Chapter 10
Structural and Thermodynamic Properties
of Au 2–58 Clusters
Yi Dong, Michael Springborg, and Ingolf Warnke
Abstract In this study, we have used a parametrized density-functional tightbinding method combined with genetic algorithms for an unbiased global optimization to study systematically neutral gold clusters with from 2 to 58 atoms.
The ground states of the clusters are identified and different descriptors are used to
analyze the properties of the clusters, including stability, overall shape, similarity,
growth patterns, and structural motifs. The vibrational heat capacity of the ground
state of neutral gold clusters at different temperatures are calculated by a newly developed method. The results show that the heat capacity is strongly size-dependent,
particularly at low temperature.
10.1 Introduction
Clusters science has been an active research area for some decades because of the
fascinating properties of the clusters. Thus, quantum-size effects combined with the
fact that the number of surface atoms relative to the total number of atoms is far
from vanishing may be held responsible for the unique, size-dependent properties
of clusters. Moreover, there is a highly non-trivial dependence of the properties on
the size and composition of the clusters. Since, on the other hand, the properties
depend sensitively on the structure of the clusters, one of the most fundamental
challenges in the study of clusters is related to the determination of their groundstate structures.
Without any further information the theoretical identification of the structure of
the ground state of a cluster of N atoms requires searching in a geometry space of
3N − 6 dimensions, which for even small values of N is hardly possible. Accordingly, even for not too large clusters, an unbiased determination of the structure of
the global total-energy minimum will easily require that very many structures are
studied whereas for each structure the calculation of the total energy is computationally demanding. Therefore, theoretical studies of the properties of the clusters have
Y. Dong (B)
Physical and Theoretical Chemistry, University of Saarland, Campus B2.2, 66123 Saarbrücken,
Germany
e-mail: y.dong@mx.uni-saarland.de
M. Hotokka et al. (eds.), Advances in Quantum Methods and Applications in
Chemistry, Physics, and Biology, Progress in Theoretical Chemistry and Physics 27,
DOI 10.1007/978-3-319-01529-3_10,
© Springer International Publishing Switzerland 2013
181
Structural and Thermodynamic Properties
of Au 2–58 Clusters
Yi Dong, Michael Springborg, and Ingolf Warnke
Abstract In this study, we have used a parametrized density-functional tightbinding method combined with genetic algorithms for an unbiased global optimization to study systematically neutral gold clusters with from 2 to 58 atoms.
The ground states of the clusters are identified and different descriptors are used to
analyze the properties of the clusters, including stability, overall shape, similarity,
growth patterns, and structural motifs. The vibrational heat capacity of the ground
state of neutral gold clusters at different temperatures are calculated by a newly developed method. The results show that the heat capacity is strongly size-dependent,
particularly at low temperature.
10.1 Introduction
Clusters science has been an active research area for some decades because of the
fascinating properties of the clusters. Thus, quantum-size effects combined with the
fact that the number of surface atoms relative to the total number of atoms is far
from vanishing may be held responsible for the unique, size-dependent properties
of clusters. Moreover, there is a highly non-trivial dependence of the properties on
the size and composition of the clusters. Since, on the other hand, the properties
depend sensitively on the structure of the clusters, one of the most fundamental
challenges in the study of clusters is related to the determination of their groundstate structures.
Without any further information the theoretical identification of the structure of
the ground state of a cluster of N atoms requires searching in a geometry space of
3N − 6 dimensions, which for even small values of N is hardly possible. Accordingly, even for not too large clusters, an unbiased determination of the structure of
the global total-energy minimum will easily require that very many structures are
studied whereas for each structure the calculation of the total energy is computationally demanding. Therefore, theoretical studies of the properties of the clusters have
Y. Dong (B)
Physical and Theoretical Chemistry, University of Saarland, Campus B2.2, 66123 Saarbrücken,
Germany
e-mail: y.dong@mx.uni-saarland.de
M. Hotokka et al. (eds.), Advances in Quantum Methods and Applications in
Chemistry, Physics, and Biology, Progress in Theoretical Chemistry and Physics 27,
DOI 10.1007/978-3-319-01529-3_10,
© Springer International Publishing Switzerland 2013
181