The electronic structures of N-heterocyclic carbenes (NHC) imidazolinylidene, thiazolinylidene, imidazolylidene, thiazolylidene, and 1,2,4-triazolylidene and their complexes with cuprous halides (CuX, X = Cl, Br, I) were investigated theoretically at the B3LYP/def2-SVP level. In contrast to other NHCs, imidazolylidene and 1,2,4-triazolylidene do not dimerize owing to the negligible coefficient of the vacant p-orbital at the carbene centre in their respective LUMOs. This is further supported by their greater thermodynamic and kinetic stabilities revealed by greater activation free energies and smaller standard free energies for their dimerization. Second-order perturbation interactions in the natural bond orbital (NBO) analysis of the NHCs indicate that six π electrons are delocalized in imidazolylidene, thiazolylidene, and 1,2,4-triazolylidene, conferring aromatic character and thereby enhancing their thermodynamic stability. NBO analysis reveals the existence of effective back bonding from a d orbital of Cu to the NHC, increasing the Wiberg bond index of the C–Cu bond to ~1.5. Owing to the large electronic chemical potential (μ) and high nucleophilicity indices, NHCs are able to transfer their electron density effectively to the cuprous halides having low μ values and high electrophilicity indices to yield stable NHC–Cu^I complexes. Large values of the Fukui function f(r) at the carbene centre of the NHCs and Cu atom of the NHC–Cu^I complexes indicate their softness. Imidazolylidene was found to be the softest, rationalizing wide use of this class of NHCs as ligands. The coordination of the NHCs to cuprous halides is either barrierless or has a very low activation free energy barrier. In the A³ reaction wherein NHC–Cu(I) complexes are used as catalyst, the reaction of NHC–CuI with phenylacetylene changes the latter into acetylide accompanied by raising the energy level of its HOMO considerably compared with the level of the uncomplexed alkyne, making its reaction with benzaldehyde barrierless.

在B3LYP上理论上研究了N-杂环卡宾（NHC）咪唑啉基亚基，噻唑啉基，咪唑基亚基，噻唑基和1,2,4-三唑基亚烷基及其与卤化亚铜（CuX，X = Cl，Br，I）的配合物的电子结构/ def2-SVP级别。与其他NHC相比，由于在各自LUMO中卡宾中心的空位p轨道系数可忽略不计，咪唑基亚烷基和1,2,4-三唑基亚烷基不二聚。其更大的热力学和动力学稳定性进一步证明了这一点，所述更大的热力学和动力学稳定性由用于它们的二聚作用的更大的活化自由能和较小的标准自由能揭示。NHC的自然键轨道（NBO）分析中的二级扰动相互作用表明，六个π电子在咪唑基，噻唑基和1,2,4-三唑基中离域，赋予芳族特性，从而增强其热力学稳定性。NBO分析揭示了从铜的轨道到NHC的有效反向键的存在，从而将C-Cu键的Wiberg键指数提高到1.5。由于大的电子化学势（μ）和高的亲核指数，NHC能够有效地将电子密度转移到具有低μ值和高亲电指数的卤化亚铜中，从而产生稳定的NHC-Cu^我很复杂。在NHC的卡宾中心和NHC-Cu ^I络合物的Cu原子上，较大的Fukui函数f（r）表示其柔软性。发现咪唑基亚烷基是最软的，合理地广泛使用了这类NHC作为配体。NHC与卤化亚铜的配位是无障碍的，或者具有非常低的无活化能垒。在使用NHC-Cu（I）配合物作为催化剂的A ³反应中，NHC-CuI与苯基乙炔的反应将后者转变为乙炔，并与未配合的炔烃相比大大提高了其HOMO的能级，使其与苯甲醛的反应无障碍。