Orbital-resolved calculations of two-center interferences in linear triatomic molecules

We perform ab initio calculations of high-harmonic spectroscopy (HHS) of two-center interference phenomena in oriented carbon-dichalcogen molecules, using time-dependent density functional theory (TDDFT). We show that by resolving the harmonic response into contributions from individual Kohn-Sham orbitals, we can extract target-specific characteristics for both the spectral amplitude and phase. We also discuss that this extraction is predicated on a careful analysis and normalization of the harmonic spectrum. Finally, we present field-free scattering calculations that mimic the recollision step in high-order-harmonic generation and allow the calculation of recombination dipole matrix elements without explicitly calculating the scattering states of a molecule. We show that the orbital-resolved TDDFT HHS results and results based on our field-free scattering calculations are in very good agreement with each other.

Figure 1

(a) Schematic of the geometry we use in TDDFT simulations. At the center of the elongated box lies the linear triatomic molecule, which is tilted at an angle $\theta$ with respect to the polarization of the driving laser field. (b) Isosurface of the highest-occupied molecular orbital (HOMO) of ${\text{CO}}_2$, aligned at an angle $\theta$ with respect to the laser polarization.

Figure 2

Normalized angle-resolved high-harmonic spectral intensities for ${\text{CO}}_2$ calculated from the combined HOMO-resolved dipole signal for different laser parameters: (a) $\lambda =2000\mathrm{nm}, I_{\circ }=60\mathrm{TW}/{\text{cm}}^2$, IR only; (b) $\lambda =2000\mathrm{nm}, I_{\circ }=20\mathrm{TW}/{\text{cm}}^2$, IR only; (c) $\lambda =1500\mathrm{nm}, I_{\circ }=60\mathrm{TW}/{\text{cm}}^2$, IR only; and (d) $\lambda =1500\mathrm{nm}, I_{\circ }=60\mathrm{TW}/{\text{cm}}^2$, IR$+$APT. The black dotted trend lines come from scattering simulations—see Fig. 6.

Figure 3

Normalized angle-resolved high-harmonic spectral intensities for (a) ${\text{CS}}_2$ and (b) ${\text{CSe}}_2$ calculated from the IR-only HOMO-resolved dipole signal, using the laser parameters $\lambda =2000\mathrm{nm}, I_{\circ }=60\mathrm{TW}/{\text{cm}}^2$ as in Fig. 2. Black dotted lines again correspond to scattering simulations.

Figure 4

(a)–(c) Angle-dependent target-specific phases for ${\text{CO}}_2, {\text{CS}}_2$, and ${\text{CSe}}_2$, respectively, using the laser parameters $\lambda =2000\mathrm{nm}$ and $I_{\circ }=60\mathrm{TW}/{\text{cm}}^2$. (d) The target-specific group delay for ${\text{CS}}_2$, calculated from the phase in (b). Black dotted lines again correspond to scattering simulations.

Figure 5

Markers: comparison of the TCI minimum in the carbon-dichalcogen family for different MIR wavelengths and intensities, as well as scattering simulations; see legend. For each datum, we report the difference between the HHG energy at which the TCI minimum is located at zero degrees and the molecule's ionization potential. The dotted curve is proportional to $1/R^2$, as predicted by scattering theory [53, 54].

Figure 6

Field-free scattering simulations, for the out-of-plane HOMO, in the carbon-dichalcogen family. (a)–(c) The angle-resolved target-specific intensity ${\sigma }_k^2$ for ${\text{CO}}_2, {\text{CS}}_2$, and ${\text{CSe}}_2$, respectively. (d) The corresponding phase ${\varphi }_k$ for ${\text{CS}}_2$.