Role of Strain and Ligand Effects in the Modification of the Electronic and Chemical Properties of Bimetallic Surfaces
J. R. Kitchin, J. K. Nørskov, M. A. Barteau, and J. G. Chen, “Role of Strain and Ligand Effects in the Modification of the Electronic and Chemical Properties of Bimetallic Surfaces”, Physical Review Letters 93(15), 156801 (2004). https://doi.org/10.1103/physrevlett.93.156801
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Question
A monolayer of one metal supported on another often adsorbs molecules very differently from either parent metal. Two mechanisms are usually invoked: strain, because the overlayer atoms adopt interatomic distances different from those in their own bulk, and the ligand effect, meaning the heterometallic bonding between surface and substrate atoms. Because the two act together in almost every real system, they had been hard to separate. The Letter asks for a simple, general picture of how strain and ligand effects each change the surface electronic structure, and how those changes carry through to surface chemistry (Kitchin et al. 2004).
Approach
The authors use periodic density functional theory (DACAPO, PW91 functional, Vanderbilt ultrasoft pseudopotentials, 350 eV plane wave cutoff) on three-layer slabs of the substrate’s close-packed facet (fcc(111), bcc(110) or hcp(0001)) in 2x2 cells, replacing the top layer with a pseudomorphic Ni, Pd or Pt monolayer. Substrates include Nb, Ta, Mo, W, Re, Ru, Ir, Os, Ni and Pt; calculations are done both with unrelaxed and with relaxed slabs. The d band is characterized by projecting the Kohn-Sham states onto atomic orbitals, giving a d-band filling, a d-band center (average energy) and a root mean squared d-band width (Kitchin et al. 2004).
To rationalize the band widths, they use a tight-binding (Harrison-type) interatomic matrix element that couples the d orbitals of a surface atom to each nearest neighbor. For each neighbor the contribution scales with the product of the two metals’ characteristic d-orbital lengths raised to the 3/2 power, divided by the fifth power of the interatomic distance, and the contributions are summed over all neighbors including subsurface ones. In this form the ligand effect enters through the numerator (the identity of the neighbors) and strain enters through the denominator (the distances). Finally, dissociative H2 adsorption energies are computed for H in a threefold site on relaxed bimetallic slabs (Kitchin et al. 2004).
Key findings
Forming the bimetallic surface changes the d-band filling by typically less than 2%, which the authors treat as negligible, and imposed strain leaves it unchanged as well. Because filling is conserved, the d-band center must shift when the width changes, as a rectangular band model predicts. Across unrelaxed and relaxed slabs the rms width and the d-band center are linearly correlated with a slope of about -1 (R2 = 0.99): a wider band sits lower in energy and a narrower band sits higher (Kitchin et al. 2004).
The rms d-band width is in turn proportional to the summed matrix element (R2 = 0.99) over a broad set of structures: pure Ni, Pd and Pt sheets, slabs and solids under isotropic and anisotropic strain, the supported monolayers, surface and subsurface alloys, and Pt-3d sandwich structures. Tensile strain lengthens bonds, lowers the matrix element, narrows the band and raises it; compressive strain does the opposite. The dissociative adsorption energy of H2 correlates with the d-band center (R2 = 0.88), with surfaces whose d-band center is higher binding hydrogen more strongly (Kitchin et al. 2004).
Ni monolayers illustrate competing effects. On W(110) Ni is under more than 10% tensile strain, yet strong Ni-W bonding broadens the band enough that it ends up wider and lower than on Ni(111), and H2 adsorbs more weakly. On Ru(0001) the strain is similar but the ligand effect weaker, so the two nearly cancel and Ni/Ru(0001) behaves almost like Ni(111). On Pt(111) the ligand effect is weakest, strain dominates, the band narrows and rises, and H binds more strongly. Matrix elements for Ni, NiPt, NiRu and NiW are 0.23, 0.17, 0.27 and 0.28 eV, with DFT widths of 1.89, 1.35, 1.76 and 2.00 eV. Using the global fit to predict these widths overestimates them by 10 to 20%, suggesting element-specific fits would do better. Relaxation sometimes changes the results substantially, but systems simply move along the same trends, since relaxation only alters interatomic distances (Kitchin et al. 2004).
Significance
The Letter reduces the strain and ligand effects to one quantity, the interatomic d-d matrix element, and shows that both act by changing the d-band width, with the d-band center following to keep the filling constant. This links the geometry and composition of a bimetallic surface to the d-band center, and through it to adsorption energies, without needing a full DFT calculation for each candidate. The authors propose this as a first step for screening bimetallic and alloy surfaces for desired electronic or chemical properties, and note the same reasoning could estimate the effect of surface reconstructions (Kitchin et al. 2004). It extends their earlier analysis of Pt-3d subsurface structures (J. Chem. Phys. 120, 10240, 2004) to a general treatment of supported monolayers.