Semiclassical Approaches in Density Functional Theory

We discuss the use of semiclassical methods in understanding, and improving, density functional theory (DFT). It has been found[1] that semiclassical approaches can explain many features of modern exchange-correlation approximations, such as the local density approximation or generalized gradient approximations. In this work, we continue this line of inquiry, showing how semiclassical approximations may be used to construct a form for the non-interacting kinetic energy density. A semiclassical approximation to the Green's function is made[2], which, when integrated appropriately, yields leading corrections to the Thomas-Fermi result. It can be regarded as a functional of the potential. We test this approximation for various 1D systems confined within a box and present the results. This, coupled with the corresponding form of the density[2], could provide an orbital-free DFT which would allow more complex systems to be studied.\newline [1] J. Perdew, A. Ruzsinszky, G.I. Csonka, O.A. Vydrov, G.E. Scuseria, L.A. Constantin, X. Zhou, and K. Burke, arXiv:0707.2088 (2007).\newline [2] W. Kohn and L.J. Sham, Phys. Rev. {\bf 137}, A1697 (1965).