Performance of one-body reduced density matrix functionals for the homogeneous electron gas

The subject of this study is the exchange-correlation-energy functional of reduced density matrix functional theory. Approximations of this functional are tested by applying them to the homogeneous electron gas. We find that two approximations recently proposed by Gritsenko, Pernal, and Baerends, J. Chem. Phys., {\bf 122}, 204102 (2005), yield considerably better correlation energies and momentum distributions than previously known functionals. We introduce modifications to these functionals which, by construction, reproduce the exact correlation energy of the homogeneous electron gas

Discontinuity of the chemical potential in reduced-density-matrix-functional theory

We present a novel method for calculating the fundamental gap. To this end, reduced-density-matrix-functional theory is generalized to fractional particle number. For each fixed particle number, $M$, the total energy is minimized with respect to the natural orbitals and their occupation numbers. This leads to a function, $E_{\mathrm{tot}}^M$, whose derivative with respect to the particle number has a discontinuity identical to the gap. In contrast to density functional theory, the energy minimum is generally not a stationary point of the total-energy functional. Numerical results, presented for alkali atoms, the LiH molecule, the periodic one-dimensional LiH chain, and solid Ne, are in excellent agreement with CI calculations and/or experimental data.Comment: 9 pages, 3 figures, version as publishe

Open shells in reduced-density-matrix-functional theory

Reduced-density-matrix-functional theory is applied to open-shell systems. We introduce a spin-restricted formulation by appropriately expressing approximate correlation-energy functionals in terms of spin-dependent occupation numbers and spin-independent natural orbitals. We demonstrate that the additional constraint of total-spin conservation is indispensable for the proper treatment of open-shell systems. The formalism is applied to the first-row open-shell atoms. The obtained ground-state energies are in very good agreement with the exact values as well as other state of the art quantum chemistry calculationsComment: 4 pages, 2 figures, corrected typo

Exchange-energy functionals for finite two-dimensional systems

Implicit and explicit density functionals for the exchange energy in finite two-dimensional systems are developed following the approach of Becke and Roussel [Phys. Rev. A 39, 3761 (1989)]. Excellent agreement for the exchange-hole potentials and exchange energies is found when compared with the exact-exchange reference data for the two-dimensional uniform electron gas and few-electron quantum dots, respectively. Thereby, this work significantly improves the availability of approximate density functionals for dealing with electrons in quasi-two-dimensional structures, which have various applications in semiconductor nanotechnology.Comment: 5 pages, 3 figure

Exchange-correlation orbital functionals in current-density-functional theory: Application to a quantum dot in magnetic fields

The description of interacting many-electron systems in external magnetic fields is considered in the framework of the optimized effective potential method extended to current-spin-density functional theory. As a case study, a two-dimensional quantum dot in external magnetic fields is investigated. Excellent agreement with quantum Monte Carlo results is obtained when self-interaction corrected correlation energies from the standard local spin-density approximation are added to exact-exchange results. Full self-consistency within the complete current-spin-density-functional framework is found to be of minor importance.Comment: 5 pages, 2 figures, submitted to PR

Optimized Effective Potential Method in Current-Spin Density Functional Theory

Current-spin density functional theory (CSDFT) provides a framework to describe interacting many-electron systems in a magnetic field which couples to both spin- and orbital-degrees of freedom. Unlike in usual (spin-) density functional theory, approximations to the exchange-correlation energy based on the model of the uniform electron gas face problems in practical applications. In this work, explicitly orbital-dependent functionals are used and a generalization of the Optimized Effective Potential (OEP) method to the CSDFT framework is presented. A simplifying approximation to the resulting integral equations for the exchange-correlation potentials is suggested. A detailed analysis of these equations is carried out for the case of open-shell atoms and numerical results are given using the exact-exchange energy functional. For zero external magnetic field, a small systematic lowering of the total energy for current-carrying states is observed due to the inclusion of the current in the Kohn-Sham scheme. For states without current, CSDFT results coincide with those of spin density functional theory.Comment: 11 pages, 3 figure

Demonstration of a beam loaded nanocoulomb-class laser wakefield accelerator.

