在本論文中，我們首先利用電子結構計算探討氫原子在鍺表面上的遷移與Diels-Alder環化反應(論文第一篇)。除此之外，我們也利用分子動力學模擬計算鍺-氫延展振動模在鍺表面的弛緩延展速率(論文第二篇)。
論文的第一個部份是關於氫原子在鍺表面的遷移計算，由電子結構計算得到氫原子在氫化鍺(111)表面沿著兩相鄰吸附位置的四條遷移路徑以及在氫化的鍺(100):2x1表面三條遷移路徑包含intradimer、interrow、intrarow遷移方向的遷移位能曲面圖以得到遷移能障。我們的結果顯示，氫原子在鍺(111)表面的遷移路徑以直接經由兩吸附位置的上空遷移最為容易，其遷移能障為36.73 kcal/mol。而其他遷移路徑的遷移能障皆較高，分別為65.28、54.64、65.28 kcal/mol。而相同的方式計算得到氫原子在氫化的矽(111)表面的遷移能障與氫原子在鍺(111)表面遷移的遷移能障結果相似，皆是直接經由兩吸附位置的上空遷移的遷移路徑具有較低的遷移能障，而其他三條遷移路徑則具較高的遷移能障。然而，氫原子在鍺(111)表面具較低遷移能障的遷移路徑，其能障值36.73 kcal/mol比氫原子在矽(111)表面相同遷移路徑低了約5.63 kcal/mol。而氫原子在鍺(100):2x1 表面 intradimer、interrow、intrarow遷移方向的遷移能障分別為24.71、59.24、43.69 kcal/mol，此結果顯示氫原子在鍺(100)表面之遷移是不等向性，此性質與在氫化的矽、鑽石(100):2x1表面不同。除此之外，根據我們結果所得到不同溫度下的擴散係數以及與矽、鑽石表面的比較也一併討論之。
論文的第二部份則解釋鍺(100)表面的Diels-Alder環化反應，由於乙炔分子的吸附是最簡單的系統，因此先探討乙炔分子吸附在鍺(100)表面四個吸附位置的穩定性。而電子結構計算也得到1,3-丁二烯在重構鍺(100):2x1表面環化反應的[4+2]與[2+2]產物的穩定性。由於環張力的影響，[4+2]產物比[2+2]產物能量穩定約16.98 kcal/mol，此結果與矽、鑽石(100)表面的環化反應相同。除此之外，我們也將1,3-丁二烯的2,3號碳原子上的氫原子取代為推、拉電子基以檢視推、拉電子基是否會改變鍺(100):2x1表面環化反應的熱穩定性。而我們的結果則顯示，推、拉電子基並不明顯影響重構鍺(100):2x1環化反應的熱穩定性。
在論文的第三部份，我們則利用根據Bloch-Redfield理論的古典分子動力學模擬來計算氫原子的第一振動激發態在氫化的鍺(111)表面的振動能量弛緩速率。在室溫下，鍺-氫的延展振動模在氫/鍺(111)表面的生活期為20000 ns，比矽-氫、碳-氫的延展振動模在氫/矽(111)、氫/鑽石(111)表面的生活期為1.7、0.03 ns分別大了四個、六個次方。我們也計算室溫下鍺-氘、鍺-氚在氘、氚/鍺(111)表面的生活期，其在室溫下的生活期分別為400及30 ns。除此之外，熱效應以及鍺-鍺-氫的彎曲振動頻率對生活期的影響也一併討論之，並比較此部份的結果與鑽石、矽(111)表面結果的異同。

In the present thesis, we examined 1) hydrogen diffusion and 2) a Diels-Alder reaction on germanium surfaces using the first principle calculation. In addition, a molecular dynamics simulation was carried out to examine the vibrational relaxation of hydrogen stretching modes on germanium surface.
For the first topic, hydrogen diffusion, potential energy curves of hydrogen migration along four paths between on-top adsorption sites on a hydrogen-covered germanium (111) surface, and the three paths including intradimer、interrow and intrarow migration paths on a hydrogen-covered germanium (100):2x1 surface, were calculated. For germanium (111) surface, the calculations gave an energy barrier height of 36.73 kcal/mol for the direct path between two on-top adsorption sites, and 65.28, 54.64, 65.28 kcal/mol for the other three paths traveling via minor adsorption sites. These results suggest that hydrogen migrate along direct paths between on-top adsorption sites on this surface. The results of the low barrier for direct path and high barriers for the other three paths are similar to the corresponding silicon (111) surface. The calculated low barrier of 36.73 kcal/mol for direct path is lower than the silicon (111) surface by 5.63 kcal/mol. For the germanium (100) surface, the calculations gave energy barrier heights of 24.71, 59.24, and 43.69 kcal/mol for the intradimer, interrow, and intrarow migration paths, respectively. These results also show that hydrogen migrations on the hydrogen-covered germanium (100) surface is anisotropic, which is different from the results on the silicon and diamond (100) surfaces. The thermal effect in diffusion constant based on the present calculated results and a comparison with silicon and diamond surfaces will be discussed.
In the second topic of examining a Diels-Alder reaction on germanium (100) surface, the stability of four adsorption sites for acetylene molecule were examined and compared first. For the Diels-Alder reaction, the energies of the [4+2] and [2+2] cycloaddition reactions between 1,3-butadiene and the reconstructed germanium (100) surface were calculated. The [4+2] product is energetically favored over the [2+2] product by 16.98 kcal/mol due to ring strain. This result is similar to the findings for the silicon and diamond (100):2x1 surfaces. In addition, the hydrogen atoms on the 2 and 3 carbon atoms were substituted with electron-donating and electron-withdrawing groups for investigation of how the substitutions alter the stability of the Diels-Alder reactions on the germanium (100) surface. It was found that the substitutions of both electron-donating and electron-withdrawing groups did not change the stability significantly. Physical reasons for this result is discussed.
Finally, in the last topic, we report the calculated lifetimes of the first hydrogen stretching excited state on a hydrogen-covered germanium (111) surface using molecular dynamics simulation based on the Bloch-Redfield theory. The lifetime was found to be 20000 nanoseconds at room temperature, four and six orders longer than the hydrogen stretches on a hydrogen-covered silicon and diamond (111) surfaces, respectively. In addition, the calculations for the Ge-D and Ge-T stretches gave lifetimes of 400 and 30 nanoseconds, respectively, at room temperature. The thermal effect, and an effect of the Ge-Ge-H bending frequency in the calculated lifetimes are discussed, and a comparison with silicon and diamond (111) surfaces is also discussed.

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