7.4.4 Calculation of High-Harmonic Generation (HHG) Spectra

The high-harmonic generation (HHG) spectrum $H(\omega )$ in the dipole acceleration form is calculated by ²⁵¹ Coccia E. et al.
Int. J. Quantum Chem.
(2016), 116, pp. 1120. Link ^{, 100} Bedurke F. et al.
J. Chem. Phys.
(2019), 150, pp. 234114. Link

where $w(t)$ is some kind of window function to improve spectrum quality, and ${\mu }_{\kappa }(t)$ is the time-dependent dipole moment component. For light polarized in the $\kappa$ direction ($\kappa \in \{x,y,z\}$), we have ${\mu }_{\lambda }(t)=0$ ($\lambda \in \{x,y,z\},\lambda \ne \kappa$), and Eq. (7.62) becomes

The incorporation of a complex absorbing potential (CAP) is frequently preferred to mitigate artifacts arising from the finite-basis approximation, see Section 7.4.2.3.

A script is provided to obtain the spectrum after the TDKS simulation is completed:

• •

  $QC/bin/tools/tdks_hhg.py

This uses Eq. (7.63) with $w(t)$ taken to be the Hamming window function. ¹⁵⁰³ Zhu Y., Herbert J. M.
J. Chem. Phys.
(2022), 156, pp. 204123. Link For $\kappa =z$, the script can be run as follows:

python3 $QC/bin/tools/tdks_hhg.py z output spectrum.txt

The file spectrum.txt produced by the processing script will contain two columns: harmonic order and logarithmic strength (arbitrary units). The harmonic order is $\omega$ divided by FIELD_FREQUENCY, and the logarithmic strength is $\log [H(\omega )]$. These data can be visualized as an $(x,y)$ plot to view the spectrum. Users of Q-Chem’s TDKS code for HHG spectra are asked to cite Ref.  1503 Zhu Y., Herbert J. M.
J. Chem. Phys.
(2022), 156, pp. 204123. Link .