Dynamics and structure of single-mode Jahn-Teller vibronic coupling in a tetrahedral environment

Ebrahim Ghelichkhani, Purdue University

Abstract

The dynamics and structure of nuclear motion in the vicinity of a conical intersection do not follow the familiar Born-Oppenheimer approximation. The separation of electronic energy level for such case are not sufficiently large to avoid bifurcation of nuclear motion onto neighboring potential surfaces. A special case of the general principle of conical intersections in polyatomic molecules is the familiar Jahn-Teller vibronic coupling problem, which is a fully developed subject in molecular spectroscopy. Single-mode JT vibronic coupling of doubly and a triply degenerate electronic states with doubly and triply degenerate vibrational modes, in a tetrahedral point group, are investigated by exact numerical solutions of the corresponding Hamiltonians. Photoelectron spectra of the lowest $\sp2$E electronic states of tetrameric molecular clusters of the Group V elements P$\sb4\sp+$, As$\sb4\sp+$, and Sb$\sb4\sp+$, are studied. The degenerate ground state, in each case, undergoes Jahn-Teller distortion in the coordinate space of the doubly degenerate vibrational normal mode. Vibronic computations are carried out for these clusters and the results are compared with experimental ones. The correspondence between experiment and vibronic model calculations place the adiabatic ionization potential of P$\sb4$ at 8.95 eV, of As$\sb4$ at 7.83, and of Sb$\sb4$ at 6.61 eV. The Jahn-Teller problem of a triply degenerate electronic state with a doubly degenerate normal mode is explored, using exact as well as numerical methods. Vibronic level structures of the diagonal T $\otimes$ e Hamiltonian are studied for both linear and linear-plus-quadratic terms. The full numerical solution to one-parameter linear T $\otimes$ t problem is worked out. The vibronic eigenlevels are computed with respect to variation of linear coupling parameter from which a few lower states are displayed in a correlation diagram. The impact of linear coupling strength on the Franck-Condon distribution of spectral intensities from a totally symmetric originating ground state is characterized. The jet-cooled ultraviolet two-photon absorption spectra of the 3s($\sp2$T$\sb2$) Rydberg states of adamantane-h$\sb{16}$, -d$\sb{16}$ are obtained in a supersonic molecular beam. The low energy features of these spectra are interpreted successfully with reference to a numerical solution of the T $\otimes$ $\tau$ JT vibronic coupling problem.

Degree

Ph.D.

Advisors

Grant, Purdue University.

Subject Area

Chemistry

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