Relation between single-particle kinetic energy and exchange energy in DFT for the inhomogeneous electron liquid in the Be atomRelation between single-particle kinetic energy and exchange energy in DFT for the inhomogeneous electron liquid in the Be atom
Faculty of Sciences. Physics
Department of Physics
Physics and chemistry of liquids. - London
48(2010):2, p. 272-278
University of Antwerp
n a recent study, the authors have used the semi empirical fine-tuned Hartree-Fock ground-state electron density n(r) of Cordero et al. [Phys. Rev. A 75, 052502 (2007)] for the Be atom to calculate the phase θ(r) from a non-linear pendulum-like equation. Since the density amplitude n(r)1/2 plus θ(r) determine, in turn, the idempotent Dirac density matrix γ(r, r'), we use n(r) and θ(r) first of all to calculate the exchange energy density eX(r) of the density functional theory (DFT). This enables us to obtain the Slater (Sl) approximation GPCH_A_429748_O_XML_IMAGES\GPCH_A_429748_O_ILM0001.gif to the exchange-only potential. A comparison can then be made, by integrating the earlier predicted exchange-correlation force -∂VXC (r)/∂r, of VXC (r) with GPCH_A_429748_O_XML_IMAGES\GPCH_A_429748_O_ILM0002.gif. Relationship to the Becke semiempirical density gradient approximation for exchange is also established. Some brief discussion of the Perdew-Burke-Ernzerhof density functional is added.