Dresden 2009 – wissenschaftliches Programm
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O: Fachverband Oberflächenphysik
O 41: Ab-initio approaches to excitations in condensed matter I
O 41.8: Vortrag
Mittwoch, 25. März 2009, 16:45–17:00, SCH 251
Discontinuity of chemical potential in reduced density matrix functional theory: open shell formulation — •N.N. Lathiotakis1,2,4, N. Helbig2,3,4, and E.K.U. Gross2,4 — 1TPCI, NHRF, Vass. Constantinou 48, Athens, Greece — 2Institut für Theoretische Physik, FU Berlin, Arnimallee 14, D14195 Berlin, Germany — 3Nano-Bio Spectroscopy group, Dpto. de Física de Materiales, Universidad del País Vasco UPV/EHU and Centro Mixto CSIC-UPV/EHU, San Sebastián, Spain — 4European Theoretical Spectroscopy Facility
In reduced-density-matrix-functional theory, approximations of the total energy as a functional of the one-body-reduced-density matrix are minimized. In an open-shell treatment, this minimization involves two Lagrange multipliers that ensure the conservation of the number of particles separately for each spin. We prove that these Lagrange multipliers are the chemical potentials, i.e. the derivatives of the total energy with respect to the numbers of spin up and spin down electrons. For the exact functional, these Lagrange multipliers show a discontinuity at integer values of the spin-resolved particle numbers which equals the fundamental gap. We test present-day RDMFT functionals for this property and find that many of them reproduce a step-like behavior, in resemblance to the exact theory. This behavior is improved in the open-shell treatment i.e. when all fractional electrons are added to the same spin. The obtained discontinuities are in very good agreement with the gaps of the studied finite systems. These promising results are a motivation for the application of RDMFT to problems like the band gaps of solids where DFT results deviate from experiments.