Figure 1

Free-energy landscapes obtained by MTD simulations and related stable configurations [Si: yellow (light gray), O: red (dark gray)]. (a) Distances of each O atom from each center of the backbonds, shown as a red $\times$, are used as collective variables (CVs). (b) Distances of each O atom from the Si atom in the first layer, marked by a red $\times$, are used as CVs. (c) Structures of each local minimum and transition state (TS) for these reaction pathways. The relative free-energy difference between the minima (A) and (B) is not determined since the reverse reaction from (B) to (A) has not been simulated: Note that the free-energy landscape in MTD simulations is obtained from the history-dependent potential added to overcome the reaction barrier.Reuse & Permissions

Figure 2

Free-energy profiles of the backbond oxidation calculated by BM approach. Pathways and corresponding free-energy profiles between the on-dimer geometry and the on-top geometry (a) and from the on-top geometry to the backbond oxidized geometry (b). The various panels show the geometries of the local minima (see text). Color code for atoms is the same as in Fig. 1.Reuse & Permissions

Figure 3

Thermally activated backbond oxidation in pairs of minimum (B) configurations. The oxidation proceeds from (a) to (b), or (c) to (d). In both cases, an O of the O${}_2$ intervenes in the backbond whereas the other O stays near the on-top site. Si dimer bonds are broken as circled in (a) and (c). Color code for atoms is the same as in Fig. 1.Reuse & Permissions

Figure 4

Spin density (a), spin-up HOKO, (c) spin-down HOKO, (d) spin-up LUKO, and (e) spin-down LUKO in the pair of minimum (B) configuration plus an O${}_2$ shown in Fig. 3c. In (a), the isosurfaces at $\pm 2\times {10}^{-3}$ $e/{\AA }^3$ are shown in orange (light gray) and green (dark gray), respectively. From (b) to (e), the isosurfaces at $\pm 2.4\times {10}^{-2}{(e/{\AA }^3)}^{1/2}$ are shown in red (dark gray) and blue (black), respectively. Color code for atoms is the same as in Fig. 1.Reuse & Permissions