A comprehensive search for the precursor dissociation of antimony tetramers on Ge͑001͒ with strain was carried out using first-principles calculations. In contrast to previous theoretical studies on Si͑001͒ ͓Phys. Rev. Lett. 97, 046103 ͑2006͔͒ and in agreement with recent experiments, we reveal a square intermediate anisotropy dissociation pathway across the surface dimer row, where the dissociation energetics and kinetics can be qualitatively altered by the strain and lead to divergent dissociation pathways and patterns with substratedimer-bond breaking due to the weak interactions between Ge-Ge and Sb-Ge bonds.It has long been known that molecular chemisorption on solid surfaces often involves intermediate precursor states and several competing dynamical processes such as dissociation, diffusion, and desorption. 1 A typical example is the reaction of group-V elements ͑e.g., As, Sb, and Bi͒ with Si and Ge surfaces. 2-18 For Sb 4 on Si͑001͒, the three-dimensional ͑3D͒ clusters can convert to flat tetramers that can then split into pairs of dimers. Scanning tunneling microscopy ͑STM͒ measurements 2-4 and density-functional theory ͑DFT͒ calculation 14 revealed a two-stage reaction process involving two distinct pathways, along and across the surface dimer row via a rhombus intermediate state. Similar but distinct reaction behavior is also observed for Sb 4 on Ge͑001͒ where STM measurements identified a pathway involving a twodimensional ͑2D͒ flat square intermediate state across the surface dimer row. 5 Such processes have attracted considerable attention because they play a key role in the epitaxial growth of Ge/Si heterostructures. [15][16][17][18] In this Brief Report, we present a comprehensive search on the dissociation energetics and kinetics of Sb 4 on Ge͑001͒ surface with biaxial strain using DFT calculations. They show sensitive dependence on the strain state of the substrate: in the absence of an external strain, Sb 4 dissociates via a square intermediate state with a bond-twisting assisted rigid rotation mechanism for the first-stage conversion and a substrate-dimer-bond-breaking assisted piecewise rotation dissociation pathway across the dimer row for the secondstage conversion. While with an applied strain, the energetics and kinetics can be qualitatively altered, leading to distinct reaction pathways and patterns due to the weak interactions between Ge-Ge and Sb-Ge bonds. For comparison, we also performed calculations for Sb 4 on Si͑001͒. In stark contrast to the case of Sb 4 on Ge͑001͒, the external strain has little effect on the dissociation behavior on Si͑001͒ due to the strong interactions between Sb-Si and Si-Si bonds.The reported calculations are carried out using VASP code 19 with ultrasoft pseudopotentials 20 and the generalized gradient approximation ͑GGA͒. 21 An energy cutoff of 200 eV for the plane-wave basis set is used. The supercell size is set to XYZ =16ϫ 32ϫ 35.72 Å 3 with ten layers of Ge in the Z direction and one layer of hydrogen to passivate the bottom Ge layer. The XY plane corr...