van der Waals corrected density functionals for cylindrical surfaces: Ammonia and nitrogen dioxide adsorbed on a single-walled carbon nanotube

Abstract

In this work, we extend the damped Zaremba-Kohn model (dZK) for long-range dispersion interaction between a molecule and a planar surface to molecules adsorbed on a curved cylindrical surface, and employ this extended model as an additive correction to the semilocal density functionals PBE (Perdew-Burke-Ernzerhof) and SCAN (strongly constrained and appropriately normed). The resulting PBE+vdW (van der Waals)-dZK and SCAN+vdW-dZK are applied to two systems, NH3 and NO2 molecules adsorbed on a single-wall carbon nanotube (CNT), for calculations of binding energies and equilibrium distances. For comparison, the results from vdW nonlocal functionals, such as SCAN+rVV10 and PBE+rVV10, are also presented. The binding energies from PBE+rVV10 (Vydrov and Van Voorhis), SCAN+rVV10, PBE+vdW-dZK, and SCAN+vdW-dZK are about 70–115 meV for the system of CNT + NH 3 and 300–500 meV for the system of CNT + NO 2 . The results from PBE+vdW-dZK and SCAN+vdW-dZK are closer to each other than those from PBE+rVV10 and SCAN+rVV10 are. The relatively closer results from PBE+vdW-dZK and SCAN+vdW-dZK indicate the consistency of our developed vdW–dZK model for cylindrical surfaces. All methods, including PBE, SCAN, PBE+rVV10, SCAN+rVV10, PBE+vdW-dZK, and SCAN+vdW-dZK, give approximately the same binding energy differences between two adsorption configurations (types I and II) for the two systems. This implies that the two adsorption sites have approximately the same adsorption stability. The exponent of the vdW interaction power law from our vdW-dZK model for the two systems is about 0 at short distance, largely due to the damping factor, and tends slowly to –4 to –4.5 at distances D about 20–50 Å. At even larger distances, the vdW power-law exponent approaches –5. This feature is very similar to the one calculated with random-phase approximation and renormalization group approaches, supporting the applicability of our methods. Our developed vdW-dZK method provides a highly efficient and reliable method for large systems with cylindrical surfaces, such as vdW interactions with nanotubes.