Time-dependent Born–Oppenheimer approximation approach for Schrödinger equation: Application to H2+

► An easy-to-compute time-dependent BO approximation approach is introduced.
► Our approach is applied to numerically solve the TDSE of a 1D H2+ model.
► The wavefunctions and HHG calculated by BO and non-BO approaches are similar.
► Our approach is feasible and precise for medium laser intensity.

We deploy a time-dependent Born–Oppenheimer approximation approach for numerically solving the time-dependent Schrödinger equation (TDSE) by reducing the wavefunction dimensionality to nuclear and electronic degrees of freedom, and apply it to a one-dimensional model of H2+. Based upon our three distinct error evaluation schemes, we quantitatively compare the wavefunctions and HHG spectra which are computed by the present approximation method, with those obtained by fully solving the TDSE. The similarities of both the wavefunctions and the HHG spectra justify that our approach is feasibly precise for medium laser intensity. It is also anticipated that this approximation can be adopted for other polyatomic molecules with a dimensionality reduction and computational simplification in calculating the time-dependent wavefunctions.