THE JAHN-TELLER EFFECT IN ICOSAHEDRAL SYMMETRY - EXTENSION OF HAM FACTORS IN STRONGLY COUPLED SYSTEMS

We extend the standard definition ol reduction factors (Ham factors) in strongly coupled Jahn-Teller (JT) systems. Our aim is to cover linear JT systems in which the vibronic ground state at strong coupling is in close proximity in energy to low-lying excited states belonging to singlet and non-trivial irreducible representations of the JT centre. Such a structure of low-lying vibronic states is present in the linear JT systems of the icosahedral orbital quartet and quintet, G and H. We calculate all the standard reduction factors as well as extended matrix elements, for the icosahedral systems G circle times g, G circle times h and H circle times g. We calculate the matrix of Ham factors needed to handle the extra multiplicity of an H operator in an H state. A direct group-theoretical approach which explains the origins of various features of our analysis is included.