本論文包含兩個異相催化反應之理論計算研究：甲醇-d4在Rh催化劑分解反應及Fischer-Tropsch(F-T)合成反應。在第一個主題中，我們計算甲醇-d4在Rh(100)、放大的Rh(100)e及球狀Rh38表面，脫氫產生CO及D2分子的反應路徑，與表面大小的相關性，且與真空實驗系統做比對。由計算結果得知，在小的表面Rh38，甲醇-d4斷O-D鍵的活化能降低，使甲醇-d4容易分解，其結果與實驗觀察一致。此外，我們計算Rh表面及團簇上CO數目對吸附能的影響。CO吸附行為在平坦Rh(100)及球狀Rh38兩種表面差異甚大，在平坦的Rh(100)及Rh(100)e表面，CO分子垂直吸附於表面，然而，在球狀Rh38表面，CO分子吸附為輻射狀，此吸附結構會造成CO在球狀Rh38表面分子間作用力較小；因此，隨著CO覆蓋率上升，在Rh38表面吸附能下降幅度較Rh(100)表面為平緩。
在第二個部分中，我們探討Fischer-Tropsch (F-T) 合成反應在Ru(0001)和Co(0001)表面的反應機構。根據計算結果可知，不論在Ru(0001)還是Co(0001)表面，CO傾向生成中間物CHO；在Co(0001)表面，CHO會繼續氫化生成CH2O及CH3O，但在Ru(0001)表面則是傾向斷C-O鍵。此兩表面路徑差異，對應在Co催化劑上有高的CH4選擇率，而在Ru催化劑則是生成含碳長鏈產物。因此，我們利用物理方法：改變表面粗糙度，及化學方法：表面加入promoter，增加Co催化劑活性作為改善。在物理方法中，我們計算波浪狀(11-20)及(1-100)表面，發現CO斷鍵在此兩表面更為容易，減少CH4選擇率。在化學方法中，探討加入Na及K金屬的Co(0001)表面，由計算結果得知，Na及K提升CHO的C-O斷鍵能力，大於氫化能力，增加F-T合成反應活性。

This thesis computationally studied two related topics in heterogeneous catalysis, methanol-d4 decomposition on Rh catalysts and Fischer-Tropsch synthesis (FTS). In the first topic we thoroughly examined the decomposition pathway from methanol-d4 to CO and D2 on the prefect and expanded Rh(100) surfaces as well as spherical-shaped Rh38, which correspond to different-sized Rh nanoclusters in the experiment. Our computational result found that smaller Rh cluster, Rh38, can better decompose methanol because of the the decreased activation energy for O-D bond scission of methanol-d4, in consistent with the experimental observation. Additionally, we examined the adsorption behavior of surface CO on those Rh surface and cluster. CO adsorption behaves differently on flat Rh(100) and spherical Rh38. Surface CO perpendicularly adsorbed on the planes of Rh(100) and Rh(100)e, whereas the adspecies radically adsorbed the sphere of Rh38 that can ease the interaction among them and Eads reduction. Thus, the Eads of surface CO decreases rather slower on smaller sized Rh38 than the Rh(100) surfaces at higher surface coverage.
In the second part, we computational examined the reaction mechanism of FTS on Ru(0001) and Co(0001) surfaces. According to the calculations, CO prefers the hydrogenation reaction forming CHO intermediate on both Ru(0001) and Co(0001) surfaces initially. Surface CHO prefers further hydrogenation forming CH2O or CH3O on Co(0001) while favors C-O bond cleavage on Ru(0001). The different reaction pathways for CHO are responsible for the higher CH4 selectivity on Co-based materials while products with longer carbon chian prefers on Ru-based catalysts. Furthermore, we used physical, such as surface roughness, and chemical, surface with promotors, methods to improve Co catalysted reactivity. In the physical method, we computed CO dissociation on step (11-20) and (1-100) surfaces and found CO can better dissociate on the surfaces to lower the CH4 selectivity. In the chemical method, FTS reactions were investigated on Co surface with with Na and K adatoms. The computed result found that adatoms can effectively promote C-O dissocation than hydrogenation of CHO to enhance FTS activity.

