Time-dependent density-functional-theory calculation of high-order-harmonic generation of H2

The observation of the isotope effect in the high-order-harmonic generation (HHG) of H-2 presents a challenge for time-dependent density-functional-theory (TDDFT) methods, since this effect is related to the dynamics of the ion created in the tunneling ionization step of HHG and it depends on the harmonic order. As an initial step toward describing this effect within current computational capacity, we benchmark a method in which the nuclear and electronic degrees of freedom are separated and both treated quantum mechanically. For the electrons two TDDFT formalisms are adopted. Although the ion-dynamics effect is not described in our method, it reproduces the measured D-2-to-H-2 HHG ratios up to the 25th harmonic when the 35th is the classical cutoff. Beyond the 25th harmonic, however, our results show substantial deviation and are sensitive to the laser intensity. A higher intensity reproduces the experimental results. Analysis reveals an R-dependent phase factor as the cause of the isotope effect in our calculation. We isolate this phase factor and propose a strong-field-approximation-phase model, which reproduces experimental data, including those for which the ion-dynamics model has to be further modified. We show that the model that we propose is intrinsically related to the ion-dynamics model. Our model provides a correction to the TDDFT approach when the ion-dynamics effect becomes significant. It also indicates that the isotope effect is not only a probe for the ion created by the external field but is ultimately a more useful probe for the ground-state nuclear wave function. For all molecules whose vertical ionization potential strongly depends on the nuclear geometry, HHG may serve as a sensitive ultrafast probe of nuclear dynamics.