Malaya Journal of Matematik, Vol. S, No. 2, 1103-1105, 2020

https://doi.org/10.26637/MJM0S20/0285

A Study on various modes of vibration in

C. Radhikaa 1

Abstract Spectroscopy deals with interaction of matter with electromagnetic energy and spectroscopists harvest wealth of information about the matter, from these interactions. Molecular Spectroscopy aims to understand the interaction of molecular energy with electromagnetic radiation possess various forms of energy due to its different kinds of motion and intermolecular interactions. For instance, it possess translational energy, rotational energy, vibrational energy etc., and these energies are quantized. Also the interactions between stem are very weak. Keywords Spectroscopy, molecular energy.

1Department of Physics, Bharath Institute of Higher Education and Research, Selaiyur, Chennai-600073, Tamil Nadu, India. Article History: Received 01 October 2020; Accepted 10 December 2020 c 2020 MJM.

Contents uids, solutions, melt, gases, films and absorbed species. It s important applications are : molecular structural determi- 1 Introduction...... 1103 nations, calculation of inter molecular and intra molecular 2 Fourier Transform Infra Red Spectroscopy...... 1103 forces, computation of degree of association in condensed phases,elucidation of molecular symmetries identification and 2.1 Molecular Vibrations...... 1103 characterization of new , deducing thermodynam- 2.2 Vibrational Modes...... 1104 ical properties of molecular system etc., Vibrational spec- 2.3 Normal Modes Of Vibrations...... 1104 troscopy has also contributed significantly to the growth of Molecular Energies • Rotational Energy • Vibrational Energy • other areas such as polymer chemistry, catalysis, fast reaction Electronic Energy dynamics, charge-transfer complex etc., 2.4 Vibrations...... 1104 Vibrational spectroscopy involves different methods, the most 3 Theory Of Infra Red Absorption ...... 1104 important of which are infrared and . Molecular vibrations which modulate the molecular dipole References...... 1105 moment, are visible in the Infrared spectrum, while those vibrations, which modulate the polarizability appear in the 1. Introduction Raman spectrum[2,3] . These two techniques yield compli- mentary information regarding molecular vibrations. Thus Spectroscopy deals with interaction of matter with electro- both these methods should necessarily used for a complete magnetic energy. Electromagnetic radiations can be allowed vibrational analysis of a . to interact with the molecular energy levels and radiations can be allowed to interact with the molecular energy levelsand investigation of these interactions can provide various infor- 2. Fourier Transform Infra Red mation regarding their rotation, charge localization, molec- Spectroscopy ular structure, symmetry, vibration etc., It is an established fact that the interactions of electromagnetic energy with the 2.1 Molecular Vibrations vibrational energy levels of the molecule provide amazing A molecule is not a rigid assembly of atoms, it can be viewed information on the molecular dynamics and vibrational spec- as a system of balls and springs of varying strengths, corre- troscopy emerge with theories and techniques to deal with sponding to the atoms and chemicalbonds of the molecule. such interactions[1,2]. There are two types of fundamental vibrations for molecules: The frontiers of vibrational spectroscopy are very wide, as Stretching, which the distance between two atoms decreases the techniques are applicable to solids, crystals, powder, liq- or increases, but the atoms remain in the same bond axis, and A Study on various modes of vibration in spectroscopy — 1104/1105

