Deviations from Born-Oppenheimer Theory in Structural Chemistry: Jahn-Teller, Pseudo Jahn-Teller, and Hidden Pseudo Jahn-Teller Effects in C₃H₃ and C₃H₃<SUP>-</SUP>

Abstract

The electronic structure and vibronic coupling in two similar molecular systems, radical C3H3 and anion C3H3-, in ground and excited states, are investigated in detail to show how their equilibrium structures, in deviation from the Born-Oppenheimer approximation, originate from the vibronic mixing of at least two electronic states, producing the Jahn-Teller UT), pseudo JT (PJT), and hidden PJT effects. Starting with the high-symmetry geometry D3h of C3H3, we evaluated its 2-fold degenerate ground electronic state 2E" and two lowest excited states 2A,' and 2E' and found that all of them contribute to the distortion of the ground state via the JT vibronic coupling problem E" e' and two PJT problems (E" + A(1)') circle star e" and (E" + E') circle times (a2" + e"); all the three active normal modes e'(1335 e"(1030 cm(-1)), and a2"(778 cm(-1)) are imaginary, meaning that all the three vibronic couplings are sufficiently strong to cause instability, albeit in different directions. The first of them, the ground state JT effect, enhances one of the C-C bonds (toward an ethylenic form with C-2v symmetry), while the two PJT effects produce, respectively, cis (a(2)" toward C-3v symmetry) and trans (e") puckering of the hydrogen atoms. As a result, C3H3 has two coexisting equilibrium configurations with different geometry. In the C3H3- anion, the ground electronic state in DA symmetry is an orbitally nondegenerate spin triplet (3)A(2)' with a group of close in energy singlet and triplet excited states in the order of (1)A(1),', (3)A(1)', E-1", E-3", and E-1'. This shows that two PJT couplings, (3A(2)' + (3)A(1)") circle times a(2)" and (3A2' + 3E") e", may influence the geometry of the equilibrium structure in the 3A2' state. Indeed, both vibrational modes, a(2)"(1034 cm(-1)) and e"(1284 cm(-1)), are imaginary in this state. Similar to the radical case, they produce, respectively, cis (a(2)") and trans (e") puckering of the hydrogen atoms, but no e' distortion of the basic C-3 triangle; the equilibrium configuration with Cs symmetry occurs along the stronger e" distortions. Another higher-in-energy triplet-state minimum with C-2v symmetry emerges as a result of a strong JTE in the excited 3E" electronic state. In addition to these APES minima with spin-triplet electronic states, the system has a coexisting minimum with a spin-singlet electronic state, which is shown to be due to the hidden PJT effect that couples two singlet excited states. The two lowest equilibrium configurations of the C3H3- anion with different geometry and spin realize a (common to all electronic e(2) configurations) magnetic and structural bistability accompanied by a spin crossover. Some general spectroscopic consequences are also noted. As a whole, this article is intended to demonstrate the efficiency of the vibronic coupling approach in rationalizing the origin of complicated structural features of molecular systems as due to a combination of nonadiabatic JT effects.