Jahn-Teller theory beyond the standard model

In the standard model of Jahn-Teller (JT) theory, the spin-free electronic Hamiltonian is expanded up to second order in normal-mode displacements, while the spinorbit (SO) coupling operator is approximated in zeroth order. In this article, the systematic extension of JT theory beyond the standard model is outlined. For the classic E x e and T(2)xt(2) JT problems in C-3v and T-d symmetry, respectively, it is shown how the conventional Taylor expansion of the spin-free Hamiltonian can be replaced by an expansion in invariant polynomials up to arbitrarily high orders. The theory of SO coupling in JT systems is extended beyond the standard model by an expansion of the Breit-Pauli SO-coupling operator up to first order in normal-mode displacements. The spectroscopic relevance of the higher-order electrostatic and the linear relativistic JT coupling terms is illustrated for the vibronic structures of the photoelectron spectra of tetrahedral P-4 and Sb-4.