本論文分為兩大主題: 一. 探討大氣中含氮的自由基。從石化燃料燃燒產生的氮氧化物由於它們具有毒性，是大氣污染物，所以相當令人感到關注，我們藉由理論計算的方法來探討其可能的反應機制，以理解燃燒產生的空氣污染。共分為兩個單元進行討論:
第一部分: 探討NCN 和NO, NS的反應機制，此反應分為四個不同路徑，其可能的產物為N2O/N2S + CN, N2 + NCO/NCS, N2 + CNO/CNS, CNN + NO/NS，分別表示為p1/p1s 到 p4/p4s。在NCN + NO的反應中，所得到的加合物，只有nitroso 加合物NCNNO的能量低於反應物，約22 kcal/mol，和實驗上觀察的一致，反應藉由加合物NCNNO快速的轉移成產物。在NS的反應中，thionitroso NCNNS和thiazyl NCNSN加合物都比反應物穩定，分別約為43和29 kcal/mol。其中五員環-NCNNS中間物當橋樑以連結此兩個加合物，而五員環-NCNNS中間物亦比反應物穩定，約為36 kcal/mol。在NS的位能曲面圖中，除了產生p4s的路徑外，所有的能障皆為負值，但在 NO中，則全為正數。產生p1 (N2 O+ CN) 的能障最低為3.8 kcal/mol，而生成p2 (N2 + NCO) 和p2s (N2 + NCS) 則是放熱最多的路徑，分別為100.94 和107.38 kcal/mol。
第二部分: 探討NCX (X=O, S) 和C2H2的反應機制，此反應分為五個不同路徑，其可能的產物為HCCO/HCCS+ HCN, HCCO/HCCS + HNC, HNCO/HNCS + C2H, HOCN/HSCN + C2H, HC2NCO/HC2NCS + H，分別表示為P1/P1s到P5/P5s。直接氫抓取反應有利於產生HNCO，而不是HOCN，但是在NCS反應，卻是HSCN比HNCS容易生成。有兩種不同的路徑產生中間物 oxazole/thiazole，但是兩種不同的路徑能障的高低在NCO和NCS反應卻相反。在高溫下，HNCO/HSCN + C2H的路徑，可能有利於進行。其它的產物路徑和實驗預測的相符合，先形成短生命週期的加合物 (adduct) NCO/NCS-C2H2，然後再快速的轉變成產物。

二. 研究有機分子成環的反應。此反應在有機合成或生物學上皆扮演重要的角色，我們藉由理論計算的方法來探討其可能的反應機制，及取代基改變對反應機制的影響。共分為兩個單元進行討論:
第一部分: 研究自由基NCO + RCCH (R= H, CH3, F, Cl, CN)的[3+2] 環加成反應，產生五員雜環oxazole。此環加成反應為異步(asynchronous)形成兩個鍵的機制，當乙炔上的其中一個氫替換成R基(R=CH3, F, Cl, CN)，反應便有立體選擇性(regioselectivity)的問題。我們使用Fukui functions和HSAB的理論來解釋不同取代基的位置選擇性，所得到的結果和位能曲面圖上的能障相符合，除了F外。反應第一步為NCO上的N原子攻擊RCCH上未取代的碳原子，然後O原子再和另一個碳原子環起來，第一步能障 (uts1) 的大小為H > F > CN > Cl >CH3 > OH > NH2 ，第二步能障 (uts2) 的大小為H > Cl > CH3 > CN > OH > F > NH2。

第二部分: Enyne-allenes在allene末端以alkenyl取代(R2=CH2CH-)的環化反應，原則上具有四種可能的位置選擇反應。第一種環化模式—藉由C2-C6 鍵的生成，產生, π-雙自由基的五員環中間物2 (Scheme 1, Path A)。第二種環化模式為已知的Myers-Saito反應—藉由C2-C7新鍵的生成，產生, π-雙自由基的六員環中間物3 (Scheme 1, Path C)。第三種模式為分子內的Diels-Alder [4+2]環加成反應，形成雙環化合物4 (Scheme 1, Path B)。最後一種模式為分子內的[2+2]環加成反應，經由雙自由基(2)形成雙環化合物5 (Scheme 1, Path D)。取代基效應對enyne-allene是有影響的，不同取代基對以上所敘述的四種模式反應，分別以不同程度降低或升高能障，而有利於某種模式的進行，分別做詳細的討論。

