Mixed Planewave and Localized Orbital Basis for Sparse-Stochastic Hybrid TDDFT

We present a mixed basis-set approach to obtain optical absorption spectra within a generalized Kohn-Sham time-dependent density functional theory framework. All occupied valence molecular orbitals (MOs) are expanded in a plane-wave (PW) basis, while unoccupied MOs are derived primarily from localized atomic basis functions. The method accelerates spectral convergence when compared to fully PW-based simulations, with a $2-3$ fold reduction in the number of unoccupied MOs entering the Casida equation. The mixed-basis is placed on a common real-space grid, enabling our previously developed deterministic/sparse-stochastic evaluation of the exact exchange operator (J. Chem. Theory Comput. 2023, 19, 9239-9247). This chemically intuitive and computationally efficient approach is validated across various molecular systems, including $π$-conjugated polymethine dyes, aromatic hydrocarbons, and a chlorophyll monomer.