We present a new nonempirical density functional generalized gradient approximation (GGA) that gives significant improvements for lattice constants, crystal structures, and metal surface energies over the most popular Perdew-Burke-Ernzerhof (PBE) GGA. The new functional is based on a diffuse radial cutoff for the exchange-hole in real space, and the analytic gradient expansion of the exchange energy for small gradients. There are no adjustable parameters, the constraining conditions of PBE are maintained, and the functional is easily implemented in existing codes. PACS numbers: 71.15.Mb, 71.45.Gm, Kohn-Sham density functional theory (DFT) [1,2] makes it possible to solve many-electron ground-state problems efficiently and accurately. The DFT is exact if the exchange-correlation (XC) energy E XC were known exactly, but there is no tractable exact expressions of E XC in terms of electron density. Numerous attempts have been made to approximate E XC , starting with the local (spin) density (LSD) approximation (LDA), which is still widely used. The generalized gradient approximations (GGAs) [3,4,5] are semilocal, seeking to improve upon LSD. Other more complicated approximations are often orbital-dependent or/and nonlocal. They suffer from computational inefficiency; it is much harder to treat them self-consistently and to calculate energy derivative quantities.The XC energy of LSD and GGAs areandrespectively. Here the electron density n = n ↑ + n ↓ , and ǫ unif XC is the XC energy density for the uniform electron gas. LSD is the simplest approximation, constructed from uniform electron gas, and very successful for solids, where the valence electron densities vary relatively more slowly than in molecules and atoms, for which GGAs [5, 6] achieved a great improvement over LSD. It is well known that LSD underestimates the equilibrium lattice constant a 0 by 1-3%, and some properties such as ferroelectricity are extremely sensitive to volume. When calculated at the LSD volume, the ferroelectric instability is severely underestimated [7,8,9]. On the other hand, GGAs tend to expand lattice constants. They well predict correct a 0 for simple metals, such as Na and K [6], however for other materials they often overcorrect LSD by predicting a 0 1-2% bigger [10] than experiment. Predicting lattice constants more accurately than LSD remains a tough issue, even for state-of-the-art meta-GGAs; nonempirical TPSS [11] only achieves moderate TABLE I: Calculated equilibrium volume V0 (Å 3 ) and strain (%) of tetragonal PbTiO3 for various GGAs comparing with experimental data at low temperature [24]. PW91 PBE revPBE RPBE Expt. V0 70.78 70.54 74.01 75.47 63.09 strain 24.2 23.9 28.6 30.1 7.1 improvement over PBE, while empirical PKZB [12] is worse than PBE. GGAs are especially poor for ferroelectrics, e.g., PBE [5] predicts the volume and strain of relaxed tetragonal PbTiO 3 more than 10% and 200% too large, respectively [13], and other GGAs [ 4,14,15] are even worse, as seen in Table I. Another more complicated functional, the nonlocal...

A piezoelectric material is one that generates a voltage in response to a mechanical strain (and vice versa). The most useful piezoelectric materials display a transition region in their composition phase diagrams, known as a morphotropic phase boundary, where the crystal structure changes abruptly and the electromechanical properties are maximal. As a result, modern piezoelectric materials for technological applications are usually complex, engineered, solid solutions, which complicates their manufacture as well as introducing complexity in the study of the microscopic origins of their properties. Here we show that even a pure compound, in this case lead titanate, can display a morphotropic phase boundary under pressure. The results are consistent with first-principles theoretical predictions, but show a richer phase diagram than anticipated; moreover, the predicted electromechanical coupling at the transition is larger than any known. Our results show that the high electromechanical coupling in solid solutions with lead titanate is due to tuning of the high-pressure morphotropic phase boundary in pure lead titanate to ambient pressure. We also find that complex microstructures or compositions are not necessary to obtain strong piezoelectricity. This opens the door to the possible discovery of high-performance, pure-compound electromechanical materials, which could greatly decrease costs and expand the utility of piezoelectric materials.

