Received 3 December 2008DOI:https://doi.org/10.1103/PhysRevLett.102.039902©2009 American Physical Society
We have improved the revised Tao-Perdew-Staroverov-Scuseria (revTPSS) meta-generalized gradient approximation (GGA) in order to remove the order of limits anomaly in its exchange energy. The revTPSS meta-GGA recovers the second-order gradient expansion for a wide range of densities and therefore provides excellent atomization energies and lattice constants. For other properties of materials, however, even the revTPSS does not give the desired accuracy. The revTPSS does not perform as well as expected for the energy differences between different geometries for the same molecular formula and for the related nonbarrier height chemical reaction energies. The same order of limits problem might lead to inaccurate energy differences between different crystal structures and to inaccurate cohesive energies of insulating solids. Here we show a possible way to remove the order of limits anomaly with a weighted difference of the revTPSS exchange between the slowly varying and iso-orbitals (one- or two-electron) limits. We show that the new regularized (regTPSS) gives atomization energies comparable to revTPSS and preserves the accurate lattice constants as well. For other properties, the regTPSS gives at least the same performance as the revTPSS or TPSS meta-GGAs.
As a partition based clustering algorithm, K-Means is widely used in many areas for the features of its efficiency and easily understood. However, it is well known that the K-Means algorithm may get suboptimal solutions, depending on the choice of the initial cluster centers. In this paper, we propose a projection-based K-Means initialization algorithm. The proposed algorithm first employ conventional Gaussian kernel density estimation method to find the highly density data areas in one dimension. Then the projection step is to iteratively use density estimation from the lower variance dimensions to the higher variance ones until all the dimensions are computed. Experiments on actual datasets show that our method can get similar results compared with other conventional methods with fewer computation tasks.
We have computed the surface energies, work functions, and interlayer surface relaxations of clean (111), (100), and (110) surfaces of Al, Cu, Ru, Rh, Pd, Ag, Pt, and Au. We interpret the surface energy from liquid metal measurements as the mean of the solid-state surface energies over these three lowest-index crystal faces. We compare experimental (and random phase approximation) reference values to those of a family of nonempirical semilocal density functionals, from the basic local density approximation (LDA) to our most advanced general purpose meta-generalized gradient approximation, strongly constrained and appropriately normed (SCAN). The closest agreement is achieved by the simplest density functional LDA, and by the most sophisticated one, SCAN+rVV10 (Vydrov-Van Voorhis 2010). The long-range van der Waals interaction, incorporated through rVV10, increases the surface energies by about 10%, and increases the work functions by about 3%. LDA works for metal surfaces through two known error cancellations. The Perdew-Burke-Ernzerhof generalized gradient approximation tends to underestimate both surface energies (by about 24%) and work functions (by about 4%), yielding the least-accurate results. The amount by which a functional underestimates these surface properties correlates with the extent to which it neglects van der Waals attraction at intermediate and long range. Qualitative arguments are given for the signs of the van der Waals contributions to the surface energy and work function. A standard expression for the work function in Kohn-Sham (KS) theory is shown to be valid in generalized KS theory. Interlayer relaxations from different functionals are in reasonable agreement with one another, and usually with experiment.
In the past decades, the speed development of the Web and a large amount of data published through the Web have made it the largest public data source in the world. The network has become a carrier of massive information. How to efficiently classify text for the acquired massive information is a hot issue of current research. The traditional machine learning algorithms for text classification have many disadvantages such as inconspicuous text features, long training period and loss of word order. This article puts forward a BERT model based method for technology information text auto-Categoriz to improve the accuracy text classification of science and technology information. The results suggest that the using method has significantly improved accuracy, recall and fl_score, and has a good Chinese text classification effect.
Density functional theory in principle predicts correct ground-state properties for all materials. However, the rocksalt structure of MnO has been obtained only by the high-level random phase approximation and diffusion Monte Carlo (DMC). Here, we propose and test for MnO, FeO, CoO, and NiO that a semilocal density functional can solve this problem by properly including both self-interaction and van der Waals corrections. The importance of the latter was previously unanticipated. The MnO structural energy difference from SCAN+$r\text{VV10+}U$ agrees well with that from DMC. Here SCAN is a recent semilocal exchange-correlation functional, $r\text{VV10}$ is the revised Vydrov-Van Voorhis long-range van der Waals correction, and the onsite Hubbard $U$ is taken from linear response.
Within the random-phase approximation (RPA) or ring sum, the ground-state correlation energy for a uniform gas of charged particles with density parameter ${\mathit{r}}_{\mathit{s}}$ tends as ${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}\ensuremath{\infty} to (-0.803 Ry) ${\mathit{r}}_{\mathit{s}}^{\mathrm{\ensuremath{-}}3/4}$. This limit holds for fermions, as for bosons and distinguishable particles. For electrons, the next term in the low-density expansion (of order ${\mathit{r}}_{\mathit{s}}^{\mathrm{\ensuremath{-}}1}$) cancels the exchange energy. Corrections to RPA must cancel the ${\mathit{r}}_{\mathit{s}}^{\mathrm{\ensuremath{-}}3/4}$ term, and can modify the ${\mathit{r}}_{\mathit{s}}^{\mathrm{\ensuremath{-}}1}$ term.
From a global perspective, the density of an atom is strongly inhomogeneous and not at all like the density of a uniform or nearly-uniform electron gas. But, from the semi-local or myopic perspective of standard density functional approximations to the exchange-correlation energy,it is not so easy to tell an atom from an electron gas. We address the following problem: Given the ground-state electron density n and orbital kinetic energy density in the neighborhood of a point r, can we construct an "inhomogeneity index" w(r) which approaches zero for weakly-inhomogeneous densities and unity for strongly-inhomogeneous ones? The solution requires not only the usual local ingredients of a meta-generalized gradient approximation (n,rn,r2n, ),but also r and r2 . The inhomogeneity index is displayed for atoms, and for model densities of metal surfaces and bulk metals. Scaling behavior and a possible application to functional interpolation are discussed.
The electrical response of molecular chains is dramatically overestimated by local and semilocal density functionals. We show that Kohn-Sham density-functional theory yields accurate linear and nonlinear polarizabilities when the exact exchange energy is employed together with the corresponding exact Kohn-Sham potential upsilonx(r). We further show that approximations to upsilonx(r) that are very accurate for the ground-state energy can nevertheless fail badly for the response because of potential barriers that have little effect on the ground-state energy but strongly affect the electron mobility.
