Eur. Phys. J. D Volume 42, Number 1 Pages 61-72 (2007) The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics Category Molecular Physics and Chemical Physics LOCAL MODES OF SILANE WITHIN THE FRAMEWORK OF STRETCHING VIBRATIONAL POLYADS H. Crogman^1, V. Boudon^1 and D.A. Sadovskií^2 1 Institut Carnot de Bourgogne, UMR 5209 CNRS-Université de Bourgogne, 9 avenue Alain Savary, B.P. 47870, 21078 Dijon, France 2 Université du Littoral, Département de physique, 59140 Dunkerque, France sadovski@univ-littoral.fr (Received 9 October 2006 / Received in final form 12 December 2006 / Published online 19 January 2007) Abstract We define stretching relative equilibria (RE) of silane and other similar tetrahedral molecules in terms of the dynamical polyad symmetry which assumes the resonance condition 1:1 between the two stretching vibrational modes $\nu_1$ and $\nu_3$ of the molecule. Exploiting symmetry and topology arguments and reducing the dimension of the classical mechanical system, we find these RE. One of them, with local symmetry C3v and minimal energy within a polyad, corresponds to the local modes. We give the upper energy limit of the local mode localization within a polyad. PACS 33.15.Mt - Rotation, vibration, and vibration-rotation constants. 33.20.Vq - Vibration-rotation analysis. DOI: 10.1140/epjd/e2007-00011-3 © EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2007