Real-time time-dependent density functional theory (rt-TDDFT) can in principle access all excitations of a many-electron system exposed to a narrow pulse. However, this requires not only an accurate and efficient integrator for the numerical integration of the time-dependent Kohn-Sham equation (TDKS) but also an accurate and efficient scheme for the harmonic analysis of the discrete time series. The situation is particularly difficult for the high end of the TDKS spectrum. It turns out that the optimized fourth-order commutator-free exponential time-propagator (oCFET4) [1] is sufficiently accurate for core excitations of systems containing heavy elements, even with the largest time step Δt determined by the sampling/undersampling theorem. However, this can only be achieved by invoking an implicit, second-order exponential predictor-corrector (iEPC2), thereby leading to iEPC2@oCFET4 [2]. The total simulation time T (which determines the resolution of the TDKS spectrum) can be shortened if the full TDKS spectrum is to be extracted batch-wise in parallel. Since the computational time is proportional to the number of time steps, T/Δt, the use of short T and large Δt naturally ensures the computational efficiency. The inner-core and valence excitations of the AtH molecule are taken as a showcase to reveal the performance of the iEPC2@oCFET4 method.

Full spectrum from real-time time-dependent density functional theory with large time step and short simulation time

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