E × e Jahn-Teller effect in the P ₄⁺ cation and its signatures in the photoelectron spectrum of P₄

The Jahn-Teller effect in the electronic ground state of the P4+ radical cation, which is one of the strongest E×e Jahn-Teller effects known in nature, has been revisited in this work with computational methods. The relevance of the Jahn-Teller coupling terms beyond second order in normal-mode displacements has been investigated. An elegant and efficient scheme based on polynomial invariant theory has been employed to expand the E×e potential energy matrix up to arbitrarily high orders in normal mode displacements. Using the state-averaged complete-active-space self-consistent-field method and a correlation consistent double-ζ basis set, an accurate ab initio adiabatic E×e Jahn-Teller potential-energy surface was obtained. It is shown that a polynomial expansion of least up to sixth order is necessary to account for the pronounced anharmonicity of the ab initio potential-energy surface for large amplitude displacements of the Jahn-Teller active vibrational mode. The vibronic structure of the X¯²E band of the photoelectron spectrum of P₄ has been computed using a time-dependent wave-packet propagation method. The results reveal the significance of the higher-order Jahn-Teller coupling terms for the high-resolution vibronic spectrum as well as for the low-resolution band shape.