To demonstrate the technique and to check convergence with respect to total simulation time, we calculated the absorption spectrum of the methionine molecule at the oxygen K-edge (Fig. ). Two different simulations are shown, using either ∆t = 0.01 a.u. or ∆t = 0.02 a.u., both of which are well within the Nyquist limit for this spectral range, which imposes a bound ∆t ≤ 0.16 a.u. at E max = 540 eV. Comparing a normal fast Fourier transform (FFT) of the time series µ λ (t k ) with a Padéaccelerated transform, we find that the Padé technique produces a much better-converged spectrum in only half the simulation time, t max = 600 a.u. (≈ 14.5 fs). Nearedge features are converged with as little as one-quarter of that time. For simulations with t max ≤ 300 a.u., clear artifacts are evident at higher energies, which diminish but do not disappear as the time step is reduced. These features provide a diagnostic to indicate that additional simulation time is required in order to converge the spectrum in a given energy range. Similar data for an ion-pair ). In the Padé-accelerated case, the spectra computed using tmax = 1200 a.u. are indistinguishable from the ones using tmax = 600 a.u. that are shown.