Recent Publications

< more | 2011 | 2010 | 2009 | 2008 | 2007 | 2006 | 2005 | 2004 | more >

  1. Title: Nuclear quantum effects on the structural properties of solids

    Author(s): Scivetti I., Hughes D., Gidopoulos N., Caro A., Kohanoff J.,

    AIP Conference Proceedings, 963, pp. 212-223 (SEP 25 2007)


  2. Title: Can Marcus theory be applied to redox processes in ionic liquids? A comparative simulation study of dimethylimidazolium liquids and acetonitrile

    Author(s): Lynden-Bell R.M.

    Journal Of Physical Chemistry B, 111, No. 36, pp. 10800-10806 (SEP 13 2007)

    doi: 10.1021/jp074298s

    Simulations of a model system of charged spherical ions in the ionic liquids dimethylimidazolium chloride, [dmim][Cl], dimethylimidazolium hexafluorophosphate, [dmim][PF6], and the polar liquid acetonitrile, MeCN, are used to investigate the applicability of Marcus theory to electrochemical half-cell redox processes in these liquids. The free energy curves for solvent fluctuations are found to be approximately parabolic and the Marcus solvent reorganization free energies and activation free energies are determined for six possible redox processes in each solvent. The similarities between the different types of solvent are striking and are attributed to the essentially long-range nature of the relevant interactions and the effectiveness of the screening of the ion potential. Nevertheless, molecular effects are seen in the variation of solvent screening potential with distances up to 2 nm.

  3. Title: Vibrational frequencies of CO on Pt(111) in electric field: A periodic DFT study

    Author(s): Lozovoi A.Y., Alavi A.

    Journal Of Electroanalytical Chemistry, 607, No. 1-2, pp. 140-146 (SEP 1 2007)

    doi: 10.1016/j.jelechem.2007.02.030

    The stretching frequency of CO adsorbed on Pt(1 1 1), vc-0, changes if an external electric field F is applied (the vibrational Stark effect). The slope dv(c-o)/dF measured in electrochemical cells, is a factor of two larger than that obtained in UHV experiments. The reasons for this discrepancy are still being debated, whereas existing DFT calculations "support" the electrochemical value. This study, on the contrary, produces a slope close to that found in UHV. The difference between our ab initio calculations and previous studies is that the latter were performed with finite clusters, whereas here the electric field is applied to a periodic supercell. This highlights the importance of the computational setup, and in particular the boundary conditions, for calculations of charged systems. (c) 2007 Elsevier B.V. All rights reserved.

  4. Title: Structure-related effects on the domain wall migration in atomic point contacts

    Author(s): Stamenova M., Sahoo S., Todorov T.N., Sanvito S.

    Journal Of Magnetism And Magnetic Materials, 316, No. 2, pp. E934-E936 (SEP 2007)

    doi: 10.1016/j.jmmm.2007.03.147

    We investigate the interplay between magnetic and structural dynamics in magnetic point contacts under current-carrying conditions. In particular we address the dependence of the results upon the specific parameterization of the elastic properties of the material. Our analysis shows a strong influence of the structural relaxation on the energy barrier for domain wall migration, but a negligible dependence of the mechanical properties on the magnetic state. These results are stable against the various material specific choices of parameters describing different transition metals. (c) 2007 Elsevier B.V. All rights reserved.

  5. Title: Nonequilibrium statistical mechanics of classical nuclei interacting with the quantum electron gas

    Author(s): Wang Y., Kantorovich L.

    Physical Review B, 76, No. 14, Art. No. 144304 (OCT 19 2007)

    doi: 10.1103/PhysRevB.76.144304

    Kinetic equations governing time evolution of positions and momenta of atoms in extended systems are derived using quantum-classical ensembles within the nonequilibrium statistical operator method (NESOM). Ions are treated classically, while their electrons quantum mechanically; however, the statistical operator is not factorized in any way and no simplifying assumptions are made concerning the electronic subsystem. Using this method, we derive kinetic equations of motion for the classical degrees of freedom (atoms) which account fully for the interaction and energy exchange with the quantum variables (electrons). Our equations, alongside the usual “Newton-like” terms normally associated with the Ehrenfest dynamics, contain additional terms, proportional to the atoms velocities, which can be associated with the “electronic friction.” Although previously electronic friction was introduced into molecular dynamics equations of atoms only using model treatments, we show that this result is general and model independent and thus must be expected in treating any system as an additional force acting on slow degrees of freedom due to coupling with the fast ones. Possible ways of calculating the friction forces, which are shown to be given via complicated nonequilibrium correlation functions, are discussed. In particular, we demonstrate that the correlation functions are directly related to the thermodynamic Matsubara Green\'s functions, and this relationship allows for the diagrammatic methods to be used in treating electron-electron interaction perturbatively when calculating the correlation functions.