(1) Palmeri, N.; Chiodo, V.; Freni, S.; Frusteri, F.; Bart, J. C. J.; Cavallaro, S. International Journal of Hydrogen Energy 2008, 33, 6627.
(2) Rabenstein, G.; Hacker, V. Journal of Power Sources 2008, 185, 1293.
(3) Jiang, R.; Guo, W.; Li, M.; Zhu, H.; Zhao, L.; Lu, X.; Shan, H. Journal of Molecular Catalysis A: Chemical 2011, 344, 99.
(4) Liu, X.; Madix, R. J.; Friend, C. M. Chemical Society Reviews 2008, 37, 2243.
(5) Min, B. K.; Friend, C. M. Chemical Reviews 2007, 107, 2709.
(6) Davis, S. E.; Ide, M. S.; Davis, R. J. Green Chemistry 2013, 15, 17.
(7) Zhang, J.; Cao, X. M.; Hu, P.; Zhong, Z.; Borgna, A.; Wu, P. The Journal of Physical Chemistry C 2011, 115, 22429.
(8) Papageorgopoulos, D. C.; Ge, Q.; King, D. A. The Journal of Physical Chemistry 1995, 99, 17645.
(9) Schulz, H. Applied Catalysis A: General 1999, 186, 3.
(10) Iglesia, E. Applied Catalysis A: General 1997, 161, 59.
(11) Khodakov, A. Y.; Chu, W.; Fongarland, P. Chemical Reviews 2007, 107, 1692.
(12) Davis, B. H. Industrial & Engineering Chemistry Research 2007, 46, 8938.
(13) de Smit, E.; Weckhuysen, B. M. Chemical Society Reviews 2008, 37, 2758.
(14) Borghard, W. G.; Bennett, C. O. Industrial & Engineering Chemistry Product Research and Development 1979, 18, 18.
(15) Garra¨ªn, D.; Lech¨®n, Y.; R¨²a, C. d. l. Smart Grid and Renewable Energy 2011, Vol.02No.02, 7.
(16) Vaidya, P. D.; Rodrigues, A. E. Chemical Engineering & Technology 2009, 32, 1463.
(17) Zhang, B.; Tang, X.; Li, Y.; Xu, Y.; Shen, W. International Journal of Hydrogen Energy 2007, 32, 2367.
(18) Zhang, Q.; Kang, J.; Wang, Y. ChemCatChem 2010, 2, 1030.
(19) Kresse, G.; Hafner, J. Physical Review B 1993, 47, 558.
(20) Ceperley, D. M.; Alder, B. J. Physical Review Letters 1980, 45, 566.
(21) Becke, A. D. The Journal of Chemical Physics 1992, 97, 9173.
(22) Kresse, G.; Hafner, J. Physical Review B 1994, 49, 14251.
(23) Kresse, G.; Furthmüller, J. Physical Review B 1996, 54, 11169.
(24) Perdew, J. P.; Wang, Y. Physical Review B 1992, 45, 13244.
(25) Blöchl, P. E. Physical Review B 1994, 50, 17953.
(26) Perdew, J. P.; Wang, Y. Phys. Rev. B 1992, 45, 13244.
(27) Burstein, G. T.; Barnett, C. J.; Kucernak, A. R.; Williams, K. R. Catal. Today 1997, 38, 425.
(28) Hamnett, A. Catal. Today 1997, 38, 445.
(29) Rostrup‐Nielsen, J. R. Catal. Rev. 2004, 46, 247.
(30) Williams, K. R.; Burstein, G. T. Catal. Today 1997, 38, 401.
(31) Akhter, S.; White, J. M. Surf. Sci. 1986, 167, 101.
(32) Chen, J.-J.; Jiang, Z.-C.; Zhou, Y.; Chakraborty, B. R.; Winograd, N. Surf. Sci. 1995, 328, 248.
