Accelerating Real-Time Time-Dependent Density Functional Theory with a Nonrecursive Chebyshev Expansion of the...

Solutions of the real-time time-dependent density functional theory (RT-TDDFT) equations provide an affordable route to understanding the electronic dynamics that underpins many spectroscopic techniques. From the solutions of the RT-TDDFT equations, it is possible to extract optical absorption and circular dichroism spectra, as well as descriptions of charge transfer and charge transport dynamics. In order to apply RT-TDDFT to increasingly large systems, it is necessary to develop methods to overcome computational bottlenecks. One current bottleneck is the [Formula: see text] cost required to form the time propagator for the RT-TDDFT equations, because of the full matrix diagonalization that is required at each time step. Here, we present a (semi)diagonalization-free formation of the propagator based on a nonrecursive Chebyshev polynomial expansion. The Chebyshev expansion relies only on matrix multiply operations which have lower computational cost and are furthermore extremely parallelizable. We demonstrate the accuracy and stability of the Chebyshev approach, and then discuss the favorable scaling of the method, compared to traditional approaches based on matrix diagonalization. The Chebyshev expansion method should enable the application of RT-TDDFT methods to large systems such as nanocrystals and biomolecules.