  The assumptions underpinning the adiabatic Born-Oppenheimer (BO)
approximation are broken for molecules interacting with attosecond laser
pulses, which generate complicated coupled electronic-nuclear wavepackets that
generally will have components of electronic and dissociation continua as well
as bound-state contributions. The conceptually most straightforward way to
overcome this challenge is to treat the electronic and nuclear degrees of
freedom on equal quantum-mechanical footing by not invoking the BO
approximation at all. Explicitly correlated Gaussian (ECG) basis functions have
proved successful for non-BO calculations of stationary molecular states and
energies, reproducing rovibrational absorption spectra with very high accuracy.
In this paper, we present a proof-of-principle study of the ability of fully
flexible ECGs (FFECGs) to capture the intricate electronic and rovibrational
dynamics generated by short, high-intensity laser pulses. By fitting linear
combinations of FFECGs to accurate wave function histories obtained on a large
real-space grid for a regularized 2D model of the hydrogen atom and for the 2D
Morse potential we demonstrate that FFECGs provide a very compact description
of laser-driven electronic and rovibrational dynamics.
