Laboratoire de Cristallographie, Résonance Magnétique et Modélisations

Quantum EXPRESSO 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. Quantum EXPRESSO 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.

Hybrid Fock exchange/density functional theory functionals have shown to be very successful in describing a wide range of molecular properties. For periodic systems, however, the long-range nature of the Fock exchange interaction and the resultant large computational requirements present a major drawback. This is especially true for metallic systems, which require a dense Brillouin zone sampling. Recently, a new hybrid functional [HSE03, J. Heyd, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 118, 8207 (2003)] that addresses this problem within the context of methods that evaluate the Fock exchange in real space was introduced. We discuss the advantages the HSE03 functional brings to methods that rely on a reciprocal space description of the Fock exchange interaction, e.g., all methods that use plane wave basis sets. Furthermore, we present a detailed comparison of the performance of the HSE03 and PBE0 functionals for a set of archetypical solid state systems by calculating lattice parameters, bulk moduli, heats of formation, and band gaps. The results indicate that the hybrid functionals indeed often improve the description of these properties, but in several cases the results are not yet on par with standard gradient corrected functionals. This concerns in particular metallic systems for which the bandwidth and exchange splitting are seriously overestimated.

The implementation of technique for full structural optimizations of complex periodic systems in the DFT-PAW package VASP, including the volume and shape of the unit cell and the internal coordinates of the atoms, together with a correction that allows an appropriate modeling of London dispersion forces, as given by the DFT-D2 approach of Grimme [Grimme, S. J. Comp. Chem. 2006, 27, 1787], is reported. Dispersion corrections are calculated not only for the forces acting on the atoms, but also for the stresses on the unit cell. This permits a simultaneous optimization of all degrees of freedom. Benchmark results on a series of prototype systems are presented and compared to results obtained by other methods and experimental data. It is demonstrated that the computationally inexpensive DFT-D2 scheme yields reasonable predictions for the structure, bulk moduli, and cohesive energies of weakly bonded materials.

We report on ab initio calculations of the two-dimensional systems ${\text{MoS}}_{2}$ and ${\text{NbSe}}_{2}$, which recently were synthesized. We find that two-dimensional ${\text{MoS}}_{2}$ is a semiconductor with a gap which is rather close to that of the three-dimensional analog, and that ${\text{NbSe}}_{2}$ is a metal, which is similar to the three-dimensional analog of this compound. We further computed the electronic structure of the two-dimensional hexagonal (graphene-like) lattices of Si and Ge and compared them with the electronic structure of graphene. It is found that the properties related to the Dirac cone do not appear in the case of two-dimensional hexagonal germanium, which is metallic, contrary to two-dimensional hexagonal silicon, also known as silicene, which has an electronic structure very similar to the one of graphene, making them possibly equivalent.

We assess the performance of recent density functionals for the exchange-correlation energy of a nonmolecular solid, by applying accurate calculations with the GAUSSIAN, BAND, and VASP codes to a test set of 24 solid metals and nonmetals. The functionals tested are the modified Perdew-Burke-Ernzerhof generalized gradient approximation (PBEsol GGA), the second-order GGA (SOGGA), and the Armiento-Mattsson 2005 (AM05) GGA. For completeness, we also test more standard functionals: the local density approximation, the original PBE GGA, and the Tao-Perdew-Staroverov-Scuseria meta-GGA. We find that the recent density functionals for solids reach a high accuracy for bulk properties (lattice constant and bulk modulus). For the cohesive energy, PBE is better than PBEsol overall, as expected, but PBEsol is actually better for the alkali metals and alkali halides. For fair comparison of calculated and experimental results, we consider the zero-point phonon and finite-temperature effects ignored by many workers. We show how GAUSSIAN basis sets and inaccurate experimental reference data may affect the rating of the quality of the functionals. The results show that PBEsol and AM05 perform somewhat differently from each other for alkali metal, alkaline-earth metal, and alkali halide crystals (where the maximum value of the reduced density gradient is about 2), but perform very similarly for most of the other solids (where it is often about 1). Our explanation for this is consistent with the importance of exchange-correlation nonlocality in regions of core-valence overlap.

