Semi-local approximations to the density functional for the exchangecorrelation energy of a many-electron system necessarily fail for lobed one-electron densities, including not only the familiar stretched densities but also the less familiar but closely-related noded ones. The Perdew-Zunger (PZ) self-interaction correction (SIC) to a semi-local approximation makes that approximation exact for all oneelectron ground-or excited-state densities and accurate for stretched bonds. When the minimization of the PZ total energy is made over real localized orbitals, the orbital densities can be noded, leading to energy errors in many-electron systems. Minimization over complex localized orbitals yields nodeless orbital densities, which reduce but typically do not eliminate the SIC errors of atomization energies. Other errors of PZ SIC remain, attributable to the loss of the exact constraints and appropriate norms that the semi-local approximations satisfy, and suggesting the need for a generalized SIC. These conclusions are supported by calculations for oneelectron densities, and for many-electron molecules. While PZ SIC raises and improves the energy barriers of standard generalized gradient approximations (GGA's) and meta-GGA's, it reduces and often worsens the atomization energies of molecules. Thus PZ SIC raises the energy more as the nodality of the valence localized orbitals increases from atoms to molecules to transition states. PZ SIC is applied here in particular to the SCAN meta-GGA, for which the correlation part is already self-interaction-free. That property makes SCAN a natural first candidate for a generalized SIC.

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The large tunability of band gaps and optical absorptions of armchair MoS2 nanoribbons of different widths under bending is studied using density functional theory and many-body perturbation GW and Bethe–Salpeter equation approaches. We find that there are three critical bending curvatures, and the non-edge and edge band gaps generally show a non-monotonic trend with bending. The non-degenerate edge gap splits show an oscillating feature with ribbon width n, with a period $$\Delta n=3$$ Δ n = 3 , due to quantum confinement effects. The complex strain patterns on the bent nanoribbons control the varying features of band structures and band gaps that result in varying exciton formations and optical properties. The binding energy and the spin singlet–triplet split of the exciton forming the lowest absorption peak generally decrease with bending curvatures. The large tunability of optical properties of bent MoS2 nanoribbons is promising and will find applications in tunable optoelectronic nanodevices.

Semi-local density functional approximations are widely used. None of them can capture the long-range van der Waals (vdW) attraction between separated subsystems, but they differ remarkably in the extent to which they capture intermediate-range vdW effects responsible for equilibrium bonds between neighboring small closed-shell subsystems. The local density approximation (LDA) often overestimates this effect, while the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) underestimates it. The strongly-constrained and appropriately normed (SCAN) meta-GGA often estimates it well. All of these semi-local functionals require an additive non-local 1 arXiv:1906.01091v2 [cond-mat.mtrl-sci] 5 Jun 2019 correction such as the revised Vydrov-Van Voorhis 2010 (rVV10) to capture the longrange part. This work reports adsorption energies and the corresponding geometry of the aromatic thiophene (C 4 H 4 S) bound to transition metal surfaces. The adsorption process requires a genuine interplay of covalent and weak binding and requires a simultaneously accurate description of surface and adsorption energies with the correct prediction of the adsorption site. All these quantities must come from well balanced short and long-range correlation effects for a universally applicable method for weak interactions with chemical accuracy.

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