797 publications from this institution
Received 5 April 2011DOI:https://doi.org/10.1103/PhysRevLett.106.179902© 2011 American Physical Society
The surface energy for several simple metals is calculated self-consistently with use of a single variational parameter whose optimal value depends on the crystal structure and the surface plane considered. The calculation clearly demonstrates the strong dependence of the electron-density profile at the metal-vacuum interface on the discreteness of the ionic density. The method is as simple numerically as the usual jellium calculations and can probably be applied readily to more complex surface problems.
The Harbola-Sahni exchange potential is the work needed to move an electron against the electric field of its hole charge distribution. We prove that it is not the exact exchange potential of density-functional theory, by showing that it yields the wrong second-order gradient expansion in the slowly varying limit. But we also discover that it yields the correct local-density approximation. Thus the Harbola-Sahni potential is a more physically correct version of the Slater potential, one that is better suited for molecular and solid-state applications. As a step in our derivation, we present the third-order gradient expansion of the exchange hole density, and discuss its structure. We also describe a new version of the Harbola-Sahni potential which corrects its path dependence. The exact exchange potential for an atom is given by the optimized potential model (OPM) of Talman and Shadwick. By using enhanced numerics, we confirm that the OPM potential satisfies the Levy-Perdew virial relation and exhibits correct -1/r behavior at large r. Numerical calculations also show that the intershell maxima in the exact exchange potential are needed to lower the total energy. These ``bumps'' are missing from the Harbola-Sahni and Slater potentials.
Binding or potential energy curves have been calculated for the ground-state diatomics H(2)(+), He(2)(+), LiH(+), H(2), N(2), and C(2), for the transition state H(3), and for the triplet first excited state of H(2) using the nonempirical density functionals from the first three rungs of a ladder of approximations: the local spin density (LSD) approximation, the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA), and the Tao-Perdew-Staroverov-Scuseria (TPSS) meta GGA. Good binding energy curves in agreement with coupled cluster or configuration interaction calculations are found from the PBE GGA and especially from the TPSS meta GGA. Expected exceptions are the symmetric radicals H(2)(+) and He(2)(+), where the functionals suffer from self-interaction error, and the exotically bonded C(2). Although the energy barrier for the reaction H(2) + H --> H + H(2) is better in PBE than in TPSS, the transition state H(3) is a more properly positioned and curved saddle point of the energy surface in TPSS. The triplet first excited state of H(2) obeys the Aufbau principle and thus is one of the exceptional excited states that are computable in principle from the ground-state functional. The PBE GGA and TPSS meta GGA are useful not only for chemical applications but also for the construction of higher-rung nonempirical functionals that can further improve the binding energy curves.
The energy of a spherical metallic particle of radius R, charged with Z excess electrons, is simply ${E}_{Z}$=${E}_{0}$-ZW+${Z}^{2}$${e}^{2}$/2(R+a), where W is the bulk work function, e is the charge of one electron, and R+a is the radial centroid of the excess charge. Consequently, the ionization energy is I=W+${e}^{2}$/2(R+a), and the electron affinity is A=W-${e}^{2}$/2(R+a). These formulas apply even to the smallest microparticle, a single monovalent atom. Thus they may be used to estimate the bulk work function W=(I+A)/2 and density parameter (Wigner-Seitz radius) ${r}_{s}$ from atomic values for I and A; ${r}_{s}$ is the solution of the equation ${r}_{s}$+a(${r}_{s}$)=${e}^{2}$/(I-A). The link between microcosm and macrocosm is further shown by the relationship ${\ensuremath{\varepsilon}}_{\mathrm{coh}\mathrm{\ensuremath{\approxeq}}\mathrm{\ensuremath{\sigma}}4\mathrm{\ensuremath{\pi}}{r}_{s}^{2}}$ between the cohesive energy ${\ensuremath{\varepsilon}}_{\mathrm{coh}}$ and the surface tension \ensuremath{\sigma}. These relationships are illustrated for atoms and small jellium spheres.
Understanding of the atomic structure and stability of nanowires (NWs) is critical for their applications in nanotechnology, especially when the diameter of NWs reduces to ultrathin scale (1-2 nm). Here, using aberration-corrected high-resolution transmission electron microscopy (AC-HRTEM), we report a detailed atomic structure study of the ultrathin Au NWs, which are synthesized using a silane-mediated approach. The NWs contain large amounts of generalized stacking fault defects. These defects evolve upon sustained electron exposure, and simultaneously the NWs undergo necking and breaking. Quantitative strain analysis reveals the key role of strain in the breakdown process. Besides, ligand-like morphology is observed at the surface of the NWs, indicating the possibility of using AC-HRTEM for surface ligand imaging. Moreover, the coalescence dynamic of ultrathin Au NWs is demonstrated by in situ observations. This work provides a comprehensive understanding of the structure of ultrathin metal NWs at atomic-scale and could have important implications for their applications.
Abstract For the strong noise interference brought by the NSP mechanism (Next Sentences Prediction) in Bert to the model, in order to improve the classification effect of the Bert model when it is used in text classification, an SOP (Sentences Order Prediction) mechanism is used to replace the Bert model of the NSP mechanism-Multi-classification of Chinese news texts. At first, use randomly sorted adjacent sentence pairs for segment embedding. Then use the Transformer structure of the Bert model to encode the Chinese text, and obtain the final CLS vector as the semantic vector of the text. Finally, connect the different semantic vectors to the multi-category Classification. After ablation experiments, the improved SOP-Bert model obtained the highest F1 value of 96.69. The results show that this model is more effective than the original Bert model on text multi-classification problems.
