我們重溫了能量谷跳躍法，這個一直以來被發展用來尋找分子或金屬叢集的最低能量結構的演算法。基於這個優秀的演算法基礎上, Yen and Lai (Ref. 33) 提出了一個新的構形最佳化方法並用來研究不同構形之間如何轉換。新方法針對了共價鍵的特性在舊方法上做了一些修正: (1) 我們限縮了構形可以被搜尋的空間大小 。(2) 我們把cut-and-splice基因運算子包含進去。改良之後的方法可以更適切的運用在共價鍵系統如碳叢集上因為可以更準確的描述離子和價電子間的偶合交互作用。內文針對此方法會做更詳盡的介紹並應用在四種不同的經驗能量勢上。我們發現碳叢集(Cn, n=3-60) 在構形上會有一連串不同的變化。從小到大分別為: 直線形狀-> 單環 -> 多環 (類平面的碗狀結構) ->籠狀(3D富勒烯)。不同能量勢預測的結果會有些許構形上的差異。 新方法在預測C60 和 C72 上比僅用Deaven and Ho 提出的cut-and-splice [ Phys. Rev. Lett. 75, 288 (1995) ] 更有效率。此外，我們發現TEA勢 [ Phys. Rev. B 71, 035211 (2005) ] 的結果能夠預測2維石墨烯( Cn, n=6,10,13,16,19,22,24,27) 的形成過程。其他經驗勢並沒有發現類似結果。在第一代Brenner 經驗勢部分, 其預測結果和Cai et al.[J. Mol. Struct. (theochem), 678, 113 (2004) ] 非常一致。第二代Brenner勢的結果則有非常規則的結構演化。和同樣使用二代Brenner勢的Kosimov等人 [Phys. Rev. B 78, 235433]比較，我們的結果更為定量。文章最後就一二代的Brenner勢的結果差異分析了其物理上的意涵為何。;Abstract
The basin hopping optimization algorithm previously developed for finding the lowest energy structures of clusters, both nonmetallic and metallic, is revisited. This state-of-the-art technique is extended by our group (Ref. 33) to carbon clusters studying their varied forms of structural transitions, changing from one cluster geometry to another. This modified optimization algorithm very recently proposed by Yen and Lai(Ref. 33) closely parallels that of the basin hopping method [D. J. Wales and J.P. Doye, J. Phys. Chem. A 101,5111 (1997)], but is discreetly designed to take into account the unique bond-order interactions of the carbon cluster through defining a spatial volume within which its lowest energy structure is searched and through introducing a cut-and-splice genetic operator into the basin hopping technique. The present modified basin hopping method is characteristically distinguishable from the nonmetallic and metallic clusters, technically more thorough in dealing the couplings of valence electrons with ions, and hence is more appropriate for carbon clusters. We discuss in this work the basis of success of the present modified basin hopping technique, and tested it by calculating the lowest energy structures of carbon clusters using four different empirical potentials. It is found here that the cluster Cn, n=3-60, undergoes a series of interesting structural transitions, i.e. its structural geometry changes, in sequence of increasing cluster size n, as linear → single ring → multi rings or quasi-two dimensional bowl-like → cage-like or three dimensional fullerene-like structure, depending on the empirical potential employed in optimization. The modified basin hopping algorithm (Ref. 33) is efficient when it is checked against the popular cut-and-splice technique of Deaven and Ho [Phys. Rev. Lett. 75, 288 (1995)] for two well-known stable carbon clusters of larger size, i.e.C60 and C72. An interesting prediction of one of the empirical potentials, due to Erhart and Albe [Phys. Rev. B71, 035211 (2005)], is its capturing of the development of two-dimensional graphene structure, i.e. the evolution of Cn for n=6, 10, 13, 16, 19, 22, 24, 27 since no such structural sequence is seen in the other three empirical potentials. Our optimization algorithm that combines with the first generation of Brenner potential yields Cn compares very well with those reported by Cai et al. [J. Mol. Struct. (Theochem) 678, 113 (2004)]. For the second generation of Brenner potential, our calculated Cns show regularity in its structural evolution. These Cn
results are more quantitatively behaved than the only similar works by Kosimov et al. [Phys. Rev. B 78, 235433 (2008); Phys. Rev. B 81, 195414 (2010)]. Finally, we draw physical implications from our comparison of Cn obtained from using the first and second generations of Brenner potentials. Keywords: carbon cluster; optimization algorithm; topological transition; fullerene.
Corresponding author: email@example.com