The majority of DFT calculations today are limited to a system size, N, of hundreds to thousands of atoms. This limitation stems from the cubic-scaling O(N3) computational complexity in conventional DFT implementations. In addition, these methods are often restricted to periodic boundary conditions, due to the use of the plane-wave basis functions. From a mechanical point of view, the properties of interest often derive from defects that involve far beyond hundreds of atoms, and cause non-periodic perturbations in the crystal structure. The size and periodicity restriction can be lifted using a real-space approach, combined with an algorithm that has linear-scaling, O(N) complexity.
Of the available linear-scaling methods for DFT, the linear-scaling spectral Gauss quadrature (LSSGQ) method (Suryanarayana et al., JMPS 2013) holds a great potential to scale to beyond millions of processors. The LSSGQ method transforms the energy and electron density from an orbital formulation into integrals with spectral measures (spectral integrals). The integrals are then approximated using a spectral Gauss quadrature rule, by means of a Krylov-subspace method known as the Lanczos iteration. We seek to reduce the computational cost of the LSSGQ method through augmenting the Krylov subspace.
Problems in Li-based batteries often exhibit coupling between large mechanical deformations and electrochemistry. Lithiation can cause volumetric expansion in the electrodes ranging from 10% to 400% depending on the material. The presence of mechanical stress can affect the electrodes in both favorable and unfavorable ways. On the one hand, it has been observed that Li-induced plastic flow in thin-film silicon anodes increases the cycle-life of the battery; there are theoretical studies that suggest mechanical pre-stress on a Li-metal anode can reduce the dendrite formation during lithiation. On the other hand, large lattice strains have led to fractures in bulk silicon anodes and delamination in composite anodes. We study the problem of dendrite formation on the Li-metal anode using O(N) DFT. Li-metal is an attractive anode material because of its specific capacity is 10 times higher than the specific capacity of carbon. However, Li-metal anodes suffer from catastrophic failures due to the dendrites that extend from the anode to the cathode. We investigate the problem of dendrite growth under both chemical and mechanical modifications.