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We investigate the statics and dynamics of spatial phase segregation process of a mixture of fermion atoms in a harmonic trap using the density functional theory. The kinetic energy of the fermion gas is written in terms of the density and its gradients. Several cases have been studied by neglecting the gradient terms (the Thomas-Fermi limit) which are then compared with the Monte-Carlo results using the full gradient corrected kinetic energy. A linear instability analysis has been performed using the random-phase approximation. Near the onset of instability, the fastest unstable mode for spinodal decomposition is found to occur at q = 0. However, in the strong coupling limit, many more modes with q ≈ KF decay with comparable time scales.

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European Physical Journal D

Statics and dynamics of phase segregation in multicomponent fermion gas

Metal ([Formula presented])-encapsulated caged clusters of Ge are studied using the ab initio pseudopotential plane-wave method and the generalized gradient approximation for the exchange-correlation energy. Depending upon the size of the [Formula presented] atom, we find Frank-Kasper polyhedral [Formula presented] for [Formula presented], Zr, Hf and capped decahedral or cubic [Formula presented] and [Formula presented] clusters for several [Formula presented] atoms. The growth behavior differs from the one found in [Formula presented] clusters. The highest-occupied–lowest-unoccupied molecular orbital gaps are, however, similarly large or even higher in some cases. [Formula presented] and [Formula presented] are magnetic. The weak interaction between the clusters makes such species attractive for cluster assembled materials. {\textcopyright} 2002 The American Physical Society.

Physical Review Letters

Metal-Encapsulated Caged Clusters of Germanium with Large Gaps and Different Growth Behavior than Silicon

Vertical and adiabatic ionization potentials of small tin clusters having upto 20 atoms are numerically estimated using ab initio quantum mechanical methods. The ground state geometries and energetics of neutral and singly positively charged clusters are obtained using ultrasoft pseudopotential plane wave method with generalized gradient approximations. The calculated ionization potentials (IPs) show good agreement with the experimental results. The IPs of Sn7 and Sn10 show local maxima that corroborate the magic behavior of these clusters as found in the mass abundance spectra and photoionization experiments. A comparative study is also made to understand the effect of different exchange correlation functionals on the IPs using Gaussian molecular orbital methods. {\textcopyright} 2002 Published by Elsevier Science B.V.

Chemical Physics Letters

Ionization potentials of small tin clusters: First principles calculations

Recently, sharply reduced magnetic moments were measured in Mn13 and Mn19 clusters with values of about 0.5 $\mu$B/atom, while other clusters had moments of 1 to 1.4$\mu$B/atom. It was postulated that this sharply reduced magnetic moment results from the icosahedral growth sequence. We confirm the stability of the icosahedral structures. The icosahedral Mn13 and Mn19 clusters have several nearly degenerate low energy states, each with a low magnetic moment. It is shown that the mixture of ferromagnetic and antiferromagnetic coupling is responsible for the low net magnetic moments.

Materials Transactions

Anomalous magnetic moments of Mn13 and Mn19 clusters

Studies of the atomic and electronic structures of Pd clusters with 2-23, 55 and 147 atoms have been carried out using the ultrasoft pseudopotential plane wave method and the spin-polarized generalized gradient approximation for the exchange-correlation energy. We find predominantly an icosahedral growth in these clusters and size dependent oscillatory magnetic moments that are not confined just to the surface atoms. Atomically closed shell 13-, 55- and 147-atom clusters have large moments of (formula presented) (formula presented) and (formula presented) respectively. But cubic (formula presented) isomer has a low moment of (formula presented) only, indicating the importance of the icosahedral structure in the development of magnetism in Pd clusters. The evolutions of the (formula presented) hybridization, the magnetic moment and the electronic structure are discussed as a function of the cluster size. The magnetic energy is found to be small. Further studies on the adsorption of H and O show that though both an increase as well as a decrease of the moment are possible, often there is a reduction in the magnetic moments of Pd clusters. A hydrogen induced metal to nonmetal transition is predicted in (formula presented) and (formula presented) clusters. {\textcopyright} 2002 The American Physical Society.

Physical Review B - Condensed Matter and Materials Physics

Icosahedral growth, magnetic behavior and adsorbate-induced metal-nonmetal transition in palladium clusters

It is well known that (formula presented) bonding in carbon can result in stable cage structures, but pure Si clusters with similar cage structures are unstable. Using first-principles calculations, we show that a dodecahedral cage of silicon can be stabilized dynamically as well as energetically by doping with Ba, Sr, Ca, Zr and Pb atoms to create structures of silicon similar to that of the smallest carbon fullerene. The stability and bonding in such cages shed light on Si clathrates in which (formula presented) is the basic building block of the structure. Moreover, the charge distributions and highest-occupied-lowest-unoccupied molecular orbital gaps for these cage structures can be tuned by changing the metal atom. This allows additional freedom for the design of nanomaterials involving Si. {\textcopyright} 2002 The American Physical Society.

First-principles calculations of metal stabilized (formula presented) cages

TRANSACTIONS-MATERIALS RESEARCH SOCIETY OF JAPAN

Phase Separation in Fermion Droplets

Results of first-principles calculations on pure and doped aluminum clusters are analyzed using the electron localization function (ELF) to obtain a real-space representation of the electronic shell structure. Our results provide a quantitative analysis of the bonding nature and localization of charge in jelliumlike metal clusters and show that similar to atoms, ELF reproduces the electronic shell structure of clusters in real space. {\textcopyright} 2001 The American Physical Society.

Real-space representation of electron localization and shell structure in jelliumlike clusters

Ab-initio calculations are performed to study interaction of hydrogen on aluminum clusters. The results show large binding energies for a single hydrogen atom on Al7 and Al13 and two hydrogen atoms on Al6. The highest occupied-lowest unoccupied molecular orbital (HOMO-LUMO) gaps of Al7 and Al13 become dramatically large by absorbing hydrogen. These large binding energies and HOMO-LUMO gaps make Al7H and Al13H clusters magic(s). The atomic structures and binding energies of Al6H2 and Al8H2 are used to explain the reason why hydrogen is likely to be dissociated only on Al6. These results are discussed in the light of available experimental data and are in very good agreement with them.

Bonding character of hydrogen in aluminum clusters

Ant colony framework is illustrated by considering dynamic optimization of six important bench marking examples. This new computational tool is simple to implement and can tackle problems with state as well as terminal constraints in a straightforward fashion. It requires fewer grid points to reach the global optimum at relatively very low computational effort. The examples with varying degree of complexities, analyzed here, illustrate its potential for solving a large class of process optimization problems in chemical engineering. © 2001 Elsevier Science Ltd. All rights reserved.