Condensed Matter Physics, 2012, vol. 15, No. 4, p. 43603:115
DOI:10.5488/CMP.15.43603
arXiv:1212.6358
Title:
Recent developments in classical density functional theory: Internal energy functional and diagrammatic structure of fundamental measure theory
Author(s):

M. Schmidt
(Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D95440 Bayreuth, Germany; H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK),


M. Burgis
(Theoretische Physik II, Physikalisches Institut, Universit{ät Bayreuth, D95440 Bayreuth, Germany),


W.S.B. Dwandaru
(H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK; Jurusan Fisika, Universitas Negeri Yogyakarta, Bulaksumur, Yogyakarta, Indonesia),


G. Leithall
(H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK),


P. Hopkins
(H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK)

An overview of several recent developments in density functional theory for classical inhomogeneous liquids is given. We show how Levy's constrained search method can be used to derive the variational principle that underlies density functional theory. An advantage of the method is that the Helmholtz free energy as a functional of a trial onebody density is given as an explicit expression, without reference to an external potential as is the case in the standard MerminEvans proof by reductio ad absurdum. We show how to generalize the approach in order to express the internal energy as a functional of the onebody density distribution and of the local entropy distribution. Here the local chemical potential and the bulk temperature play the role of Lagrange multipliers in the EulerLagrange equations for minimiziation of the functional. As an explicit approximation for the freeenergy functional for hard sphere mixtures, the diagrammatic structure of Rosenfeld's fundamental measure density functional is laid out. Recent extensions, based on the KierlikRosinberg scalar weight functions, to binary and ternary nonadditive hard sphere mixtures are described.
Key words:
density functional theory, HohenbergKohn theorem, Rosenfeld functional
PACS:
61.25.f, 61.20.Gy, 64.70.Ja
