Mohammad Reza Darafsheh,a*
Ali Reza Ashrafi,b and Arash Darafshehc
a Department of Mathematics, Statistics and Computer Science, Faculty of Science, University of Tehran, Tehran, Iran. E-mail: firstname.lastname@example.org
b Department of Mathematics, Faculty of Science, University of Kashan, Kashan, Iran
c Faculty of Science, Shahid Beheshti University, Tehran, Iran
The non-rigid molecule group theory in which the dynamical symmetry operations are defined as physical operations is applied to determine the character table for the full non-rigid molecule group (f-NRG) of tetramethylethylene. We show that the f-NRG of this molecule is a group of order 324, the structure of which is formed as the wreath product Z3∿(Z2×Z2), in which Z3 is the cyclic group of order 3 and Z2 denotes the cyclic group of order two. Using the group theory package GAP, we calculate the conjugacy classes and character table of this molecule.
Key words: non-rigid molecule group, tetramethylethylene, wreath product, character table