Shell model breathing

Figure 1. Schematic representation of the dipolar/breathing shell model for polarizability.

There is a further refinement of the shell model that is occasionally used, known as the breathing shell model (Schroder 1966). He re the shell is given a finite variable radius on which the short-range repulsive potential acts. In addition a harmonic restoring force is included about the equilibrium radius. The coupling of forces via variable radii creates a many body force that allows for the change in ionic environments between different materials. 

Catlow CRA, Cormack AN (1987) Computer modelling of silicates. Int Rev in Phys Chem 6 227-250 Catlow CRA, Faux ID, Norgett Ml (1976) Shell and breathing shell model calculations for defect formation energies and volrrmes in magnesirrm oxide. J. Phys. C Solid State Phys. 9 419-429. 

VRT Energy Transfer. Breathing Shell Model and Effective Mass Method... 

Phonon dispersion curves in the directions A, 2, and A ([ 00], [0 ], and calculated using an overlap shell model and compared with the experimental data [3, 4] for r-L ([%, ]) are shown in Fig. 92. The labels II and indicate whether the polarization of the transverse branches In the [0 ] direction Is parallel to [0T1] or to [100], respectively, Zeyher, Kress [8]. Phonon dispersion curves along r-L, r-X, and T-K calculated on a nine-parameter breathing shell model are also in good agreement with the Raman data for r-L [7], cf. [6]. 

An interesting extension of the shell model is the deformable shell model or breathing shell model introduced by SCHRODER [4.16]. This model allows for radial deformations of the shells in the course of lattice vibrations which leads to three-body interactions and, correspondingly, the model does not predict the Cauchy relations [4.46]. 

The frequency dependence of the damping and shift of the TO-mode at q = 0 has also been calculated for NaCl [5.50]. A breathing shell model was used to provide frequencies and eigenvectors necessary for these calculations. The influence of anharmonicity on the TO and LO optical phonons at q = 0 has been studied experimentally by means of the far-infrared dielectric response for 18 alkali and thallium halides [5.51], for the silver and thallium halides... 

There exist a variety of extensions of the basic shell model. One variation for molecular systems uses an anisotropic oscillator to couple the core and shell charges,thus allowing for anisotropic polarizability in nonspherical systems. Other modifications of the basic shell model that account for explicit environment dependence include a deformable or breathing shelF ° and shell models allowing for charge transfer between neighboring sites. 

Schroder K-P, Sauer J, Leshe M, Catlow CRA, Thomas JM (1992) Bridging hydroxyl-groups in zeohtic catalysts - a computer simulation of their stracture, vibrational properties and acidity in protonated faujasites (H-Y zeohtes). Chem Phys Lett 188 320-325 Schroder U (1966) A new model for lattice dynamics ( breathing shell modef). Solid State Cormnun 4 347-349... 

Since the Raman effect in these rocksalt structures measures the weighted phonon density of states, it is desirable to compute this entity. Cclio et al. (1981) used an 8 parameter shell model with defonnable ions in the spirit of Bilz et al. (1979). They decomposed the density of states into a T breathing part and a quadrupolar deformability of the Se ion. The parameters were adjusted u.sing the lattice constant, the... 

Zhang, H. and Bukowinski, M.S.T. (1991) Modified potential-induced-breathing model of potentials between closed shell ions Phys. Rev. B44, 2495-2503. 

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