Correlation Energy Densities: E Pluribus Unum

Van der Waals Coefficients for Nanostructures: Fullerenes Defy Conventional Wisdom

“…Recently, in an extension of our earlier work [12,13], we have found [14,15] a way to estimate the van der Waals coefficients accurately between large quasispherical nanostructures, by modeling them as classical solid spheres or spherical shells of uniform valence electron density, with the outer radii fixed by accurate values for the static dipole polarizability of each nanostructure. Ref.…”

“…Ref. [15] also discovered numerically that the size-dependence of 6 C was the expected 2 n (the number of ways of pairing one atom in object A with one in B) for solid nanocluster pairs A n -A n , but showed a much stronger increase with the number of atoms n for single-walled fullerene pairs C n -C n . Here we will derive the asymptotic ( ) ∞ → n dependence of the van der Waals coefficients of all orders for both kinds of nanostructures, arguing that large fullerenes are unsuited to description either by atom pair potentials or by standard nonlocal van der Waals correlation energy functionals, and explaining why.…”

“…Ref. [15] presented the needed formulas for the coefficients of all orders, neglecting the energy gap except insofar as it affects the outer radius via Eq. (5) below.…”

Two avenues to self-interaction correction within Kohn—Sham theory: unitary invariance is the shortcut

“…While x σ (r) of Eq. (21) seems to be a satisfactory iso-orbital indicator, it does display an orderof-limits problem [45]: …”

“…x σ (r) is an ingredient of self-correlation free meta-GGA's including those of Refs. [44] and [45], and of local hybrids [39] and hyper-GGA's [38]. (21), plotted as a function of the distance from the center of two spherical densities, the Ne atom and a jellium cluster with 34 electrons having the average valence electron density of Na (r s = [3/(4πn)] 1/3 = 3.93 bohr).…”