Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set

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.

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QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials

We have developed and implemented a selfconsistent density functional method using standard norm-conserving pseudopotentials and a flexible, numerical linear combination of atomic orbitals basis set, which includes multiple-zeta and polarization orbitals. Exchange and correlation are treated with the local spin density or generalized gradient approximations. The basis functions and the electron density are projected on a real-space grid, in order to calculate the Hartree and exchange-correlation potentials and matrix elements, with a number of operations that scales linearly with the size of the system. We use a modified energy functional, whose minimization produces orthogonal wavefunctions and the same energy and density as the Kohn-Sham energy functional, without the need for an explicit orthogonalization. Additionally, using localized Wannier-like electron wavefunctions allows the computation time and memory required to minimize the energy to also scale linearly with the size of the system. Forces and stresses are also calculated efficiently and accurately, thus allowing structural relaxation and molecular dynamics simulations.

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The SIESTA method for ab initio order-N materials simulation

Recent extensions of the DMol3 local orbital density functional method for band structure calculations of insulating and metallic solids are described. Furthermore the method for calculating semilocal pseudopotential matrix elements and basis functions are detailed together with other unpublished parts of the methodology pertaining to gradient functionals and local orbital basis sets. The method is applied to calculations of the enthalpy of formation of a set of molecules and solids. We find that the present numerical localized basis sets yield improved results as compared to previous results for the same functionals. Enthalpies for the formation of H, N, O, F, Cl, and C, Si, S atoms from the thermodynamic reference states are calculated at the same level of theory. It is found that the performance in predicting molecular enthalpies of formation is markedly improved for the Perdew–Burke–Ernzerhof [Phys. Rev. Lett. 77, 3865 (1996)] functional.

From molecules to solids with the DMol3 approach

This article reviews the current status of lattice-dynamical calculations in crystals, using density-functional perturbation theory, with emphasis on the plane-wave pseudopotential method. Several specialized topics are treated, including the implementation for metals, the calculation of the response to macroscopic electric fields and their relevance to long-wavelength vibrations in polar materials, the response to strain deformations, and higher-order responses. The success of this methodology is demonstrated with a number of applications existing in the literature.

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Phonons and related crystal properties from density-functional perturbation theory

Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.

Electronic Structure: Basic Theory and Practical Methods

We present a theoretical study of the structural and electronic properties of pseudomorphic Si/Ge interfaces, in which the layers are strained such that the lattice spacing parallel to the interface is equal on both sides. The self-consistent calculations, based on the local density functional and ab initio pseudopotentials, determine the atomic structures and strains of minimum energy, and the lineup of the Si and Ge band structures. The presence of the strains causes significant shifts and splittings of the bulk bands. We derive values for the band discontinuities for (001), (111), and (110) interfaces under different strain conditions, and discuss the validity of the density-functional methods for the analysis of the interface problem. Spin-orbit splitting effects in the valence bands are included a posteriori. We express our results in terms of discontinuities in the valence bands, and deformation potentials for the bulk bands, and compare them with recent experiments on Si/${\mathrm{Si}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Ge}}_{\mathrm{x}}$ heterostructures.

Theoretical calculations of heterojunction discontinuities in the Si/Ge system.

A simple phenomenological theory of the elastic constants of sphalerite structure crystals is presented and shown to apply within reasonable errors to the known experimental constants. The theory utilizes a form for bond-stretching ($\ensuremath{\alpha}$) and bending ($\ensuremath{\beta}$) forces first used by Keating, to which are added effective point-ion Coulombic forces. Also it is pointed out that regularities in the experimental elastic constants of these crystals are readily explained in terms of the ionicity ${f}_{i}$ defined by Phillips and Van Vechten. Of particular note are the shear constants which decrease markedly with ionicity. It is found that this decrease is described quantitatively by $\frac{\ensuremath{\beta}}{\ensuremath{\alpha}}\ensuremath{\propto}(1\ensuremath{-}{f}_{i})$, which confirms the interpretation of $\ensuremath{\beta}$, since bond-bending forces should vanish in the ionic limit ${f}_{i}\ensuremath{\rightarrow}1$. Other equally simple formulas for the forces in terms of only the bond length and ${f}_{i}$ are shown to predict all the constants with a rms accuracy of 10%.

Elastic Properties of ZnS Structure Semiconductors

Recent developments in and around the SIESTA method of first-principles simulation of condensed matter are described and reviewed, with emphasis on (i) the applicability of the method for large and varied systems, (ii) efficient basis sets for the standards of accuracy of density-functional methods, (iii) new implementations, and (iv) extensions beyond ground-state calculations.

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The SIESTA method; developments and applicability.

The stress theorem presented previously by the present authors is derived in detail and is related to the virial and force theorems. Stress fields are considered in two alternative forms, both of which give the same macroscopic stress and forces on nuclei when integrated over appropriate surfaces. A crucial concept is interactions that ``cross'' surfaces. Explicit forms of the stress field within the local-density approximation are given, together with a generalization of the approximate Liberman form for pressure. Reciprocal-space expressions and ab initio calculations are considered in detail in an accompanying paper.

Richard M. Martin

Papers

Electronic Structure: Basic Theory and Practical Methods

Theoretical calculations of heterojunction discontinuities in the Si/Ge system.

Elastic Properties of ZnS Structure Semiconductors

The SIESTA method; developments and applicability.

Quantum-mechanical theory of stress and force.