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.

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