The post-Born-Oppenheimer regime: dynamics of electronic motion in molecules by attosecond few-cycle spectroscopy

Dynamics of electronic motion when the nuclei are clamped is discussed and shown to be always described as a superposition of adiabatic electronic states. These states are stationary when the nuclei are clamped but their superposition leads to multiply periodic motion where the natural frequencies are the differences in the energies of the adiabatic electronic states. When one or more of the frequencies are low and the atoms are allowed to move, the electronic rearrangement is commensurate with the motion of the nuclei. This is the usual breakdown of the Born-Oppenheimer approximation. But when the electronic frequencies are higher there is an electronic motion before the nuclei move. The motion can be demonstrated through expectation values such as the multipole moments of the charge distribution. Such superposition states will be excited when the laser pulse width in energy exceeds the spacings of the states. For low-lying valence excited or low Rydberg states this requires a femtosecond or shorter laser pulse. Since the carrier frequency has to be comparable to the excitation energy, the required laser pulses must span only a few cycles.