797 publications from this institution
Despite silicon being of great technological importance, an understanding of its behavior across the phase diagram is still lacking, especially near liquid-solid coexistence. The difficulty in describing silicon near coexistence from first principles lies in discriminating between the metallic and covalent bonds present in the material. Using the strongly constrained and appropriately normed (SCAN) density functional, which can describe a wide variety of bonds with quantitative accuracy, we report a thorough investigation of liquid silicon in the vicinity of liquid-solid coexistence using ab initio molecular dynamics simulations. We observe a structural transition in the supercooled regime that is rooted in a change in the electronic structure of the material. This transition is found to occur at a higher temperature than previous predictions. We also discuss implications of the observed change in interatomic interactions for empirical models of transitions between two distinct liquids.
Abstract Is the uniform electron gas unstable against charge and spin density waves (CDW's and SDW's) of infinitesimal amplitude, which break the translational symmetry of the Hamiltonian? Within density functional theory, a CDW of wavevector Q ≈︁ 1.1(2 k F ) appears at low densities. The local spin density approximation (LSDA) for exchange and correlation places the transition at r s ≈︁ 30, while inclusion of the next term in the gradient expansion suppresses the transition to densities as low as r s ≈︁ 200. The best estimate is that the CDW appears out of the uniform ferromagnetic phase of jellium at r s ≈︁ 70; this is also where Ceperley, in a recent calculation with correlated wave functions, found Wigner crystallization. Although no SDW in jellium is predicted within LSDA, the calculated uniform spin susceptibility diverges at r s ≈︁ 35, close to the highest density ( r s ≈︁ 26) at which Ceperley found ferromagnetism.
Results from numerical tests of nine approximate exchange–correlation energy functionals are reported for various systems—atoms, molecules, surfaces, and bulk solids. The functional forms can be divided into three categories: (1) the local spin density (LSD) approximation, (2) generalized gradient approximations (GGAs), and (3) meta-GGAs. In addition to the spin densities and their first gradients, the input to a meta-GGA includes other semilocal information such as Laplacians of the spin densities or orbital kinetic energy densities. We present a way to visualize meta-GGA nonlocality which generalizes that for GGA nonlocality, and which stresses the different meta-GGA descriptions of iso-orbital and orbital overlap regions of space. While some of the tested approximations were constructed semiempirically with many parameters fitted to chemical data, others were constructed to incorporate key properties of the exact exchange–correlation energy. The latter functionals perform well for both small and extended systems, with the best performance achieved by a meta-GGA which recovers the correct gradient expansion. While the semiempirical functionals can achieve high accuracy for atoms and molecules, they are typically less accurate for surfaces and solids. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 889–909, 1999
The authors consider the application of ab initio single-configuration orbital theories to predict the existence and energies of autodetaching states or resonances in atoms and molecules. Numerical results are given for the (ns)2 resonances in H- and He. In some cases (e.g. He) the conventional orbital theories (either Hartree-Fock or the local spin density approximation for exchange and correlation) give useful results, but the important autodetaching states of negative ions are usefully described only by the new self-interaction-corrected (SIC) version of the local spin density approximation. The authors also discuss how a (1s)2 resonance appears and then disappears in a two-electron ion as the nuclear charge Z is reduced below 1. The SIC calculation for this system displays an analogue to the 'bound state in the continuum' which Stillinger (1966) found for Z approximately=0.9.
͓S0163-1829͑98͒03908-
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 non-metals. 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 (TPSS) 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.