(33) Francis, S. M.; Corneille, J.; Goodman, D. W.; Bowker, M. Surf. Sci. 1996, 364, 30.
(34) Gibson, K. D.; Dubois, L. H. Surf. Sci. 1990, 233, 59.
(35) Hrbek, J.; DePaola, R. A.; Hoffmann, F. M. J. Chem. Phys. 1984, 84, 2818.
(36) Huberty, J. S.; Madix, R. J. Surf. Sci. 1996, 360, 144.
(37) Kizhakevariam, N.; Stuve, E. M. Surf. Sci. 1993, 286, 246.
(38) Lazaga, M. A.; Wickham, D. T.; Parker, D. H.; Kastanas, G. N.; Koel, B. E. ACS Symp. Ser. 1993, 523, 90.
(39) Outka, D. A.; Madix, R. J. J. Am. Chem. Soc. 1987, 109, 1708.
(40) Sexton, B. A. Surf. Sci. 1981, 102, 271.
(41) Wang, J.; Masel, R. I. J. Am. Chem. Soc. 1991, 113, 5850.
(42) Ammon, C.; Bayer, A.; Held, G.; Richter, B.; Schmidt, T.; Steinrück, H.-P. Surf. Sci. 2002, 507-510, 845.
(43) Morkel, M.; Kaichev, V. V.; Rupprechter, G.; Freund, H.-J.; Prosvirin, I. P.; Bukhtiyarov, V. I. J. Phys. Chem. B 2004, 108, 12955.
(44) Zhang, C. J.; Hu, P. J. Chem. Phys. 2001, 115, 7182.
(45) Borasio, M.; Fuente, O. R. d. l.; Rupprechter, G.; Freund, H.-J. J. Phys. Chem. B 2005, 109, 17791.
(46) Fuente, O. R. g. d. l.; Borasio, M.; Galletto, P.; Rupprechter, G.; Freund, H.-J. Surf. Sci. 2004, 566-568, 740.
(47) Habermehl-Ćwirzeń, K.; Lahtinen, J.; Hautojärvi, P. Surf. Sci. 2005, 598, 128.
(48) Vinod, C. P.; Niemantsverdriet, J. W.; Nieuwenhuys, B. E. Phys. Chem. Chem. Phys. 2005, 7, 1824.
(49) Matolínová, I.; Johánek, V.; Mysliveček, J.; Prince, K. C.; Skála, T.; Škoda, M.; Tsud, N.; Vorokhta, M.; Matolín, V. Surf. Interface Anal. 2011, 43, 1325.
(50) Wang, G.-C.; Zhou, Y.-H.; Nakamura, J. J. Chem. Phys. 2005, 122, 044707.
(51) Antolini, E.; Salgado, J. R. C.; Gonzalez, E. R. Appl. Catal. B: Environ. 2006, 63, 137.
(52) Panja, C.; Saliba, N.; Koel, B. E. Surf. Sci. 1998, 395, 248.
(53) Sheu, B.-R.; Chaturvedi, S.; Strongin, D. R. J. Phys. Chem. 1994, 98, 10258.
(54) Dilara, P. A.; Vohs, J. M. Surf. Sci. 1994, 321, 8.
(55) Kim, K. S.; Barteau, M. A. Surf. Sci. 1989, 223, 13.
(56) Mensch, M. W.; Byrd, C. M.; Cox, D. F. Catal. Today 2003, 85, 279.
(57) Mullins, D. R.; Robbins, M. D.; Zhou, J. Surf. Sci. 2006, 600, 1547.
(58) Houtman, C.; Barteau, M. A. Langmuir 1990, 6, 1558.
(59) Parmeter, J. E.; Xudong, J.; Goodman, D. W. Surf. Sci. 1990, 240, 85.
(60) Solymosi, F.; Berkó, A.; Tarnóczi, T. I. Surf. Sci. 1984, 141, 533.
(61) Choi, Y.; Liu, P. Journal of the American Chemical Society 2009, 131, 13054.
