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.

We use first-principles calculations to study structural, vibrational, and superconducting properties of ${\mathrm{H}}_2\mathrm{S}$ at pressures $P\ge 200\mathrm{GPa}$. The inclusion of zero-point energy leads to two different possible dissociations of ${\mathrm{H}}_2\mathrm{S}$, namely $3{\mathrm{H}}_2\mathrm{S}\to 2{\mathrm{H}}_3\mathrm{S}+\mathrm{S}$ and $5{\mathrm{H}}_2\mathrm{S}\to 3{\mathrm{H}}_3\mathrm{S}+{\mathrm{HS}}_2$, where both ${\mathrm{H}}_3\mathrm{S}$ and ${\mathrm{HS}}_2$ are metallic. For ${\mathrm{H}}_3\mathrm{S}$, we perform nonperturbative calculations of anharmonic effects within the self-consistent harmonic approximation and show that the harmonic approximation strongly overestimates the electron-phonon interaction ($\lambda \approx 2.64$ at 200 GPa) and $T_c$. Anharmonicity hardens H─S bond-stretching modes and softens H─S bond-bending modes. As a result, the electron-phonon coupling is suppressed by 30% ($\lambda \approx 1.84$ at 200 GPa). Moreover, while at the harmonic level $T_c$ decreases with increasing pressure, the inclusion of anharmonicity leads to a $T_c$ that is almost independent of pressure. High-pressure hydrogen sulfide is a strongly anharmonic superconductor.

Harmonic calculations based on density-functional theory are generally the method of choice for the description of phonon spectra of metals and insulators. The inclusion of anharmonic effects is, however, delicate as it relies on perturbation theory requiring a considerable amount of computer time, fast increasing with the cell size. Furthermore, perturbation theory breaks down when the harmonic solution is dynamically unstable or the anharmonic correction of the phonon energies is larger than the harmonic frequencies themselves. We present here a stochastic implementation of the self-consistent harmonic approximation valid to treat anharmonicity at any temperature in the nonperturbative regime. The method is based on the minimization of the free energy with respect to a trial density matrix described by an arbitrary harmonic Hamiltonian. The minimization is performed with respect to all the free parameters in the trial harmonic Hamiltonian, namely, equilibrium positions, phonon frequencies, and polarization vectors. The gradient of the free energy is calculated following a stochastic procedure. The method can be used to calculate thermodynamic properties, dynamical properties, and even anharmonic corrections to the Eliashberg function of the electron-phonon coupling. The scaling with the system size is greatly improved with respect to perturbation theory. The validity of the method is demonstrated in the strongly anharmonic palladium and platinum hydrides. In both cases, we predict a strong anharmonic correction to the harmonic phonon spectra, far beyond the perturbative limit. In palladium hydrides, we calculate thermodynamic properties beyond the quasiharmonic approximation, while in PtH, we demonstrate that the high superconducting critical temperatures at 100 GPa predicted in previous calculations based on the harmonic approximation are strongly suppressed when anharmonic effects are included.

Resistivity saturation is observed in many metallic systems with large resistivities—when the resistivity has reached a critical value, its further increase with temperature is substantially reduced. This typically happens when the apparent mean free path is comparable to the interatomic separations—the Ioffe-Regel condition. Recently, several exceptions to this rule have been found. This colloquium first reviews experimental results and early theories of resistivity saturation. It then describes more recent theoretical work, addressing cases both where the Ioffe-Regel condition is satisfied and where it is violated. In particular, the authors show how the (semiclassical) Ioffe-Regel condition can be derived quantum mechanically under certain assumptions about the system and why these assumptions are violated for high-$T_c$ cuprates and alkali-doped fullerides.