The problem of numerical accuracy in the calculation of vibrational frequencies of crystalline compounds from the hessian matrix is discussed with reference to alpha-quartz (SiO(2)) as a case study and to the specific implementation in the CRYSTAL code. The Hessian matrix is obtained by numerical differentiation of the analytical gradient of the energy with respect to the atomic positions. The process of calculating vibrational frequencies involves two steps: the determination of the equilibrium geometry, and the calculation of the frequencies themselves. The parameters controlling the truncation of the Coulomb and exchange series in Hartree-Fock, the quality of the grid used for the numerical integration of the Exchange-correlation potential in Density Functional Theory, the SCF convergence criteria, the parameters controlling the convergence of the optimization process as well as those controlling the accuracy of the numerical calculation of the Hessian matrix can influence the obtained vibrational frequencies to some extent. The effect of all these parameters is discussed and documented. It is concluded that with relatively economical computational conditions the uncertainty related to these parameters is smaller than 2-4 cm(-1). In the case of the Local Density Approximation scheme, comparison is possible with recent calculations performed with a Density Functional Perturbation Theory method and a plane-wave basis set.

The partitioning of space with Hirshfeld surfaces enables the analysis of fingerprint molecular interactions in crystalline environments. This study uses the decomposition of the crystal contact surface between pairs of interacting chemical species to derive an enrichment ratio. This quantity enables the analysis of the propensity of chemical species to form intermolecular interactions with themselves and other species. The enrichment ratio is obtained by comparing the actual contacts in the crystal with those computed as if all types of contacts had the same probability to form. The enrichments and contact tendencies were analyzed in several families of compounds, based on chemical composition and aromatic character. As expected, the polar contacts of the type H⋯N, H⋯O and H⋯S, which are generally hydrogen bonds, show enrichment values larger than unity. O⋯O and N⋯N contacts are impoverished while H⋯H interactions display enrichment ratios which are generally close to unity or slightly lower. In aromatic compounds, C⋯C contacts can display large enrichment ratios due to extensive π⋯π stacking in the crystal packings of heterocyclic compounds. C⋯C contacts are, however, less enriched in pure (C,H) hydrocarbons as π⋯π stacking is not so favourable from the electrostatic point of view compared with heterocycles. C⋯H contacts are favoured in (C,H) aromatics, but these interactions occur less in compounds containing O, N or S as some H atoms are then involved in hydrogen bonds. The study also highlights the fact that hydrogen is a prefered interaction partner for fluorine.

The central-zone vibrational spectrum of alpha-quartz (SiO2) is calculated by building the Hessian matrix numerically from the analytical gradients of the energy with respect to the atomic coordinates. The nonanalytical part is obtained with a finite field supercell approach for the high-frequency dielectric constant and a Wannier function scheme for the evaluation of Born charges. The results obtained with four different Hamiltonians, namely Hartree-Fock, DFT in its local (LDA) and nonlocal gradient corrected (PBE) approximation, and hybrid B3LYP, are discussed, showing that B3LYP performs far better than LDA and PBE, which in turn provide better results than HF, as the mean absolute difference from experimental frequencies is 6, 18, 21, and 44 cm(-1), respectively, when a split valence basis set containing two sets of polarization functions is used. For the LDA results, comparison is possible with previous calculations based on the Density Functional Perturbation Theory and usage of a plane-wave basis set. The effects associated with the use of basis sets of increasing size are also investigated. It turns out that a split valence plus a single set of d polarization functions provides frequencies that differ from the ones obtained with a double set of d functions and a set of f functions on all atoms by on average less than 5 cm(-1).

Topological analysis of the experimental electron density rho(r) in hydrogen-bonding regions has been carried out for a large number of organic compounds using different multipole models and techniques. Relevant systematic relationships between topological properties at the critical points and the usual geometric parameters are pointed out. Results involving X-ray data only and joint X-ray and neutron data, as well as special hydrogen bonding cases (symmetric, bifurcated, peptide bonds, etc.) are included and analysed in the same framework. A new classification of hydrogen bonds using the positive curvature of the electron density at the critical point [lambda(3)(r(CP))] is proposed.

