Molecular symmetry with quaternions

A new and relatively simple version of the quaternion calculus is offered w hich is especially suitable for applications in molecular symmetry and stru cture. After introducing the real quaternion algebra and its classical matr ix representation in the group SO(4) the relations with vectors in 3-space and the connection with the rotation group SO(3) through automorphism. prop erties of the algebra are discussed. The correlation of the unit quaternion s with both the Cayley-Klein and the Euler parameters through the group SU( 2) is presented. Besides rotations the extension of quaternions to other im portant symmetry operations, reflections and the spatial inversion, is give n. Finally, the power of the quaternion calculus for molecular symmetry pro blems is revealed by treating some examples applied to icosahedral symmetry . (C) 2001 Elsevier Science B.V. All rights reserved.