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

Abstract

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.

Real-Time Probing of Electron Dynamics Using Attosecond Time-Resolved Spectroscopy

“…This is at the core of so-called post-Born-Oppenheimer dynamics (5). Cederbaum and coworkers (104)(105)(106)(107)(108)(109)(110)(111) and Levine and coworkers (4,5,102,(112)(113)(114)(115)(116) performed extensive theoretical calculations that model charge migration processes in various polyatomic molecules.…”

“…A metal such as copper serves as the condensed-phase example: An electron traveling in the conduction band at the Fermi velocity (2) can traverse a distance equal to its lattice constant in ∼230 as. Correlation-driven electrons and holes in polyatomic molecules or widely spaced electronic superposition states are predicted to evolve on suboptical-cycle timescales (3)(4)(5)(6)(7)(8)(9). Generating attosecond pulses that can take snapshots of these processes is a prerequisite for understanding electron dynamics that precede, and perhaps even dictate, longer-time nuclear vibrational dynamics.…”

Attosecond pumping of nonstationary electronic states of LiH: Charge shake-up and electron density distortion

“…The relatively long vibrational period in LiH allows us to use a clamped nuclei computation. Otherwise, effects of nuclear motion must be included [12,[26][27][28][29]. The LiH molecule is small enough that an all-electron computation with an overly large basis set is possible.…”

Coherence revival during the attosecond electronic and nuclear quantum photodynamics of the ozone molecule

“…6 by the corresponding excited-state differential charge density at the FC point, Eq. (15). This local picture with respect to the nuclear coordinates illustrates the electron dynamics of the molecule at early times (during 5-6 fs), as long as the nuclear wave packets remain in the vicinity of the FC point.…”