirror system (iv) IR radiation detector

Fig.6 Block diagram of a dispersive IR spectrometer

reference

sample

IR source

IRdetector

Amplification

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The IR radiations from source, after reflections at flat mirrors and rotating mirrors pass through reference and sample. Transmitted light is amplified and then detected by IR detector.

4.4 Detectors There are three categories of detector;

• Thermal • Pyroelectric • Photoconducting

5. Summary

• Discussed about spectroscopy • Information about IR spectroscopy provided • Definition of vibrational modes and normal modes of vibration given • Basics of IR spectroscopy discussed in very brief • What is the source of interaction of electromagnet waves with molecules discussed in brief • Block diagram of IR spectrometer is given and various parts of it are mentioned

CHEMISTRY PAPER No.13 : MODULE No.24

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