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Real-time time-dependent density functional theory (RT-TDDFT) is known to behindered by the very small time step (attosecond or smaller) needed in thenumerical simulation due to the fast oscillation of electron wavefunctions,which significantly limits its range of applicability for the study ofultrafast dynamics. In this paper, we demonstrate that such oscillation can beconsiderably reduced by optimizing the gauge choice using the paralleltransport formalism. RT-TDDFT calculations can thus be significantlyaccelerated using a combination of the parallel transport gauge and implicitintegrators, and the resulting scheme can be used to accelerate any electronicstructure software that uses a Schr\"odinger representation. Using absorptionspectrum, ultrashort laser pulse, and Ehrenfest dynamics calculations forexample, we show that the new method can utilize a time step that is on theorder of $10\sim 100$ attoseconds in a planewave basis set, and is no less than$5\sim 10$ times faster when compared to the standard explicit 4th orderRunge-Kutta time integrator. Thanks to the significant increase of the size ofthe time step, we also demonstrate that the new method is more than 10 timesfaster in terms of the wall clock time when compared to the standard explicit4th order Runge-Kutta time integrator for silicon systems ranging from 32 to1024 atoms

Fast real-time time-dependent density functional theory calculations with the parallel transport gauge