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Linear scaling methods for density-functional theory (DFT) simulations areformulated in terms of localised orbitals in real-space, rather than thedelocalised eigenstates of conventional approaches. In local-orbital methods,relative to conventional DFT, desirable properties can be lost to some extent,such as the translational invariance of the total energy of a system withrespect to small displacements and the smoothness of the potential energysurface. This has repercussions for calculating accurate ionic forces andgeometries. In this work we present results from \textsc{onetep}, our linearscaling method based on localised orbitals in real-space. The use of psincfunctions for the underlying basis set and on-the-fly optimisation of thelocalised orbitals results in smooth potential energy surfaces that areconsistent with ionic forces calculated using the Hellmann-Feynman theorem.This enables accurate geometry optimisation to be performed. Results forsurface reconstructions in silicon are presented, along with three examplesystems demonstrating the performance of a quasi-Newton geometry optimisationalgorithm: an organic zwitterion, a point defect in an ionic crystal, and asemiconductor nanostructure.

Accurate ionic forces and geometry optimisation in linear scaling density-functional theory with local orbitals