Equilibrium configurations of large nanostructures using the embedded saturated-fragments stochastic density functional theory

An ab initio Langevin dynamics approach is developed based on stochastic density functional theory (sDFT) within a new embedded saturated fragment formalism, applicable to covalently bonded systems. The forces on the nuclei generated by sDFT contain a random component natural to Langevin dynamics, and its standard deviation is used to estimate the friction term on each atom by satisfying the fluctuation-dissipation relation. The overall approach scales linearly with the system size even if the density matrix is not local and is thus applicable to ordered as well as disordered extended systems. We implement the approach for a series of silicon nanocrystals (NCs) of varying size with a diameter of up to 3 nm corresponding to N_e = 3000 electrons and generate a set of configurations that are distributed canonically at a fixed temperature, ranging from cryogenic to room temperature. We also analyze the structure properties of the NCs and discuss the reconstruction of the surface geometry.