Density functional molecular dynamical simulations have been performed on Ga17 and Ga13 clusters to understand the recently observed higher-than-bulk melting temperatures in small gallium clusters [Phys. Rev. Lett. 91, 215508 (2003)]]. The specific-heat curve, calculated with the multiple-histogram technique, shows the melting temperature to be well above the bulk melting point of 303 K, viz., around 650 and 1400 K for Ga17 and Ga13, respectively. The higher-than-bulk melting temperatures are attributed mainly to the covalent bonding in these clusters, in contrast with the covalent-metallic bonding in the bulk.

We report the results of detailed thermodynamic investigations of the Sn 20 cluster using densityfunctional molecular dynamics. These simulations have been performed over a temperature range of 150 to 3000 K, with a total simulation time of order 1 ns. The prolate ground state and low-lying isomers consist of two tricapped trigonal prism (TTP) units stacked end to end. The ionic specific heat, calculated via a multihistogram fit, shows a small peak around 500 K and a shoulder around 850 K. The main peak occurs around 1200 K, about 700 K higher than the bulk melting temperature, but significantly lower than that for Sn 10 . The main peak is accompanied by a sharp change in the prolate shape of the cluster due to the fusion of the two TTP units to form a compact, near spherical structure with a diffusive liquidlike ionic motion. The small peak at 500 K is associated with rearrangement processes within the TTP units, while the shoulder at 850 K corresponds to distortion of at least one TTP unit, preserving the overall prolate shape of the cluster. At all temperatures observed, the bonding remains covalent.

Recent experimental reports bring out extreme size sensitivity in the heat capacities of gallium and aluminum clusters. In the present work we report results of our extensive ab initio molecular dynamical simulations on Ga30 and Ga31, the pair which has shown rather dramatic size sensitivity. We trace the origin of this size sensitive heat capacities to the relative order in their respective ground state geometries. Such an effect of nature of the ground state on the characteristics of heat capacity is also seen in case of small gallium and sodium clusters, indicating that the observed size sensitivity is a generic feature of small clusters.

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The finite temperature behavior of small Silicon (Si10, Si15, and Si20) and Tin (Sn10 and Sn20) clusters is studied using isokinetic Born-Oppenheimer molecular dynamics. The lowest equilibrium structures of all the clusters are built upon a highly stable tricapped trigonal prism unit which is seen to play a crucial role in the finite temperature behavior of these clusters. Thermodynamics of small tin clusters (Sn10 and Sn20) is revisited in light of the recent experiments on tin clusters of sizes 18-21 [G. A. Breaux et. al. Phys. Rev. B 71 073410 (2005)]. We have calculated heat capacities using multiple histogram technique for Si10, Sn10 and Si15 clusters. Our calculated specific heat curves have a main peak around 2300 K and 2200 K for Si10 and Sn10 clusters respectively. However, various other melting indicators such as root mean square bond length fluctuations, mean square displacements show that diffusive motion of atoms within the cluster begins around 650 K. The finite temperature behavior of Si10 and Sn10 is dominated by isomerization and it is rather difficult to discern the temperature range for transition region. On the other hand, Si15 does show a liquid like behavior over a short temperature range followed by the fragmentation observed around 1800 K. Finite temperature behavior of Si20 and Sn20 show that these clusters do not melt but fragment around 1200 K and 650 K respectively.

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Heat capacities have been measured as a function of temperature for aluminum clusters with 31-48 atoms, complimenting previous measurements for larger clusters. Peaks in the heat capacities (due to the latent heat) indicate melting transitions. Large size-dependent fluctuations in the melting temperatures are found in the 31-48 atom size regime, with the lowest melting temperature differing from the highest by close to 400 K. There are also large variations in the latent heats; some clusters show prominent peaks in their heat capacities, whereas for others the peak is virtually absent. A first effort is made to explain the main features of these results by investigating the geometries of the clusters using first principles density functional methods. It appears that clusters that show strong first-order phase transitions have geometries with more uniform bonding (i.e., more similar bond energies and bond lengths) than clusters that lack a strong first-order phase transition. The variation in the melting temperature is associated with the core-surface connectivity and the average coordination of the atoms in the cluster.

We have obtained the ground state and the equilibrium geometries of Au(n) (-) and Au(n-1)Cu(-) in the size range of n=13-19. We have used first principles density functional theory within plane wave and Gaussian basis set methods. For each of the cluster we have obtained at least 100 distinct isomers. The anions of gold clusters undergo two structural transformations, the first one from flat cage to hollow cage and the second one from hollow cage to pyramidal structure. The Cu doped clusters do not show any flat cage structures as the ground state. The copper doped systems evolve from a general 3D structure to hollow cage with Cu trapped inside the cage at n=16 and then to pyramidal structure at n=19. The introduction of copper atom enhances the binding energy per atom as compared to gold cluster anions.