Double­well potential energy surface in the interaction between h­BN and Ni(111) potential energy surface in the interaction

. Density functional theory calculations with non-local correlation functionals, properly accounting for dispersion forces, predict the presence of two minima in the interaction energy between h -BN and Ni(111). These can be described as a physisorbed state with no corrugation of the h -BN structure, and a chemisorbed state exhibiting noticeable corrugation and shorter distance of h -BN to the metallic support. The latter corresponds indeed to the one reported in most experiments. The relative stability of the two minima depends on the specific density functional employed: of those investigated here only the optB86b-vdW yields the correct order of stability. We also demonstrate that the effect of the metal support on the Raman frequency of the chemisorbed boron nitride monolayer cannot be reduced to the associated strain. This is important because the Raman frequency has been proposed as a signature to identify h -BN monolayers from multilayered samples. Our analysis shows that such signatures would be strongly dependent on the nature of the support – h -BN interaction.


INTRODUCTION
In the last two decades, the epitaxial growth of few-layers of hexagonal boron nitride (h-BN) on the (111) surface of face-centered cubic (fcc) metals such as Au, Cu, Rh, Pt, Pd, Ir, and Ni has been widely studied. [1][2][3][4][5][6][7][8][9] The motivation for these studies is that h-BN/metal interfaces have potential applications in areas such as protective coating, transparent membranes, or deep ultraviolet emitters. 10-12 Recent theoretical investigations have also suggested that metal-supported nanosheets of h-BN might be active for both CO oxidation and oxygen reduction reaction (ORR). 13, 14 Indeed, the combined experimental and theoretical study of Uosaki et al. demonstrated that h-BN supported on Au(111) surface has much better catalytic activity for ORR than a pure Au(111) electrode. 2 These authors suggested that defective h-BN nanosheets with edge sites play an important role in the ORR. The theoretical work of Gao and coworkers 15 showed that the energy barrier for the ORR depends on the type of defects, which also play an important role at enhancing the stability the h-BN/metal heterostructures. 3 The interaction between h-BN and metal surfaces is complex even in the absence of defects, as it involves strain effects, dispersion interactions, and electronic redistribution.
Early experimental studies by Rokuta et al. demonstrated that orbital hybridization at the Ni(111) and h-BN nanosheets interface generates metallic bands. 16 Other transition metal substrates, including Rh(111) and Pt(111) surfaces, have been also reported to modify the electronic properties of supported h-BN in a similar way. 17,18 Theoretical studies have suggested that the metallic behavior of h-BN when supported on metal substrates can be due to the mixing of d orbitals of the metal with the 2p orbitals of N and B of h-BN. 2,19 The Ni(111) surface is an interesting substrate for atomically-thin layers of h-BN since the lattice constant of the former (249 pm) 20 almost perfectly matches that of the latter (251 pm), i.e., their degree of incommensurability is below 0.8%. 21 It has been suggested that the h-BN monolayer on Ni(111) overcomes the small lattice mismatch by introducing a slightly rumpled structure, allowing the formation of a commensurate p(1×1) system. 16 Most of the recent theoretical work about this interface has been devoted to the catalytic activity towards the CO oxidation and ORR. 13,15 In these studies, the dispersion has been treated empirically under the so-called D2 method on top of semi-local density functionals (in the generalized gradient approximation), which may miss relevant features. Here, we investigate the interface geometry and electronic structure of h-BN layers supported on the Ni(111) surface using nonlocal correlation functionals, optB88-vdW and optB86b-vdW, which offer more robust descriptions of dispersion interactions. We will show that a double-well potential energy surface exists for the interaction of h-BN with the metal support, with two minima that can be identified as chemisorption and physisorption states, respectively. In addition, we discuss the effect of the Ni support on the Raman signal of h-BN, which is important given that Raman peaks can be used experimentally to identify the presence of h-BN monolayers, in contrast with h-BN bulk. 22 4

