RESONANT X-RAY-SCATTERING BEYOND THE BORN-OPPENHEIMER APPROXIMATION -SYMMETRY-BREAKING IN THE OXYGEN RESONANT X-RAY-EMISSION SPECTRUM OF CARBON-DIOXIDE

Although resonant x-ray scattering of molecules fulfills strict electr onic symmetry selection rules, as now firmly proven by. spectra of dia tomic molecules, the accumulated body of data for polyatomic molecules indicates that an apparent breaking of these rules represents the com mon situation rather than the exception. The CO2 molecule provides a g ood example of symmetry breaking, with the. oxygen x-ray emission spec tra showing strong intensity for transitions that are forbidden by the parity selection rule. We present time-independent and time-dependent theories for frequency-dependent resonant x-ray scattering beyond, th e Born-Oppenheimer approximation in order to explore under what circum stances one can anticipate symmetry breaking in the spectra of polyato mic molecules. The theory starts out from the Kramers-Heisenberg dispe rsion relation and is generalized for vibrational degrees of freedom a nd for nonadiabatic coupling of the electronic (vibronic) states, incl uding the frequency dependency of, the scattering cross section. Diffe rent Limiting cases and few-level models are considered. The symmetry breaking is proven to be the result of pseudo-Jahn-Teller-Like vibroni c coupling between near-degenerate core-excited states. Thus vibromic interaction over the antisymmetric vibrational mode between the ''brig ht'' 1 sigma(g)(-1)2 pi(u)(-1) and ''dark'' 1 sigma(u)(-1)2 pi(u)(-1) intermediate states of CO2 allows transitions otherwise forbidden. The measurements and theory demonstrate that the symmetry-selective chara cter of the resonant x-ray emission is strongly frequency dependent. T he strong intensity of ''dipole-forbidden'' transitions in the pi oxy gen K spectrum at resonance is reduced monotonically with the detuning of the excitation energy from resonance, and the spectra become ''sym metry purified.'' Simulations with full vibronic coupling predict this feature of the x-ray scattering experiment and a few-level model expl ains the energy dependence of the symmetry selection and the symmetry purification at large detuning energies in the limit of narrowband pho ton excitation. (C) 1997 American Institute of physics.