Applications in Vibrational Spectroscopy

The chapter is roughly divided into three sections. In the first (Sections 6.2 and 6.3) we look at the background theory of vibrational spectroscopy, including the selection rules for IR and Raman spectroscopy. We can already use reducible representations and the reduction formula to determine the symmetry labels for the vibrational modes of any molecule. 

Molecular Symmetry David J. Willock 2009 John Wiley Sons, Ltd. ISBN 978-0-470-85347-4 

Telescope Imaging Spectrograph (STIS) observations of HD 37903 showing vibrational fine structure of the UV region of the spectrum. The observed lines are evidence of UV absorption by vibrationally excited H2. (Source Meyer DM, Lauroesch JT, Sofia Uj, Draine BT, Bertoldi F 

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Neural network methods require a fixed length representation of the data to be processed. Vibrational spectra recorded usually fulfill this requirement. With most applications in vibrational spectroscopy, the spectral range and resolution are fixed, and a comparison of spectra from different sources is directly possible. Appropriate scaling of the spectra allows handling different resolutions to obtain the same number of components in a descriptor. Digitized vibrational spectra typically contain absorbance or transmission values in wave-number format. Most of the spectrometers provide the standardized spectral data format JCAMP-DX developed by the Working Party on Spectroscopic Data Standards from the International Union of Pure and Applied Chemistry (lUPAC) [48]. 

Sathayanarayana DN (2004) Theory and application. In Vibrational spectroscopy. New Age International, New Delhi... 

In this chapter we will explore further the symmetry operations that are used to describe molecular structure. New operations are introduced to complete the set used in molecular symmetry. Particular sets of operations often recur, with many molecules having the same collection of operations. Once we establish how the properties of a molecule depend on the set of valid operations, this will mean that we can actually infer the properties of many related molecules of the same symmetry. The sets of operations are referred to as point groups, and our main task in this chapter is to introduce the concept of a point group. The formal construction of the point groups most commonly used in chemistry is carried out in Chapter 3. The properties of the point groups, and their application in vibrational spectroscopy and MO theory, are then the subject of the remainder of the book. 

Applications in Vibrational Spectroscopy 177 Then apply the reduetion formula to show that... 

Applications in Vibrational Spectroscopy 201 Table 6.14 The projection operator applied to the proposed generating function (bi — b ). 

Applications in Vibrational Spectroscopy 215 In the B2 vibration, 63 must have a zero coefficient, so that... 

Chapters 4 and 5 introduce the concepts of group theory, which makes symmetry indispensible for understanding many areas of chemistry. This book concentrates on applications in vibrational spectroscopy and molecular orbital theory and so illustrative examples are drawn from these areas. 

Chapter 6 covers applications in vibrational spectroscopy, specifically dealing with infra-red and Raman. The chapter explains how symmetry is used to rationalise experimental data to help determine the shape and structure of molecules. To do this some background on the physical origin of spectral bands and the role of symmetry in determining selection rules is given. 

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