本計劃擬研究兩項議題。第一項議題為建構一可靠高效能的電腦模擬方法，使得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現象，得以解決。亞穩動力 (metadynamics) 模擬為眾多強化採取樣品法之一。本計劃擬從統計力學理論角度出發，利用亞穩動力模擬的技巧，探究並將它用具化。有別於一般人採用較為嚴峻的Born-Oppenheimer分子動力學模擬，雖使用現成的軟體執行之，但需要的電腦計算時間仍然冗長以及耗費，本計劃因此提議用泛密度函數緊密捆綁density functional tight-binding (DFTB) 理論，先計算其能量E_DFTB，再與本研究室自行研發的布朗分子動力學模擬方法結合，來執行傳統等溫下之分子動力學模擬(Nosé-Hover等溫法)。在此設計下，此時系統是以聚集變數空間 (collective variable space) 來描述，取代慣用之能量組態 (configurational energy space) 空間。另外，本計劃也將帶有歷史關係式之電位勢V_G加到E_DFTB，讓 (V_G+E_DFTB) 成為偏離即定路徑之電位勢，然後將之引入並進行亞穩動力模擬。在本計劃裏，我們利用亞穩動力模擬探討n個原子之Au_n叢集，建構在聚集變數空間之自由能能量面與電位勢能之能量面，尤其是探究二維演化至三維的議題。本計劃的第二項議題為研究尺寸稍大 (n>30) 之Au_n金叢集之最低能量值結構。在這方面，我們將測試兩組DFTB參數，計算個別在DFTB理論之E_DFTB ，並與本研究室自行發展的最佳化演算法，進行一系列且有系統的計算金叢集之穩定結構。 ;This project targets at two specific themes. The first theme concerns with developing a molecular dynamics (MD) simulation scheme so that the long-standing kinetic problems due to high barriers between metastable states which cause the system being trapped in local minima and hence resulting in significantly long timescales in simulations can be circumvented. The metadynamics MD simulation is one of the numerous enhanced sampling methods and will be theoretically investigated and implemented in the present project. Although there are softwares programmed along the line of the ab initio Born-Oppenheimer MD simulation but the approach is still computationally tedious and expensive. Here we propose the density functional tight-binding (DFTB) theory which is used to calculate the energy function E_DFTB of a cluster and combine it with the Brownian-type MD method developed previously by us to perform the MD simulation as a Nose–Hoover thermostat. This canonical MD simulation which in essence is the configurational energy space will be transposed to a collective variable (CV) space. Then, by amending E_DFTB of the canonical MD simulation algorithm with a history dependent potential VG thereby constructing a biased potential (E_DFTB + V_G), we perform the metadynamics MD simulation for the cluster Au_n consisting of a number n of Au atoms. Both the free energy surface and potential energy surface of Au_n in the CV space will constructed and they are analyzed specifically to study the issue of the bidimensional to tridimensional transition. The second theme is about finding the lowest energy of structures of Au_n clusters of larger size (n>30). We shall investigate in this context using two sets of DFTB parameters to calculate their respective E_DFTB and combine the latter with an elegant optimization algorithm developed very recently by our group to carry out a systematic study of the change of geometry of Au_n.
