在最近純金屬叢集最低能量結構最佳化的計算中，我們採用泛密度函數緊密捆綁（DFTB） 理論計算能量函數和修改式盆地跳槽 （MBH） 演算法來尋找全域最小能量值。在此 DFTB/MBH 最佳化方法預測下，發現有多個鑄幣金屬叢集，其最低能量的幾何形狀都具有對掌性，亦即前述每個金屬叢集皆有相同的能量值，但卻有兩種幾何形狀呈現出鏡像對稱性，雖是互為鏡像，卻無法完全重疊。此兩個不重疊鏡像叢集我們稱之為鏡像異構物 (enantiomers)。這個源自DFT架構下的DFTB理論，這次計算所偶然發現的左右鏡像異構物在物理學中是相當罕見的。這個意外的發現也促使我們想深一層去探究鏡像異構物是如何從一個鏡像異構物過渡到另一個鏡像異構物的基本機制。也是在這樣欲瞭解後者的動態行為的前提下，我們採用了等溫布朗型分子動力學電腦模擬（MD），來研究一個鏡像異構物，比如左，是如何轉移到右鏡像異構物，並希望從電腦模擬生成和記錄的原子配置推斷出鏡像異構物轉換的機制。為了更深入研究鏡像異構物的動態行為，我們專注於兩個有效分辨左右鏡像異構物的參數。第一個參數是超快形狀識別相似性指數(ultrafast shape recognition index) ζ，而第二個參數是豪斯多夫對掌性測量（HCM）。在本計劃中，我們將展示如何利用 ζ-HCM 兩參數，詳細介紹怎樣精巧地從MD資料中先快速搜尋亞穩態對稱結構，並從連同左右鏡像異構物推斷出一個反應座標。所得之反應座標可以提供有趣的資訊如鏡像異構物轉換速率、發生頻率、鏡像異構物轉換機制與原子之間的關係等。除了將這種新方法應用於仍在進行中的金、銀鏡像異構物叢集，我們也將研究鑄幣銅金屬叢集，因銅金屬叢集現在文獻上已經有新的DFTB參數化參數。 ;In very recent calculations of lowest-energy structural conformations of pure metallic clusters, using the density functional tight-binding (DFTB) theory to calculate the energy function and the modified basin hopping (MBH) algorithm to find global minimum, it was predicted by this DFTB/MBH minimization method that the optimized geometries of several coinage pure clusters exhibit chiral property, i.e. each of these clusters has a same energy value but assumes two shapes having mirror-image symmetry but are non-superimposable. The latter two clusters have been called enantiomers. This accidental discovery of left-right enantiomers at the DFT-based DFTB theory level is uncommon in physics and has motivated us to inquire into the underlying mechanism of transition from one enantiomer to another. It is on the premise to understand the enantiomeric dynamics that we employ the isothermal Brownian-type molecular dynamics (MD) simulation to investigate how an enantiomer, say left, transits to its right enantiomer, deducing the mechanism of these enantiomeric transitions from reading the generated atomic configurations. To delve into the transition dynamics, we pay due attention to two useful parameters in order to effectively differentiate the left and right enantiomers. The first parameter is the ultrafast shape recognition similarity index ζ and the second one is the Hausdorff chirality measure (HCM) parameter. We show in this project how the ζ-HCM pair can expediently be used to search for the intermediate symmetrical structure from the MD simulations data recorded and deduce from it a reaction coordinate that can provide more information on such interesting issues as transition rate between enantiomers, the frequency of enantiomeric transitions, the mechanism of transition and its connection with atoms involved,.., etc. In addition to applying this new method to the on-going chiral cluster sAu and Ag, we shall study as well the remaining coinage metal Cu where new DFTB parametrization is now available in the literature.
