  We present a novel function fitting method for approximating the propagation
of the time-dependent electric dipole moment from real-time electronic
structure calculations. Real-time calculations of the electronic absorption
spectrum require discrete Fourier transforms of the electric dipole moment. The
spectral resolution is determined by the total propagation time, i.e. the
trajectory length of the dipole moment, causing a high computational cost. Our
developed method uses function fitting on shorter trajectories of the dipole
moment, achieving arbitrary spectral resolution through extrapolation.
Numerical testing shows that the fitting method can reproduce high-resolution
spectra using short dipole trajectories. The method converges with as little as
100 a.u. dipole trajectories for some systems, though the difficulty converging
increases with the spectral density. We also introduce an error estimate of the
fit, reliably assessing its convergence and hence the quality of the
approximated spectrum.
