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Section Time-Dependent::Propagation
Type integer
Default etrs

This variable determines which algorithm will be used to approximate the evolution operator $U(t+\delta t, t)$. That is, given $\psi(\tau)$ and $H(\tau)$ for $\tau \le t$, calculate $t+\delta t$. Note that in general the Hamiltonian is not known at times in the interior of the interval $[t,t+\delta t]$. This is due to the self-consistent nature of the time-dependent Kohn-Sham problem: the Hamiltonian at a given time $\tau$ is built from the "solution" wavefunctions at that time.

Some methods, however, do require the knowledge of the Hamiltonian at some point of the interval $[t,t+\delta t]$. This problem is solved by making use of extrapolation: given a number $l$ of time steps previous to time $t$, this information is used to build the Hamiltonian at arbitrary times within $[t,t+\delta t]$. To be fully precise, one should then proceed self-consistently: the obtained Hamiltonian at time $t+\delta t$ may then be used to interpolate the Hamiltonian, and repeat the evolution algorithm with this new information. Whenever iterating the procedure does not change the solution wavefunctions, the cycle is stopped. In practice, in Octopus we perform a second-order extrapolation without a self-consistency check, except for the first two iterations, where obviously the extrapolation is not reliable.

The proliferation of methods is certainly excessive. The reason for it is that the propagation algorithm is currently a topic of active development. We hope that in the future the optimal schemes are clearly identified. In the mean time, if you do not feel like testing, use the default choices and make sure the time step is small enough.


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