| 摘要: | 在與第一原理方法相較的情況下，奈米叢集理論之研究中採用的密度泛函緊束縛（ Density Functional Tight-Binding, DFTB ） 理論，可促使模擬時間尺度在可負擔之計算成本下獲得延長，並在準確性上達到接近之優勢。我們透過改進版的谷域跳躍（ modified basin-hopping ）優化演算法，發現 DFTB 對金銀銅之小型叢集所預測之最低能量結構，爲擁有鏡像對稱的 Cu12 、 Cu14 、 Cu19 、Ag14 、 Ag17 、 Ag20 、 Au10 、 Au15 和 Au18 。利用昊斯多夫鏡像計量（ Hausdorff chirality measure ）與超快速形狀識別技術（ ultra-fast shape recognition technique ）的分析，鏡像結構得以在數學架構內精準地被描述。兩者巧妙的串聯應用亦有助於尋找一對鏡像結構中之非鏡像中間結構，從而獲得納入向量考量的反應坐標（ reaction coordinates ），再用來闡明在布朗型恆溫分子動力學模擬下 Cu14 、 Au10 與 Au15 的鏡像變相。 經由振動頻率的計算顯示，該相變機制可歸因於，鏡像異構物之間的簡正模態，經由其中間結構，促進了這些相變。在 Au18 的案例中，其各個鏡像結構之間存在著能量障壁，我們演示了亞穩動力（ metadynamics ）技術擁有跨越其能量障壁的能力，也證明了在低維度的自由能景觀（ free energy landscape ， FEL ）中存在著變相途徑。本論文的第二部分中，我們運用基於自適應方法取得的最新 DFTB 參數，對 n = 3-20 範圍內不帶電金叢集進行結構研究，重新探討由二維轉換至三維叢集之臨界粒子數 nc 。透過對訂定的 DFTB 參數之表現進行分析與比較，評估發現其與文獻中的結構爲一致，而且該參數適合金 叢集之計算。 亞穩動力所探索接近 nc 之金叢集顯示， FEL 具有能量谷域之間被能量障壁區分之特徵，並包含金叢集結構性熵（ entropy ）與焓（ enthalpy ）之資訊。;The use of density functional tight-binding (DFTB) in the theoretical studies of nanoclusters opened up access to longer timescales in simulation at an affordable computing cost and with little trade off in accuracy against ab initio or first principle methods. The purported global minimum (GM) structures of small Cu, Ag and Au clusters at the DFTB level, predicted by a modified basin-hopping global optimization algorithm, have revealed the existence of GM structures manifesting in chiral pairs Cu12 , Cu14 , Cu19 , Ag14 , Ag17 , Ag20 , Au10 , Au15 and Au18 . These chiral structures are studied by the Hausdorff chirality measure and ultra-fast shape recognition technique to ascertain their chiral nature in a mathematical formalism, in addition to an adroit and tandem use of both methods in identifying intermediate structures that point to suitable reaction coordinates derived from vectorial considerations to elucidate the enantiomeric transitions in Cu14 , Au10 and Au15 that are observable with a Brownian-type isothermal molecular dynamics simulation. Calculation of vibrational frequencies suggests the transition mechanisms are attributable to normal modes facilitating transitions between enantiomers via the identified intermediate structures. In the case of Au18 , where chiral states are hindered by hypothesized high energy barriers betweenthem, metadynamics has demonstrated its biasing abilities to overcome such barriers and shown the existence of transition pathways in an expressive lower dimension in the free energy landscape. In the second segment of this thesis, a systematic study of static neutral Aun structures in the range n = 3-20, using a recent DFTB parametrization available based on an adaptive scheme, is conducted to revisit the critical size, nc where the dimensionality transition of planar-nonplanar Au clusters occurs. The quality of said DFTB parametrization is assessed, and found to be adequate and consistent against structures reported in the literature. The energy landscapes of Aun close to nc explored by metadynamics are characterized by distinct regions of energy wells separated by barriers, and carry with them valuable information encompassing both the conformational enthalpy and conformational entropy of Au clusters. |