We find an unexpected tetragonal-to-monoclinic-to-rhombohedral-to-cubic phase transition sequence induced by pressure, and a morphotropic phase boundary in a pure compound using first-principles calculations. Huge dielectric and piezoelectric coupling constants occur in the transition regions, comparable to those observed in the new complex single-crystal solid-solution piezoelectrics such as Pb(Mg(1/3)Nb(2/3))O3-PbTiO3, which are expected to revolutionize electromechanical applications. Our results show that morphotropic phase boundaries and giant piezoelectric effects do not require intrinsic disorder, and open the possibility of studying this effect in simple systems.

Detailed study of the equation of state, elasticity, and hardness of selected superconducting transition-metal nitrides reveals interesting correlations among their physical properties. Both the bulk modulus and Vickers hardness are found to decrease with increasing zero-pressure volume in NbN, HfN, and ZrN. The computed elastic constants from first principles satisfy c11 > c12 > c44 for NbN, but c11 > c44 > c12 for HfN and ZrN, which are in good agreement with the neutron scattering data. The cubic ␦-NbN superconducting phase possesses a bulk modulus of 348 GPa, comparable to that of cubic boron nitride, and a Vickers hardness of 20 GPa, which is close to sapphire. Theoretical calculations for NbN show that all elastic moduli increase monotonically with increasing pressure. These results suggest technological applications of such materials in extreme environments.elasticity ͉ elastic constants ͉ equations of state ͉ hardness ͉ binary compounds H ard superconducting materials are of considerable interest for specific electronic applications. Superconductivity has been discovered in diamond, generally believed to be the hardest material having very high shear and bulk moduli (1, 2), with a superconducting transition temperature (T c ) near 4 K when doped with boron (3). However, the transition-metal compounds having the sodium chloride (B1) structure (e.g., NbN, NbC, ZrN, or HfN) are also hard superconductors but with relatively higher T c s. The transition temperatures of solid solutions of NbN and NbC can reach a maximum value of 17.8 K, which is close to those found for the cubic A15-type compounds such as Nb 3 Sn and V 3 Si (4). The refractory characteristics of these transitionmetal nitrides and carbides have been applied as coatings to increase the wear resistance, for instance, in cutting tools as well as for magnetic storage devices. The unusual hardness enhancement in these materials has been theoretically shown to originate from a particular -band of bonding states between the nonmetal p orbitals and the metal d orbitals that strongly resists shearing strains (5). At the moment, there is a need to investigate elastic and mechanical properties of these superconductors under simulated extreme working conditions.Here, we report both experimental and theoretical studies of the equation of state, elasticity, and hardness of selected superconducting transition-metal nitrides. We find that the cubic ␦-NbN superconducting phase possesses a bulk modulus of 348 GPa, comparable to that of cubic boron nitride, and a Vickers hardness of 20 GPa, which is close to sapphire (Al 2 O 3 ) (6). The results indicate that these nitrides are good candidates for engineering hard superconducting materials. Experimental and Theoretical DetailsEquations of state studies were based on angle-dispersive synchrotron powder x-ray diffractometry with a diamond anvil cell. The diffraction experiments were carried out at the synchrotron beam line 16ID-B of the Advanced Photon Source High Pressure Collaborative Access Team. A 500 ϫ 500-m ...

Owing to its remarkable electronic and transport properties, graphene has great potential of replacing silicon for next-generation electronics and optoelectronics; but its zero bandgap associated with Dirac fermions prevents such applications. Among numerous attempts to create semiconducting graphene, periodic patterning using defects, passivation, doping, nanoscale perforation, etc., is particularly promising and has been realized experimentally. However, despite extensive theoretical investigations, the precise role of periodic modulations on electronic structures of graphene remains elusive. Here we employ both the tight-binding modeling and first-principles electronic structure calculations to show that the appearance of bandgap in patterned graphene has a geometric symmetry origin. Thus the analytic rule of gap-opening by patterning graphene is derived, which indicates that if a modified graphene is a semiconductor, its two corresponding carbon nanotubes, whose chiral vectors equal graphene's supercell lattice vectors, are both semimetals.

