【作者】 石元坤；

【导师】 李振华；

【作者基本信息】 复旦大学 ， 物理化学， 2011， 硕士

【摘要】 自从分子动力学(Molecular Dynamics, MD)建立以来,它就被广泛应用于复杂体系的反应动力学研究当中。例如最经典的氢气与氟原子的撞击反应,蛋白质折叠等等。然而,应用分子动力学方法对金属簇的物理化学性质研究是一个近年来刚刚兴起的领域,目前研究还较少。作为一个典型例子,金属团簇如铝,金在高温下的动力学表现是目前实验研究多相催化过程中广泛涉及到的热点问题。目前,关于这个问题的研究尚处于初步探索阶段。因此,开展金属团簇如金或铝在高温下的动力学研究不仅可以拓展分子动力学的应用领域,而且可以加深人们对反应过程中催化剂中心变化的认识,为实验上开发新一代有效催化剂提供重要的理论依据。由于从头计算的时间成本过高,精准经验势能面的缺乏加上实验手段的局限性,目前人们对于催化剂尺度的金属颗粒的静态结构及动态性质并没有很深入的认识。因此,本论文的主要工作是围绕用分子动力学研究金属团簇展开的,主要以铝和金这两个体系作为模型体系,用分子动力学配合经验势能面为研究手段,研究金属簇在高温下的动力学性质。在此基础上,重点研究了以下几个问题：铝纳米簇碰撞的微分截面的模式分析：我们系统性的研究了铝簇撞击的微分截面。通过对撞击参数,反应物产物角动量,中间体形状、温度、角动量,产物分布的分析,归纳总结得出铝簇间撞击的反应规律。我们发现铝簇的反应中间体多为椭球状,并且该反应对产物的选择性受动力学和热力学同时控制。我们基于模拟观察到的铝簇中间体的独特形状,结合微分截面模式的分析,提出了一个新模型来解释铝簇的微分截面模式。基于这一工作,我们发现NPB这一势能面的函数形式在描述金属簇的反应动力学上有良好表现,可以在其他金属簇上开展进一步研究。适合金簇计算的密度泛函理论筛选：为了建立构建势能面所需的结构能量库,我们系统性的研究了各类密度泛函理论计算金簇的表现。我们发现对于金元素,相对论效应对于准确计算金簇的结构及能量是至关重要的。我们发现,通过旋轨耦合计算考虑的相对论效应会高估金簇的原子化能,而考虑HF交换能则会低估金簇的原子化能。基于这一发现,我们挑选出了TPSSh作为计算金簇较有效的泛函,并且进一步的研究发现旋轨耦合对于金簇的原子能的校正与金簇大小及其所含金原子的配位数有线性关系。这一发现可能可以用来解释长久以来理论界计算金簇的一大困惑,即金的平面型结构转换至立体结构问题。金簇的平面型结构至立体结构的转换：我们通过前期工作所建立的精准数据库与小基组重新计算结果间的比较,确立了用M06和TPSSh这两个方法来计算Au6-Au13,并将所得结果与文献建议的M06-L的计算结果相比较。我们发现在考虑了旋轨耦合效应以后,M06及TPSSh的计算结果在金簇的平面型结构至立体结构的转换上显示出了一致性结果,而相比之下M06-L的结果则较为不确定。并且,我们再一次验证了旋轨耦合显著降低高对称性结构的相对能量,因此使得部分金簇结构倾向于高对称性的结构,说明了旋轨耦合效应对于计算金簇的重要性。并且,通过与仅有的关于Au7实验数据与计算结果间的对比,我们认为Au,可能是中性金簇最后一个平面型结构占主导的簇。金簇势能面的初步建立：基于前期工作所得到的精确结构能量数据库以及所确立的计算方法,我们对Au2-Au4进行了势能面扫描,所获得数据通过差分进化算法用于拟合NPB势能面。我们初步获得了比较精确的势能面。更多还原

【Abstract】 Molecular Dynamics (MD) has been widely applied to the investigation of reaction dynamics of prototype reactions and complex systems, for example H2+F, and protein folding. However, reliable investigation of physical and chemical properties of metal cluster via MD method is still absent. As promising material and catalyst, the dynamic properties of metal clusters like aluminum and gold clusters under high temperature is the hot spot of experiments. Therefore, study of the dynamic properties of metal clusters like gold and aluminum clusters under high temperature will not only broaden the application area of molecular dynamics but also deepen our comprehension of the change of catalysis center during the catalytic process and provide theoretical evidence and knowledge for experimental development of novel catalysts.Owing to the expensive cost of ab-initio calculations, the deficiency of accurate classical potential energy surface, and lack of experimental methods, the structure and dynamic properties of metal clusters in the catalytic process are still unclear to us. Thus, this thesis mainly focuses on the collision between of alluminum clusters via molecular dynamics simulation and the building of accurate semi-classical potential energy surface for gold clusters:Analysis of differential cross section (DCS) of collisions between aluminum clusters:Through the investigation of correlation between different observable variables, such as angular momentum of products and reactants, the temperature, shape, and angular momentum of the reaction intermediates, and product distribution, we have summarized the general rule of collision between aluminum clusters, which may also be applied to the collisions between other metal clusters. Based on the finding that the intermediate of the collisions is ellipsoid sphere and the selectivity over products is controlled by both kinetic and thermodynamics factors, we proposed a novel model to explain the DCS patterns of aluminum cluster collisions. Moreover, this work shows that NPB, a new form of potential energy surface, is able to describe the dynamics behavior of aluminum clusters well and can be applied to other systems as well.Validation of density functional theories for the calculation of gold clusters: In the purpose of building the database required by PES construction, we have systematically studied the performance of various density functional theories for the calculation of gold clusters. It turns out that Spin-Orbit (SO) coupling overestimates the cohesive energy of gold clusters, while Hartree-Fock exchange underestimates the cohesive energy of gold clusters. Due to the cancelling effect between SO effect and HF exchange TPSSh was found to be the best method for gold clusters. Through further study of the relationship between SO correction to atomization energy (ΔESO) and the size of the gold clusters (Natom) and the number of Au-Au bonds (Nbond), a simple linear equation betweenΔESO and Natom and Nbond has been found, which may help to solve the puzzle regarding to the transition point of gold clusters from two-dimensional (2D) structures to three-dimensional (3D) structures.Transition of gold clusters from 2D structures to 3D structures:Two methods, M06 and TPSSh which have good performance in the calculations of gold clusters have been used to study Au6-Au13 clusters and the results were compared to those calculated by M06-L which was recommended by previous studies indicating that M06-L can reproduce the 2D-3D transition points of ionic gold clusters observed by experiments. It turns out that SO coupling is very important on the determination of the 2D-3D transition of gold clusters and both M06 and TPSSh give the same result on this issue. However, the performance of M06-L is not very satisfactory. Furthermore, it was also found in the present study that SO coupling prefers high symmetry geometries. Finally, through the comparison between experimental and calculation results, Au7 was found to be the largest neutral gold cluster dominated by planar structures.Building of gold potential energy surface:We have scanned the potential energy surface of Au2-Au4 using the accurate SO TPSSh method which was validated in the previous benchmark calculations. The resulting energies were fitting into NPB via differential revolution method. The fitting is very successful and the error is only 0.015 eV/cluster.更多还原