  6. Title: Competition of charge density waves and superconductivity in Sulfur

    Author(s): Degtyareva O., Magnitskaya M.V., Kohanoff J., Profeta G., Scandolo S., McMahon M.I., Gregoryanz E.,

    Physical Review Letters, 99, Art. No. 155505 (OCT 15 2007)

    doi: 10.1103/PhysRevLett.99.155505

    Full Text

    A one-dimensional charge-density wave (CDW) instability is shown to be responsible for the formation of the incommensurate modulation of the atomic lattice in the high-pressure phase of sulfur. The coexistence of, and competition between, the CDW and the superconducting state leads to the previously observed increase of Tc up to 17 K, which we attribute to the suppression of the CDW instability, the same phenomenology found in doped layered dichalcogenides.

  7. Title: Simulations of ionic liquids, solutions, and surfaces

    Author(s): Lynden-Bell R.M., Del Popolo M.G., Youngs T.G.A., Kohanoff J., Hanke C.G., Harper J.B., Pinilla C.C.

    Accounts of Chemical Research, 40, No. 11, pp. 1138-1145 (OCT 2007)

    doi: 10.1021/ar700065s

    We have been using atomistic simulation for the last 10 years to study properties of imidazolium-based ionic liquids. Studies of dissolved molecules show the importance of electrostatic interactions in both aromatic and hydrogen-bonding solutes. However, the local structure strongly depends upon ion–ion and solute–solvent interactions. We find interesting local alignments of cations at the gas–liquid and solid–liquid interfaces, which give a potential drop through the surface. If the solid interface is charged, this charge is strongly screened over distances of a few nanometres and this screening decays on a fast time scale. We have studied the sensitivity of the liquid structure to force-field parameters and show that results from ab initio simulations can be used in the development of force fields.

  8. Title: Clusters, liquids, and crystals of dialkyimidazolium salts. A combined perspective from a initio and classical computer simulations

    Author(s): Del Popolo M.G., Kohanoff J., Lynden-Bell R.M., Pinilla C

    Accounts of Chemical Research, 40, No. 11, pp. 1156-1164 (NOV 2007)

    doi: 10.1021/ar700069c

    We summarize results obtained by a combination of ab initio and classical computer simulations of dialkylimidazolium ionic liquids in different states of aggregation, from crystals to liquids and clusters. Unusual features arising from the competition between electrostatic, dispersion, and hydrogen-bonding interactions are identified at the origin of observed structural patterns. We also discuss the way Bronsted acids interact with ionic liquids leading to the formation of hydrogen-bonded anions.

  9. Title: Dynamical simulation of inelastic quantum transport

    Author(s): McEniry E.J., Bowler D.R., Dundas D., Horsfield A.P., Sanchez C.G., Todorov T.N.

    Journal Of Physics-Condensed Matter, 19, No. 19, Art. No. 196201 (MAY 16 2007)

    doi: 10.1088/0953-8984/19/19/196201

    A method for correlated quantum electron-ion dynamics is combined with a method for electronic open boundaries to simulate in real time the heating, and eventual equilibration at an elevated vibrational energy, of a quantum ion under current flow in an atomic wire, together with the response of the current to the ionic heating. The method can also be used to extract inelastic current voltage corrections under steady-state conditions. However, in its present form the open-boundary method contains an approximation that limits the resolution of current-voltage features. The results of the simulations are tested against analytical results from scattering theory. Directions for the improvement of the method are summarized at the end.

  10. Title: Polarization relaxation in an ionic liquid confined between electrified walls

    Author(s): Pinilla C., Del Popolo M.G., Kohanoff J., Lynden-Bell R.M.