Bending (deformation), in which the position of the atom point masses. changes relative to the original bond axis. Each of the vibra- According to the Classical Theory, 2 tional motions of the molecule occurs with a certain frequency, Erot = 1/2 Iω which is characteristic of the molecule and of the particular Where I is the moment of inertia and ω is the angular velocity bond[3]. The energy involved in a particular vibration is char- of rotating molecule. acterized by the amplitude of the vibration, so that higher the vibrational energy, the larger amplitude of the motion. 2.3.3 Vibrational Energy According to the results of Quantum mechanics only certain This type of energy is associated with the oscillation of atoms vibrational energies are allowed to the molecule, and thus which are considered as point masses about only certain amplitudes are allowed. Associated with each equilibrium positions. The vibrational energy of a molecule is of the vibrational motions of the molecule, there is a series Evib= hγ(v+1/2) Where γ is the vibrational frequency and v is of energy levels. Transition between these vibrational energy the positive integer called the vibrational quantum number. levels in molecules occurs upon the absorption of electromag- netic radiation having energy equal to the difference in energy 2.3.4 Electronic Energy of levels involved. This is observed to lie in the IR region of This type of energy is associated with the motion of electrons the spectrum, IR spectroscopic deals with such transitions be- while considering the nuclei of atoms fixed points. The in- tween vibrational energy levels in molecules and is therefore crease in the electronic energy of molecule occurs due to an constitute a part of vibrational spectroscopy. increase in kinetic energy and potential energy of the electron of the molecule [3,4]. 2.2 Vibrational Modes An individual atom has three degrees of freedom in the Carte- sian coordinates (x,y,z) necessary to describe its position with 2.4 Vibrations respect to a fixed point in a molecule of N atoms has 3N Bond Vibration It denotes an increment (δr)in the bond degrees of freedom. Included in the 3N count are 3 transla- length of a diatomic molecule during a vibration. The vibra- tion vectors are along the bond and are define by the coordi- tional (x,y,z) and 3 rotational (Rx,Ry,Rz )modes. For a non linear molecule the remaining (3N-6) will be normal vibra- nate (δr). r is used to denote the stretching frequency. tional modes. In the case of linear molecules, there can be no rotation about the molecular axissince all nuclei lie on the Angle deformation It represents a change in the inter- axis, hence there are (3N-5) normal modes. Of these (3N-6) bond angle and the displacement vectors are perpendicular vibrational modes, (N-1) modes are bond stretching vibrations to the bond. The coordinate (δα) defines the angle bending and other (2N-5), (2N-4) for linear molecule modes are angle vibration. bending vibrations. Among them (3N-6) or (3N-5) normal mode of vibration, those that produce net change in the dipole moment of the Wagging A change in the angle between a bond or the molecule may result in IR activity and those that give polar- folding of a plane about a line through it defines a wagging izability changes may give rise to Raman activity. Naturally, mode. some vibrations can be both IR and RAMAN active. 3. Theory Of Infra Red Absorption 2.3 Normal Modes Of Vibrations Diatomic molecule has only stretching vibrations while poly IR radiation is not energetic enough to cause electronic transi- atomic molecules have stretching as well as deformation vibra- tion but the absorption of such radiation can cause vibrational tions[4]. The number of stretching vibrations is equal to the and rotational transitions. As a molecule vibrates, a regular number of valence bonds in the molecule and the remaining fluctuation in the dipole moment occurs establishing a field vibrations are deformation modes. Depending on the type of that can interact with the electric field of the IR radiation. If movement of the constituent nuclei of a molecule, the modes the frequency of the radiation exactly matches a natural vibra- may be termed as bending, rocking, wagging or torsional tional frequency of a molecule then a net transfer of energy modes. occurs and there is a resultant change in the amplitude of molecular vibration [5], which is reflected in a change in the 2.3.1 Molecular Energies radiation power monitored at a detector. This means that the A molecule may possess internal energy which can be divided IR spectrum of a molecule is characteristic of the compound in to three energies rotational energies and may be used for identification [6]. As a technique IR vibrational energies and electronic energies. spectroscopy is extremely useful because it is possible to look E =E + E + E int elec vib rot at intra molecular vibration such as stretching, bending, tor- 2.3.2 Rotational Energy sions and ring puckering and intermolecular vibration means This type of energy is associated with the overall rotation of interaction between two or more molecules such as in Vander the molecule with atoms considered as fixed Waals complexes and hydrogen bonding [7].

1104 A Study on various modes of vibration in spectroscopy — 1105/1105

Acknowledgement I am thankful to honorable chair- man Pro-chancellor, Vice Chancellor, Registrar, Dean R&D and Dean Engineering of Bharath University for their con- tinuous support and encouragement given to carry out this research work.

References [1] G. Herberg, Molecular spectra and molecular struc- ture, Von Nostrand Reinhold Company, New York, Vol II (1945) [2] Bernhard Schrader, Lnfrared& Raman, Spectroscopy, VCH Pub, Inc., New York, (1995). [3] D.N. Sathyanarayana, Vibrational Spectroscopy, New age International (P) limited, New Delhi, (1996) [4] N.B. Colthup, L.H.Daly, S.E. Wiberely, Introduction to Infra red & Raman Spectroscopy, Academic Press, New York, (1964). [5] D.A. Skoog, J.L. Leary, Principles of Instrumental Anal- ysis, Sannders College Publishing ,Toronto, (1992) [6] A.D. Cross, R.A. Jones,An Introduction to practical Infra red Spectroscopy, Butterworths& co London (1969) [7] A. Finch, P.N. Gates, F.N. Dickson, F.F. Bentley, Chemi- cal Applications of Far Infrared spectroscopy, academic Press, London, (1970).

????????? ISSN(P):2319 − 3786 Malaya Journal of Matematik ISSN(O):2321 − 5666 ?????????

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