本論文用定溫Brownian-type分子動力學模擬，進行有限系統的金屬叢集電腦計算。在此計算中，抽取出長時間序列的金屬叢集原子結構，用以研究金屬叢集的熱力學性質。 而從這些數據之中，再把一小群的原子(大小比金屬叢集小)轉換成四個數字去表達，而這四個數字我們稱為common neighbor label(CNL)。然而，在同一個金屬叢集結構裡，不同的原子群結構卻可能會被表示成相同的CNL。因此，我們將這些CNL的”簡併”數目，給一個相對應的abundance值。所以當金屬叢集在基態的結構時，我們可以得到一組固定的CNL和其各自對應的abundance來描述其結構。而隨著溫度的增加，將會產生更多不同的原子結構，如此會使原始結構的CNL所對應之abundance值改變，並且也會產生新的CNL還有其相對應的abundance。 在本篇論文裡，我們使用上述的方法產生了不同溫度的時間序列資料。接著利用統計上的時間序列分析方法，來處理這些資料。從這個方法中，可以得到CNL和CNL的關聯矩陣。假使在CNL的關聯性之間,可以清楚的區分出強關聯性和弱關聯性，則可從其中將它們分離出來，再從這些強關聯性的中做進一步的分類，而得到一組一組的CNL，我們稱其為effective variable。也確實，在我們的系統中，可以清楚的區分出強關聯性和弱關聯性。 隨著溫度的改變，effective variable也會產生變化，而這些的變化中加上effective variable本身所包含的意義，我們得到一些關係對應到前置峰(prepeak)和主峰(principal peak)的位置。所以，最後我們以三種材料Ag14、Cu14、Cu13Au1得到的結果和比熱圖作一個比較。 The isothermal Brownian-type molecular dynamics simulation previously developed for studying the thermal and dynamic properties of metallic clusters was applied to generate long-time series data from which are recorded the time development of atomic configurations. A group of atoms of a smaller size(than the cluster), which we call the common neighbor label (CNL) and designate by four numeric digits, is canvassed by the common neighbor analysis. The latter analysis describes the geometrical symmetries of the CNL and assigns to it an abundance value which is the number of “degenerate” four digits characterizing a same CNL. When the cluster is in the ground state, the number of CNLs and their corresponding abundances are fixed. As temperature increases, different kinds of atomic activities such as vibration, migrational relocation, permutational and topological isomer transition etc. manifest depending on their lowest energy structure. As a result, the abundances of original CNLs will change and new CNLs with their respective abundances are created. Tracking down these CNLs and their associated abundance values as a function of time at given temperature as well as the thermal variations of them shed light on the cluster dynamics. A novel statistical time series analysis which utilizes the long-time series data sets is exploited to understand the cluster dynamics. The method uses both the short- and long-time clustering. Based on these temporal statistics recorded at given temperature, we choose a long-time window to generate CNL-CNL correlation matrices. If the statistical correlations among the CNLs can be well categorized into weakly and strongly ones, as indeed possible in clusters, one can then sort out so-called effective variables which are collections of CNLs exhibiting high correlation behaviors. It is found here that certain effective variables show subtleties in their temperature dependences and these traits bear a delicate thermal relation to prepeaks and main peaks seen in clusters Ag14, Cu14 and Cu13Au1. We therefore infer from the temperature changes of effective variables the temperatures at which the prepeak and principal peak appear and they are compared with those determined from the specific heat data. In this work, we consider four metallic clusters, i.e. Ag14, Cu13, Cu14 and Cu13Au1.