    Journal Of Physical Chemistry B, 111, No. 18, pp. 4877-4884 (MAY 10 2007)

    doi: 10.1021/jp067184+

    The response of a room temperature molten salt to an external electric field when it is confined to a nanoslit is studied by molecular dynamics simulations. The fluid is confined between two parallel and oppositely charged walls, emulating two electrified solid-liquid interfaces. Attention is focused on structural, electrostatic, and dynamical properties, which are compared with those of the nonpolarized fluid. It is found that the relaxation of the electrostatic potential, after switching the electric field off, occurs in two stages. A first, subpicosecond process accounts for 80% of the decay and is followed by a second subdiffusive process with a time constant of 8 ps. Diffusion is not involved in the relaxation, which is mostly driven by small anion translations. The relaxation of the polarization in the confined system is discussed in terms of the spectrum of charge density fluctuations in the bulk.

  11. Title: Neutral and charged 1-butyl-3-methylimidazolium triflate clusters: Equilibrium concentration in the vapor phase and thermal properties of nanometric droplets

    Author(s): Ballone P., Pinilla C., Kohanoff J., Del Popolo M.G.

    Journal Of Physical Chemistry B, 111, No. 18, pp. 4938-4950 (MAY 10 2007)

    doi: 10.1021/jp067484r

    Ground state energy, structure, and harmonic vibrational modes of 1-butyl-3-methylimidazolium triflate ([bmim][Tf]) clusters have been computed using an all-atom empirical potential model. Neutral and charged species have been considered up to a size (30 [bmim][Tf] pairs) well into the nanometric range. Free energy computations and thermodynamic modeling have been used to predict the equilibrium composition of the vapor phase as a function of temperature and density. The results point to a nonnegligible concentration of very small charged species at pressures (P similar to 0.01 Pa) and temperatures (T >= 600 K) at the boundary of the stability range of [bmim][Tf]. Thermal properties of nanometric neutral droplets have been investigated in the 0 <= T <= 700 K range. A near-continuous transition between a liquidlike phase at high T and a solidlike phase at low T takes place at T similar to 190 K in close correspondence with the bulk glass point T-g similar to 200 K. Solidification is accompanied by a transition in the dielectric properties of the droplet, giving rise to a small permanent dipole embedded into the solid cluster. The simulation results highlight the molecular precursors of several macroscopic properties and phenomena and point to the close competition of Coulomb and dispersion forces as their common origin.

  12. Title: Quantum annealing of an ising spin-glass by Green's function Monte Carlo

    Author(s): Stella L., Santoro G.E.,

    Physical Review E, 75, No. 3, Art. No. 036703 (March 2007)

    doi: 10.1103/PhysRevE.75.036703

    We present an implementation of quantum annealing (QA) via lattice Green's function Monte Carlo (GFMC), focusing on its application to the Ising spin glass in transverse field. In particular, we study whether or not such a method is more effective than the path-integral Monte Carlo- (PIMC) based QA, as well as classical simulated annealing (CA), previously tested on the same optimization problem. We identify the issue of importance sampling, i.e., the necessity of possessing reasonably good (variational) trial wave functions, as the key point of the algorithm. We performed GFMC-QA runs using such a Boltzmann-type trial wave function, finding results for the residual energies that are qualitatively similar to those of CA (but at a much larger computational cost), and definitely worse than PIMC-QA. We conclude that, at present, without a serious effort in constructing reliable importance sampling variational wave functions for a quantum glass, GFMC-QA is not a true competitor of PIMC-QA.

  13. Title: Monte Carlo study of thermodynamic properties and clustering in the bcc Fe-Cr system

    Author(s): Lavrentiev M.Y., Drautz R., Nguyen-Manh D., Klaver T.P.C., Dudarev S.L.

    Physical Review B, 75, No. 1, Art. No. 014208 (JAN 2007)

    doi: 10.1103/PhysRevB.75.014208

    Iron-chromium alloys are characterized by a complex phase diagram, by the small negative enthalpy of mixing at low Cr concentrations in the bcc alpha-phase of Fe, and by the inversion of the short-range order parameter. We present Monte Carlo simulations of the binary Fe-Cr alloy based on the cluster expansion approximation for the enthalpy of the system. The set of cluster expansion coefficients is validated against density functional calculations of energies of small clusters of chromium in bcc structure. We show that in the limit of small Cr concentration the enthalpy of mixing remains negative up to fairly high temperatures, and individual Cr atoms remain well separated from each other. Clustering of Cr atoms begins at concentrations exceeding approximately 10% at 800 K and 20% at 1400 K, with Cr-Fe interfaces being parallel to the [110] planes. Calculations show that the first and the second short-range order parameters change sign at approximately 10.5% Cr, in agreement with experimental observations. Semi-grand-canonical ensemble simulations used together with experimental data on vibrational entropy of mixing give an estimate for the temperature of the top of the alpha-alpha(') miscibility gap. We find that the complex ordering reactions occurring in Fe-Cr, as well as the thermodynamic properties of the alloy, can be reasonably well described using a few concentration-independent cluster expansion coefficients.

