Infrared Spectroscopy of Symmetric and Spherical Spindles for Space Observation 1

Pierre-Richard Dahoo, Azzedine Lakhlifi

• Verlag: Wiley-ISTE
• Jahr: 2021
• ISBN:
  9781119824053
• Auflage: 1
• Thema: Physical Sciences
• Thema: Spectroscopy & Spectrum Analysis

This book is dedicated to the description and application of various different theoretical models to identify the near and mid-infrared spectra of symmetric and spherical top molecules in their gaseous form.

Theoretical models based on the use of group theory are applied to rigid and non-rigid molecules, characterized by the phenomenon of tunneling and large amplitude motions. The calculation of vibration-rotation energy levels and the analysis of infrared transitions are applied to molecules of ammonia (NH3) and methane (CH4). The applications show how interactions at the molecular scale modify the near and mid-infrared spectra of isolated molecules, under the influence of the pressure of a nano-cage (the substitution site of a rare gas matrix, clathrate, fullerene or zeolite) or a surface, and allow us to identify the characteristics of the perturbing environment.

This book provides valuable support for teachers and researchers but is also intended for engineering students, working research engineers and Masters and doctorate students.

1
Group Theory in Infrared Spectroscopy

This chapter reviews the use of group theory methods for the study of a molecule using infrared (IR) spectroscopy. The application of group theory involves the use of character tables in the theory of representation of a point symmetry group associated with a molecule. The focus is on the elements of the theory of representation, which are used in the following chapters for the study of ammonia (NH₃) molecules (an example of a symmetric top), and methane (CH₄) (an example of a spherical top), and their isotopologues. Elements of the tensor operator algebra are also reviewed for the study of CH₄ within the framework of tensor formalism. The permutation-inversion group CNPI is also presented with reference to NH₃, in order to distinguish between the symmetry group based on the geometry of the molecule, i.e. on its symmetry elements, and the permutation group of the identical nuclei.

1.1. Introduction

The point symmetry group of a molecule reflects the geometric form of the molecule. It is well adapted to the Hamiltonian of Schrödinger’s equation, the energy operator which is the sum of the kinetic energy operator and the potential energy operator of the molecule, since it is built on space variables of the position of the electrons and nuclei. When the transformations involving identical nuclei exchanges are taken into account, the point symmetry group is not adapted to the study of the symmetries of the wave function which includes quantum variables related to the spins of identical nuclei when describing a vibration–rotation state for a given electronic state. The identical particle permutation group, which is the symmetric group S_n (not to be confused with th...