A Unified Hamiltonian Formalism of Jahn-Teller and Pseudo-Jahn-Teller Problems in Axial Symmetries

A formalism for expansions of all Jahn-Teller and pseudo-Jahn-Teller Hamiltonian operators in all axial symmetries is presented. The formalism provides Hamiltonian expansions up to arbitrarily high order and including an arbitrary number of vibra?tional modes, which are of arbitrary types. It consists of three equations and two tables. The formalism is user-friendly since it can be used without understanding its derivation. An example of E00 3 ⊗ e 0 1 Jahn-Teller interaction of cycloheptatrienyl cation is used to demonstrate the correctness of the formalism. A Python program is devel?oped to automate the generation of Hamiltonian expansions for all axial Jahn-Teller and pseodo-Jahn-Teller problems, , and interface the expansions to quantum dynamics simulation program. This is the first unified Hamiltonian formalism for axial Jahn?Teller and pseudo-Jahn-Teller problems. And it is the only one.