| 摘要: | 在本論文，主要研究Si13與Si14團簇與鹼土族金屬(AEM =Be、Mg、Ca)結合後的構型與鍵結情況，包含其吸附與鑲嵌狀態。BeSi14，MgSi13、14，CaSi13、14並沒有發現穩定的鑲嵌狀態(AEM@Si13、14)。所以在此也只有進行由最穩定的BeSi13吸附狀態轉化為最穩定之Be@Si13。其結構最佳化//單點能量的運算分別利用B3LYP/6-311G*//B3LYP/6-311++G(3df)，此為常見的加快其運算速度的方式；此方法也用於尋找過度態上。之後利用賀須費爾電荷(HCs)計算團簇裡的各原子的帶電性，梅爾鍵級(MBOs)計算其鍵結強度，Mayer total valences (MTVs)計算各原子的鍵結容量。在研究過程中發現含有Be的團簇之MTV值常為高過3，大於理論值2，而且在鑲嵌況態下還會更高，再對照HCs與分子軌域後發現此原因可能為回饋鍵結所造成。而在MgSi13、14和CaSi13、14中共價特性減弱，而且Ca-Si鍵結較Mg-Si鍵結更傾向於離子性鍵結。其結果顯示當原子總數相同時BeSi13、14具有最高的結合能而MgSi13、14則為最低，CaSi13、14則介於中間。離子性的增加更能穩定CaSi13、14一如BeSi13、14中的共價性，甚至導致其結合能有時可以趨近於BeSi13、14。最後也將最穩定之BeSi13轉變為最穩定Be@Si13的過程推導而出。
In this study, we investigated the structures and bonding properties of Si13 and Si14 based early alkaline earth metal (AEM) binary clusters (AEM = Be, Mg, Ca), including their exohedral and endohedral isomers. BeSi14, MgSi13,14 and CaSi13,14 were found not to have stable caged structures (AEM@Si13,14). Therefore, we also only searched for the conversion pathways from the most stable BeSi13 adsorptive precursor to the Be@Si13 at the global minimum of potential energy surface. Geometric relaxations//single point energies were carried out at the B3LYP/6-311G*//B3LYP/6-311++G(3df) level, which is a common strategy to speed up optimizations while allow us to obtain finer cluster energies; the same method was applied to transition-state search. Hirshfeld charges (HCs) were to show atomic charge partition in clusters; Mayer bond orders (MBOs) were employed to analyze bond strength and Mayer total valences (MTVs) were to represent the bonding capacity of an atom.Our results showed that Be is commonly hypervalent with MTV > 3, higher than the expected value 2, especially in those endohedrons. HCs and molecular orbitals indicated that back-donation from hosts facilitated such hypervalency.
MgSi13,14 and CaSi13,14 have less covalent characteristic, while Ca-Si bonds are more ionic than Mg-Si. The consequence was that BeSi13,14 have the highest binding energies and MgSi13,14 have the lowest, CaSi13,14 are in between when the total numbers of atoms are same. The ionicity in CaSi13,14 must also contributes to cluster stability as the covalency in BeSi13,14, and sometime can give a binding energy pretty close to that of BeSi13,14. Finally, we also used the QST3 and intrinsic reacrion coordinate methods to locate and confirm the transition state between the most stable adsorptive BeSi13 precursor and the most stable encaged Be@Si13 product. |
