Among the computationally efficient semilocal density functionals for the exchange-correlation energy, meta-generalized-gradient approximations (meta-GGAs) are potentially the most accurate. Here, we assess the performance of three new meta-GGAs (revised Tao-Perdew-Staroverov-Scuseria or revTPSS, regularized revTPSS or regTPSS, and meta-GGA made simple or MGGA_MS), within and beyond their "comfort zones," on Grimme's big test set of main-group molecular energetics (thermochemistry, kinetics, and noncovalent interactions). We compare them against the standard Perdew-Burke-Ernzerhof (PBE) GGA, TPSS, and Minnesota M06L meta-GGAs, and Becke-3-Lee-Yang-Parr (B3LYP) hybrid of GGA with exact exchange. The overall performance of these three new meta-GGA functionals is similar. However, dramatic differences occur for different test sets. For example, M06L and MGGA_MS perform best for the test sets that contain noncovalent interactions. For the 14 Diels-Alder reaction energies in the "difficult" DARC subset, the mean absolute error ranges from 3 kcal mol(-1) (MGGA_MS) to 15 kcal mol(-1) (B3LYP), while for some other reaction subsets the order of accuracy is reversed; more generally, the tested new semilocal functionals outperform the standard B3LYP for ring reactions. Some overall improvement is found from long-range dispersion corrections for revTPSS and regTPSS but not for MGGA_MS. Formal and universality criteria for the functionals are also discussed.

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. with outer radius R and thickness t. The result is C-2k = -c(k) (t/R)root 4 pi 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, -C-6/d(6) - C-8/d(8)- ..., can be summed analytically, diverging only for d <= 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. DOI:10.1103/PhysRevA.86.062714