To start the AMB algorithm one needs to initialize

f(y,t) \equiv \dfrac{1}{i}(\hat{H}(\{\varphi_n\},t)-\langle H\rangle_n)\varphi_n(\bm{r},t)

for four time steps back: f_{k-1}, f_{k-2}, f_{k-3}, f_{k-4}.

Starting from a stationary state

In the case of a stationary state, \varphi_n are eigenstates of the hamiltonian, and the instantaneous quasi-particle energies are equal to quasiparticle energies E_n=\textrm{const}. Then, as long as the hamiltonian does not depend we obtain:

f_{k-1}=f_{k-2}=f_{k-3}=f_{k-4}=0

To use this prescription for initialization of ABM algorithm you need to select in the input file:

selfstart               0        # use Taylor expansion for first 5 steps? 

Starting from a non-stationary state

In this case, we need to generate the first five steps using single step method. In case of td-wslda we use a method based Taylor expansion of the evolution:

\varphi_n(\bm{r},t+\Delta t) = e^{-i(\hat{H}(\{\varphi_n\},t)-\langle H\rangle_n)\Delta t}\varphi_n(\bm{r},t)\approx \sum_{k=0}^{4}\frac{(-i\Delta t)^k}{k!}(\hat{H}(\{\varphi_n\},t)-\langle H\rangle_n)^k\varphi_n(\bm{r},t)

where we expanded the evolution operator into Taylor series up to the same order as the precision of the ABM algorithm.

In order to use the Taylor expansion method for the generation of the first five steps you need to select in the input file:

selfstart               1        # use Taylor expansion for first 5 steps?