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7.4 Real-Time SCF Methods

7.4.4 Calculation of High-Harmonic Generation (HHG) Spectra

(May 7, 2024)

The high-harmonic generation (HHG) spectrum H(ω) 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(ω)=κ=x,y,z12π|d2μκ(t)dt2w(t)e-iωt𝑑t|2 (7.53)

where w(t) is some kind of window function to improve spectrum quality, and μκ(t) is the time-dependent dipole moment component. For light polarized in the κ direction (κ{x,y,z}), we have μλ(t)=0 (λ{x,y,z},λκ), and Eq. (7.53) becomes

H(ω)=12π|d2μκ(t)dt2w(t)e-iωt𝑑t|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

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 κ=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 ω divided by FIELD_FREQUENCY, and the logarithmic strength is log[H(ω)]. 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.