Adsorption of n-butane on Cu(100), Cu(111),Au(111), and Pt(111): Van der Waals density-functional study Kyuho Lee, 1,2,3 Yoshitada Morikawa, 1,2,4, * and David C. Langreth 3 1 The Institute of Scientific and Industrial Research (ISIR), Osaka University, 8-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan 2 CREST, Japan Science and Technology Agency (JST), 4-1-8, Honcho, Kawaguchi, Saitawa 332-0012, Japan 3 Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854-8019, USA 4 Research Institute for Computational Science (RICS), National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba Central 2, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan Received 26 September 2009; revised manuscript received 10 September 2010; published 29 October 2010 The adsorption of n-butane on Cu100, Cu111, Au111, and Pt111 is studied as a prototypical phys- isorption system of organic molecule-metal interface by using a fully nonlocal Van der Waals density func- tional vdW-DFM. Dion et al., Phys. Rev. Lett. 92, 246401 2004 and a second version of it vdW-DF2. Adsorption energies and heights are compared with experiments and conventional local local-density approxi- mation and semilocal generalized gradient approximation functionals. The adsorption energies and heights predicted by vdW-DF2 agree most favorably with known estimates. Lateral intermolecular interactions at a full coverage are calculated to be about 25% of total adsorption energy. A summation up to the second-nearest- neighbor pairs, i.e., six contacting neighbors, is enough to make the pairwise sum converged. DOI: 10.1103/PhysRevB.82.155461 PACS numbers: 68.43.-h, 82.65.+r, 31.15.eg I. INTRODUCTION The adsorption of n-butane CH 3 CH 2 CH 2 CH 3 , a linear- shape fully saturated hydrocarbon with four carbon atoms, on transition-metal TM surfaces is a typical weak phys- isorption system, and Van der Waals vdW interaction is the only attractive force between the nonpolar molecule and the metal surfaces. Despite the weak interaction, a noticeable softening of CH stretching mode has been observed 1,2 which has a relevance to the catalytic C-H bond activation mecha- nism of dehydrogenation. 3 As a prototypical weak physisorp- tion system of inert small organic molecules on TM surfaces, it has been studied for several decades and well characterized. 4–8 In order to understand this weakly interacting system by using density-functional theory DFT calculations, however, we need an accurate exchange-correlation energy functional which can describe the vdW interaction correctly because local or semilocal description of conventional DFT function- als cannot treat this nonlocal correlation effect properly. 9 In general, the local-density approximation LDA overbinds and the semilocal generalized gradient approximation GGA underbinds. For hard materials the error is relatively small in comparison to its bond strength. For the weak physisorption of molecules on TM surfaces, however, the relative error is extremely amplified. The energetics and structural properties predicted by LDA or GGA deviate significantly from the reality. 10,11 For vdW systems, local or semilocal functionals loose its predictive power. Correct description of vdW interaction will extend the applicability of DFT to a larger extent of sparse materials and hence there have been enormous efforts to overcome this deficiency. 12–20 Among them here we employ the vdW-DF, 13 a nonempirical universal functional which does not require any empirical fitting parameters for each atomic element. The functional has been successfully applied to many sys- tems, including small molecules, 21–23 layered structures, 24 molecular adsorption on surfaces, 24–32 potassium intercala- tion in graphite, 33 molecular crystal of polyethylene, 34 and so on. For a recent comprehensive review, refer to the review paper of Langreth and co-workers. 35 In this paper, we study the adsorption energy and height of n-butane on Cu100, Cu111, Au111, and Pt111 by using vdW-DF and its recent revised version vdW-DF2. 36 The adsorption energies calculated by vdW-DF and vdW- DF2 are found to be in a good agreement with experiments. 5,37–39 The adsorption height predicted by vdW- DF2 is also improved beyond GGA and vdW-DF. II. COMPUTATIONAL METHOD The calculations are performed by using ABINIT Ref. 40 code with a plane-wave basis set and Troullier-Martins 41 norm-conserving pseudopotentials. We adapted an imple- mentation of the efficient vdW-DF algorithm 42 from SIESTA Refs. 43 and 44 for use within a modified version of AB- INIT. A kinetic-energy cutoff of 50 Ry is used. The scalar- relativistic correction is included in the pseudopotentials for transition metals. For k-space integrations, a 4  6  1 Monkhorst-Pack mesh is used. For the partial occupation of metallic bands, we use the second-order Methfessel-Paxton scheme with a 0.07 eV broadening width. With this setup the total energies are converged within 0.01 eV. The vdW-DF total energy E tot vdW-DF is calculated as a post- GGA perturbation to a self-consistent calculation with Perdew-Burke-Ernzerhof PBE functional. The adsorption energy correction from fully self-consistent calculation is negligible 22 1%. Self-consistent PBE charge densities are used to evaluate E tot vdW-DF , E tot vdW-DF = E tot PBE - E x PBE + E x revPBE - E c PBE + E c LDA + E c vdW-DF , 1 where E tot PBE is a PBE total energy, E x PBE is a PBE exchange energy, E x revPBE is a revPBE Ref. 45 exchange energy, and PHYSICAL REVIEW B 82, 155461 2010 1098-0121/2010/8215/1554616 ©2010 The American Physical Society 155461-1