Jürgen Furthmüller

Abstract: We present an efficient scheme for calculating the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrices will be discussed. Our approach is stable, reliable, and minimizes the number of order ${\mathit{N}}_{\mathrm{atoms}}^{3}$ operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special ``metric'' and a special ``preconditioning'' optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calculations. It will be shown that the number of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order ${\mathit{N}}_{\mathrm{atoms}}^{2}$ scaling is found for systems containing up to 1000 electrons. If we take into account that the number of k points can be decreased linearly with the system size, the overall scaling can approach ${\mathit{N}}_{\mathrm{atoms}}$. We have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable. \textcopyright{} 1996 The American Physical Society.

Abstract: We present a detailed description and comparison of algorithms for performing ab-initio quantum-mechanical calculations using pseudopotentials and a plane-wave basis set. We will discuss: (a) partial occupancies within the framework of the linear tetrahedron method and the finite temperature density-functional theory, (b) iterative methods for the diagonalization of the Kohn-Sham Hamiltonian and a discussion of an efficient iterative method based on the ideas of Pulay's residual minimization, which is close to an order Natoms2 scaling even for relatively large systems, (c) efficient Broyden-like and Pulay-like mixing methods for the charge density including a new special ‘preconditioning’ optimized for a plane-wave basis set, (d) conjugate gradient methods for minimizing the electronic free energy with respect to all degrees of freedom simultaneously. We have implemented these algorithms within a powerful package called VAMP (Vienna ab-initio molecular-dynamics package). The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semi-conducting surfaces, phonons in simple metals, transition metals and semiconductors) and turned out to be very reliable.

Abstract: In this work we derive closed expressions for the head of the frequency-dependent microscopic polarizability matrix in the projector-augmented wave (PAW) methodology. Contrary to previous applications, the longitudinal expression is utilized, resulting in dielectric properties that are largely independent of the applied potentials. The improved accuracy of the present approach is demonstrated by comparing the longitudinal and transversal expressions of the polarizability matrix for a number of cubic semiconductors and one insulator, i.e., Si, SiC, AlP, GaAs, and diamond (C), respectively. The methodology is readily extendable to more complicated nonlocal Hamiltonians or to the calculation of the macroscopic dielectric matrix including local field effects in the random phase or density functional approximation, which is demonstrated for the previously mentioned model systems. Furthermore, density functional perturbation theory is extended to the PAW method, and the respective results are compared to those obtained by summation over the conduction band states.

Abstract: (a) Ioffe Physico-Technical Institute, Russian Academy of Science, Polytekhnicheskaya 26, 194021 St. Petersburg, Russia (b) Institut für Festkörpertheorie and Theoretische Optik, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, D-07743 Jena, Germany (c) Department of Electronics and Information Science, Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, Kyoto 606-8585, Japan (d) Institute of Solid State and Semiconductor Physics, Belarus Academy of Sciences, Brovki 17, 220072 Minsk, Belarus (e) LfI, University of Hannover, Schneiderberg 32, D-30167 Hannover, Germany

Abstract: The phonon dispersion relations of diamond and graphite are calculated using an ab initio force constant method. The force constants are calculated via a self-consistent supercell approach in the local-density approximation in terms of the Hellmann-Feynman forces induced by the displacement of a single atom in the supercell. For diamond our ab initio results are in very good agreement with the neutron inelastic scattering and Raman data. For graphite we find good agreement with the neutron data for the low-energy modes as well as with the reflections electron energy loss spectroscopy (REELS) and optical data at higher energies. Significant differences to the predictions of semi-empirical models appear.

Abstract: We present a detailed description and comparison of algorithms for performing ab-initio quantum-mechanical calculations using pseudopotentials and a plane-wave basis set. We will discuss: (a) partial occupancies within the framework of the linear tetrahedron method and the finite temperature density-functional theory, (b) iterative methods for the diagonalization of the Kohn-Sham Hamiltonian and a discussion of an efficient iterative method based on the ideas of Pulay's residual minimization, which is close to an order Natoms2 scaling even for relatively large systems, (c) efficient Broyden-like and Pulay-like mixing methods for the charge density including a new special ‘preconditioning’ optimized for a plane-wave basis set, (d) conjugate gradient methods for minimizing the electronic free energy with respect to all degrees of freedom simultaneously. We have implemented these algorithms within a powerful package called VAMP (Vienna ab-initio molecular-dynamics package). The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semi-conducting surfaces, phonons in simple metals, transition metals and semiconductors) and turned out to be very reliable.

Abstract: QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.

Abstract: A modification of the nudged elastic band method for finding minimum energy paths is presented. One of the images is made to climb up along the elastic band to converge rigorously on the highest saddle point. Also, variable spring constants are used to increase the density of images near the top of the energy barrier to get an improved estimate of the reaction coordinate near the saddle point. Applications to CH4 dissociative adsorption on Ir~111! and H2 on Si~100! using plane wave based density functional theory are presented. © 2000 American Institute of Physics. @S0021-9606~00!71246-3#

Abstract: VESTA is a three-dimensional visualization system for crystallographic studies and electronic state calculations. It has been upgraded to the latest version, VESTA 3, implementing new features including drawing the external mor­phology of crystals; superimposing multiple structural models, volumetric data and crystal faces; calculation of electron and nuclear densities from structure parameters; calculation of Patterson functions from structure parameters or volumetric data; integration of electron and nuclear densities by Voronoi tessellation; visualization of isosurfaces with multiple levels; determination of the best plane for selected atoms; an extended bond-search algorithm to enable more sophisticated searches in complex molecules and cage-like structures; undo and redo in graphical user interface operations; and significant performance improvements in rendering isosurfaces and calculating slices.

Abstract: First-principles simulation, meaning density-functional theory calculations with plane waves and pseudopotentials, has become a prized technique in condensed-matter theory. Here I look at the basics of the suject, give a brief review of the theory, examining the strengths and weaknesses of its implementation, and illustrating some of the ways simulators approach problems through a small case study. I also discuss why and how modern software design methods have been used in writing a completely new modular version of the CASTEP code.