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.

- 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

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- 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]

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- 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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