COMPUTATIONAL METHODS
Density functional theory (DFT) calculations were carried out using plane wave basis sets as implemented in the VASP code. 23, 24 The projected augmented wave (PAW) method 25,26 was used to describe the effect of core electron on the valence electron density. The number of plane waves in the calculations was limited by a kinetic energy cutoff of 410 eV. In order to sample the Brillouin zone, a Monkhorst-Pack 27 k-point grid of 7×7×1 was used throughout the simulations involving the metal slabs. The Methfessel-Paxton smearing method of first order was used with an energy width of σ = 0.2 eV; total energies were extrapolated to σ=0.
For the calculation of densities of states (DOS) we used the tetrahedron method with Blöchl corrections. The threshold for forces acting on ions was set to 0.005 eV Å −1 . Test calculations with a lower threshold, of 0.001 eV Å −1 , led to zero or negligible effect on the computed interaction energies, corrugation and separation between the Ni substrate and the monolayer.
To compensate for the use of an asymmetric slab, all simulations included a dipole correction as implemented in VASP, based on a method proposed by Makov and Payne. 28 Following the approach of a previous DFT investigation of graphene on this metal substrate, 29  We compared results obtained from calculations with various functionals including the generalized gradient approximation (GGA) in the formulation by Perdew-Burke-Ernzerhof 5 (PBE), 31 as well as their empirical corrections by Grimme's method (D2 and D3) 32,33 to account for dispersion. We also consider the optB88-vdW and optB86b-vdW functionals where dispersion is treated with explicit non-local correlation, 34 as developed and implemented in VASP by Klimeš et al. 35 The interaction energy ( int ) of h-BN adsorbed on the Ni(111) surface was computed as: where interface is the total energy of the h-BN/Ni(111) slab, including n formula units of h-BN; Eh-BN is the energy per formula unit of a free-standing (unstrained) h-BN sheet, and surf is the total energy of the clean Ni(111) slab.
The energy barrier and potential energy surface between the chemisorption and physisorption minima was obtained using the nudged elastic band method. 36  structure. In a similar system, graphene on Ni(111) surfaces, high-resolution X-ray photoelectron spectroscopy (HR-XPS) have detected the coexistence of bridge and top-fcc structures. 29 Hence, we have also considered bridge geometries, where the B-N bond sits on top, fcc, and hcp sites, generating three additional arrangements. Due to the presence of two atomic species in the monolayer, two non-equivalent interfaces can be formed, which we call Interface A and Interface B. These interfaces cannot be converted into one another by a simple translation. As a result, twelve high-symmetry configurations/interfaces were explicitly considered, six for each interface (Figure 1).  In our study, the initial automatic search with the optB88-vdW method, as described above, found only physisorbed states (Figure 2). However, if we start from the same N(top)-B(fcc) configuration, but manually placing the monolayer closer to the Ni substrate and relaxing the ions using a less aggressive optimizer (we used the quasi-Newton method), the optB88-vdW simulation was able to converge to a minimum at shorter distances. In this local minimum, the corrugation value is estimated as 7.2 pm with the B atom closer to Ni substrate, in good agreement with the XPD measurements. 9 Moreover, the interlayer separation h-BN monolayer-Ni as 221 pm, in line with LEED 30 and TEM 37 reports. The geometry of this interface configuration thus corresponds to a chemisorbed state, even if it has a weaker interaction (by ~10 meV/atom) than the physisorbed state calculated with the same functional. In order to understand the relationship between the two minima, we also investigated the transition from one to the other using the nudged band elastic (NEB) method ( Figure 3). The two minima are separated by a small energy barrier of ~1.6 meV/atom.
The coexistence of two minima in the potential energy surface, one corresponding to a physisorbed state, at a longer distance and with little corrugation, and one corresponding to a chemisorbed state, at shorter distance and with significant corrugation, is physically plausible. For example, it has been recently found that two distinguishable adsorption wells coexist at the interface between graphene and silicon oxide, although in that case the chemisorption well was reached experimentally only under ultra-high pressure. 49 In the same way, it is possible that the two   Table 1. Interestingly, all these functionals predict the existence of both local minima thus reinforcing the present theoretical prediction. Moreover, the formation of the interface, in either the physisorbed or chemisorbed state, is energetically favorable (negative formation energy) for all functionals except for PBE, which does not account for the stabilizing dispersion interactions, and thus incorrectly lets the strain effect to dominate.
Interestingly, the only functional that correctly identifies the chemisorbed state as more stable than the physisorbed state is the optB86b-vdW functional, as observed for graphene/Ni(111).
In fact, this functional predicts a very shallow physisorbed minimum, with a barrier of less than 0.1 meV/atom to transit to the chemisorbed minimum (Figure 3). In future work, it would be interesting to also test other recently developed functionals, like the PBE-vdW surf 12 functional, which can account for the nonlocal screening within the bulk. 50 However, recent investigations of molecular adsorption at metal surfaces 51,52 have shown that the PBE+vdW surf and the optB88-vdW functionals, while based on different approximations, lead to nearly equivalent quantitative agreement in adsorption energies and equilibrium distances. The optB88-vdW functional, which in Ref. 53 we found to be particularly good in the description of free-standing h-BN, can lead to a chemisorbed minimum for h-BN on Ni(111), although it does not identify it as the most favorable minimum for adsorption. For compatibility with our previous work where we investigated the origin of Raman signature in monolayers of h-BN, 53 we will discuss below the addition of extra layers and the Raman 13 frequencies of supported h-BN as calculated with the optB88-vdW (at the correct chemisorbed minimum), such that it facilitates the comparison between the free-standing and supported systems.  16   Therefore, a detailed understanding of the nature of the h-BN/support interaction is necessary to elucidate the origin of Raman shifts in specific supported h-BN systems.

CONCLUSIONS
In summary, we have shown that non-local correlation functionals predict the presence of two minima in the interaction energy between h-BN and Ni(111): one geometrically flat that can be identified as a physisorbed state and one with appreciable corrugation of the h-BN lattice and shorter interface distance, which can be identified as a chemisorbed state. Both empirically-corrected GGA functionals and non-local correlation functionals can locate the two minima in the potential energy surface, but only the optB86b-vdW is able to give the correct order of stability.
In the chemisorbed state, which is the one reported in most experiments, there is significant charge transfer from Ni to h-BN, which becomes metallic. We have found that the