本計劃屬三年期計劃的第三年，亦即延續前兩年[MOST106-2112-M-008-015及MOST107-2112-M-008-021]的工作，主要發展亞穩動力 (metadynamics) 分子動力(MMD)電腦模擬，應用在建構金屬叢集之自由能能量面。至目前為止，這項工作穩定進行中，我們除結合本研究室自行研發的等溫下布朗分子動力(MD)模擬方法(Nosé-Hover等溫法)，本計劃所提議使用之泛密度函數緊密捆綁density functional tight-binding理論用於計算金屬叢集能量EDFTB以及將帶有歷史關係式之電位勢VG加到EDFTB，再以 (VG+EDFTB) 成為偏離即定路徑之電位勢進行MMD模擬，也首次以低維度聚集變數空間 (collective variable space) 來描述金屬叢集之結構變化，取代原先正则系综MD模擬法之多維度能量組態空間 (configurational energy space)。對於本計劃前兩年的工作重點，主要測試MMD模擬應用在探究n個原子之金叢集，持別是分析金叢集在聚集變數空間之自由能能量面，瞭解其二維演化至三維的過渡現象。而分析結果顯示，進一步研究各種不同大小的金屬叢集，尤其是尺寸較大之金屬叢集，有助於瞭解亞穩態之間的轉變現象過程中的隱含物理。另外，本計劃將持續研究常發生在電位勢介於亞穩狀態間的高障礙，造成物理系統被圈套在電位勢谷，也因此導致電腦模擬時間延長的問題。為此，本計劃也擬採用MMD模擬的技巧，具體展示如何解決前述發生在MD電腦模擬所遭遇到的高障礙窘境。在此問題上，我們選擇了Au15,Au18, Ag14 和Ag20為探討對象，因為這四個金屬叢集根據本研究室自行開發的最佳化(DFTB/MBH)演算法，發現它們具有手征對稱，亦即每個叢集都各有兩個叢集共同擁有一相同能量值，但各別叢集之結構卻呈現左右對稱。而我們初步測試Au18，發現使用等溫下布朗MD模擬方法，無法揭開此叢集之左右對稱，推測是高障礙使然。 ;As part of a 3-year project and a continuation of two preceding projects to implement the metadynamics molecular dynamics (MMD) simulation method to calculate the free energy landscape of metallic clusters, we have progressed steadily in our plan and have in fact successfully combined the three main ingredients, namely, the isothermal Brownian-type MD method, the density functional tight-binding (DFTB) theory which is used to calculate the energy function EDFTB of a cluster, and the amendment of EDFTB in the canonical MD simulation algorithm with a history dependent potential VG thereby constructing a biased potential (EDFTB + VG) for MMD simulation. The original canonical MD simulation method which, in essence, spanning the multi-dimensional configurational energy space, is now transposed to a lower dimensional collective variable (CV) space. The newly developed MMD simulation method was tested and applied to understand specifically the issue of the bidimensional to tridimensional transition in n-atom Aun cluster analyzing its free energy landscapes in the CV-space. Further critical evaluation on several other clusters especially the larger sized ones will help to understand the underlying physics of transitions between metastable states. This third-year project is to continue delving deeper into the long-standing kinetic problems due to high barriers between local minima in the potential energy landscape that cause the system to being trapped and hence resulting in significantly long timescales in simulations. A skilledly use of MMD simulation scheme can be applied to resolve this numerical dilemma and several case studies including clusters Au15, Au18 Ag14 and Ag20 will be investigated. These clusters are chosen because of the chiral symmetry that the DFTB/MBH optimization algorithm developed by our group predicted them to possess. Our preliminary testing on one of them, Au18 using the isothermal Brownian-type MD simulation has shown that the MD simulation is unable to unravel these two same lowest-energy minima. We conjecture this failure is due to high barriers between local minima in the potential energy landscape.
