Friday, April 26, 2013

Choice of time-step and total propagation time in TDDFT software Octopus

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,

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

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