Overall, the Ru/ZrO2 model catalyst consists of a three-layer [112 ̅ 0] oriented Ru nanorod with a (3  3) super cell of Ru(0001), which is positioned on a five-layer (1  3) super cell of ZrO2(111) (see Figure ). The bottom two layers of ZrO2 were fixed, while the Ru atoms and the uppermost three layers of the ZrO2(111) support were relaxed for optimization. Subsequently, we constructed Ru/ZrO2-x catalysts with varying O-vacancy concentrations and distributions by removing specified lattice oxygen atoms. Systems with individual O-vacancies were modeled by removing one lattice oxygen atom per unit cell. We investigated O-vacancies located in different positions: in the uppermost layer and deeper layers underneath the Ru nanorod, as well as in the top layer of the support adjacent to the Ru nanorod. Among the 15 O atoms in the uppermost layer, labeled as ni (i=1-15) in Figure , nine (from 1i to 9i) are covered by the Ru nanorod, denoted as 'lattice-O atoms underneath the Ru nanorod'. The remaining six O-atoms, labeled from 10i to 15i, were distributed on both sides of the Ru nanorod without direct contact with the Ru nanorod. Furthermore, O-vacancies underneath the edge of Ru nanorod in deeper layer, i.e., on ii, iii, or iv sites, were created as depicted in Figure . The distance between these O-vacancies and the nearest Ru atom increases from 3.89 Å to 5.14 Å and 6.29 Å, respectively. underneath or aside the Ru nanorod, ii, iii, and iv denote positions in deeper layers underneath the Ru nanorod. Formation of O-vacancies on positions 1i, 2i, 3i, 4i, and 5i leads to oxygen vacancy (Ov) clusters 1VO, 2VO, 3VO, 4VO, and 5VO with 1 -5 O-vacancies in the top layer underneath the Ru nanorod, as illustrated in the schematic representation in Table in our previous report. O-vacancies on positions 1i, 17i, 18i, and 14i lead to O-vacancy clusters 1VO, 2VO, 3VO, and 4VO in the top layer of the support directly adjacent to the Ru nanorod. Finally, positions ii, iii, and iv refer to newly formed Ov sites in the deeper layers underneath the Ru nanorod, which starting from the Ov at site 1i contribute to the formation of the Ov clusters 1VO, 2VO, 3VO, and 4VO.