Metal adsorbate interactions and the convergence of density functional calculations

Abstract

The adsorption of metal atoms on nanostructures, such as graphene and nanotubes, plays an important role in catalysis, electronic doping, and tuning material properties. Quantum chemical calculations permit the investigation of this process to discover desirable interactions and obtain mechanistic insights into adsorbate behavior, of which the binding strength is a central quantity. However, binding strengths vary widely in the literature, even when using almost identical computational methods. To address this issue, we investigate the adsorption of a variety of metals onto graphene, carbon nanotubes, and boron nitride nanotubes. As is well-known, calculations on periodic structures require a sufficiently large system size to remove interactions between periodic images. Our results indicate that there are both direct and indirect mechanisms for this interaction, where the latter can require even larger system sizes than typically employed. The magnitude and distance of the effect depends on the electronic state of the substrate and the open-or closed-shell nature of the adsorbate. For instance, insulating substrates (e.g., boron nitride nanotubes) show essentially no dependence on system size, whereas metallic or semi-metallic systems can have a substantial effect due to the delocalized nature of the electronic states interacting with the adsorbate. We derive a scaling relation for the length dependence with a representative tight-binding model. These results demonstrate how to extrapolate the binding energies to the isolated-impurity limit.Graphene, carbon nanotubes (CNTs), and boron nitride nanotubes (BNNTs) have exceptional mechanical, thermal, and electronic properties. These materials are thus the subject of intense research. Adsorption studies range from hydrogen and fluorine to metals of the 3d, 4d, and 5d series [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Among the latter are many density functional theory (DFT) studies examining the behavior of single metal atoms. These, however, show variation in the binding strengths up to several electron volts [5]. In part, this is due to differences in the methods employed, such as spin-polarized versus non-spin-polarized calculations, ultrasoft pseudo-potentials versus projector augmented wave methods (PAWs), or the use of LDA versus GGA exchange functionals. However, even studies employing almost identical techniques yield different results. For example, comparing the investigations of Manadé et al. [5], Pašti et al. [3] and Liu et al. [7] with respect to 3d metal adsorption, which all employed the same computational package, the (GGA-PBE) exchange-correlation functional, and PAWs, as well as a 4 × 4 graphene super cell, there are differences of up to 0.56 eV.Here, we investigate the binding energy dependence on the system size for various 3d metals on graphene, CNTs, and BNNTs by means of DFT. We aim to identify the cell size required to obtain, or extrapolate to, the isolated impurity limit, as well as understand related sources of error. Up...