Calculation Of Density Change

The program tddft_iter is able to compute induced densities and induced electric fields. The aim of this tutorial is to describe the parameters that affect these tasks.

By default, the program tddft_iter computes polarizability tensor $P_{ij}(\omega)$ for a set of frequencies $\{ \omega \}$ by an iterative algorithm. In this algorithm, each frequency is treated individually in an iterative process. As a consequence, the calculation can be done for an arbitrary set of frequencies with a possibility of reducing the amount of work by a meaningful limiting of the frequency set. For instance, if one knows that a molecule has a large gap, then one can cease to compute polarizabilities at low frequencies. The other purpose of this tutorial is to tell how the parameters are chosen for doing these type of optimizations.

There are a set of parameters to define frequency grid. Currently, only equidistant grid is supported. However, this frequency grid can be limited from above and below. The most physically appealing way of defining the frequency grid would be to define its spacing $\Delta \omega$ and number of frequency points $N_{\omega}$

The grid spacing is defined through the parameter d_omega_win1 in the Input file

d_omega_win1  0.1

By default, electron volts (eV) are used for input/output of energies. Hence, the last chunk of input sets frequency spacing of 0.1 eV.

The number of frequencies in the frequency grid is set via parameter nff.

d_omega_win1  0.1
nff  1000

The example above sets frequency spacing to 0.1 eV and number of frequency points to 1000. The grid will range from 0.1 eV to 100 eV.

We can further limit a set of frequencies by specifying minimum and maximum frequencies for iterative TDDFT calculation. This is done through parameters omega_min_tddft and omega_max_tddft.

d_omega_win1  0.1
nff  1000
omega_min_tddft  2.0 
omega_max_tddft 5.0

For instance, in the example above, the frequency set will be limited from below by 2 eV and from above by 5 eV. Hence, the set of frequencies will be $\{\omega\}$=$\{ 2.0, 2.1, 2.2 \ldots 5.0 \}$ eV, i.e. it will contain only 31 frequencies.
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