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WIREs Comput Mol Sci
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Linear‐scaling self‐consistent field methods for large molecules

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Abstract Over the last decades, linear‐scaling quantum–chemical methods (QM) have become an important tool for studying large molecular systems, so that already with modest computer resources molecules with more than a thousand atoms are well in reach. The key feature of the methods is the reduction of the steep scaling of the computational effort of conventional ab initio schemes to linear while reliability and accuracy of the underlying quantum–chemical approximation is preserved in the most successful schemes. This review gives a brief overview of selected linear‐scaling approaches at the Hartree–Fock and density‐functional theory level with a particular emphasis on density matrix‐based approaches. The focus is not only on energetics, but also on the calculation of molecular properties providing an important link between theory and experiment. In addition, the usefulness of linear‐scaling QM approaches within quantum mechanical/molecular mechanical (QM/MM) hybrid schemes is briefly discussed. WIREs Comput Mol Sci 2013, 3:614–636. doi: 10.1002/wcms.1138 This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods

McWeeny purification transformation: f(x) = 3x2 − 2x3.

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Sparsity pattern of (a) MO‐coefficient matrix and (b) density matrix for a DNA‐16 system (HF/6‐31G*, 1052 atoms, 10,764 basis functions). Significant elements larger than 10−7 are represented in black color.

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Conventional self‐consistent‐field algorithm.

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