  14. Title: Lattice melting and rotation in perpetually pulsating equilibria

    Author(s): Pichon C., Lynden-Bell D., Pichon J., Lynden-Bell R.

    Physical Review E, 75, No. 1, Art. No. 011125 (JAN 2007)

    doi: 10.1103/PhysRevE.75.011125

    Systems whose potential energies consists of pieces that scale as r(-2) together with pieces that scale as r(2), show no violent relaxation to Virial equilibrium but may pulsate at considerable amplitude forever. Despite this pulsation these systems form lattices when the nonpulsational "energy" is low, and these disintegrate as that energy is increased. The "specific heats" show the expected halving as the "solid" is gradually replaced by the "fluid" of independent particles. The forms of the lattices are described here for N <= 18 and they become hexagonal close packed for large N. In the larger N limit, a shell structure is formed. Their large N behavior is analogous to a gamma=5/3 polytropic fluid with a quasigravity such that every element of fluid attracts every other in proportion to their separation. For such a fluid, we study the "rotating pulsating equilibria" and their relaxation back to uniform but pulsating rotation. We also compare the rotating pulsating fluid to its discrete counterpart, and study the rate at which the rotating crystal redistributes angular momentum and mixes as a function of extra heat content.

  15. Title: Phase diagrams and surface properties of modified water models

    Author(s): Alejandre J., Lynden-Bell R.M.

    Molecular Physics, 105, No. 23, pp. 3029-3033 (DEC 2007)

    doi: 10.1080/00268970701733405

    The surface properties and phase diagrams are examined for a number of modified water models. In the 'bent' family of models where the bond angle is decreased and the network structure is lost the surface tension is lower than in SPC/E water and the critical temperature is lower. In the 'hybrid' family of models which are hybrids between SPC/E water and a Lennard-Jones liquid the surface tension and the critical temperature are higher that in SPC/E water. These properties correlate well with the varying ability of the liquids to dissolve hard spheres. The surface potential, on the other hand, is slightly smaller in magnitude in the hybrid models than in SPC/E water because there is slightly less alignment of the dipoles in the surface layer. The degree of molecular alignment in the surface and the consequent surface potential drop is much lower in magnitude in the bent models than in SPC/E water.

  16. Title: Does Marcus theory apply to redox processes in ionic liquids? A simulation study

    Author(s): Lynden-Bell R.M.

    Electrochemistry Communications, 9, No. 8, pp. 1857-1861 (AUG 2007)

    doi: 10.1016/j.elecom.2007.04.010

    Simulation studies on a model system of a spherical ion with various charges in two imidazolium ionic liquids and in acetonitrile are compared. The average vertical ionisation potentials as a function of the charge on the ion are similar for all three systems. The Landau free energies of each system as a function of the vertical ionisation potential are computed and are close to being parabolic. Results are shown for the solvent reorganisation energies and for the activation free energies. The similarities of all these quantities are interpreted in terms of continuum models. However, the dynamics are likely to be very different in a polar liquid and in an ionic liquid as in the former case screening occurs by reorientation of molecules and in the latter case it occurs by translation of ions. (c) 2007 Elsevier B.V. All rights reserved.

  17. Title: Local and semilocal density functional computations for crystals of 1-alkyl-3-methyl-imidazolium salts

    Author(s): Del Popolo M.G., Pinilla C., Ballone P.

