Approximation Schemes to Include Nuclear Motion in Laser-Driven Ab Initio Electron Dynamics: Application to High Harmonic Generation.

The quantum mechanical description of many-electron dynamics in molecules driven by short laser pulses is at the heart of theoretical attochemistry. In addition to the formidable time-dependent electronic structure problem, the field faces the challenge that nuclear motion, ideally also treated quantum mechanically, may not be negligible, but scales enormously in effort. As a consequence, most first-principles calculations on ultrafast electron dynamics in molecules are done within the fixed-nuclear approximation. For laser-pulse excitation in H 2 + , where an "exact" treatment of the coupled nuclear-electron dynamics is possible, it has been shown that nuclear motion can have a nonnegligible impact on high harmonic generation (HHG) spectra (Witzorky et al. , J. Chem. Theor. Comput. 2021, 17 , 7353-7365). It is not so clear, however, how to include (quantum) nuclear motion also for more complicated molecules, with more electrons and/or nuclei, in particular when the electronic structure is described by correlated, multistate wavefunction methods such as the time-dependent configuration interaction (TD-CI). In this work, we suggest a scheme in which the Born-Oppenheimer potential energy surfaces of a molecule are approximated by model potentials (harmonic and asymptotic, as an expansion in 1/ R ), obtained from only a few ab initio calculations, with the prospect to treat complex molecular systems. The method is tested successfully for HHG by few-cycle laser pulses for the "exact" H 2 + reference. It is then applied for diatomic molecules with more electrons and for a two-dimensional model of the water molecule using TD-CIS (S = single) for the electronic structure part.