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.

Q uantum ESPRESSO is an integrated suite of open-source computer codes for quantum simulations of materials using state-of-the-art electronic-structure techniques, based on density-functional theory, density-functional perturbation theory, and many-body perturbation theory, within the plane-wave pseudopotential and projector-augmented-wave approaches. Q uantum ESPRESSO owes its popularity to the wide variety of properties and processes it allows to simulate, to its performance on an increasingly broad array of hardware architectures, and to a community of researchers that rely on its capabilities as a core open-source development platform to implement their ideas. In this paper we describe recent extensions and improvements, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software.

Working in the Wannier representation, we derive an expression for the orbital magnetization of a periodic insulator. The magnetization is shown to be comprised of two contributions, an obvious one associated with the internal circulation of bulklike Wannier functions in the interior, and an unexpected one arising from net currents carried by Wannier functions near the surface. Each contribution can be expressed as a bulk property in terms of Bloch functions in a gauge-invariant way. Our expression is verified by comparing numerical tight-binding calculations for finite and periodic samples.

We derive a multi-band formulation of the orbital magnetization in a normal periodic insulator (i.e., one in which the Chern invariant, or in two dimensions (2D) the Chern number, vanishes). Following the approach used recently to develop the single-band formalism [Thonhauser, Ceresoli, Vanderbilt, and Resta, Phys. Rev. Lett. 95, 137205 (2005)], we work in the Wannier representation and find that the magnetization is comprised of two contributions, an obvious one associated with the internal circulation of bulklike Wannier functions in the interior and an unexpected one arising from net currents carried by Wannier functions near the surface. Unlike the single-band case, where each of these contributions is separately gauge invariant, in the multi-band formulation only the sum of both terms is gauge invariant. Our final expression for the orbital magnetization can be rewritten as a bulk property in terms of Bloch functions, making it simple to implement in modern code packages. The reciprocal-space expression is evaluated for 2D model systems and the results are verified by comparing to the magnetization computed for finite samples cut from the bulk. Finally, while our formal proof is limited to normal insulators, we also present a heuristic extension to Chern insulators (having nonzero Chern invariant) and to metals. The validity of this extension is again tested by comparing to the magnetization of finite samples cut from the bulk for 2D model systems. We find excellent agreement, thus providing strong empirical evidence in favor of the validity of the heuristic formula.

Zirconia $\left({\mathrm{ZrO}}_2\right)$ and hafnia $\left({\mathrm{HfO}}_2\right)$ are leading candidates for replacing ${\mathrm{SiO}}_2$ as the gate insulator in complementary metal-oxide semiconductor technology. Amorphous versions of these materials ($a\text{−}{\mathrm{ZrO}}_2$ and $a\text{−}{\mathrm{HfO}}_2$) can be grown as metastable phases on top of a silicon buffer; while they tend to recrystallize during subsequent annealing steps, they would otherwise be of considerable interest because of the promise they hold for improved uniformity and electrical passivity. In this work, we report our theoretical studies of $a\text{−}{\mathrm{ZrO}}_2$ and $a\text{−}{\mathrm{HfO}}_2$ by first-principles density-functional methods. We construct realistic amorphous models using the “activation-relaxation” technique of Barkema and Mousseau. The structural, vibrational, and dielectric properties of the resulting models are analyzed in detail. The overall average dielectric constant is computed and found to be comparable to that of the monoclinic phase.