Density-based embedding for multiscale simulations
Materials properties are to a large extent determined by lattice defects. In order to model the defects, multiscale methods such as QM/MM are often required. However, QM/MM simulations for metals are particularly challenging owing to the existence of delocalized electronic states at QM/MM interface, which renders standard QM/MM coupling approaches such as cutting/saturating covalent bonds across the interface ineffective or invalid. To address this challenge, we have recently developed two QM/MM methods for metallic systems based on charge density embedding. In the first method [1,2,3], the QM/MM coupling is achieved by adding an embedding potential to the Kohn-Sham (KS) Hamiltonian of the QM subsystem. This embedding potential captures the coupling between QM and MM subsystems and is defined as the functional derivative of QM/MM interaction energy with respect to charge density, evaluated by orbital-free DFT (OFDFT). In the second method, the presence of the MM subsystem is formulated by a constraint potential added to the KS Hamiltonian of the QM subsystem. The QM/MM coupling problem is recast into a constraint DFT problem for the QM subsystem. The second QM/MM method  is formally exact and does not depend on OFDFT. Both QM/MM methods will be reviewed and their applications including extended defects on mechanical properties and catalysis for core/shell nanoparticles will be presented.