(62) Kapur, N.; Hyun, J.; Shan, B.; Nicholas, J. B.; Cho, K. The Journal of Physical Chemistry C 2010, 114, 10171.
(63) Pushpa, R.; Ghosh, P.; Narasimhan, S.; Gironcoli, S. d. Phys. Rev. B 2009, 79, 165406.
(64) Parmeter, J. E.; Xudong, J.; Goodman, D. W. Surface Science 1990, 240, 85.
(65) Stroppa, A.; Mittendorfer, F.; Andersen, J. N.; Parteder, G.; Allegretti, F.; Surnev, S.; Netzer, F. P. The Journal of Physical Chemistry C 2009, 113, 942.
(66) Zhao, X.; Zhang, R.; Ling, L.; Wang, B. Applied Surface Science 2014, 320, 681.
(67) Huang, S.-C.; Lin, C.-H.; Wang, J. H. J. Phys. Chem. C 2010, 114, 9826.
(68) Lin, C.-H.; Chen, C.-L.; Wang, J.-H. J. Phys. Chem. C 2011, 115, 18582.
(69) Kapur, N.; Hyun, J.; Shan, B.; Nicholas, J. B.; Cho, K. J. Phys. Chem. C 2010, 114, 10171.
(70) F. Fischer, H. T. Brennst.-Chem. 1923, 4, 276.
(71) F. Fischer, H. T. Brennst.-Chem. 1926, 7, 97.
(72) Eilers, J.; Posthuma, S. A.; Sie, S. T. Catalysis Letters 1990, 7, 253.
(73) Knottenbelt, C. Catalysis Today 2002, 71, 437.
(74) Prieto, G.; Martínez, A.; Concepción, P.; Moreno-Tost, R. Journal of Catalysis 2009, 266, 129.
(75) Bezemer, G. L.; Radstake, P. B.; Koot, V.; van Dillen, A. J.; Geus, J. W.; de Jong, K. P. Journal of Catalysis 2006, 237, 291.
(76) Nurunnabi, M.; Murata, K.; Okabe, K.; Inaba, M.; Takahara, I. Catalysis Communications 2007, 8, 1531.
(77) Nurunnabi, M.; Murata, K.; Okabe, K.; Inaba, M.; Takahara, I. Applied Catalysis A: General 2008, 340, 203.
(78) Stenger, H. G.; Satterfield, C. N. Industrial & Engineering Chemistry Process Design and Development 1985, 24, 411.
(79) Miller, D.; Moskovits, M. Journal of the American Chemical Society 1989, 111, 9250.
(80) Kaukasoina, P.; Lindroos, M.; Hu, P.; King, D. A.; Barnes, C. J. Physical Review B 1995, 51, 17063.
(81) Jenkins, S. J.; King, D. A. Journal of the American Chemical Society 2000, 122, 10610.
(82) Görling, A.; Ackermann, L.; Lauber, J.; Knappe, P.; Rösch, N. Surface Science 1993, 286, 26.
(83) Xu, X.-C.; Su, J.; Tian, P.; Fu, D.; Dai, W.; Mao, W.; Yuan, W.-K.; Xu, J.; Han, Y.-F. The Journal of Physical Chemistry C 2015, 119, 216.
(84) Rofer-DePoorter, C. K. Chemical Reviews 1981, 81, 447.
(85) Maitlis, P. M.; Zanotti, V. Chemical Communications 2009, 1619.
(86) Jun Cheng , P. H., Peter Ellis , Sam French , Gordon Kelly , and C. Martin Lok J. Phys. Chem. C 2008, 112, 6082.
(87) Shetty, S.; van Santen, R. A. Catalysis Today 2011, 171, 168.
(88) Wu, M. C.; Goodman, D. W. Journal of the American Chemical Society 1994, 116, 1364.
(89) Kua, J.; Faglioni, F.; William A. Goddard, I. J. Am. Chem. Soc. 2000, 122, 2309.