Miguel Marques marques at teor.fis.uc.pt
Thu Aug 23 12:25:46 WEST 2007

```  Hi,

The choice of the time-step and of the total propagation time are
independent, so let's start by the first:

*) the time-step determines two things. First, the maximum frequency we
can have in the spectrum. This is not a big probably, as the time-steps
that one typically uses are more than enough to reach the X-ray regime.
So, the limiting factor is the stability of the propagation. It is easy
to estimate the order of magnitude of the time-step: it should be enough
to resolve the electronic motion. As this is of the order of the
attosecond, also the time step will have to be of this order of
magnitude. Technically, for the methods we mostly use, the time-step is
also connected to the mesh spacing. The smaller the mesh spacing, the
smaller will have to be the time-step (delta t ~ 1/(delta x)^2).

So, the best strategy is to choose the largest time-step that yields a
stable propagation. This is done by trial and error. Just choose a
time-step (of the order of 0.005 hbar/eV), and then propagate for 20-50
iterations. If it explodes (i.e., if the energy is not well conserved),
decrease the time-step. Otherwise try to increase it.

*) Regarding the total propagation time. This is related to the
resolution of the spectrum (the width of a bound-bound peak is inversely
proportional to the total propagation time). Typically, one chooses the
total propagation time such that the peaks are "well defined". Usually a
width of around 0.2 eV is more than enough for most practical purposes.
So, just run for some iterations (10000, for example), and calculate the
spectrum. If it "looks" OK, with the peaks well defined, just stop
there, otherwise just increase the total propagation time. Don't forget
that you can restart the TD calculation, so this is basically
pain-free ;)

hope this helped,
Miguel

P.S. Maybe one of you could copy this to the wiki...

On Fri, 2007-08-17 at 13:01 +0800, jingjing zhou wrote:
>  Hello,
> 'Assessment of exchange-correlation functionals for the calculation
> of dynamical properties of small clusters in time-dependent density
> functional theory'
> published in JOURNAL OF CHEMICAL PHYSICS 115,  7(2001)
> There is a question hinder me.
> Hope you can help me!
> In you article,the time step is 0.0025 hbar/eV ,and the total
> propagation
> are 50 hbar/eV for the sodium clusters and 25 hbar/eV for the silicon
> clusters respectively.
> The problem is  i don't know how to decide this parameters: time step
> and
> total propagation.With the change of the time step and total
> propagation,
> the dipole stength change correspondingly.So what method can be use