Central Atom Model

The above is not intended to be a definitive list but rather to indicate some of the more commonly used models at the present time. Other, more historical, models have been used extensively, for example the polymerisation models of Toop and Samis (1962) and Masson (1965), the models of Flood (1954), Richardson (1956) and Yokakawa and Niwa (1969). More recently the central atom model by Satsri and Lahiri (1985, 1986) and the complex model of Hoch and Arpshofen (1984) have been proposed. Each has been used with some success in lower-order systems, but the extension to multicomponent systems is not always straightforward. 

A critical part of the calculations is to calculate the tie-line at the interface corresponding to local equilibrium, and Enomoto (1992) used the central atoms model to predict the thermodynamic properties of a and 7. Some assumptions were made concerning the growth mode and the calculation of this tie-line is dependent on whether growth occurred under the following alternative conditions ... 

Eno] Enomoto, M., Aaronson H.I., Calculation of a+y Phase Boundaries in Fe-C-X Systems from the Central Atoms Model , Calphad, 9, 43-58 (1985) (Phase Relations, Calculation, 31)... 

The thermodynamic activity of carbon in ferrite alloys were measured at 712°C, 0.24 to 2.93 mass% Mo and 0 to 0.2 mass% C by [1986Wad]. The molybdenum-carbon interaction in the a was analyzed using the central atoms model, and the interaction parameter was determined as = -100 2. The Ti phase was in equilibrium with a phase over the carbon activity range from 0.045 to 0.156. The (3 phase was in equilibrium with ferrite at the carbon activity of 0.51. According to the measurements, the a + (3 + Ti equilibrium takes place at ac = 0.45. 

Eno] Calculation (central atoms model) Ferrite and austenite phase boundaries... 

Fig. 1. The time evolution (top) and average cumulative difference (bottom) associated with the central dihedral angle of butane r (defined by the four carbon atoms), for trajectories differing initially in 10 , 10 , and 10 Angstoms of the Cartesian coordinates from a reference trajectory. The leap-frog/Verlet scheme at the timestep At = 1 fs is used in all cases, with an all-atom model comprised of bond-stretch, bond-angle, dihedral-angle, van der Waals, and electrostatic components, a.s specified by the AMBER force field within the INSIGHT/Discover program.

Various other ways to incorporate the out-of-plane bending contribution are possible. For e3plane bend involves a cakulation of the angle between a bond from the central atom and the plane defined by I he central atom and the other two atoms (Figure 4.10). A value of 0° corresponds to all four atoms being coplanar. A third approach is to calculate the height of the central atom above a plane defined by the other three atoms (Figure 4.10). With these two definitions the deviation of the out-of-plane coordinate (be it an angle or a distance) can be modelled Lt ing a harmonic potential of the form... 

Valence shell electron pair repulsion (VSEPR) model (Section 110) Method for predicting the shape of a molecule based on the notion that electron pairs surrounding a central atom repel one another Four electron pairs will arrange them selves in a tetrahedral geometry three will assume a trigo nal planar geometry and two electron pairs will adopt a linear arrangement... 

In this section we apply this model to predict the geometry of some rather simple molecules and polyatomic ions. In all these species, a central atom is surrounded by from two to six pairs of electrons. 

Figure 7.5 (page 177) shows the geometries predicted by the VSEPR model for molecules of the types AX2 to AX. The geometries for two and three electron pairs are those associated with species in which the central atom has less than an octet of electrons. Molecules of this type include BeF2 (in the gas state) and BF3, which have the Lewis structures shown below ... 

In many molecules and polyatomic ions, one or more of the electron pairs around the central atom are unshared. The VSEPR model is readily extended to predict the geometries of these species. In general—... 

Geometries of molecules such as these can be predicted by the VSEPR model The results are shown in Figure 7.8 (page 181). The structures listed include those of all types of molecules having five or six electron pairs around the central atom, one or more of which may be unshared. Note that—... 

The VSEPR model applies equally well to molecules in which there is no single central atom. Consider the acetylene molecule, C2H2. Recall that here the two carbon atoms are joined by a triple bond ... 

VSEPR model Valence Shell Electron Pair Repulsion model, used to predict molecular geometry states that electron pairs around a central atom tend to be as far apart as possible, 180-182... 

In this section, we construct a model of molecular shape empirically, which means that we base it on rules suggested by experimental observations rather than on more fundamental principles. We proceed in three steps. First, we set up the basic nodel for simple molecules without lone pairs on the central atom. Then, we elude the effects of lone pairs. Finally, we explore some of the consequences of ecular shape. 

A molecule with only two atoms attached to the central atom is BeCl2. The Lewis structure is CI — Be — CE, and there are no lone pairs on the central atom. To be as far apart as possible, the two bonding pairs lie on opposite sides of the Be atom, and so the electron arrangement is linear. Because a Cl atom is attached by each bonding pair, the VSEPR model predicts a linear shape for the BeCL molecule, with a bond angle of 180° (4). That shape is confirmed by experiment. 

When there is more than one central atom in a molecule, we concentrate on each atom in turn and match the hybridization of each atom to the shape at that atom predicted by VSEPR. For example, in ethane, C2H6 (38), the two carbon atoms are both central atoms. According to the VSEPR model, the four electron pairs around each carbon atom take up a tetrahedral arrangement. This arrangement suggests sp hybridization of the carbon atoms, as shown in Fig. 3.14. Each... 

Below are ball-and-stick models of two molecules. In each case, indicate whether or not there must be, may be, or cannot be one or more lone pairs of electrons on the central atom ... 

If the central atom has different groups or atoms around it, or if one or more of the vertices of the polyhedron is occupied by a lone pair, then variations in bond angles will occur such that distorted polyhedral arrangements are obtained. In its quantitative forms, the VSEPR model parameterizes each individual interaction and makes very accurate predictions of the distortions which are to be expected. 

C09-0133. Among the halogens, only one known molecule has the formula X 7. It has pentagonal bipyramidal geometry, with five Y atoms in a pentagon around the central atom X. The other two Y atoms are in axial positions. Draw a ball-and-stick model of this compound. Based on electron-electron repulsion and atomic size, determine the identities of atoms X and Y. Explain your reasoning. (Astatine is not involved. This element is radioactive and highly unstable.)... 

---