The structural properties of graphite, such as the interlayer equilibrium distance, the elastic constant, and the net layer binding energy, are obtained using the adiabatic-connection fluctuation-dissipation theorem in the random phase approximation. Excellent agreement is found with the available experimental data; however, our computed binding energy of 48 meV per atom is somewhat smaller than the one obtained by quantum Monte Carlo methods. The asymptotic behavior of the interlayer dispersion interaction, previously derived from analytic approximations, is explicitly demonstrated to follow a d-3 behavior at very large distances.

The method proposed by Tkatchenko and Scheffler [Phys. Rev. Lett. 102, 073005 (2009)] to correct density functional calculations for the missing van der Waals interactions is implemented in the Vienna ab initio simulation package (vasp) code and tested on a wide range of solids, including noble-gas crystals, molecular crystals ($\ensuremath{\alpha}$-N${}_{2}$, sulfur dioxide, benzene, naphthalene, cytosine), layered solids (graphite, hexagonal boron nitride, vanadium pentoxide, MoS${}_{2}$, NbSe${}_{2}$), chain-like structures (selenium, tellurium, cellulose I), ionic crystals (NaCl, KI), and metals (nickel, zinc, cadmium). In addition to the original formulation expressing the van der Waals (vdW) corrections as pairwise potentials whose strength is derived from the rescaled polarizabilities of the neutral free atoms, the self-consistently screened ($\text{TS}+\text{SCS}$) [Phys. Rev. Lett. 108, 236402 (2012)] variant of the method involving electrodynamic response effects has been examined. Analytical expressions for the forces acting on the atoms and for the components of the stress tensor needed for the relaxation of the volume and shape of the unit cell using the $\text{TS}+\text{SCS}$ method are derived. While the calculated structures are reasonably close to experiment, the van der Waals corrections to the binding energies are often found to be overestimated in comparison with experimental data. The $\text{TS}+\text{SCS}$ approach leads to significantly better results in some problematic cases, such as the binding energy of graphite. However, there is room for further improvements, in particular for strongly ionic systems.

Slightly attractive: The attractive and anisotropic nature of the ClCl interaction in C(6)Cl(6) is experimentally demonstrated from an expansion of the electron density rho(r) around the chlorine nuclei. The interaction is explained in a model in which there is a bonding attraction involving electron-deficient (see picture, blue) and electron-rich (red) regions of adjacent Cl atoms.

The structural and elastic properties of orthorhombic black phosphorus have been investigated using first-principles calculations based on density functional theory. The structural parameters have been calculated using the local density approximation (LDA), the generalized gradient approximation (GGA), and with several dispersion corrections to include van der Waals interactions. It is found that the dispersion corrections improve the lattice parameters over LDA and GGA in comparison with experimental results. The calculations reproduce well the experimental trends under pressure and show that van der Waals interactions are most important for the crystallographic $b$ axis in the sense that they have the largest effect on the bonding between the phosphorus layers. The elastic constants are calculated and are found to be in good agreement with experimental values. The calculated ${C}_{22}$ elastic constant is significantly larger than the ${C}_{11}$ and ${C}_{33}$ parameters, implying that black phosphorus is stiffer against strain along the $a$ axis than along the $b$ and $c$ axes. From the calculated elastic constants, the mechanical properties, such as bulk modulus, shear modulus, Young's modulus, and Poisson's ratio are obtained. The calculated Raman active optical phonon frequencies and their pressure variations are in excellent agreement with available experimental results.

Long-range exchange and correlation effects, responsible for the failure of currently used approximate density functionals in describing van der Waals forces, are taken into account explicitly after a separation of the electron-electron interaction in the Hamiltonian into short- and long-range components. We propose a ``range-separated hybrid'' functional based on a local density approximation for the short-range exchange-correlation energy, combined with a long-range exact exchange energy. Long-range correlation effects are added by a second-order perturbational treatment. The resulting scheme is general and is particularly well adapted to describe van der Waals complexes, such as rare gas dimers.

Using the GW approximation, we study the electronic structure of the recently synthesized hydrogenated graphene, named graphane. For both conformations, the minimum band gap is found to be direct at the $\ensuremath{\Gamma}$ point, and it has a value of 5.4 eV in the stable chair conformation, where H atoms attach C atoms alternatively on opposite sides of the two-dimensional carbon network. In the metastable boat conformation the energy gap is 4.9 eV. Then, using a supercell approach, the electronic structure of graphane was modified by introducing either a hydroxyl group or an H vacancy. In this last case, an impurity state appears at about 2 eV above the valence-band maximum.

