Van der Waals Density Functionals

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    Calculating van der Waals interactions in extended systems where the electronic density is sufficiently sparse is of great importance for many applications. When using Density Functional Theory, several approaches are available:

     - Adding an empirical dispersion potential to the usual DFT Kohn-Sham equations (DFT-D method)[1].
     - Using Maximally-Localized Wannier Functions (DFT-WF method)[2].
     - Taking long-range exchange-correlation interactions directly into account within DFT (vdW-DF method)[3].
    

    The original method proposed by Dion et al. scales very heavily with the size of the system. The developers of SIESTA have thus proposed an approximation[4] that scales more reasonably.

    Several functionals have been developed on this basis since then:

     - optB86B, optB88, and optPBE-vdW[5].
     - vdW-DF2[6].
     - ...
    

    Since 2015, ESL contributors have been collaborating with the developers of a parallel C implementation of the vdW-DF approach, codename Libvdwxc[7].

    References

    1. S. Grimme., Accurate description of van der waals complexes by density functional theory including empirical corrections, J. Comput. Chem., 25(12), 1463-1473, (2004)
    2. A. Ambrosetti, P.L. Silvestrelli, van der Waals interactions in density functional theory using Wannier functions: Improved C6 and C3 coefficients by a different approach, Phys. Rev. B 85, 073101 (2012)
    3. M. Dion, H. Rydberg, E. Schröder, D. C. Langreth, and B. I. Lundqvist, van der Waals Density Functional for General Geometries, Phys. Rev. Lett. 92, 246401 (2004)
    4. G. Román-Pérez, J. M. Soler, Efficient implementation of a van der Waals density functional: Application to double-wall carbon nanotubes, Phys. Rev. Lett. 103, 096102 (2009)
    5. J. Klimeš, D. R. Bowler, and A. Michaelides, Chemical accuracy for the van der Waals density functional, J. Phys.: Cond. Matt. 22, 022201 (2010)
    6. K. Lee, E. D. Murray, L. Kong, B. I. Lundqvist, and D. C. Langreth, Higher-accuracy van der Waals density functional, Phys. Rev. B 82, 081101 (2010)
    7. A.H. Larsen, M. Kuisma, J.L. Öfgren, Y. Pouillon, P. Erhart, P. Hyldgaard, libvdwxc: A library for exchange–correlation functionals in the vdW-DF family, arXiv:1703.06999v1 (2017)