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Locality of compact one-electron orbitals expanded strictly in terms of localsubsets of basis functions can be exploited in density functional theory (DFT)to achieve linear growth of computation time with systems size, crucial inlarge-scale simulations. However, despite advantages of compact orbitals thedevelopment of practical orbital-based linear-scaling DFT methods has long beenhindered because a compact representation of the electronic ground state isdifficult to find in a variational optimization procedure. In this work, weshow that the slow and unstable optimization of compact orbitals originatesfrom the nearly-invariant mixing of compact orbitals that are mostly but notcompletely localized within the same subsets of basis functions. We alsoconstruct an approximate Hessian that can be used to identify the problematicnearly-invariant modes and obviate the variational optimization along themwithout introducing significant errors into the computed energies. This enablesus to create a linear-scaling DFT method with a low computational overhead thatis demonstrated to be efficient and accurate in fixed-nuclei calculations andmolecular dynamics simulations of semiconductors and insulators.

Robust linear-scaling optimization of compact localized orbitals in density functional theory