Laser-plasma wakefield accelerators have seen tremendous progress, now capable of producing quasi-monoenergetic electron beams in the GeV energy range with few-femtoseconds bunch duration. Scaling these accelerators to the nanocoulomb range would yield hundreds of kiloamperes peak current and stimulate the next generation of radiation sources covering high-field THz, high-brightness X-ray and γ-ray sources, compact free-electron lasers and laboratory-size beam-driven plasma accelerators. However, accelerators generating such currents operate in the beam loading regime where the accelerating field is strongly modified by the self-fields of the injected bunch, potentially deteriorating key beam parameters. Here we demonstrate that, if appropriately controlled, the beam loading effect can be employed to improve the accelerator's performance. Self-truncated ionization injection enables loading of unprecedented charges of ∼0.5 nC within a mono-energetic peak. As the energy balance is reached, we show that the accelerator operates at the theoretically predicted optimal loading condition and the final energy spread is minimized.Higher beam quality and stability are desired in laser-plasma accelerators for their applications in compact light sources. Here the authors demonstrate in laser plasma wakefield electron acceleration that the beam loading effect can be employed to improve beam quality by controlling the beam charge

A functional of the one-body-reduced density matrix derived from the homogeneous electron gas: Performance for finite systems

An approximation for the exchange-correlation energy of reduced-density-matrix-functional theory was recently derived from a study of the homogeneous electron gas (N.N. Lathiotakis, N. Helbig, E.K.U. Gross, Phys. Rev. B 75, 195120 (2007)). In the present work, we show how this approximation can be extended appropriately to finite systems, where the Wigner Seitz radius r_s, the parameter characterizing the constant density of the electron gas, needs to be replaced. We apply the functional to a variety of molecules at their equilibrium geometry, and also discuss its performance at the dissociation limit. We demonstrate that, although originally derived from the uniform gas, the approximation performs remarkably well for finite systems.Comment: 5 pages, 2 figuere

Discontinuity of the chemical potential in RDMFT for open-shell systems

We employ reduced density-matrix functional theory in the calculation of the fundamental gap of open-shell systems. The formula for the calculation of the fundamental gap is derived with special attention to the spin of the neutral and the charged systems. We discuss the effects of different functionals as well as the changes due to different basis sets. Also, we investigate the importance of varying the natural orbitals for the calculation of the fundamental gapComment: 9 pages, 6 figures, submitted to Phys. Rev.

Revisiting the role of H+ in chemotactic signaling of sperm

© 2004 Solzin et al. This article is distributed under the terms of the Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License. The definitive version was published in Journal of General Physiology 124 (2004): 115-124, doi:10.1085/jgp.200409030.Chemotaxis of sperm is an important step toward fertilization. During chemotaxis, sperm change their swimming behavior in a gradient of the chemoattractant that is released by the eggs, and finally sperm accumulate near the eggs. A well established model to study chemotaxis is the sea urchin Arbacia punctulata. Resact, the chemoattractant of Arbacia, is a peptide that binds to a receptor guanylyl cyclase. The signaling pathway underlying chemotaxis is still poorly understood. Stimulation of sperm with resact induces a variety of cellular events, including a rise in intracellular pH (pHi) and an influx of Ca2+; the Ca2+ entry is essential for the chemotactic behavior. Previous studies proposed that the influx of Ca2+ is initiated by the rise in pHi. According to this proposal, a cGMP-induced hyperpolarization activates a voltage-dependent Na+/H+ exchanger that expels H+ from the cell. Because some aspects of the proposed signaling pathway are inconsistent with recent results (Kaupp, U.B., J. Solzin, J.E. Brown, A. Helbig, V. Hagen, M. Beyermann, E. Hildebrand, and I. Weyand. 2003. Nat. Cell Biol. 5:109–117), we reexamined the role of protons in chemotaxis of sperm using kinetic measurements of the changes in pHi and intracellular Ca2+ concentration. We show that for physiological concentrations of resact (<25 pM), the influx of Ca2+ precedes the rise in pHi. Moreover, buffering of pHi completely abolishes the resact-induced pHi signal, but leaves the Ca2+ signal and the chemotactic motor response unaffected. We conclude that an elevation of pHi is required neither to open Ca2+-permeable channels nor to control the chemotactic behavior. Intracellular release of cGMP from a caged compound does not cause an increase in pHi, indicating that the rise in pHi is induced by cellular events unrelated to cGMP itself, but probably triggered by the consumption and subsequent replenishment of GTP. These results show that the resact-induced rise in pHi is not an obligatory step in sperm chemotactic signaling. A rise in pHi is also not required for peptide-induced Ca2+ entry into sperm of the sea urchin Strongylocentrotus purpuratus. Speract, a peptide of S. purpuratus may act as a chemoattractant as well or may serve functions other than chemotaxis.This work was supported by a grant from the Deutsche Forschungsgemeinschaft