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What’s the point of linear-scaling electronic structure methods?

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It is over 20 years since Yang proposed the first “divide-and-conquer” linear-scaling method [1]. Since then there has been a lot of fuss about the development of O(N) methods but relatively little to show for it in terms of practical applications. In this talk I will suggest why this is the case and how it may be addressed.

First, I will briefly outline the scheme implemented in the ONETEP code [2], focussing on the in situ optimisation of local orbitals that enables plane-wave accuracy to be achieved. I will suggest that the resulting “non-orthogonal generalised Wannier functions” may be used in a manner similar to maximally localised Wannier functions e.g. to interpolate band structure.

Second, I will suggest three strategies for exploiting the capability of linear-scaling methods to perform large-scale electronic structure calculations, each illustrated with an example. 1. low-dimensional systems where the configuration space to be explored is relatively simple, with reference to simulations of entire polar semiconductor nanorods that are amenable to O(N) methods. 2. the role of linear-scaling methods in a multiscale approach, such as the fitting of classical force fields to explore configuration space by molecular dynamics, as shown by the prediction of amyloid fibril structure using computational NMR spectroscopy. 3. theoretical spectroscopy to establish a direct link between simulation and experiment involving recent development of local orbital methods for performing time-dependent density-functional theory calculations to obtain optical absorption spectra.

[1] Phys. Rev. Lett. 66, 1438 (1991)
[2] www.onetep.org

This talk is part of the Theory of Condensed Matter series.

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