We point out a simplifying but mildly inconsistent assumption of the Perdew-Burke-Ernzerhof (PBE) correlation functional, which should be corrected when evaluating the high-density limit of the PBE energy for nonsinglet systems under uniform density scaling. The discussion also concerns high-density limits of all density functionals that use PBE as an ingredient, including the Tao-Perdew-Staroverov-Scuseria (TPSS) approximation. We revisit the nonrelativistic correlation energies of isoelectronic atomic ions in the limit of infinite nuclear charge and explain small discrepancies between the PBE and TPSS values of these limits existing in the literature.
The Tao-Perdew-Staroverov-Scuseria (TPSS) meta-generalized-gradient-approximation (MGGA) and its revised version, the revTPSS, are implemented self-consistently within the framework of the projector-augmented-wave (PAW) method, using a plane wave basis set. Both TPSS and revTPSS yield accurate atomization energies for the molecules in the AE6 set, better than those of the standard Perdew-Burke-Ernzerhof (PBE) generalized-gradient-approximation. For lattice constants and bulk moduli of 20 diverse solids, revTPSS performs much better than PBE, and on average as well as PBEsol and Armiento-Mattsson (AM05), GGAs designed for solids. The latter two overestimate the atomization energies for molecules to an unacceptable degree. However, the revTPSS presents only a slight improvement over PBEsol for the prediction of cohesive energies for solids, and some deterioration with respect to PBE. We also study the magnetic properties of Fe, for which both TPSS and revTPSS predict the right ground-state solid phase, the ferromagnetic body-centered-cubic (bcc) structure, with an accurate magnetic moment.
The dynamic multipole polarizabilities and thus the second-order van der Waals coefficients ${C}_{2k}$ of all orders are known exactly for the interaction between two classical spherical conducting shells, each of uniform electron density $\ensuremath{\rho}$ with outer radius $R$ and thickness $t$. The result is ${C}_{2k}=\ensuremath{-}{c}_{k}(t/R)\sqrt{4\ensuremath{\pi}\ensuremath{\rho}}{[{(2R)}^{2}]}^{k}$. The ${c}_{k}$ approach a limiting constant value, so the infinite series for the van der Waals interaction at separation $d$, $\ensuremath{-}{C}_{6}/{d}^{6}\ensuremath{-}{C}_{8}/{d}^{8}\ensuremath{-}\ensuremath{\cdots}$, can be summed analytically, diverging only for $d\ensuremath{\le}2R$. This divergence can be removed without changing the asymptotic series. Real quasispherical objects like nanoclusters, fullerenes, and even atoms can be approximated by this spherical-shell model, with $R$ fixed by the true static dipole polarizability. Once $t/R$ is fixed, all the higher coefficients are determined by just ${C}_{6}$ and ${C}_{8}$. Finally, we compare the exact ${C}_{2k}$ to those from a pair interaction model, which works for solid spheres ($t=R$) but not for fullerenes.
The transition metal dichalcogenides exhibit polymorphism; i.e. both 2H and 1T' crystal structures, each with unique electronic properties. These two phases can coexist within the same monolayer microstructure, producing 2H/1T' interfaces. Here we report a systematic investigation of the energetics of the experimentally most important MoS2 heterophase interfaces and edges. The stable interface and edge structures change with chemical potential (these edges/interfaces are usually non-stoichiometric). Stable edges tend to be those of highest atomic density and the stable interfaces correspond to those with local atomic structure very similar to the 2H crystal. The interfacial energies are lower than those of the edges, and the 1T' edges have lower energy than the 2H edges. Because the 1T' edges have much lower energy than the 2H edges, a sufficiently narrow 1T' ribbon will be more stable than the corresponding 2H ribbon (this critical width is much larger in MoTe2 than in MoS2). Similarly, a large 2H flake have an equilibrium strip of 1T' along its edge (again this effect is much larger in MoTe2 than in MoS2). Application of tensile strains can increase the width of the stable 1T' strip or the critical thickness below which a ribbon favors the 1T' structure. These effects provide a means to phase engineer transition metal dichalcogenide microstructures.
In a recent paper [Phys. Rev. B $63,$ 224115 (2001)], we proposed two equations of state based upon microscopic insight into the cohesion of a solid: the stabilized jellium equation of state (SJEOS) and its augmented version (ASJEOS). In this Reply, we address the issues raised by Holzapfel in his Comment on that paper. We show that, according to the number of independent fitting parameters used, our ASJEOS is comparable with Holzapfel's third-order adapted polynomial (AP3) and that the ASJEOS performs slightly better than AP3 for the materials (Al, Li, and Mo) and pressure range $(P\ensuremath{\lesssim}15\mathrm{Mbar})$ discussed in our paper. We compare the advantages and the disadvantages of ASJEOS and AP3, and discuss the behavior of the equations of state as they approach the strong-compression and strong-expansion limits.
The density functional theory of Hohenberg, Kohn, and Sham has been used to derive an exact variational expression for the spin susceptibility (χ) of an inhomogeneous electron gas. This variational expression allows one to simultaneously treat band and exchange correlation effects among the conduction electrons and, furthermore, includes the influence of core electrons on the latter. The use of a simple trial function and a local approximation for the exchange correlation functional in the variational expression results in a simple formula for χ (lower bound). The above approach is developed in parallel and compared with the self consistent single particle equations for a magnetized paramagnetic system including exchange correlation. These equations are used to obtain explicit expressions for the paramagnetic response functionals for noninteracting and interacting systems.
