Combining Linear-Scaling DFT with Subsystem DFT in Born Oppenheimer and Ehrenfest Molecular Dynamics Simulations: From Molecules to a Virus in Solution

In this work, methods for the efficient simulation of large systems embedded in a molecular environment are presented. These methods combine linear-scaling (LS) KohnSham (KS) density functional theory (DFT) with subsystem (SS) DFT. LS DFT is efficient for large subsystems, while SS DFT is linear scaling with a smaller prefactor for large sets of small molecules. The combination of SS and LS, which is an embedding approach, can result in a 10-fold speedup over a pure LS simulation for large systems in aqueous solution. In addition to a ground-state BornOppenheimer SS+LS implementation, a time-dependent density functional theory-based Ehrenfest molecular dynamics (EMD) using density matrix propagation is presented that allows for performing nonadiabatic dynamics. Density matrix-based EMD in the SS framework is naturally linear scaling and appears suitable to study the electronic dynamics of molecules in solution. In the LS framework, linear scaling results as long as the density matrix remains sparse during time propagation. However, we generally find a less than exponential decay of the density matrix after a sufficiently long EMD run, preventing LS EMD simulations with arbitrary accuracy. The methods are tested on various systems, including spectroscopy on dyes, the electronic structure of TiO2 nanoparticles, electronic transport in carbon nanotubes, and the satellite tobacco mosaic virus in explicit solution.