Electronic structure methods

Here is a list of some of the computational techniques used by Psi-k members in their research. Links to relevant review articles are given. The list of methods is evidently incomplete at the moment, and it is hoped to expand it presently.

  1. Density functional theory (DFT)
    Density functional theory is the main workhorse of the community. It is based on the Hohenberg-Kohn theorem — which states that all observables determined by the ground state density — and the Kohn-Sham approach — which maps the full many body problem onto an effective non-interacting problem — allowing the calculation (at least in principle) of the exact ground state density and energy. A more detailed introduction to density functional theory can be found here. A selection of other relevant articles and books might include:

    • Density functional theory: past, present, … future” by R.O. Jones (Sep 2014 Psi-k Scientific Highlight of the Month) [link]
    • Perspective: fifty years of density functional theory in chemical physics” by A. Becke, J. Chem. Phys. 140, 18A301 (2014) [link]
    • Perspective on density functional theory” by K. Burke, J. Chem. Phys. 136, 150901 (2012) [link]
    • A chemist’s guide to density functional theory” by W. Koch and M.C. Malthausen (Wiley, 2001)
    • Kohn-Sham density functional theory: predicting and understanding chemistry” by F.M. Bickelhaupt and E.J. Barends, Reviews in Computational Chemistry 15 (2000) [link]
    • “Density functional theory of atoms and molecules” by  R. G. Parr and W. Yang (Oxford University Press, New York, 1989)

  3. GW-Approximation
    The GW method is based on the Hedin equations, which fully determine the many-body problem in terms of the Green’s function, describing the quasiparticles of a system.  A full solution of these equations turns out to be impossible, and the more tractable GW approximation arises from truncating them and neglecting the so-called vertex function. The remaining expression for the self-energy of the system consists of the Greens function G and the screened Coulomb interaction W. More information is available here.

    • New method for calculating the one-particle Green’s function with application to the electron-gas problem” by L. Hedin, Phys. Rev. 139, A796 (1965) [link]
    • Quasiparticle calculations in solids” by W.G. Aulbur, L. Jönsson and J.W. Wilkins, Solid State Physics 54, 1 [link]
    • The GW Method” by F. Aryasetiawan and O. Gunnarsson, Rep. Prog. Phys. 61, 237 (1998)  [link]
    • Correlation effects in solids from first principles” by  F. Aryasetiawan [link]
    • Electron correlation in the solid state” edited by N.H. March (World Scientific, 1999) [link]

  5. Quantum Monte Carlo (QMC)
    ‘Quantum Monte Carlo’ encompasses a set of techniques linked by their common use of the random sampling Monte Carlo method to handle the multi-dimensional integrals that arise in the various formulations of the many-body problem. The method is in principle capable of giving exact solutions to the full many-body Schrödinger equation. Although exact solutions cannot normally be found in practice due to, e.g., the necessity of making the fixed-node approximation, and although the method is computationally expensive, QMC provides a useful, highly-accurate benchmark with excellent scaling with system size and with number of computer processors. Some relevant review articles are:

    • Quantum Monte Carlo and related methods” by B.M. Austin, D.Y. Zubarev, and W.A. Lester, Chem. Rev. 112 ,  263 (2012) [link]
    • Applications of quantum Monte Carlo methods in condensed systems” by Jindřich Kolorenč and Lubos Mitas, Rep. Prog. Phys. 74, 026502 (2011) [link]
    • Continuum variational and diffusion quantum Monte Carlo calculations” by R.J. Needs, M.D. Towler, N.D. Drummond, and P. López Ríos, J. Phys.: Cond. Mat. 22, 023201 (2009) [link]
    • Petascale computing opens up new vistas for quantum Monte Carlo”  by M.J. Gillan, M.D. Towler and D. Alfè (Feb 2011 Psi-k Scientific Highlight of the Month) [link]
    • Quantum Monte Carlo for atoms, molecules and solids“, W.A. Lester Jr., L. Mitas, and B. Hammond, Chem. Phys. Lett. 478, 1 (2009) [link]
    • Quantum Monte Carlo simulations of solids” (2001) by M. Foulkes, L. Mitás, R.J. Needs and G. Rajagopal, Rev. Mod. Phys. 73, 33 (2001) [link]

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Ab initio (from electronic structure) calculation of complex processes in materials