本論文以密度泛函理論(Density Functional Theory，DFT)中的B3LYP方法，研究Ge11與Ge12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，來做最佳化及相對穩定性之討論計算研究。一般而言，Be是Be、Mg、Ca三者中最能和Ge形成共價鍵的元素。其結構最佳化//單點能量的運算法為B3LYP/6-31G*//B3LYP/6-311++G(3df)，此方法也用於尋找過度態上。在各複合團簇中Be的賀須菲爾電荷(HC)是極小的正值，甚至可能是負值Be-Ge的梅爾鍵級(MBO)較大，金屬與Ge之間的共價性隨鹼土族原子序增加而遞減。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。在CaGe11和CaGe12中，Ca-Ge的MBO比對應的Be-Ge和Mg-Ge小，但吸附能(Ead)卻比MgGe11、MgGe12高，因為MBO低估了離子性，而這離子性顯示在Ca比其他金屬具有較明顯之正電荷。
比較同n的AEM-Gen複合團簇會發現，結合能(BE)並未隨金屬不同而有太明顯差異，這顯示結合能的主要貢獻來自母團簇的穩定度而非鹼土金屬的吸附，其中Ge12是比Ge11穩定的母團簇。同樣的情形，當金屬改變時，吸附能確有明顯的改變，顯示Be還是最佳的吸附原子，而Mg是最差的吸附原子，因為Mg-Ge的共價性比Be-Ge差，離子性也比Ca-Ge差，由最穩定的BeGe12吸附前趨物並最穩定的Be@Ge12經過一個過渡狀態。
We have used the B3LYP of density functional theory (DFT) and a simple basis set 6-31G* to optimize the structures of the hybrid clusters formed by adsorptions of alkaline earth metal(AEM) on Ge11 and Ge12 . Generally, Be has the best capability of forming covalent bonds with
Ge among Be、Mg、Ca. Geometric relaxations//single point energies were carried out at the B3LYP/6-31G*//B3LYP/6-311++G(3df) level; the same method was applied to transition-state search.Our results showed that Be is commonly hypervalent with MTV > 3, higher than the expected value 2, especially in those endohedrons. Hirshfeld charges(HCs) and molecular orbitals indicated that back-donation from hosts facilitated such hypervalency.
In CaGe11 and CaGe12 ,Ca-Ge bonds have small Mayer bond orders(MBO) but metal adsorption energies (Ead) are higher than in MgGe11 and MgGe12 because MBOs underestimate the bond ionicities, which are revealed by the obviously positive HCs of Ca atoms.
The binding energies (BE) in MGen are comparable with different M and the same n , meaning the contribution of metal adsorption is not significant to the complete dissociation, but the greater stability of Ge12 than Ge11 . However, Eads in MGen (also different M and same n) imply that Be adsorbs strongly on Gen, then in Ca, and then in Mg. Mg-Ge has less covalency than Be-Ge and less iconicity than Ca-Ge that make Mg the weakest adsorbate.
