Charged deformed clusters

Liquid-Drop Model for Neutral and Charged Deformed Clusters... 

Yannouleas C and Landman U 1995 Barriers and deformation In fission of charged metal clusters J. Phys. Chem. 99 14577... 

The long-range repulsion may result in limitation of the cluster size [87, 88]. Coulomb repulsion tries to break charged spherical clusters or introduce an ellipsoidal deformation [89,90]. In 1935, Weizsacker studied the stability of the atomic nucleus by analyzing the potential energy of the charged spherical cluster , [91]. In the case when the cluster is Ailed by N primary particles with radius r and charge Ze, the value of includes the volume u, surface u, and electrostatic e> terms ... 

For the more tight clusters SiO2 C70 and CS2 C7o, the local minimum of the PES corresponds to symmetric structure D h, the M(SiO) and R CS) distances are, respectively, 0.013 and 0.045 A shorter and their vstr frequencies experience a blue shift by 80 cm-1 (Si-O) and 145-245 cm-1 (C-S). As in the above clusters, the frequency of the deformation vibration nu e ) is red shifted by 78 (SiCA) and 145 (CS2) cm-1. Like the C-O and Be-F bonds, the Si-O bonds compressed in the cage become more polar. In the CS2 C7o cluster, a noticeable charge is transferred from the cage to the sulfur atoms, each of which acquires about 0.01 e (Table 11). 

Deformation density calculations [66] based on X-ray and neutron diffraction data indicated a substantial electron deficiency in the sulphur valence shell. Kappa refinement based on the point charge model relates a positive charge close to 1.8 to the sulphur, and about -1.0 on each of the sulphate oxygen atoms [66]. The comparison of these results to those obtained from MO cluster model calculations, provides an indication of the goodness of the applied atomic basis sets. Such a comparison is presented in Table 4. 

Figure 1. Total energy and the Mulliken charge on an oxygen atom of an SiOj -4e cluster for (a) Td, (b) Csv and (o) D2d deformation modes. The Si-O-e" " angle is set to 180°. Solid circles represent the cluster calculation, solid lines are the fitted potentials, and the broken lines are guides to the eye. In (b) the Mulliken charge shown by the dashed line is for the oxygen ion moved during the calculation, while that shown by the dotted line is for the fixed oxygen ions. 1 Hartree = 2.6255 X 10 kJ/mol.

We performed Hartree-Fock self-consistent-field (HF-SCF) calculation and obtained PES s corresponding to T, Csv and Did deformation modes of the cluster as shown in Fig. l(a)-(c).Douhle-zeta basis functions, which express each valence orbital of the atom with two functions, are employed with two d functions for silicon and p functions for the negative ion state of oxygen. We assume no electron orbitals around the point charges. 

Figure 2. Net potential energy surfaees for Td deformation of an SiOj -4e eluster calculated using (a) fixed charges Qi, and (b) electron charge density p(r). The full circles are the cluster calculation. The solid line is for the 0-e+ distances of 1.65A, and the dashed line is for 3.30A. The energy difference of these two net potential energy surfaces is shown with dotted lines.

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