Theoretical studies of thermodynamic properties of clusters at low temperatures

两个现有的计算机程序包，即，嵌入原子方法和参数化密度泛函方法，应如此扩展，以确定更低能量的异构体的集群，这样的振动特性，在谐波近似下，可以确定。随后，应计算配分函数，并由此确定各种热力学量，如熵、自由能和热容作为团簇大小和温度的函数。这些方法应应用于不同的系统，即，NaN，CuN，AuN，AlN和Ni-Cu团簇，其结果将用于解决以下问题：通过熵效应的温度是否会导致幻数的变化？温度会导致相同团簇大小的不同同分异构体的相对总能量的变化吗？多个不同的、能量相近的异构体的共存对团簇的性质有多重要？在热容中可以看到“幻数”，即，魔团是不是特别坚硬，因此热容特别低？电子自由度对于热力学量有多重要，即，由于电子激发能通常远大于kT，因此人们可能会认为电子与热力学量无关？在什么样的近似水平上，我们才能充分描述团簇的热力学性质作为温度和大小的函数？

Two existing computer program packages, i.e., an embedded atom method and a parameterized density-functional method, shall be so extended that more energetically lowest isomers of clusters can be determined, and so that vibrational properties, withín a harmonic approximation, can be determined. Subsequently, the partition function shall be calculated and from this various thermodynamic quantities, like entropy, free energy, and heat capacity as a function of cluster size and temperature, shall be determined. The methods shall be applied on different systems, i.e., NaN, CuN, AuN, AlN and Ni-Cu clusters and the results shall be used in addressing the following questions: Does temperature via entropy effects lead to changes in the magic numbers? Does temperature lead to changes in the relative total energies of different isomers of the same cluster size? How important is the co-existence of more different energetically close isomers for the properties of the clusters? Can the ‘magic numbers’ be seen in heat capacities, i.e., are the magic clusters particularly rigid and have, therefore, particularly low heat capacities? How important are electronic degrees of freedom for the thermodynamic quantities, i.e., since electronic excitation energies most often are much larger than kT, one may expect the electrons to be irrelevant for the thermodynamic quantities? At which level of approximation does one get an adequate description of the thermodynamic properties of the clusters as a function of temperature and size?