There are two major themes in this thesis.
I. The study of nitrogen-containing radicals in the gas phase. It is of great interest because of the role these species play in the formation and removal of NOx pollutants in combustion processes. We report the possible reaction pathways of nitrogen-containing radicals by a theoretical method. There are two major paths in the subject and are given as follow.
Part 1: Quantum-chemical calculations on the mechanisms of reaction of NCN with NO and NS. Possible mechanisms were classified according to four pathways yielding products in four possible groups: N2O/N2S + CN, N2 + NCO/NCS, N2 + CNO/CNS, and CNN + NO/NS, labeled in order from p1/p1s to p4/p4s. The local structures, transition structures and potential-energy surfaces with respect to the reaction coordinates are calculated, and the barriers are compared. In the reaction NCN + NO formation of only the nitroso adduct NCNNO is predicted to have an energy lower than that of reactants, by 21.89 kcal/mol; that adduct undergoes rapid transformation into the products, in agreement with experimental observation. For the NS counterpart, both thionitroso NCNNS and thiazyl NCNSN adducts have energies much lower than those of reactants, by 43 and 29 kcal/mol, respectively, and a five-membered-ring NCNNS (having energy lower than the reactants by 36 kcal/mol) acts as a bridge in connecting these two adducts. The net energy barriers leading to product channels other than p4s are negative for the NS reaction, whereas those for the NO analogue are all positive. The channel leading to p1 (N2O + CN) has the lowest energy (3.81 kcal/mol), whereas the channel leading to p2 (N2+ NCO), or p2s (N2 + NCS) is the most exothermic (100.94 or 107.38 kcal/mol, respectively).
Part 2: The reaction mechanisms for NCX (X = O, S) with C2H2 . The possible reaction mechanisms of NCO + C2H2 investigated in this study were categorized into five different pathways leading to the five possible final products: HCCO + HCN, HCCO + HNC, HNCO + C2H, HONC + C2H, and HC2NCO + H, labeled in order from P1 to P5, respectively. Similar calculations were also carried out for the NCS counterpart, and the energy barriers as well as the products were compared. Direct hydrogen abstraction is favored in the formation of HNCO instead of HOCN. In contrast, it is much easier to form HSCN rather than HNCS. There are two different paths for the oxazole/thiazole formation as an intermediate, and the order of energy barriers of these two paths is opposite in NCO and NCS. The product channel of HNCO/ HSCN + C2H may be kinetically favored at higher temperature. Other product channels are consistent with the experimental prediction of the formation of initial short-lifetime NCO/NCS-C2H2 adducts which then undergo rapid transformation into the products.

II. The study of the cyclizations and cycloadditions of some organic reaction. Since they are important in synthesis and in biology. We investigated these reactions by a theoretical method. There are also two sections regarding to the subject studied and are rendered below.
Section 1: The [3 + 2] cycloaddition reaction of NCO + RCCH (R = H, CH3, F, Cl, CN), producing a five-membered ring heterocyclic oxazole. An asynchronous two-bond formation mechanism was found, which led to a certain regioselectivity in the products when the substituted alkyne was used as a reactant. The preferable reactive sites of RCCH in various substituents are calculated by employing the Fukui functions and HSAB theory, and the results are in good agreement (except R = F) with the calculated energy barriers of the transition states in the potential energy surfaces. The N atom of NCO attacks the unsubstituted carbon atom of RCCH first, followed by the ring closure of the O atom with the other carbon atom to form the substituted oxazole. The order of the calculated first transition barriers (uts1) in the substituted alkynes (RCCH) is R = H > F > CN > Cl > CH3, and that for the second transition barriers (uts2), R = H > CH3 > CN > Cl > F. The reason for the decreased transition barriers of the substituted alkynes is analyzed.
Section 2: The cyclization of enyne-allenes incorporating alkenyl substituents (R1 = CH2CH- ) at the allene terminus which in principle possess four possible regioalternatives. One mode of cyclization is a formation of five-membered ring between C2 and C6 on a biradical pathway yielding the , π-biradical 2(Scheme 1, path A). The second mode, known as the Myers-Saito reaction, forms the new bond between C2 and C7 leading to a , π-biradical 3(Scheme 1, path C). The third mode is novel intramolecular formal Diels-Alder cycloaddition leading to bicyclic compound 4 (Scheme 1, path B). The last mode is intermolecular [2+2] cycloaddition via diradical (2) forming a bicyclic compound 5 (Scheme 1, path D). Subsituent effect are significant for the enyne-allenes. For R=CH3, t-Bu, the barrier of the C2-C7 cyclization increases more than the C2-C6 cyclization because of the steric effect. For R=Ph, NH2, O-, NO2, CN, the barrier of the C2-C6 cyclization decreases and becomes lower than the C2-C7 cyclization because of the mesomeric effect. It is noted that when R=NH2 and O-, there will be no one-step [4+2] transition state, instead, the [2+2] cycloaddition becomes possible. Solvent effect plays an important role in the [4+2] cycloaddition reaction, and the stronger polarity of the solvent such as DMSO or H2O the larger the influence to the reaction barriers.

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