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to incorporate one or more approximations. For instance, one may choose to study
only small(er) clusters or clusters of selected sizes and/or structures. Furthermore,
by employing empirical potentials that depend only on the interatomic distances it
may become possible to study more structures and/or larger systems at the cost of
possible inaccuracies due to the approximate descriptions of the interatomic interactions. As a compromise, parametrized methods that include electronic degrees of
freedom can be used. Besides the use of such approximate methods for the determination of the total energy for a given structure, various approaches for the determination of the structure of the global total-energy minimum have been suggested.
These include Simulated Annealing, the Basin-Hopping method, and Genetic Algorithms [1–9].
Gold clusters constitute a special case that has attracted much attention partly because of their application as catalysts and in nanoscience, and partly because these
systems provide a useful model system with surprising results for theoretical studies. However, it has turned out to be particularly difficult to determine the properties
of gold cluster because the calculated structures depend very sensitively on the applied methods [10, 11], which is to a much lesser extent the case for most other
elemental clusters. Therefore, the reported theoretical results for gold clusters show
a particularly large scatter and a strong dependence on the approximations of the
calculations.
Interesting information on the clusters can be obtained by studying their thermodynamic properties, both experimentally and theoretically. This includes the melting
of small clusters [12–14] but also their low-temperature properties can provide useful information.
In this contribution we shall present results of a theoretical study of the properties of gold clusters. We shall partly review our earlier results on the structural
and energetic properties of gold clusters [15] and, in addition, present and apply a
new method for studying the vibrational contributions to the thermodynamic lowtemperature properties of the clusters. Our computational methods will be described
in Sect. 10.2, followed by a discussion of the results in Sect. 10.3. Finally, our results
are summarized in Sect. 10.4.
10.2 Computational Method
10.2.1 Parametrized Density-Functional Method
In the present work the total energy and the electronic properties of a given structure were calculated using a parametrized tight-binding density-functional (DFTB)
method [16]. According to this method, the relative total energy of a compound with
a chosen structure can be written as the difference of the orbital energies of the compound ({ε i }, with i being an orbital index) minus those of the isolated atoms ({ε im }
Y. Dong et al.
to incorporate one or more approximations. For instance, one may choose to study
only small(er) clusters or clusters of selected sizes and/or structures. Furthermore,
by employing empirical potentials that depend only on the interatomic distances it
may become possible to study more structures and/or larger systems at the cost of
possible inaccuracies due to the approximate descriptions of the interatomic interactions. As a compromise, parametrized methods that include electronic degrees of
freedom can be used. Besides the use of such approximate methods for the determination of the total energy for a given structure, various approaches for the determination of the structure of the global total-energy minimum have been suggested.
These include Simulated Annealing, the Basin-Hopping method, and Genetic Algorithms [1–9].
Gold clusters constitute a special case that has attracted much attention partly because of their application as catalysts and in nanoscience, and partly because these
systems provide a useful model system with surprising results for theoretical studies. However, it has turned out to be particularly difficult to determine the properties
of gold cluster because the calculated structures depend very sensitively on the applied methods [10, 11], which is to a much lesser extent the case for most other
elemental clusters. Therefore, the reported theoretical results for gold clusters show
a particularly large scatter and a strong dependence on the approximations of the
calculations.
Interesting information on the clusters can be obtained by studying their thermodynamic properties, both experimentally and theoretically. This includes the melting
of small clusters [12–14] but also their low-temperature properties can provide useful information.
In this contribution we shall present results of a theoretical study of the properties of gold clusters. We shall partly review our earlier results on the structural
and energetic properties of gold clusters [15] and, in addition, present and apply a
new method for studying the vibrational contributions to the thermodynamic lowtemperature properties of the clusters. Our computational methods will be described
in Sect. 10.2, followed by a discussion of the results in Sect. 10.3. Finally, our results
are summarized in Sect. 10.4.
10.2 Computational Method
10.2.1 Parametrized Density-Functional Method
In the present work the total energy and the electronic properties of a given structure were calculated using a parametrized tight-binding density-functional (DFTB)
method [16]. According to this method, the relative total energy of a compound with
a chosen structure can be written as the difference of the orbital energies of the compound ({ε i }, with i being an orbital index) minus those of the isolated atoms ({ε im }