Heat Capacities and Magic Numbers in Metal Clusters

Using our own {\it Aufbau/Abbau} method in performing umbiased structure optimization of isolated M$_N$ clusters (with M being a metal) together with the {\it Embedded-Atom} method for the calculation of the total energy of a given structure, we have optimized the structure of Ni$_N$, Cu$_N$, and Au$_N$ clusters with $N$ up to 150. By analysing the total energy as a function of $N$ particularly stable clusters, corresponding to the so-called magic numbers, are identified. Subsequently, we use the harmonic approximation in calculating the vibrational frequencies for each value of $N$. These are finally using in calculating the molar vibrational heat capacity $\bar C_V$ as a function of temperature $T$. It is been discussed whether, for a given $T$, $\bar C_V$ shows a dependence on $N$ that correlates with the occurrence of magic numbers. An explanation for the observations is being offered.