Structure, reactivity, and electronic properties of V-doped Co clusters

Structures and physicochemical properties of V-doped ${\text{Co}}_{13}$ clusters have been studied in detail using density-functional-theory-based first-principles method. We have found anomalous variation in stability of the doped clusters with increasing V concentration, which has been nicely demonstrated in terms of energetics and electronic properties of the clusters. Our study explains the nonmonotonic variation in reactivity of ${\text{Co}}_{13-m}{\text{V}}_m$ clusters toward ${\text{H}}_2$ molecules as reported experimentally [Nonose et al., J. Phys. Chem. 94, 2744 (1990)]. Moreover, it provides useful insight into the cluster geometry and chemically active sites on the cluster surface, which can help to design better catalytic processes.

Figure 1

(Color online) Structures of optimal HCP, icosahedron, and cuboctahedron of pure ${\text{Co}}_{13}$ cluster (from left to right, respectively). The first entry in the parenthesis gives the isomeric position (“0” means minimum-energy state) and the second entry corresponds to relative energy to the minimum-energy state.

Figure 2

(Color online) Structures of optimal icosahedron, optimal cuboctahedron, and two HCP geometries (from left to right) for ${\text{Co}}_{12}\text{V}$ cluster. Green (black) dot represents Co atom, while yellow (gray) dot represents V atom. The entries in the parentheses have the same meaning as in Fig. 1.

Figure 3

(Color online) $A$, $B$, and $C$ represent the three inequivalent homotops in icosahedral ${\text{Co}}_{10}{\text{V}}_3$ structure having one V atom always at the center. The three structures are the optimal structures for the respective three types. The entries in the parentheses have the same meaning as in Fig. 1. Color convention for atoms is the same as in Fig. 2.

Figure 4

(Color online) $A$, $B$, $C$, and $D$ represent the four probable homotops in icosahedral ${\text{Co}}_9{\text{V}}_4$ structure having one V atom at the center and two of the remaining three V atoms are closest to each other on the surface, while the position of the fourth V atom is varied. The four structures represented above are the optimal structures for the respective four types. The entries in the parentheses have the same meaning as in Fig. 1. Color convention for atoms is the same as in Fig. 2.

Figure 5

Cohesive energy of the minimum-energy structures of ${\text{Co}}_{13-m}{\text{V}}_m$ clusters with respect to the cohesive energy of minimum-energy pure ${\text{Co}}_{13}$ cluster. The dashed line is the reference fixed at the cohesive energy of pure ${\text{Co}}_{13}$. Inset shows the second difference $\left({\Delta }_{2}E\right)$ in cohesive energy [as defined in Eq. (2)] for ${\text{Co}}_{12}\text{V}$, ${\text{Co}}_{11}{\text{V}}_2$, and ${\text{Co}}_{10}{\text{V}}_3$.

Figure 6

(Color online) Total DOS per atom, Co projected DOS per atom, V-projected DOS per atom, and total $d$-projected DOS per atom for the optimal structures of ${\text{Co}}_{12}\text{V}$, ${\text{Co}}_{11}{\text{V}}_2$, ${\text{Co}}_{10}{\text{V}}_3$, and ${\text{Co}}_9{\text{V}}_4$. The smearing width is fixed at 0.1 eV. Vertical line through zero is the Fermi energy $\left(E_F\right)$.

Figure 7

(Color online) Total DOS of the central V atom in the optimal structures of ${\text{Co}}_{12}\text{V}$, ${\text{Co}}_{11}{\text{V}}_2$, ${\text{Co}}_{10}{\text{V}}_3$, and ${\text{Co}}_9{\text{V}}_4$. The Fermi energy $\left(E_F\right)$ is fixed at zero.

Figure 8

(Color online) The calculated minimum-energy chemisorption structures with ${\text{H}}_2$ on the minimum-energy structures of ${\text{Co}}_{13-m}{\text{V}}_m$ $\left(m=0–4\right)$. It is clearly seen that hollow site on the surface is preferred by chemisorbed hydrogen. Color convention is the same as in Fig. 2 with small pink colored dots representing H atom.

Figure 9

The calculated chemisorption energy [using Eq. (4)] for ${\text{Co}}_{13-m}{\text{V}}_m{\text{H}}_2$ clusters.