Clusters population analysis

The halo globular cluster system also provides valuable information, since accurate distances, and hence reliable ages, can be derived. Mackey Gilmore (2004) recently acquired and compiled a new, nearly complete, internally consistent set of photometric studies of the globular cluster population in both the Milky Way and its satellite galaxies they deduce, from analysis of HB morphol-ogy, age, abundance and structural information, somewhat more relaxed limits... 

So, the final procedure can be described as follows we calculate an initial guess performing an ROHF calculation of the isolated and neutral cluster. Then, we add both the cluster charge and the background set of charges. If the value of the operator differs from 0.75 only at the third digit, we take this solution as acceptable and proceed to the MP2 calculation and population analysis. If the spin contamination is too large, we try to use different initial solutions until an acceptable solution is reached. 

For the C02 Cjo cluster, the translational frequencies e = 54 cm-1 and a [ = 122 cm-1 are smaller than for C2H2 C7o both these vibrations are coupled to the deformation vibrations of the guest and the cage. According to the Mulliken population analysis, there is some electron density redistribution and an increase of polarity of the both M-X bonds in the encapsulated guests, as compared to the free molecules BeF2 and CO2 (induced polarization). 

The effects of particle size on the critical thickness for ferroelectricity of nanoscale BaTiCh particles were investigated using a first-principles method and population analysis. Models composed of a small Ba8Ti706 cluster and a point charge array surrounding the cluster were used for the calculations, with the size of each... 

The simplified and convenient self-consistent-charge (SCC) - scheme is used to obtained an approximate SCF potential. By the use of Mulliken population analysis , we estimate the effective charge on each atom in the cluster from the orbital population and also estimate the strength of the covalent bonding between atoms from the overlap population. 

For a characterization of the electronic structure, the spatial electron density distributions, the bond order between atoms and ionicities of each atom in the cluster are estimated according to the Mulliken population analysis [35]. The overlap population, (2 ., of electrons between two atoms v and v is defined as,... 

Mxdliken population analysis was used for the evaluation of the net charge of each atom and the bond overlap populations of each cluster. The Fermi energy Ep of each cluster was evaluated as the midpoint of the energy gap between the highest occupied molecular orbital (HOMO) and the lowest xmoccupied molecular orbital (LUMO). In order to discuss the bonding nature, we used the familiar chemist s bond order which is the sum of the bond overlap populations between each pair of atoms in the cluster. 

In the present work, the multiplet structmre of ruby was calculated using a (CrAli4048) cluster shown in Fig. 1 (cluster model). This cluster consists of 63 atoms and is larger than the one consisting of 41 atoms adopted in our previous report (2). The results of the Mulliken population analysis (6) showed that the compositions of the impurity-state orbitals calculated for the present cluster are slightly different from those for the previous cluster. Although the difference is quite small (1.4 1.6 % for the Cr 3d composition in the t g states), this time we adopted the larger one for better accuracy. 

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