The performance of hybrid organic perovskite (HOP) for solar energy conversion is driving a renewed interest in their light emitting properties. The recent observation of broad visible emission in layered HOP highlights their potential as white-light emitters. Improvement of the efficiency of the material requires a better understanding of its photophysical properties. We present in-depth experimental investigations of white-light (WL) emission in thin films of the (C6H11NH3)2PbBr4. The broadband, strongly Stokes shifted emission presents a maximum at 90 K when excited at 3.815 eV, and below this temperature coexists with an excitonic edge emission. X-rays and calorimetry measurements exclude the existence of a phase transition as an origin of the thermal behavior of the WL luminescence. The free excitonic emission quenches at low temperature, despite a binding energy estimated to 280 meV. Time-resolved photoluminescence spectroscopy reveals the multicomponent nature of the broad emission. We analyzed the dependence of these components as a function of temperature and excitation energy. The results are consistent with the existence of self-trapped states. The quenching of the free exciton and the thermal evolution of the WL luminescence decay time are explained by the existence of an energy barrier against self-trapping, estimated to ∼10 meV.

When either electron or hole doped at concentrations x approximately 0.1, the LaFeAsO family displays remarkably high temperature superconductivity with Tc up to 55 K. In the most energetically stable Q-->M=(pi,pi,0) antiferromagnetic (AFM) phase comprised of tetragonal-symmetry breaking alternating chains of aligned spins, there is a deep pseudogap in the Fe 3d states centered at the Fermi energy arising from light carriers (m* approximately 0.25-0.33), and very strong magnetophonon coupling is uncovered. Doping (of either sign) beyond x approximately 0.08 results in heavy carriers per Fe (by roughly an order of magnitude) with a large Fermi surface. Calculated Fe-Fe transverse exchange couplings Jij(R) reveal that exchange coupling is strongly dependent on both the AFM symmetry and on the Fe-As distance.

Dehydration of the hybrid compound [Ni3(OH)2(tp)2(H2O)4] (1) upon heating led to the sequential removal of coordinated water molecules to give [Ni3(OH)2(tp)2(H2O)2] (2) at T1 = 433 K and thereafter anhydrous [Ni2(OH)2(tp)] (3) at T2 = 483 K. These two successive structural transformations were thoroughly characterized by powder X-ray diffraction assisted by density functional theory calculations. The crystal structures of the two new compounds 2 and 3 were determined. It was shown that at T1 (433 K) the infinite nickel oxide chains built of the repeating structural unit [Ni3(μ3-OH)2](4+) in 1 collapse and lead to infinite porous layers, forming compound 2. The second transformation at T2 (483 K) gave the expected anhydrous compound 3, which is isostructural with Co2(OH)2(tp). These irreversible transitions directly affect the magnetic behavior of each phase. Hence, 1 was found to be antiferromagnetic at TN = 4.11 K, with metamagnetic behavior with a threshold field Hc of ca. 0.6 T. Compound 2 exhibits canted antiferromagnetism below TN = 3.19 K, and 3 is ferromagnetic below TC = 4.5 K.

The electronic structure of the superconducting material LaOFeP is investigated by means of ab initio calculations using density functional theory. The concept of two-dimensional building blocks as well as Bader analysis are used to obtain more insight about the charge transfer in this layered material. The band structure and the Fermi surface are presented in order to be compared with future experiments. It is found that the intralayer chemical bonding present a significant part of covalency, whereas the interlayer bonding is almost completely ionic. Also, four sheets of the Fermi surface have a significant two-dimensional character.

An adiabatic-connection fluctuation-dissipation theorem approach based on a range separation of electron-electron interactions is proposed. It involves a rigorous combination of short-range density-functional and long-range random phase approximations. This method corrects several shortcomings of the standard random phase approximation and it is particularly well suited for describing weakly bound van der Waals systems, as demonstrated on the challenging cases of the dimers Be2 and Ne2.