Searching....

# 7.4.4 Calculation of High-Harmonic Generation (HHG) Spectra

(May 7, 2024)

The high-harmonic generation (HHG) spectrum $H(\omega)$ in the dipole acceleration form is calculated by 241 Coccia E. et al.
Int. J. Quantum Chem.
(2016), 116, pp. 1120.
, 95 Bedurke F. et al.
J. Chem. Phys.
(2019), 150, pp. 234114.

 $H(\omega)=\sum_{\kappa=x,y,z}\frac{1}{2\pi}\left|\int\frac{d^{2}\mu_{\kappa}(t% )}{dt^{2}}w(t)e^{-i\omega t}dt\right|^{2}$ (7.53)

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 $\mu_{\lambda}(t)=0$ ($\lambda\in\{x,y,z\},\lambda\neq\kappa$), and Eq. (7.53) becomes

 $H(\omega)=\frac{1}{2\pi}\left|\int\frac{d^{2}\mu_{\kappa}(t)}{dt^{2}}w(t)e^{-i% \omega t}dt\right|^{2}$ (7.54)

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. (7.54) with $w(t)$ taken to be the Hamming window function. 1459 Zhu Y., Herbert J. M. J. Chem. Phys. (2022), 156, pp. 204123. 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.  1459 Zhu Y., Herbert J. M.
J. Chem. Phys.
(2022), 156, pp. 204123.
.