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WIREs Comput Mol Sci
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Challenges in large scale quantum mechanical calculations

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During the past decades, quantum mechanical methods have undergone an amazing transition from pioneering investigations of experts into a wide range of practical applications, made by a vast community of researchers. First principles calculations of systems containing up to a few hundred atoms have become a standard in many branches of science. The sizes of the systems which can be simulated have increased even further during recent years, and quantum‐mechanical calculations of systems up to many thousands of atoms are nowadays possible. This opens up new appealing possibilities, in particular for interdisciplinary work, bridging together communities of different needs and sensibilities. In this review we will present the current status of this topic, and will also give an outlook on the vast multitude of applications, challenges, and opportunities stimulated by electronic structure calculations, making this field an important working tool and bringing together researchers of many different domains. WIREs Comput Mol Sci 2017, 7:e1290. doi: 10.1002/wcms.1290

Overview of the popular methods used in simulations of systems with atomistic resolution, showing the typical length scales over which they are applied as well as the degree of transferability of each method, i.e., the extent to which they give accurate results across different systems without re‐tuning. On the left hand side we have the Quantum Chemistry methods which are highly transferable but only applicable to a few tens of atoms; on the right hand side we see the less transferable (semi‐)empirical methods, which can however express reliable results (as they are parameterized for) for systems containing millions of atoms; and in the middle we see the methods—in particular linear‐scaling DFT—which can bridge the gap between the two regimes. The vertical divisions and corresponding background colors give an indication of the fields in which the methods are typically applied, namely chemistry, materials science, biology, and an intermediary regime (‘bridging the length scale gap’) between materials science and biology. The line colors indicate whether a method is QM or MM, while the typical regime for QM/MM methods is indicated by the shaded region. In the top left the region wherein efforts to improve the quantum mechanical treatment are focussed, that is the quest to climb ‘Jacob's ladder’ by developing new and improved exchange‐correlation functionals, is also highlighted. Some representative systems for the different regimes are depicted along the bottom: the amino acid tryptophan with a multi‐resolution grid, a defective Si nanotube with an extended KS wavefunction, DNA with localized orbitals, and the protein mitochondrial NADH:ubiquinone oxidoreductase.
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Plot showing the HOMOs of two neighboring molecules calculated using a fragment approach. Their nearest neighbors extracted from a large disordered host‐guest morphology are also depicted. Using this setup, one can calculate transfer integrals which take into account the environment.
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Organic light‐emitting diodes (OLED) device configuration illustrating the target goal of the EXTMOS project: simulating the full device from the molecular composition of the different layers.
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Dispersion of the molecular dipole moment of water molecules within a droplet of 1800 atoms, with statistics taken over 50 snapshots of an MD simulation. The dipole is calculated based on the atomic monopoles and dipoles, and these were obtained from (a) a classical simulation using POLARIS(MD), (b) a DFT simulation using BIGDFT, and (c) a combined QM/MM approach.
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Partial density of states for the DNA within the system depicted in Figure . The red curve was generated treating the entire system on a QM level, whereas the green curve only treated the DNA plus a shell of 4 Å on a QM level, with the remaining solvent atoms replaced by a multipole expansion. In order to allow for a better comparison, the QM/MM curve was shifted such that its HOMO energy coincides with the one of the full QM approach.
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Visualization of a DNA fragment containing 11 base pairs, surrounded by a solvent of water and Na ions (giving in total 15,613 atoms), with periodic boundary conditions.
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Left: Isosurface of one Kohn‐Sham orbital for a water droplet consisting of 1500 atoms. Right: density matrix in the x dimension, i.e., F(x, y 0, z 0; x′, y 0, z 0), for the same system.
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Structure and Mechanism > Computational Materials Science
Electronic Structure Theory > Ab Initio Electronic Structure Methods
Electronic Structure Theory > Density Functional Theory

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