Accelerating Realtime TDDFT with Block-Orthogonalized Manby–Miller Embedding Theory

Realtime time-dependent density-functional theory (RT-TDDFT) is one of the most practical techniques available to simulate electronic dynamics of molecules and materials. Promising applications of RT-TDDFT to study nonlinear spectra and energy transport demand simulations of large solvated systems over long time scales, which are computationally quite costly. In this paper, we apply an embedding technique developed for ground-state SCF methods by Manby and Miller to accelerate realtime TDDFT. We assess the accuracy and speed of these approximations by studying the absorption spectra of solvated and covalently split chromophores. Our embedding approach is also compared with less accurate, less costly QM/MM charge embeddings. We find that by mixing levels of detail the embedded mean-field theory scheme is a simple, accurate, and effective way to accelerate RT-TDDFT simulations

Origin of the Size-Dependent Stokes Shift in CsPbBr₃ Perovskite Nanocrystals

The origin of the size-dependent Stokes shift in CsPbBr₃ nanocrystals (NCs) is explained for the first time. Stokes shifts range from 82 to 20 meV for NCs with effective edge lengths varying from ∼4 to 13 nm. We show that the Stokes shift is intrinsic to the NC electronic structure and does not arise from extrinsic effects such as residual ensemble size distributions, impurities, or solvent-related effects. The origin of the Stokes shift is elucidated via first-principles calculations. Corresponding theoretical modeling of the CsPbBr₃ NC density of states and band structure reveals the existence of an intrinsic confined hole state 260 to 70 meV above the valence band edge state for NCs with edge lengths from ∼2 to 5 nm. A size-dependent Stokes shift is therefore predicted and is in quantitative agreement with the experimental data. Comparison between bulk and NC calculations shows that the confined hole state is exclusive to NCs. At a broader level, the distinction between absorbing and emitting states in CsPbBr₃ is likely a general feature of other halide perovskite NCs and can be tuned via NC size to enhance applications involving these materials