利用元始計算中Hartree-Fock (HF)的level來研究鹼金屬離子嵌入至Benzene、polycyclic aromatic hydrocarbons (PAH)、C60和CNT這些分子。在M+--benzene這系統中其距離與HF的相對能量關係其結果呈現出：金屬離子Li+、Na+、K+當其在距離分別為2.0、2.4、2.8 Å處，其HF值會有一個最小量，且其嵌入苯環所需克服的能障分別為294、940及2194 kcal/mol。相同的研究在金屬離子嵌入至PAH、C60和CNT這些系統時，所得到的結果亦是大同小異。
　　為了比較鋰離子嵌入不同尺寸的環，因此對五圓環、七圓環和八圓環的嵌入來進行研究，結果發現其主要的差別在於：隨著環的尺寸越大，鋰離子嵌入環所需克服的能障越小，其所能佔據最鄰近環的位置取決於環的尺寸而定，約距離環1.8~2.0Å之間。
　　上述研究若在幾何結構最佳化的條件下運算，所形成的Cation-π complex，其束縛能會隨陽離子半徑越大而越小，M+-benzene其結果為41 kcal/mol(Li)、27 kcal/mol(Na)、17 kcal/mol(K)，M+-PAH也有相同的傾向。為了得到更可靠的結果，因此在有條件限制Optimized的條件下研究距離與相對能量的關係。這方法讓我們能藉由結果分析環的擴張程度。在M+-benzene其環上的C-C鍵長擴張了9.7 %(Li)、23.7 %(Na)，在M+-PAH其其環上的C-C鍵長則是擴張了9.7 %(Li)。

　　Ab initio calculations at Hartree-Fock (HF) level have been performed on benzene, polycyclic aromatic hydrocarbons (PAH), C60 and carbon nanotubes (CNT) intercalated by alkaline metal ions. HF energies of the M+--benzene systems calculated at various distances reveal a minimum near 2.0, 2.4 and 2.8 Å for M= Li, Na and K, respectively. The energy barriers for the metal ions to pass through the benzene ring are respectively 294, 940 and 2194 kcal/mol. The same studies carried out on PAH, C60 and CNT systems present quite similar results including the energy-distance relation, location of minimum energy and energy barriers.

　　For comparison purpose, extended studies have been conducted on five-, seven-, and eight-member aromatic rings. The major difference arising from ring sizes is found for the energy barriers, i.e. this quantity decreases significantly with increasing sizes. The preferred space for metal ion intercalation is in the range, 1.8~2.0Å, depending on the sizes of the ring under this study.

　　The above-stated cation-complexes have then been recalculated by allowing full optimization for benzene and PAH. The calculated binding energies decrease in the trend of the sizes of metal ions in M+--benzene: 41 kcal/mol(Li), 27 kcal/mol(Na), 17 kcal/mol(K). The same trend has been found for the M+--PAH series. In order to get more reliable results, such as energy barriers, the geometry optimization procedure is recommended as long as it is feasible computationally. More importantly it allows us to calculate the extents of the ring expansion due to intercalation of these ions. For M+-benzene, it is found that the C-C bond is lengthened by 9.7 and 23.7 % for M=Li and Na, respectively. In the Li+-PAH system, a lengthening of C-C bond by 9.3% is found.

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