针对铜表面化学反应，我们发展了一套铜-碳体系的密度泛函紧束缚(DFTB)参数。测试结果表明这套参数可以很好的描述吸附铜或碳原子前后铜表面的几何结构和能量。基于这套参数，我们对Cu(111)表面的碳二聚化过程进行了分子模拟研究。即使在高温下，直接的分子动力学模拟也很难观察到碳二聚体的形成。这是因为高温下铜表面显著的结构弛豫一定程度上阻止了二聚化。为了研究高温下铜表面碳二聚化的机理，我们进行了赝动力学模拟。发现在二聚化的过程中，碳原子形成C-Cu-C桥状结构以后，会绕中间Cu原子转动，最后形成碳二聚体。1300 K下碳二聚化的自由能垒约0.9 eV。 Cu has been widely used as a substrate material for graphene growth. To understand the atomistic mechanism of growth, an efficient and accurate method for describing Cu-C interactions is necessary, which is the prerequisite of any possible large-scale molecular simulation studies. The semi-empirical density-functional tight-binding (DFTB) method has a solid basis from the density functional theory (DFT) and is believed to be a good tool for achieving a balance between efficiency and accuracy. However, existing DFTB parameters cannot provide a reasonable description of the Cu surface structure. At the same time, DFTB parameters for Cu-C interactions are not available. Therefore, it is highly desirable to develop a set of DFTB parameters that can describe the Cu-C system, especially for surface reactions. In this study, a parametrization for Cu-C systems within the self-consistent-charge DFTB (SCC-DFTB) framework is performed. One-center parameters, including on-site energy, Hubbard, and spin parameters, are obtained from DFT calculations on free atoms. Two-center parameters can be calculated based on atomic wavefunctions. The remaining repulsive potential is obtained as the best compromise to describe different kinds of systems. Test calculations on Cu surfaces and Cu-or C atom-adsorbed Cu surfaces indicate that the obtained parameters can generate reasonable geometric structures and energetics. Based on this parameter set, carbon dimerization on the Cu(111) surface has been investigated via molecular dynamics simulations. Since they are the feeding species for graphene growth, it is important to understand how carbon dimers are formed on the Cu surface. It is difficult to observe carbon dimerization in brute-force MD simulations even at high temperatures, because of the surface structure distortion. To study the dimerization mechanism, metadynamics simulations are performed. Our simulations suggest that carbon atoms will rotate around the bridging Cu atom after a bridging metal structure is formed, which eventually leads to the dimer formation. The free energy barrier for dimerization at 1300 K is about 0.9 eV. The results presented here provide useful insights for understanding graphene growth
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