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We present a new method to accelerate real time-time dependent densityfunctional theory (rt-TDDFT) calculations with hybrid exchange-correlationfunctionals. For large basis set, the computational bottleneck for large scalecalculations is the application of the Fock exchange operator to thetime-dependent orbitals. Our main goal is to reduce the frequency of applyingthe Fock exchange operator, without loss of accuracy. We achieve this bycombining the recently developed parallel transport (PT) gauge formalism andthe adaptively compressed exchange operator (ACE) formalism. The PT gaugeyields the slowest possible dynamics among all choices of gauge. When coupledwith implicit time integrators such as the Crank-Nicolson (CN) scheme, theresulting PT-CN scheme can significantly increase the time step fromsub-attoseconds to 10-100 attoseconds. At each time step $t_{n}$, PT-CNrequires the self-consistent solution of the orbitals at time $t_{n+1}$. We useACE to delay the update of the Fock exchange operator in this nonlinear system,while maintaining the same self-consistent solution. We verify the performanceof the resulting PT-CN-ACE method by computing the absorption spectrum of abenzene molecule and the response of bulk silicon systems to an ultrafast laserpulse, using the planewave basis set and the HSE functional. We report thestrong and weak scaling of the PT-CN-ACE method for silicon systems rangingfrom 32 to 1024 atoms, with up to 2048 computational cores. Compared tostandard explicit time integrators such as the 4th order Runge-Kutta method(RK4), the PT-CN-ACE can reduce the Fock exchange operator application bynearly 70 times, thus reduce the overall wall clock time time by 46 times forthe system with 1024 atoms. Hence our work enables hybrid functional rt-TDDFTcalculations to be routinely performed with a large basis set for the firsttime.

Fast real-time time-dependent hybrid functional calculations with the parallel transport gauge and the adaptively compressed exchange formulation