797 publications from this institution
The recently proposed rSCAN functional [ <i>J. Chem. Phys.</i> 2019 150, 161101] is a regularized form of the SCAN functional [ <i>Phys. Rev. Lett.</i> 2015 115, 036402] that improves SCAN's numerical performance at the expense of breaking constraints known from the exact exchange-correlation functional. We construct a new meta-generalized gradient approximation by restoring exact constraint adherence to rSCAN. The resulting functional maintains rSCAN's numerical performance while restoring the transferable accuracy of SCAN.
In this paper, a paper-based ultracapacitors were fabricated by the rod-rolling method with the ink of carbon nanomaterials, which were synthesized by arc discharge under various magnetic conditions. Composites of carbon nanostructures, including high-purity single-walled carbon nanotubes (SWCNTs) and graphene flakes were synthesized simultaneously in a magnetically enhanced arc. These two nanostructures have promising electrical properties and synergistic effects in the application of ultracapacitors. Scanning electron microscope, transmission electron microscope, and Raman spectroscopy were employed to characterize the properties of carbon nanostructures and their thin films. The sheet resistance of the SWCNT and composite thin films was also evaluated by four-point probe from room temperature to the cryogenic temperature as low as 90 K. In addition, measurements of cyclic voltammetery and galvanostatic charging/discharging showed the ultracapacitor based on composites possessed a superior specific capacitance of up to 100 F/g, which is around three times higher than the ultracapacitor entirely fabricated with SWCNT.
A commonly cited reason for the success of the local spin density (LSD) approximation is that it correctly accounts for short wavelength contributions to the exchange-correlation energy. We show that this result, while true in several limits and for several approximations to these fluctuations, is not exact in general, with an analytic demonstration on a specific system (Hooke's atom). Nevertheless, we find that LSD is rather accurate for small separations.
The electronic exchange energy as a functional of the density may be approximated as ${E}_{x}[n]={A}_{x}\ensuremath{\int}{d}^{3}r{n}^{\frac{4}{3}}F(s)$, where $s=\frac{|\ensuremath{\nabla}n|}{2{k}_{F}n}$, ${k}_{F}={(3{\ensuremath{\pi}}^{2}n)}^{\frac{1}{3}}$, and $F(s)={(1+1.296{s}^{2}+14{s}^{4}+0.2{s}^{6})}^{\frac{1}{15}}$. The basis for this approximation is the gradient expansion of the exchange hole, with real-space cutoffs chosen to guarantee that the hole is negative everywhere and represents a deficit of one electron. Unlike the previously publsihed version of it, this functional is simple enough to be applied routinely in self-consistent calculations for atoms, molecules, and solids. Calculated exchange energies for atoms fall within 1% of Hartree-Fock values. Significant improvements over other simple functionals are also found in the exchange contributions to the valence-shell removal energy of an atom and to the surface energy of jellium within the infinite barrier model.
The SCAN (strongly constrained and appropriately normed) meta-generalized gradient approximation (meta-GGA), which satisfies all 17 exact constraints that a meta-GGA can satisfy, accurately describes equilibrium bonds that are normally correlated. With symmetry breaking, it also accurately describes some sd equilibrium bonds that are strongly correlated. While sp equilibrium bonds are nearly always normally correlated, the C2 singlet ground state is known to be a rare case of strong correlation in an sp equilibrium bond. Earlier work that calculated atomization energies of the molecular sequence B2, C2, O2, and F2 in the local spin density approximation (LSDA), the Perdew-Burke-Ernzerhof (PBE) GGA, and the SCAN meta-GGA, without symmetry breaking in the molecule, found that only SCAN was accurate enough to reveal an anomalous under-binding for C2. This work shows that spin symmetry breaking in singlet C2, the appearance of net up- and down-spin densities on opposite sides (not ends) of the bond, corrects that under-binding, with a small SCAN atomization-energy error more like that of the other three molecules, suggesting that symmetry-breaking with an advanced density functional might reliably describe strong correlation. This article also discusses some general aspects of symmetry breaking, and the insights into strong correlation that symmetry-breaking can bring.
