In this work, we present modifications to the well-known basin hopping (BH) optimization algorithm [D. J. Wales and J. P. Doye, J. Phys. Chem. A 101, 5111 (1997)] by incorporating in it the unique and specific nature of interactions among valence electrons and ions in carbon atoms through calculating the cluster's total energy by the density functional tight-binding (DFTB) theory, using it to find the lowest energy structures of carbon clusters and, from these optimized atomic and electronic structures, studying their varied forms of topological transitions, which include a linear chain, a monocyclic to a polycyclic ring, and a fullerene/cage-like geometry. In this modified BH (MBH) algorithm, we define a spatial volume within which the cluster's lowest energy structure is to be searched, and introduce in addition a cut-and-splice genetic operator to increase the searching performance of the energy minimum than the original BH technique. The present MBH/DFTB algorithm is, therefore, characteristically distinguishable from the original BH technique commonly applied to nonmetallic and metallic clusters, technically more thorough and natural in describing the intricate couplings between valence electrons and ions in a carbon cluster, and thus theoretically sound in putting these two charged components on an equal footing. The proposed modified minimization algorithm should be more appropriate, accurate, and precise in the description of a carbon cluster. We evaluate the present algorithm, its energy-minimum searching in particular, by its optimization robustness. Specifically, we first check the MBH/DFTB technique for two representative carbon clusters of larger size, i.e., C60 and C72 against the popular cut-and-splice approach [D. M. Deaven and K. M. Ho, Phys. Rev. Lett. 75, 288 (1995)] that normally is combined with the genetic algorithm method for finding the cluster's energy minimum, before employing it to investigate carbon clusters in the size range C3-C24 studying their topological transitions. An effort was also made to compare our MBH/DFTB and its re-optimized results carried out by full density functional theory (DFT) calculations with some early DFT-based studies.

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We perform isothermal Brownian-type molecular dynamics simulations to obtain the velocity autocorrelation function and its time Fourier-transformed power spectral density for the metallic cluster Ag(17)Cu(2). The temperature dependences of these dynamical quantities from T = 0 to 1500 K were examined and across this temperature range the cluster melting temperature T(m), which we define to be the principal maximum position of the specific heat is determined. The instantaneous normal mode analysis is then used to dissect the cluster dynamics by calculating the vibrational instantaneous normal mode density of states and hence its frequency integrated value I(j) which is an ensemble average of all vibrational projection operators for the jth atom in the cluster. In addition to comparing the results with simulation data, we look more closely at the entities I(j) of all atoms using the point group symmetry and diagnose their temperature variations. We find that I(j) exhibit features that may be used to deduce T(m), which turns out to agree very well with those inferred from the power spectral density and specific heat.

The isothermal Brownian-type molecular dynamics simulation was applied to study the melting scenario of noblemetal-based bimetallic clusters. The failure of the simulation results to portend a compatible melting temperature, T melt , which is defined in the specific heat CV at its principal peak and in the Lindermann-like parameter at the temperature which it exhibits drastic change, has prompted us to calculate the velocity autocorrelation function VACF or its Fourier-transform, the power spectrum as another useful variable for describing cluster melting. Two bimetallic clusters, namely Ag13Au1 and Ag13Cu1, were selected for illustration. We effected comparative studies of the thermal and dynamic properties of the Ag13Au1, Ag13Cu1 and Ag14 and explored isothermally the VACF and spectral density of individual atoms in each of these clusters as well as the corresponding whole cluster. We examined, in particular, the influence of the impurity atoms Au and Cu. It is observed that the CV of Ag14 displays a prepeak which is absent in Ag13Au1 and Ag13Cu1. The physical origin of this prepeak feature was studied and its presence is ascribed to the migrational relocation of the adatom in the cluster. From the temperature change of VACF and spectral density, we deduced T melt . It is found that the calculated T melt inferred from VACF and power spectrum agrees quite well with that determined from the main peak position of CV .

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