After the wavefunction has been initialized, the first TD-ADGA iteration is carried out before the time-propagation starts. This "extra" iteration is carried out since the density used to converge the zeroth iteration might vary from the density of y 0 . This is because the initial density of the zeroth iteration can be any density supplied by the user or an average density obtained from a VSCF calculation, while the current density has been calculated using the space-smoothened one-mode densities of the initial state (there is no time-smoothening since no time has passed at which the one-mode density can be smoothened over). Using the new density, new TD-ADGA integrals are calculated and then each integration box is checked for convergence by checking against the conditions in Eq. 38 and Eq. 41. If one or more integration boxes are no longer converged or if the one-mode grids should be extended, new SPs are requested by the TD-ADGA algorithm and after these have been calculated a new PES is fitted. The TD-ADGA integrals are then re-calculated and convergence of the integration boxes checked again. This procedure is repeated until all integration boxes are converged at which point the time-integration can begin.