    Journal Of Chemical Physics, 126, No. 14, Art. No. 144705 (APR 14 2007)

    doi: 10.1063/1.2715571

    The accuracy and reliability of popular density functional approximations for the compounds giving origin to room temperature ionic liquids have been assessed by computing the T=0 K crystal structure of several 1-alkyl-3-methyl-imidazolium salts. Two prototypical exchange-correlation approximations have been considered, i.e., the local density approximation (LDA) and one gradient corrected scheme [PBE-GGA, Phys. Rev. Lett. 77, 3865 (1996)]. Comparison with low-temperature x-ray diffraction data shows that the equilibrium volume predicted by either approximations is affected by large errors, nearly equal in magnitude (similar to 10%), and of opposite sign. In both cases the error can be traced to a poor description of the intermolecular interactions, while the intramolecular structure is fairly well reproduced by LDA and PBE-GGA. The PBE-GGA optimization of atomic positions within the experimental unit cell provides results in good agreement with the x-ray structure. The correct system volume can also be restored by supplementing PBE-GGA with empirical dispersion terms reproducing the r(-6) attractive tail of the van der Waals interactions. (c) 2007 American Institute of Physics.

  18. Title: The Computational Modeling of Alloys at the Atomic Scale: From Ab Initio and Thermodynamics to Radiation-Induced Heterogeneous Precipitation

    Author(s): Caro A., Caro M., Klaver T.P.C. Sadigh B., Lopasso E.M., Srinivasan S.G.

    JOM Journal of the Minerals, Metals and Materials Society, 59, No. 4, pp. 52-57 (APR 2007)

    doi: 10.1007/s11837-007-0055-y

    Full Text

    This paper describes a strategy to simulate radiation damage in FeCr alloys wherein magnetism introduces an anomaly in the heat of formation of the solid solution. This has implications for the precipitation of excess chromium in the α′ phase in the presence of eterogeneities. These complexities pose many challenges for atomistic (empirical) methods. To address such issues the authors have developed a modified manybody potential by rigorously fitting thermodynamic properties including free energy. Multi-million atom displacement Monte Carlo simulations in the transmutation ensemble, using the new potential, predict that thermodynamically grain boundaries, dislocations, and free surfaces are not preferential sites for α′precipitation.

  19. Title: Robust nonadiabatic molecular dynamics for metals and insulators

    Author(s): Stella L., Meister M., Fisher A. J., Horsfield A. P.

    Journal of Physical Chemistry, 127, No. 21, Art. No. 214104 (4 December 2007)

    doi: 10.1063/1.2801537

    We present a new formulation of the correlated electron-ion dynamics (CEID) scheme, which systematically improves Ehrenfest dynamics by including quantum fluctuations around the mean-field atomic trajectories. We show that the method can simulate models of nonadiabatic electronic transitions and test it against exact integration of the time-dependent Schrödinger equation. Unlike previous formulations of CEID, the accuracy of this scheme depends on a single tunable parameter which sets the level of atomic fluctuations included. The convergence to the exact dynamics by increasing the tunable parameter is demonstrated for a model two level system. This algorithm provides a smooth description of the nonadiabatic electronic transitions which satisfies the kinematic constraints (energy and momentum conservation) and preserves quantum coherence. The applicability of this algorithm to more complex atomic systems is discussed.

  20. Title: Magnetocaloric effect in metamagnetic systems

    Author(s): Triguero C., Porta M., Planes A.

    Physical Review B, 76, No. 9, pp. 094415- (24 September 2007)

    doi: 10.1103/PhysRevB.76.094415

    We propose a model to account for the magnetocaloric effect associated with field-driven first-order magnetic transitions. The model is based on an Ising model for the magnetic degrees of freedom which are coupled to lattice vibrations. The coupling is introduced within the framework of a bond proportion model, which assumes that nearest-neighbor pairs of antiparallel and parallel spins have different stiffness. The model is solved by means of a variational mean field technique and it is found that, for strong enough coupling, it displays a field-induced first-order magnetic transition. The magnetocaloric properties are obtained and results are compared with experimental results reported for systems undergoing metamagnetic transitions.

  21. Title: Evolucao estrutural de nanotubos de oxidos de vanadio: efeito da temperatura

    Author(s): Ferreira O.P., Alves O.L., Souza Filho A.G., Santos E.J.G., Mendes Filho J.

    Chemical Physics Letters, 437, No. 1-3, pp. 79-82 (22 March 2007)

    doi: 10.1016/j.cplett.2007.01.071

    The interaction of 2,3,7,8-tetrachlorinated dibenzo-p-dioxin (dioxin) with carbon nanotubes is analyzed by ab initio methods. The structural and electronic properties of the dioxin interacting with the pristine, defective and B-, N-, and Si-doped SWNTs are considered by studying different geometries. We have found that the dioxin interacts with a pure carbon nanotube although it depends on the geometry of the molecule approximation, increasing if the tube is defective.

