我們利用空間週期性來探討一氧化氮(NO)吸附在19顆雙二十面體的銠(Rh19)及鎳(Ni19)金屬奈米團簇上來進行斷鍵反應。其中，在雙二十面體的結構上具備一rhombus-center的結構，而當一氧化氮分子分別吸附在Rh19 、Ni19的rhombus-center位置上，其吸附能為-2.53 eV與-2.78 eV，且一氧化氮其鍵長會由氣態時的1.16 Å分別被拉長至1.33Å與1.35 Å，此時，一氧化氮分子在銠金屬團簇rhombus-center位置上進行斷鍵所需克服的活化能為0.24 eV，而在相同位置上，在鎳金屬團簇上所需克服的活化能則為0.42 eV。因此，我們也利用電子分析方法(LDOS、Charge-difference)來研究一氧化氮與奈米團簇(Rh19 、Ni19)間的電子性質，其結果指出雙二十面體團簇所具有”凹陷型”(rhombus-center)特殊的結構能夠降低一氧化氮斷鍵的活化能。 藉由金屬奈米結構對於催化反應的影響，接下來我們繼續探討有關於二氧化碳分子分別在銠(111)表面、不同結構的13顆銠金屬奈米團簇(Rh13)與不同結構的13顆銠金屬團簇坐落於氧化石墨烯(Rh13/UGO)上進行分解反應之活性。在我們的計算結果中，因銠金屬團簇坐落於氧化石墨烯上的吸附能小於銠金屬團簇的凝聚能，故銠金屬奈米團簇會傾向以奈米結構存在而不致於分散於氧化石墨烯上。因此，我們系統性將二氧化碳分子吸附於銠(111)表面、13顆銠金屬奈米團簇與13顆銠金屬團簇坐落於氧化石墨烯上，發現二氧化碳分子吸附在13顆正二十面體銠金屬團簇坐落於氧化石墨烯(Rh13-Ih/UGO)上有最大的吸附能-1.18 eV，此時二氧化碳分子中的碳-氧鍵由氣態的1.17Å被拉長至1.29Å。接著，當二氧化碳分子在13顆正二十面體銠金屬團簇坐落於氧化石墨烯上進行斷鍵之活化能為0.45eV，相較於二氧化碳在無支撐物下的13顆正二十面體銠金屬團簇(Rh13-Ih)上去進行斷鍵反應之能障還要低約0.38eV，這也表示藉由開鍊式氧化石墨烯的幫助可以更有效提升銠金屬奈米團簇活性來轉化二氧化碳分子。 最後，為了瞭解底層支撐物對於金屬團簇催化活性的影響，故我們藉由探討乙烷、丙烷以及正丁烷等烷類分子於13顆低對稱性銠金屬團簇(Rh13-Ls¬)進行直接脫氫反應之活性，並且與13顆銠金屬團簇分別坐落於開鍊式氧化石墨烯(Rh13-Ls/UGO)、二氧化銥(Rh13-Ls/ IrO2)和二氧化鈦(Rh13-Ls/ TiO2)所形成三種不同系統來作系統性比較。 而在我們的計算結果中，這三種烷類的吸附能分別在四個不同系統中所呈現之大小依序為：Rh13-Ls/UGO ≈ Rh13-Ls/ TiO2 > Rh13-Ls > Rh13-Ls/ IrO2。 另外，當乙烷、丙烷以及正丁烷分子於Rh13-Ls/UGO系統上去進行第一步脫氫(末端氫)反應(CnH2n+2 → CnH2n+1 + H)分別形成乙烷基(-C2H5)、丙烷基(-C3H7)及正丁烷基(-C4H9)，其所需活化能大小分別為0.21、0.22 和 0.16 eV；其所需能障皆為所有系統中最小的；反之，若在Rh13-Ls/ IrO2系統中，其脫氫反應所需活化能卻是四個系統中最大。因此，從計算出來顯示，我們了解到13顆銠金屬團簇可以藉由開鍊式氧化石墨烯的幫助來活化烷類分子，藉以提升脫氫反應之活性。而本論文中也利用詳細的電子分析(LDOS，Bader-charge和charge-difference等)來輔助我們了解其原因。

We applied density-functional theory (DFT) to investigate the adsorption and dissociation of NO on Rh19 and Ni19 clusters with a double-icosahedral (DI) structure. The transition structures of the NO dissociating on the potential-energy surfaces were derived with the nudged-elastic-band (NEB) method. The adsorption energies of NO molecules on the rhombus-center region of DI clusters are -2.53 eV and -2.78 eV with the N-O bond elongated to 1.33Å and 1.35 Å, respectively, on Ni19 and Rh19, compared to 1.16 Å of the gaseous NO counterpart. The barriers to the dissociation of N-O on both DI-Rh19 (Ea = 0.24 eV) and DI-Ni19 (Ea = 0.42 eV) clusters are small, indicating that the rhombus-center region of DI metal clusters might activate the scission of the N-O bond. To understand the size effects of the rhodium nanocluster, we first investigated the catalytic activity of various rhodium nanoclusters (Rhn, n = 1, 4, 5, 8, 13 amd 14) on unzipped graphene oxide (Rhn/UGO). The calculated result exhibited that the catalytic activity of CO2 dissociation on Rh13/UGO systems is better than other systems. The catalytic activity of various structures of Rh13 clusters on unzipped graphene oxide (Rh13/UGO) has been further investigated for comparison with Rh13 nanoclusters and Rh(111) surfaces. In, addition, the binding energy of Rh atoms on UGO is less than the cohesive energy (- 5.75 eV) of bulk Rh, indicating that the Rh atoms adsorbed on UGO tend to collect into clusters. We systematically calculated the energies of adsorption of CO2 on Rh13 nanoclusters in various stable shapes on unzipped graphene oxide; Rh13-Ih/UGO had the largest energy (where the Ih representing icosahedral shape), -1.18 eV, with the C–O bond being elongated from 1.17 to 1.29 Å; the barrier for dissociation of CO2 on Rh13-Ih/UGO is, accordingly, the smallest (Ea = 0.45 eV), indicating that Rh13-Ih/UGO might act as an effective catalyst to adsorb and to activate the scission of the C-O bond of CO2 .
We finally discussed the adsorption and dehydrogenation of alkanes (CnH2n+2, n = 2, 3, 4) on a low-symmetry Rh13 cluster (Rh13-Ls) in comparing with the system of the same cluster (Rh13-Ls) but supported on either an unzipped graphene-oxide (UGO) sheet (Rh13-Ls/UGO), or an IrO2 (110) surface (Rh13-Ls/IrO2), or TiO2 (110) surface (Rh13-Ls/TiO2) to understand the different support effects between Rh13-Ls and the various supports. The adsorption energies, calculated with density-functional theory, of these alkanes follow the order Rh13-Ls/UGO ≈ Rh13-Ls/ TiO2 > Rh13-Ls > Rh13-Ls/ IrO2. Our proposed reaction path for the dehydrogenation of ethane, propane and butane on Rh13-Ls/UGO has the first barriers of height 0.21, 0.22 and 0.16 eV, respectively, to form -C2H5, -C3H7 and -C4H9. In comparing with the barriers on Rh13-Ls、Rh13-Ls/ TiO2 and Rh13-Ls/ IrO2, we found that the barrier on Rh13-Ls/UGO is the lowest for all alkanes. We also studied the electronic properties, such as charge differences, density of states, electron localization functions and interaction energies, to explain the interaction between adsorbates and substrates, using density-functional theory (DFT).

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