A dynamical optimization of the minimum energy cluster structures of Na, K, Rb, and Cs clusters was performed using a many-body potential based on local density calculations. The energetics and vibrational analysis of the neutral clusters in the size range 8ϽNϽ310 were calculated, including the free energy as a function of the cluster size and the melting temperature. The fission process due to Coulomb forces of 2ϩ, 3ϩ, and 4ϩ charged alkali-metal clusters was studied extensively using molecular dynamics. We show that the cluster size at which multiply charged clusters undergo fission depends strongly on the cluster temperature. Three phases in the temperature-size-phase plane are identified corresponding to unstable, metastable, and stable clusters. These regions are bound by the spontaneous size at zero temperature and the critical size at the critical temperature. The cluster critical size exhibits a power law dependence on the total charge, which is in excellent agreement with experiments. The energy barriers that the clusters need to undergo fission are reported as a function of cluster size. The limitations of the liquid drop model are indicated in light of the dynamical findings. ͓S0163-1829͑98͒05624-0͔
We have used all-electron local ͑LDA͒ and nonlocal ͑GGA͒ approximations to the density-functional theory to determine binding energies, equilibrium geometries, vibrational frequencies, and magnetic properties of Rh N clusters (Nр6). We present careful tests on the Rh 2 dimer that compare results as calculated with a large ͑18-single Gaussian͒ and a very large ͑23-single Gaussian͒ basis sets. While the smaller set of Gaussians leads to underconverged results, we find that the large basis set leads to converged results that are also in excellent agreement with the experimental data available for Rh 2. The ground state of Rh 2 is confirmed to be a quintuplet, the trigonal Rh 3 is predicted to be a sextuplet, Rh 4 in its tetrahedral configuration is a singlet, Rh 5 sextuplet is a square pyramid, and Rh 6 septuplet is the octahedron. Results from several excited states are calculated and presented as well. It is found that LDA overestimates the binding energy but that GGA corrects this deficiency and predicts longer bond lengths. ͓S1050-2947͑98͒12909-8͔
Polypyrrole is a conjugated polymer prototype of conducting polymers. The energetically preferred spatial conformation of n-pyrrole oligomers (n=1-24) in both the reduced and oxidized phases is obtained and analyzed in this paper within the hybrid density functional theory. Binding energies, gap energies, radius of gyration, end-to-end distance, and vibrational frequencies are reported as functions of oligomer length. Reduced n-pyrrole are bent chains for all sizes showing a dramatic departure from planarity. Vibrational spectra of n-pyrrole oligomers indicate the presence of two fairly size-insensitive frequency regions, which increase in intensity with increasing oligomer size. Several oxidation levels were analyzed for n-pyrrole through the distribution of the carbon-carbon bond orders and single/double bond lengths. It is shown that the oxidation level is directly related to the way positive charge localizes along the n-pyrrole oligomer chain. If charge/n<13, the oligomers are bent and charge is delocalized; if charge/n>/=13, the oligomers are planar and charge notoriously localizes in n/charge regions along the backbone. Calculations with electronegative dopants show that charge localizes in the neighborhood of the dopant. It is demonstrated that one localized state in the gap between the highest occupied and lowest-unoccupied states appears for every +2e in the oxidation level. The band structure of infinite reduced polypyrrole gives a band gap energy in excellent agreement with experiment. The evolution of the band gap and the charge-localized band as a function of polypyrrole oxidation level is reported.
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