Locality of compact one-electron orbitals expanded strictly in terms of local subsets of basis functions can be exploited in density functional theory (DFT) to achieve linear growth of computation time with systems size, crucial in large-scale simulations. However, despite advantages of compact orbitals the development of practical orbital-based linear-scaling DFT methods has long been hindered because a compact representation of the electronic ground state is difficult to find in a variational optimization procedure. In this work, we showed that the slow and unstable optimization of compact orbitals originates from nearly-invariant mixing of occupied orbitals with the states that are mostly but not fully localized within the local vector subspace. We proposed a simple and practical method for identifying and removing the problematic nearly-invariant modes using an approximate Hessian and, as a result, developed a robust linear-scaling optimization procedure with a low computational overhead. We demonstrated the new method is highly efficient yet accurate in fixed-nuclei calculations and molecular dynamics simulations for a variety of systems ranging from semiconductors to insulators.
Robust linear-scaling optimization of compact localized orbitals in density functional theory
© 2024 · www.khaliullin.com