The Jahn-Teller effect in icosahedral symmetry: extension of Ham factors in strongly coupled systems

We extend the standard definition of 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 quarter and quintet, G and H. We calculate all the standard reduction factors as well as extended matrix elements, for the icosahedral systems G(X)g, G(X)h and H(X)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.