Axial charge separation in small diameter, partially strained silicon nanowires is predicted from ab initio calculations with electrons and holes located in different ends of the wires. We show that this effect can be understood from the topologies of near-gap wave functions, and that it is enhanced by quantum confinement. The possibility of utilizing partial strain for charge separation at the nanoscale opens up a new avenue for designing solar cells by morphology control, where effectively a type-II homojunction is formed and charge separation is facilitated by thermalization.

The elastic properties of the B1-structured transition-metal nitrides and their carbide counterparts are studied using the ab initio density functional perturbation theory. The linear response results of elastic constants are in excellent agreement with those obtained from numerical derivative methods, and are also consistent with measured data. We find the following trends: (1) Bulk moduli B and tetragonal shear moduli G ′ = (C11 − C12)/2, increase and lattice constants a0 decrease rightward or downward on the Periodic Table for the metal component or if C is replaced by N; (2) The inequality B > G ′ > G > 0 holds for G = C44; (3) G depends strongly on the number of valence electrons per unit cell (ZV ). From the fitted curve of G as a function of ZV , we can predict that MoN is unstable in B1 structure, and transition-metal carbonitrides (e.g. ZrCxN1−x) and di-transition-metal carbides (e.g. HfxTa1−xC) have maximum G at ZV ≈ 8.3.PACS numbers: 62.20. Dc, 71.15.Mb, 74.70.Ad Elasticity describes the response of a crystal under external strain and provides key information of the bonding strength between nearest-neighbor atoms. The information obtained from accurate calculation of elasticity is essential for understanding the macroscopic mechanical properties of solids and for the design of hard materials. Nowadays it is possible to calculate elasticity using ab initio quantum-mechanical techniques, and ab initio calculations have proven to be very powerful in not only providing accurate elastic constants or moduli in good agreement with measurements [1] but also predicting elasticity at extreme conditions of high temperatures and high pressures [2,3], which are not easily accessible to experiment but have wide applications in the fields ranging from solid-state physics to seismology. Most previous ab initio calculations of elasticity used finite strain methods within the framework of the density-functional theory (DFT). The development of density-functional perturbation theory (DFPT) makes it possible now to obtain elastic constants directly and more accurately [4,5].Transition-metal nitrides and carbides in the rocksalt (B 1 ) structure are widely used for cutting tools, magnetic storage devices, generators and maglev trains due to their high hardness, high melting points and oxidation resistance [6]. These excellent properties are associated with their unusual electronic bonding. The relatively high superconducting transition temperature in some of these compounds, reaching nearly 18 K in NbC 1−x N x [8], indicates a strong electron-phonon interaction. Many theoretical studies of their electronic structure [7,9,10,11,12,13] have revealed an unusual mixture of covalent, metallic, and ionic contributions to bonding which must ultimately lie at the root of their unusual properties. Specifically, it was found [11] that the hardness enhancement of these materials can be understood on a fundamental level in terms of their electronic band structures. But the general trends of elasticity and electronic structure amon...

We calculated the desorption energy of MgH(2) clusters using the highly accurate quantum Monte Carlo (QMC) approach, which can provide desorption energies with chemical accuracy (within approximately 1 kcal/mol) and therefore provides a valuable benchmark for such hydrogen-storage simulations. Compared with these QMC results, the most widely used density functional theory (DFT) computations (including a wide range of exchange-correlation functionals) cannot reach a consistent and suitable level of accuracy across the thermodynamically tunable range for MgH(2) clusters. Furthermore, our QMC calculations show that the DFT error depends substantially on cluster size. These results suggest that in simulating metal-hydride systems it is very important to apply accurate methods that go beyond traditional mean-field approaches as a benchmark of their performance for a given material, and QMC is an appealing method to provide such a benchmark due to its high level of accuracy and favorable scaling (N(3)) with the number of electrons.