Bond charge model

Weber, W. (1977) Adiabatic bond charge model for the phonons in diamond. Phys. Rev. B 15, 4789-803. 

While the above affords a fundamental route for the future, a more immediately practical approach is provided by modelling the charge density according to bond charge models. One example of these will be given below, from the work of Parr and his colleagues. 

Unfortunately, 6j8p[tr + exc] is not yet known to great accuracy. So direct quantititive study based on equation (156) has not yet proved possible to chemical accuracy. Therefore, Ray et al.91 have presented results of two kinds of calculation to illustrate the idea of electronegativity neutralization. First, they discuss the idea in the context of the simple bond charge model for diatomic molecules developed by Parr and his co-workers, one example of which was discussed in Section 13. Then they show how the idea can be developed from two alternative primitive hypotheses on the effects of charge transfer on electronegativity. 

Electronegativity Equalization in Bond Charge Model of Diatomic Molecules.—... 

Pasternak92 has considered electronegativity in the simple bond charge model of diatomic molecules. While his definition is not based on equation (156) it is not at variance with it, and Parr et al. base their first treatment of electronegativity neutralization on it. Then one can obtain a reasonable estimate of the electronegativity of AB from the electronegativity of separate atoms A and B and one can also describe the effect of heteropolarity on force constants and bond lengths. 

In the simple bond charge model for the diatomic AB, the natural definition of the electronegativity of atom A, in the final molecule after charge transfer, has the form... 

The temperature dependence of the spin-lattice relaxation time corresponding to the inelastic scattering of phonons by the Ge quadrupole moment in Ge single crystals is calculated in the framework of the adiabatic bond charge model. The results obtained agree with the experimental data. " ... 

The concept of softness is associated with polarizability. The larger the chemical system is, the softer it will be. This correlation of softness with polarizability can be found directly from a bond charge model [65 68] where softness is found to be proportional to the internuclear distance of a molecule [69-72]. To extend this definition (Eq. (28)) to open systems, the system is considered as a member of a grand canonical ensemble with bath parameters /t, v( T ), and temperature 0. This definition of S in such an ensemble can be written in terms of a number fluctuation formula [64] ... 

Lone Pair and Bond Charge Models for Fluorohydrocarbons... 

A simple bond-charge model of both homonuclear 114a) and hetero-nuclear 114b) neutral diatomic molecules has been developed by Parr, using a Fues-t5q>e vibrational potential (7/5)... 

The various methods to calculate the vibrational frequencies and force constants from ab-initio data on diatomic molecules is represented in Sections 5 A to K. It is seen that the various approximations yield results which fluctuate from molecule to molecule, although the order of magnitude is mostly correct. It is clear, however, that it is not at the present moment possible to calculate co and ke of molecules to such a d ee of accuracy that the factors which contribute to the intemudear forces in molecules can be pinpointed and compared. This is perhaps the reason why semi-empirical models continue to be exploited, e.g. the simple bond-charge model (electrostatic) model for P.E.-curves of homonudear diatomic molecules of Parr and Borckmann (114) based upon the Fues potential from which the famous Birge-Mecke relation is derived ... 

Parr RG, Borkman RF (1968) Simple bond-charge model for potentitil-eneigy curves of homonuclear diatomic molecules. 1 Chem Phys 49 1055-1058... 

Fig. tr.1-22 SiC. Phonon dispersion curves for the 3C, 2H, 4H, and 6H modifications obtained from a bond-charge model calculation [1.22]. Symbols represent experimental data. The different types of lines indicate different polarization states... 

A CNDO calculation gave fa = 0.97 mdyn/A [25]. A modified INDO calculation [26] and a calculation based on a simple bond-charge model [27] gave unsatisfactory results. 

The phonon dispersion curves of all covalent semiconductors with diamond or sphalerite structure show one characteristic feature from which only diamond itself is an exception the TA phonon branches have very low frequencies and are very flat away from the zone center, although the corresponding shear moduli (slopes of w(q) at q = 0) have rather high values. Examples of dispersion curves for Ge and GaAs are shown in Figs.4.13,14. This behaviour is most easily understood with the bond charge model which has been developed for the lattice dynamics of covalent materials. 

Fig.4 13. Phonon dispersion of Ge. The calculated frequencies (solid lines) are based on the bond charge model (4.127) containing 4 parameters only [4.17]. Dashed lines depict the results from the shell model of [4.10]...

In the bond charge model, the effect of the metal-like binding is described by central forces between nearest-neighbour ions while the covalent bonding is described by interactions involving the BC s [4.51,52]. In the adiabatic bond charge model of WEBER [4.17,18], the constraint that the BC s are fixed on the midway positions between the atoms is removed. Instead, they are allowed to move adiabatically like the electronic shells in the shell... 

Fig.4.15. Charge distribution of the bond charge model in a tetrahedrally coordinated compound. Each "ion" carries a charge +2Ze while the bond charge (BC) is -Ze...

An adiabatic bond charge model for covalent crystals has also been put forward by JOHNSON [4.53] and by JOHNSON and MOORE [4.54] in contrast to WEBER S model, all interactions in Johnsons model are purely electrostatic. Finally, it should be mentioned that bond charge models have also been used to study the vibrations of diatomic and polyatomic molecules [4.55,56]. 

---