Electron-nuclear quantum dynamics of diatomic molecules: nonadiabatic signatures in molecular spectra

The Born–Oppenheimer approximation is the fundamental approximation in the quantum-mechanical description of molecules, and holds true in most applications for ground-state properties and to a lesser extent for excited states. In situations where the coupling of electronic and nuclear motion becomes significant, for example, in strong-field induced time-dependent processes, the electron-nuclear interaction must be described beyond the Born–Oppenheimer picture. Presented here are multiconfiguration electron-nuclear dynamics simulations with and without a laser pulse excitation for the diatomic molecules H${}_2$, HeH$+$, LiH, BeH$+$, Li${}_2$, and N${}_2$, taking into account electron-nuclear coupling. The computational approach allows a direct propagation of the electron-nuclear wave function, thus avoiding the construction of potential energy surfaces. With this approach, ground-state and time-dependent properties, including equilibrium bond lengths, dipole moments, and electronic, vibrational, and high-harmonic spectra are obtained. For some of the diatomics, manifestations of nonadiabatic effects are observed in the high-harmonic spectra, where both an uptake of nuclear motion and electronic excitation into higher-lying excited states can occur, resulting in an effective driving force that displaces the nuclei from the equilibrium position. Isotope effects can also be observed in electronic excitation spectra.