Y Origin Of Symmetry-Forbidden High-Order Harmonic Generation In The Time-Dependent Kohn-Sham Formulation

We find, for two-electron closed-shell systems (H-2 molecule, 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 evenorder 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.