Theoretical study of the odd–even-order harmonic generation for asymmetric ions in non-Born–Oppenheimer approximation

We calculated the harmonic spectra generated from the asymmetric molecules of HD⁺ and HeH²⁺. It is found that HD⁺produces only odd harmonics, while HeH²⁺ produces both odd and even harmonics. Further analysis reveals that for both HD⁺ and HeH²⁺, the nuclear dipole acceleration can generate even harmonics, but it is three orders of magnitude lower than that of the electron. Hence, the electronic dipole acceleration dominates the harmonic generation. For HD⁺, the electronic dipole acceleration only contributes to the generation of odd harmonics, but for HeH²⁺ it contributes to the generation of both odd and even harmonics. Besides, one concept of the broken degree of system-symmetry is proposed to explain the different odd-even property between the harmonic spectra of HD⁺ and HeH²⁺.