本論文以理論計算的方法，探討四到六員的環狀nitrenium ions及其對等結構之等電子系統(isoelectronic systems)：環狀的carbenes和環狀的borenide anions，在不同自旋重態(multiplicity)之下，部份結構及能量上的特性，同時也計算中心原子置換為第三週期的系統(Al, Si, P)，觀察其變化情形。主要的計算方法為密度泛函數理論當中的B3LYP方法，最高的basis set層級則是6-311+G(d,p)，此外部份關於電子軌域混成組態的細節，則以NBO program輔助取得。
計算的結果，在結構方面，可看到環狀系統雖然受到部份限制，但仍舊維持著和開環系統相同的特性，也就是於三重態之下的結構具有較大的中心鍵角(指的是carbenes系統當中，methylenic carbon和相鄰兩原子所形成之夾角)。三個不同族的系列，大致上都具有相近的結構特性，但在飽和的五員環系列，則有些微特殊的區別。
而在能量方面，我們主要觀察到兩個較為有趣的現象：一是無論在飽和系列或者是在不飽和的系列當中，中心原子為第三週期的系統，均呈現較大的singlet-triplet energy differences；二是在不飽和的系統之下，四到六員環的singlet-triplet energy differences呈現系統性的變化趨勢，環越大的系統會相對呈現越小的singlet-triplet energy differences，但在飽和系統當中，則出現較不一樣的趨勢，是在五員環的時候，呈現出最大的singlet-triplet energy differences。

In this thesis, we studied the geometric and energetic properties of 4-6 membered cyclic nitrenium ions and the isoelectronic systems (cyclic car-benes and cyclic borenide anions) by theoretical calculation methods. In addition, we substituted the central atoms for the 3rd period elements (Al, Si, P). We performed our calculation by using the B3LYP/6-311+G(d,p) method. The detailed information about electronic properties and the hybrid-dizations of the systems were obtained from NBO calculations.

The results of our work can be discussed in two major ways: geometric and energetic points of view. Geometrically, we find the cyclic systems maintain geometric characteristics similar to the open-chain systems. The central angles (the angle between the neighboring atoms beside the methylenic carbon) in the geometries at triplet state are always larger. Roughly speaking, the important geometric characteristics of each ring size do not change a lot with different central atoms in studied groups (IIIA, IVA, VA group). But, we find that there are certain subtle and interesting differences in saturated 5-membered ring systems (with central atoms in different groups).

Energetically, we find two interesting points about energetic cha-racteristics. The first, the systems with central atoms of 3rd period (Al, Si, P) always present larger singlet-triplet energy differences in both saturated and unsaturated series. The second, the singlet-triplet energy differences change systematically from 4 to 6 membered ring systems in unsaturated series. The larger ring systems present smaller singlet-triplet energy differences. But it’s somewhat different in saturated series. In saturated series, it presents the largest singlet-triplet energy differences in a 5-membered ring system with all kinds of central atoms. We will discuss all the issues stated above.

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