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

Abstract

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.

Role of resonance-enhanced multiphoton excitation in high-harmonic generation of N2: A time-dependent density-functional-theory study

“…It was shown that this "SFA-phase" formula reproduces the measured D 2 -to-H 2 HHG ratio [41]. It is much less costly to evaluate Eq.…”

“…(12) involves repeatedly solving TDDFT equations for different R values. In recent work on H 2 , the error caused by using the SFA-phase formula is estimated to be within 7% for similar laser parameters [41]. We expect the error in the case of N 2 to be even smaller, because |d(R,ω)| is more flat as a function of R for N 2 than for H 2 due to the flatter I p (R) of N 2 .…”

“…Earlier work on H 2 showed that HHG spectra calculated at the equilibrium distance differ considerably from HHG spectra calculated with molecular vibration taken into account [41]. The reason is that for H 2 the vertical I p (R) varies significantly over R, which causes the phase φ(ω,R) of HHG to oscillate over R as well.…”

Time-dependent density-functional-theory study of the suppressed tunneling ionization of vanadium

“…v σ,l (r,t)P l (z/r), (21) where P l is lth-order Legendre function and z is the z coordinate. Induced potentials v σ,l P l , l = 0,1, .…”

“…The quantum action A[ ] has a stationary point at the TD density of the system, and hence from the Euler equation we get the working equations [20,21]. When we project Eq.…”