Dynamical symmetries and selection rules in high-harmonic generation spectroscopy of nonlinear molecules

In this work we have computed high-harmonic generation (HHG) spectra of H₂O and NH₃, interacting with linearly polarised pulses in different orientations. All the calculations have been carried out using the real-time time-dependent configuration interaction with single excitations (RT-TD-CIS) method with a Gaussian basis set. The selection rules in the HHG spectra, as computed with RT-TD-CIS, are interpreted in the framework of dynamical symmetries (DSs). These symmetries emerge as a combination of the temporal properties of the driving pulse and the spatial characteristics of the molecular electronic Hamiltonian and of the pulse. Moreover, multiple-orbital effects have been observed and analyzed. The findings underscore the pivotal role of DSs in shaping the HHG response, highlighting their ability to bridge the complex interactions between molecular structure, electronic transitions, and the pulse. We show that Gaussian-based RT-TD-CIS is a reliable tool to study the HHG spectra of aligned nonlinear molecules, and the role of ionisation/recombination channels in the dynamics.