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Workshops

Fundamentals of Density Functional Theory for T> 0 : Quantum meets Classical

May 20, 2019 to May 23, 2019
Location : CECAM-HQ-EPFL, Lausanne, Switzerland
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Organisers

  • James Dufty (University of Florida, USA)
  • Samuel B. Trickey (University of Florida, USA)
  • Robert Evans (University of Bristol, United Kingdom)
  • James Lutsko (CENOLI, Univ. Libre de Bruxelles, Belgium)

Supports

   CECAM

Description

The aim of this workshop is to bring together leading members of two virtually independent communities of researchers working on Density Functional Theory: the quantum DFT community studying  electronic systems  mostly at zero temperature and the classical DFT community concerned with multicomponent and/or multiphase atomic, molecular and colloidal systems at non-zero temperatures. The broad objectives here include both exploration of enhanced formal developments and the potential for shared computational expertise with a particular focus on the developing interface between the two domains devoted to the subject of warm, dense matter. The format will include both formal talks and scheduled discussion sessions allowing for in-depth exploration of the various topics. 

The classical and quantum DFT communities start with the same basic theorems but have developed completely independent approaches to the goal of turning these into practical computational tools. The objectives of the workshop will be devoted to exploring the different approaches taken to shared conceptual challenges including the following:

  • Formal theory: How exact bounds, inequalities and exact sum rules are used to guide the development of  functionals. 
  • Functional developments: The distinctive approaches to going beyond the local density approximation developed in the two communities. 
  • Comparison of two-point functionals:  use of nonlocal functionals;  the classical limit of the quantum functionals. 
  • Computational methods: State of the art techniques in each domain for solving the nonlinear Euler-Lagrange equation.
  • Complex states (mixtures, phase transitions, coexistence): Warm dense matter includes coexisting atomic, molecular and free charge states. In principle these are treated by Coulomb interactions but in practice by the use of pseudo potentials, or average charge numbers. Classical mixtures have phenomenological potentials (usually pair potentials) representing the interactions among different constituents or species. Is there a middle ground for improved, practical descriptions?
  • Stucture (pair correlations, density response function): use of correlation and response functions, via the Ornstein-Zernike and related equations, to develop free energy functionals. 
  • Collaboration: problems at the interface and across the classical/quantum boundaries e.g. multi-scale modeling. 

References

"Inhomogeneous Electron Gas", P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).

"Thermal Properties of the Inhomogeneous Electron Gas", N. D. Mermin, Phys. Rev. 137, A1441 (1965).

"Self-Consistent Equations Including Exchange and Correlation Effects", W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965) .

"The nature of the liquid-vapour interface and other topics in the statistical mechanics of non-uniform, classical fluids", R. Evans, Adv. Phys. 28, 143 (1979).

"Recent Developments in Classical Density Functional Theory", J.F. Lutsko, Adv. Chem. Phys. 144, 1 (2010).

"Theory of Simple Liquids: with Applications to Soft Matter" , J-P. Hansen and I.R. McDonald (Academic 2013).

"New developments in classical density functional theory", R. Evans, M. Oettel, R. Roth and G. Kahl, Special Issue of J. Phys. Condens. Matt. 28, 240401 (2016).

"T>0 Ensemble-state Density Functional Theory via Legendre Transform", H. Eschrig, Phys. Rev. B 82, 205120 (2010).

"Innovations in Finite-Temperature Density Functionals," V.V. Karasiev, T. Sjostrom, D.Chakraborty, J.W. Dufty, F.E. Harris, K. Runge, and S.B. Trickey, in "Frontiers and Challenges in Warm Dense Matter", F. Graziani et al. eds., (Springer, Heidelberg, 2014) 61-85.

"Warming Up Density Functional Theory", Justin C Smith, Francisca Sagredo, Kieron Burke Frontiers of Quantum Chemistry 249--271 (2018); arXiv 1701.00873.