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Title: A survey on application of representation theory to molecular vibration

Representations Theory is used extensively in many of the physical sciences as every physical system has a symmetry group G. Various differential equations determine the vibration of a molecule, and the symmetry group of the molecule acts on the space of solutions of these equations. In this paper we use CH{sub 4} (methane) molecule, which has four hydrogen atoms at the corners of a regular tetrahedron, and a carbon atom at the center of the tetrahedron. The four hydrogen atoms in CH{sub 4} are permuted by the action of the symmetry group and this action fixes the carbon atom. At each of the 5 vertices, we assign three unit vectors, called the standard basis vectors in directions of the three edges which are joined to the vertex. The symmetry group G of the molecules permutes the 15 standard basis vectors, so we may regard Q{sup 15} as a GG By expressing Q{sup 15} as a direct sum of irreducible GG-modules, the problem of finding the normal modes of vibration is reduced to that of computing the eigenvectors of some small matrices.
Authors:
;  [1]
  1. Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung (Indonesia)
Publication Date:
OSTI Identifier:
22265987
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1589; Journal Issue: 1; Conference: ICMNS 2012: 4. international conference on mathematics and natural sciences: Science for health, food and sustainable energy, Bandung (Indonesia), 8-9 Nov 2012; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ATOMS; CARBON; DIFFERENTIAL EQUATIONS; EIGENVECTORS; HYDROGEN; METHANE; SYMMETRY GROUPS; VECTORS