Application of Screened Hybrid Density Functional Theory to Ammonia Decomposition on Silicon

Abstract

Cluster geometry optimizations were performed as follows. Our Si 21 H 20 and Si 9 H 12 geometries were B3LYP/6-311++G(3df,2pd) optimized without constraints, while Si 6 H 12 and Si 2 H 4 geometries were obtained from the optimized Si 21 H 20 . The Si 21 H 20 center dimer was isolated and modified into the Si 6 H 12 cluster. The Si 6 H 12 bare cluster was obtained from the bare Si 21 H 20 cluster. The complex, transition state guess and product geometries were obtained analogously. The 6-silicon atoms in the following geometry optimizations and transition state searches were kept frozen (other coordinates unconstrained) to retain the geometric orientation about the dimer bond modeling the silicon surface. The bare Si 2 H 4 cluster was also obtained from the Si 21 H 20 center dimer by replacing the four second-layer silicon atoms with hydrogen atoms. The complex, transition state guess and product geometries were obtained analogously. The two-silicon dimer atoms in the following geometry optimizations and transition state searches were kept frozen. Four dihedral and two angles were also frozen as listed (by the optimized coordinates) retaining the geometric orientation about the dimer bond.Tables I-IV compares selected geometric parameters from our B3LYP/6-311++G(3df,2pd) calculations to previous literature. Results are reported for an isolated silicon cluster ("bare cluster"), NH 3 adsorbed onto the cluster ("complex"), "transition structure" and "product" for dissociated ammonia chemisorbed NH * 3 → NH * 2 + H * (asterisks denoting surface bound species). Cartesian coordinates for the series of clusters and atom numbering are reported in Supporting Information II. Tables report distances inÅ and angles in degrees.To calculate the tilt angle θ tilt , a plane is first defined by the four-silicon atoms (in the secondlayer) bonded to the two-silicon dimer atoms in the Si 21 H 20 and Si 9 H 12 clusters (through constraints Si 6 H 12 is equivalent to Si 21 H 20 ). The Si 2 H 4 plane is defined by the four-hydrogen atoms in the second-layer; and the Si(100)-2x2 slab plane is defined by the two-translation vectors. The θ tilt is then the angle adjacent to the plane resulting from the vertical separation ('z ' direction) in the coordinates of the silicon 'up' and 'down' atoms.The B3LYP Si 9 H 12 geometries from Surface Science, 2000 469, 9 (in Table II) used a mixed basis set: 6-311++G(2d,p) on chemically active atoms, 6-31G(d) on subsurface Si and terminating

Simulating periodic trends in the structure and catalytic activity of coinage metal nanoribbons

“…This is clear from the HSE06 potential energy surfaces, which shows the corresponding AO‐basis PBE results with dotted lines. This result generalizes our previous studies of reactions over Au, and our and other workers' indications of this behavior over nonmetallic catalysts. These results strongly motivate continued exploration of meta‐GGAs and screened hybrids for modeling heterogeneous catalysis.…”

“…While small metal clusters [34][35][36][37] or embedded clusters [38] can often be treated with accurate ab initio methods, calculations on periodic nanowires or slabs are typically restricted to density functional theory (DFT) calculations using inexpensive generalized gradient approximations (GGAs) for the many-body exchange-correlation correction. [39] We [31,40,41] and others [42][43][44][45][46][47][48][49][50][51] have shown that GGAs' well-known systematic underestimate of chemical reaction barriers [52] transfer over to reactions on surfaces. Our studies of silicon [40] and graphene [41] surfaces suggest that new meta-GGA [53][54][55] and screened hybrid [56,57] approximations can improve these systematic errors.…”

“…[39] We [31,40,41] and others [42][43][44][45][46][47][48][49][50][51] have shown that GGAs' well-known systematic underestimate of chemical reaction barriers [52] transfer over to reactions on surfaces. Our studies of silicon [40] and graphene [41] surfaces suggest that new meta-GGA [53][54][55] and screened hybrid [56,57] approximations can improve these systematic errors. However, to our knowledge, the only application of these functionals to reaction barriers on periodic metal structures is our recent study of H 2 dissociation over gold.…”

Topological analysis of the electron delocalization range

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