Origin of symmetry-forbidden high-order harmonic generation in the time-dependent Kohn-Sham formulation

We find, for two-electron closed-shell systems (${\mathrm{H}}_{2}$ molecule, $\mathrm{He}$ atom), symmetry-forbidden peaks in the high-order harmonic spectra obtained by the time-dependent Kohn-Sham equations, and clarify their origin. It turns out that fixation of the number of Kohn-Sham orbitals and their occupations gives rise to unphysical transition paths and, therefore, incorrect populations of the one-electron excited states, which leads to even-order harmonics in systems with inversion symmetry. We show that the time-dependent natural Kohn-Sham and time-dependent configuration interaction equations do not suffer from this shortcoming.