7.4 Real-Time SCF Methods

7.4.3 Calculation of Absorption Spectra

(June 30, 2021)

The absorption cross-section σii(ω) for light polarized in the i direction (i{x,y,z}) can be obtained from the imaginary part () of the frequency-dependent polarizability, αii(ω): 1256 Zhu Y., Herbert J. M.
J. Chem. Phys.
(2018), 148, pp. 044117.
Link

σii(ω)=(4πωc)[αii(ω)]. (7.35)

A rotationally-averaged absorption spectrum A(ω) is then simply

A(ω)=13[σxx(ω)+σyy(ω)+σzz(ω)] (7.36)

within the electric dipole approximation. Components αij(ω) of the frequency-dependent polarizability tensor 𝜶(ω) are obtained from the Fourier transform () of the time-dependent dipole moment component μi(t), for a perturbing field j in the j direction: 1256 Zhu Y., Herbert J. M.
J. Chem. Phys.
(2018), 148, pp. 044117.
Link

αij(ω)=[μi(t)][j(t)]. (7.37)

To compute the spectrum in Eq. (7.36), three TDKS simulations are required, with separate perturbations in the x, y, and z directions. (Some excitations may be missing from one or more of these simulations, if symmetry causes the matrix element Ψn|j|Ψ0 to vanish.)

Two different scripts are provided to obtain the spectrum after the TDKS simulation is completed. One of them ($QC/bin/tools/tdks_fft.py) uses the Fourier transform method in Eq. (7.37) directly while the other ($QC/bin/tools/tdks_pade.py) makes use of Padé approximants to obtain comparable spectra with shorter propagation times. The scripts can be run as follows:

$QC/bin/tools/tdks_fft.py output spectrum.txt
$QC/bin/tools/tdks_pade.py output spectrum.txt

The file spectrum.txt produced by the processing script will contain two columns: frequency (eV) and strength (arbitrary units). This data can be visualized as an x-y plot to view the spectrum.

Example 7.18  TDKS job using a CW field and a CAP.

$molecule
   0 1
   H    0.000000   0.000000   0.000000
   H    0.000000   0.000000   0.750000
$end

$rem
   BASIS                6-31G
   EXCHANGE             gen
   SYMMETRY             false
   TDKS                 true
   UNRESTRICTED         true
   LRC_DFT              true
   OMEGA                300
   INCFOCK              0
   PURECART             2222
   SCF_CONVERGENCE      9
   PRINT_GENERAL_BASIS  true
$end

$xc_functional
   C  PBE   1.00
   X  wPBE  1.00
   X  HF    0.00
$end

$tdks
   DT                   0.05
   MAXITER              5
   PROPAGATOR           MMUT
   FIELD_VECTOR         1 1 1
   FIELD_TYPE           cw
   FIELD_FREQUENCY      1.55
   FIELD_AMP            0.0001
   DO_CAP               true
   CAP_TYPE             atom_centered_spherical
   CAP_R0               12.0    ! should be in bohr/a.u.
   CAP_ETA              8.0
$end

View output