摘要
We consider the Thomas-Fermi-von Weizsacker energy functional,with the Wang-Teter correction,and present an efficient real space method for Orbital-Free Density Functional Theory.It is proved that the energy minimizer satisfies a second order quasilinear elliptic equation,even at the points where the electron density vanishes.This information is used to construct an efficient energy minimization method for the resulting constrained problem,based on the truncated Newton method for unconstrained optimization.The Wang-Teter kernel is analyzed,and its behavior in real space at short and far distances is determined.A second order accurate discretization of the energy is obtained using finite differences.The efficiency and accuracy of the method is illustrated with numerical simulations in an Aluminium FCC lattice.
基金
I would like to thank Prof.Weinan E for suggesting this problem to me.I would also like to thank Prof.Emily A.Carter,and the members of her group,in particular Gregory Ho and Vincent Ligneres,for explaining to me some of the intricacies of OFDFT.The simulations presented in this article were carried out in an HP workstation purchased with funds provided by NSF grant DMS-0411504
in a Beowulf cluster purchased by the Mathematics department at UCSB with funds provided by an NSF SCREMS grant DMS-0112388
and in an SGI Altix system located at the CNSI Computer Facilities at UCSB,purchased with funds provided by NSF grant CHE-0321368.
