本研究以Density Functional Theory (DFT)中的B3LYP方法，搭配較簡單的6-31G*基底函數，做最佳化及相對穩定性之討論研究。一般而言，Be是Be、Mg、Ca三者中最能和Ge形成共價鍵的元素。這反應在複合團簇中Be的賀須菲爾電荷(Hirshfield charge, HC)是極小的正值，還有Be-Ge的梅爾鍵級(Mayer bond order, 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CaGe9和CaGe10中，Ca-Ge的MBO比對應的Be-Ge和Mg-Ge小，但吸附能(Ead)卻比MgGe9、MgGe10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(Alkaline Earth Metal-Gen)複合團簇會發現，結合能(BE)並未隨金屬不同而有明顯差異，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Ge10是比Ge9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。團簇中金屬的HC與其MTV大致程相反趨勢，除了含Ca的團簇以外，含Be及Mg的基態團簇的ΔEg與Ead和BE大致呈現相似的變化走向。
We have used the B3LYP 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 Ge9 and Ge10. Generally, Be has the best capability of forming covalent bonds with Ge among Be、Mg、Ca. Such covalency is reflected in the trivially positive Hirshfeld charges (Hirshfield charge, HC) of Be atoms and large Mayer bond order (Mayer bond order, MBO) of Be-Ge bonds. The covalency decreases as metal atoms move down in the AEM group. In CaGe9 and CaGe10 , Ca-Ge bonds have small MBO but their metal adsorption energies (Ead) are higher than in MgGe9 and MgGe10 because MBOs underestimate the bond ionicity, which are revealed by the obviously positive HCs of Ca atoms. The binding energies (BE) in MGen are comparable with different M for the same n, meaning the contribution of metal adsorption is not significant to the complete dissociation into separated atoms and it is mainly due to the greater stability of Ge10 than Ge9 . 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. The trends of metal HCs and MTVs are opposite with each other. Beside CaGe9 and CaGe10, the ΔEg, Ead, and BE of ground state BeGe9,10 and MgGe9,10 vary in the similar trend.