  22. Title: Atomistic study of ordinary 1/2 < 110] screw dislocations in single-phase and lamellar gamma-TiAl

    Author(s): Katzarov I.H., Cawkwell M.J., Paxton A.T., Finnis M.W.

    Philosophical Magazine, 87, No. 12, pp. 1795-1809 (2007)

    doi: 10.1080/14786430601080252

    Full Text

    Computer simulation of the core structure and glide of ordinary 1/2 [110] screw dislocations in single-phase L1(0) TiAl and in two lamellae forming a twin gamma/gamma-interface has been performed using recently constructed Bond-Order Potentials (BOPs). BOPs represent a semi-empirical, numerically efficient scheme that works within the orthogonal tight-binding approximation and is able to capture the directionality of bonding. We have studied dislocation glide in perfect L10 TiAl and along a twin interface, transmission of an ordinary screw dislocation between lamellae, and the core structure, mobility and detachment of an interfacial 1/2 [110] screw dislocation from a twin boundary under applied shear stresses in directions parallel and perpendicular to a (111) plane. Our results show that the glide of ordinary 1/2 [110] straight screw dislocations under applied stresses in L1(0) TiAl is characterized by zigzag movement on two conjugated {111} planes. The non-planar core of the 1/2 (110] screw dislocation is distorted asymmetrically when the elastic centre of the dislocation is close to a twin gamma/gamma-interface and the dislocation moves on one of the (111) planes, depending on the magnitude of the corresponding Schmid factor. Ordinary dislocations become ordinary interfacial dislocations when they reach the interface. With increasing applied stress they can glide into the adjacent lamella, leaving no remnant interfacial dislocation.

  23. Title: Interstitials in FeCr alloys studied by density functional theory

    Author(s): Klaver T.P.C., Olsson P., Finnis M.W.

    Physical Review B, 76, pp. 214110- (2007)

    doi: 10.1103/PhysRevB.76.214110

    Density functional theory calculations have been used to study relaxed interstitial configurations in FeCr alloys. The ionic and electronic ground states of 69 interstitial structures have been determined. Interstitials were placed in alloys with up to 14 at. % Cr. Cr atoms were either monatomically dispersed or clustered together within a periodically repeated supercell consisting of 4 4 4 cubes of bcc unit cells. The distance between the interstitials and Cr atoms was varied within the supercells. It is shown that Cr atoms beyond third-nearest-neighbor distance from the interstitial can still have an interaction with it of up to 0.9 eV. The multibody nature of the Cr-Cr interactions causes the Cr-interstitial interaction to be strongly concentration dependent. The Cr-Cr interaction in defect-free alloys is also dependent on the overall Cr concentration. The effective Cr-Cr repulsion is weaker in alloys than in an environment of pure Fe. Apart from the Cr concentration, the Cr-interstitial interaction also depends on the dispersion level of Cr atoms beyond third-nearestneighbor distance from the interstitial. The formation energy differences between dumbbell interstitials with different orientations are independent of the Cr concentration. We show that the long-range influence of Cr atoms on the interstitial is not due to the interstitial strain field protruding into Cr-rich parts of the supercells. The Fermi-level and band energies were found not to be the sole governing parameter in determining the formation energies. Implications for the construction of empirical potentials are discussed.

  24. Title: Glucose solvation by the ionic liquid 1,3-dimethylimidazolium chloride: A simulation study

    Author(s): Youngs T.G.A., Hardacre C., Holbrey J.D.,

    J. Phys. Chem. B, 111, pp. 13765-13774 (2007)

    doi: 10.1021/Jp076728k

  25. Title: Structure and solvation in ionic liquids

    Author(s): Hardacre C., Holbrey J.D., Nieuwenhuyzen M., Youngs T.G.A.,

    Acc. Chem. Res., 40, pp. 1146-1155 (2007)

    doi: 10.1021/ar700068x

  26. Title: Macroscopic limit of time-dependent density-functional theory for adiabatic local approximations of the exchange-correlation kernel

    Author(s): Gruening M., Gonze X.

    Physical Review B, 76, pp. 035126- (2007)