Icosahedral hybrid orbitals

A set of twelve equivalent icosahedral hybrid orbitals pointing from the ce ntre to the corners of a regular icosahedron has been obtained. Such hybrid s can be used to explain the geometry of twelve-coordinate complexes of a r are-earth atom. Using group theoretical considerations, it is shown that th ese hybrids can be constructed by linear combination of one s, three p, fiv e d and three f-orbitals. Bearing in mind that the twelve hybrids have iden tical shape but are oriented differently in space, their mathematical expre ssions have been obtained by applying geometrical transformations to the sp (3)d(5)f(3) hybrid pointing along the positive z-axis. In order to obtain e legant mathematical expressions, the x, y and z axes have been chosen to be coincident with three orthogonal binary axes of the icosahedron. (C) 2000 Elsevier Science B.V. All rights reserved.