Multisite Interactions in Lattice-Gas Models of Adsorbates: Reconciling Adatom Relaxations at Steps

In a lattice-gas (LG) framework for (111) cubic surfaces, pair interactions cannot distinguish A and B steps, but an orientation-dependent three adatom (trio) interaction can, as we verify with VASP for Cu(111).\footnote{TJS et al., PRB a){\bf 70}('04)245404, b){\bf 71}('05)245414, c){\bf 73}('06)115426.}$^b$ However, on Pt(111), small clusters considerably underestimate the difference.\footnote{Feibelman, Surf.\ Sci.\ {\bf 463}('00)L661; Michely et al., ibid.\ {\bf 256}('91)217.} For a sequence of overlayer configurations, we explore the role of lateral relaxations and how they complicate LG analysis. On Cu(100) our prior VASP calculations of a particular trio interaction energy (E$_{\rm d}$) gave a large positive value.$^{3c}$ This nearly cancels the attractive second-neighbor interaction energy (E$_2$), leading to a discrepancy between theory and experiment of step stiffness anisotropy.$^{3a}$ Relaxations at step edges greatly reduce this repulsion. Since position-dependent interactions are improper in LG models, we show how to deal with this phenomenon using a quarto interactions. We comment on extensions to (110) faces and analytic expressions for step stiffness.