The accuracy of the Perdew-Burke-Ernzerhof and Tao-Perdew-Staroverov-Scuseria density functionals for describing noncovalent interaction energies in small water clusters is studied by testing 11 basis sets on a reduced test set proposed by Dahlke and Truhlar (J. Phys. Chem. B 2005, 109, 15677). We have also tested variants of the Perdew-Burke-Ernzerhof functional and the Becke98 hybrid functional. While moderate basis sets give converged density functional theory results for covalent dissociation energies, this is not true for noncovalent interaction energies. Our results show that density functionals give converged interaction energies with aug-cc-pVTZ and aug-cc-pVQZ basis sets. Gradual simplification of the basis set introduces an increasing overbinding effect. The best agreement with the high-level result was obtained by the Perdew-Burke-Ernzerhof functional at the basis set limit. The converged Tao-Perdew-Staroverov-Scuseria interaction energies show a systematic underbinding effect that can be compensated by a somewhat systematic overbinding basis set effect of smaller basis sets such as 6-31+G(d,2p). The inclusion of the diffuse functions in the oxygen basis set is very important, while the inclusion of the f functions practically does not influence the results. Improvement can be obtained by adding more hydrogen p functions to the 6-31+G basis set.
Local and semilocal density functional approximations for the exchange-correlation energy fail badly in the zero-thickness limit of a quasi-two-dimensional electron gas, where the density variation is rapid almost everywhere. Here we show that a fully nonlocal fifth-rung functional, the inhomogeneous Singwi-Tosi-Land-Sjölander (STLS) approach, which employs both occupied and unoccupied Kohn-Sham orbitals, recovers the true two-dimensional STLS limit and appears to be remarkably accurate for any thickness of the slab (and thus for the dimensional crossover). We also show that this good behavior is only partly due to the use of the full exact exchange energy.
If the electron-electron repulsion in an atom or molecule were very weak, it could be treated by orbital-based perturbation theory. If this repulsion were very strong, it could be treated in a model of strict correlation. A simple interaction strength interpolation between these two limits, at fixed electron density, can describe the reality that lies between the extremes. By working entirely within a sophisticated density functional approximation, the meta-generalized gradient approximation, we find that the interpolation error is only about 0.1% for the exchange-correlation energy and about 4 kcal/mole = 0.17 eV for the atomization energy. We also find that real systems probably lie close to the radius of convergence of density functional perturbation theory.
For a uniform electron gas of density n=${\mathit{n}}_{\mathrm{\ensuremath{\uparrow}}}$+${\mathit{n}}_{\mathrm{\ensuremath{\downarrow}}}$=3/4\ensuremath{\pi}${\mathit{r}}_{\mathit{s}}^{3}$=\ensuremath{\pi}${\mathit{k}}_{\mathit{s}}^{6}$/192 and spin polarization \ensuremath{\zeta}=(${\mathit{n}}_{\mathrm{\ensuremath{\uparrow}}}$-${\mathit{n}}_{\mathrm{\ensuremath{\downarrow}}}$)/n, we study the Fourier transform \ensuremath{\rho}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathit{c}}$(k,${\mathit{r}}_{\mathit{s}}$,\ensuremath{\zeta}) of the correlation hole, as well as the correlation energy ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$(${\mathit{r}}_{\mathit{s}}$,\ensuremath{\zeta})=${\mathcal{F}}_{0}^{\mathrm{\ensuremath{\infty}}}$dk \ensuremath{\rho}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathit{c}}$/\ensuremath{\pi}. In the high-density (${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}0) limit, we find a simple scaling relation ${\mathit{k}}_{\mathit{s}}$\ensuremath{\rho}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathit{c}}$/\ensuremath{\pi}${\mathit{g}}^{2}$\ensuremath{\rightarrow}f(z,\ensuremath{\zeta}), where z=k/${\mathit{gk}}_{\mathit{s}}$, g=[(1+\ensuremath{\zeta}${)}^{2/3}$+(1-\ensuremath{\zeta}${)}^{2/3}$]/2, and f(z,1)=f(z,0). The function f(z,\ensuremath{\zeta}) is only weakly \ensuremath{\zeta} dependent, and its small-z expansion -3z/${\mathrm{\ensuremath{\pi}}}^{2}$+4 \ensuremath{\surd}3 ${\mathrm{z}}^{2}$/${\mathrm{\ensuremath{\pi}}}^{2}$+... is also the exact small-wave-vector (k\ensuremath{\rightarrow}0) expansion for any ${\mathit{r}}_{\mathit{s}}$ or \ensuremath{\zeta}. Motivated by these considerations, and by a discussion of the large-wave-vector and low-density limits, we present two Pad\'e representations for \ensuremath{\rho}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathit{c}}$ at any k, ${\mathit{r}}_{\mathit{s}}$, or \ensuremath{\zeta}, one within and one beyond the random-phase approximation (RPA). We also show that \ensuremath{\rho}\ifmmode\bar\else\textasciimacron\fi{} $_{\mathit{c}}^{\mathrm{RPA}}$ obeys a generalization of Misawa's spin-scaling relation for ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}^{\mathrm{RPA}}$, and that the low-density (${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}\ensuremath{\infty}) limit of ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}^{\mathrm{RPA}}$ is \ensuremath{\sim}${\mathit{r}}_{\mathit{s}}^{\mathrm{\ensuremath{-}}3/4}$.
