AB Molecules

Ab initio Calculations on Molecules containing Five or Six Atoms 

Ionization potentials calculated by the ASCF24 method were studied by Guest and Saunders,29 who found that this combined SCF procedure successfully accounts for the relaxation energies computed by independent ASCF calculations. 

AB4 Molecules.—It is convenient to divide these molecules into tetrahalides AX4, where X=F, Cl, Br, or I, and AY4, where Y=0 or S. In view of the successes of minimal basis set SCF calculations in the prediction of qualitatively correct molecular geometries,3 71-73 we should first refer to an important paper by Ungemach and Schaefer.74 These authors also point out that usually DZ basis sets provide geometry predictions approaching quantitative accuracy, and the addition of polarization functions to the basis set had very little effect on the geometrical predictions. 

The authors have shown, however, that for AB4 molecules these general conclusions may not be valid. We refer to specific examples below, but it is clear that for AB4 species the predicted geometries are very sensitive to the choice of basis set. It is particularly difficult to distinguish between square-pyramidal (Civ) and detached octahedral (C2V) geometries. Examples are given in the following sections. 

BF4 and CF4. The only calculation75 found on BF4 involved a rather small basis set SCF study. Although several papers have dealt with CF4 at a minimal basis set level, the more extended basis set results of Brundle et al.76 dementi et al.,77 and Adams and Clark78 have not been improved upon. 

Adams and Clarkused a large basis set of better than DZ quality and calculated core binding energies and shifts for several fluoro- and chloro-methanes, including CFi- These were obtained using Koopmans theorem, hole state calculations, and equivalent cores calculations, the latter giving the best results for minimal basis sets, but there was little difference between the three methods for the more extended basis sets. NF4+ was also studied in this paper. 

---

There is, of course, a mass of rather direct evidence on orientation at the liquid-vapor interface, much of which is at least implicit in this chapter and in Chapter IV. The methods of statistical mechanics are applicable to the calculation of surface orientation of assymmetric molecules, usually by introducing an angular dependence to the inter-molecular potential function (see Refs. 67, 68, 77 as examples). Widom has applied a mean-held approximation to a lattice model to predict the tendency of AB molecules to adsorb and orient perpendicular to the interface between phases of AA and BB [78]. In the case of water, a molecular dynamics calculation concluded that the surface dipole density corresponded to a tendency for surface-OH groups to point toward the vapor phase [79]. 

Table 5.1 Hypothetical Step-Growth Polymerization of 10 AB Molecules ...

Figure 5.5. Schematic representation of compatible and incompatible systems, (a) Fab Fab - Fbb Mixture compatible, (b) Faa bb > ab- Molecules separate...

The difference is clearly seen for a spur initially containing two dissociations of AB molecules into radicals A and B (Pimblott and Green, 1995). Considering the same reaction radii for the reactions A + A, A + B, and B + B and the same initial distributions of radicals, the statistical ratio of the products should be 1 4 1 for A2 AB B2, since there is one each of A-A and B-B distances but there are four A-B distances. For n dissociations in the spur, this combinatorial ratio is n(n - l)/2 n2 n(n - l)/2, whereas deterministic kinetics gives this ratio always as 1 2 1. Thus, deterministic kinetics seriously underestimates cross-recombination and overestimates molecular products, although the difference tends to diminish for bigger spurs. Since smaller spurs dominate water radiolysis (Pimblott and Mozumder, 1991), many authors stress the importance of stochastic kinetics in principle. Stochasticity enters in another form in... 

For an octahedral ABS molecule such as SF6, the valence-shell orbitals are considered to be the s, p, and d orbitals of the central atom. It is easy to see that a regular octahedron has a center of symmetry so... 

Catlow and Stoneham (1983) have shown that ionic term corresponds to the difference of the diagonal matrix elements of the Hamiltonian of an AB molecule in a simple LCAO approximation (Haa cf. section 1.18.1), whereas the covalent energy gap corresponds to the double of the off-diagonal term Hab—i e.,... 

In the first case, the rate of attachment of AB molecules to the surface is proportional to the partial pressure of AB. Moreover, the rate is proportional to the vacant sites concentration. So, the rate of attachment is... 

Each Ab molecule consists of four protein chains - two light chains and two heavy chains. The chains are covalently linked to each other by disulfide bridges. The four chains come together in the shape of a Y with the ends of the arms of the Y, the amino termini of the... 

As an example of an AB molecule, we will discuss the planar symmetrical molecule BC1, which belongs to the B point group. First we assign to each chlorine atom a pair of mutually perpendicular... 

Now let us consider the important case of an octahedral AB molecule. If We associate two mutually perpendicular vectors with each atom B as in Fig. 11-4.3, we obtain the following character for rhTb ... 

The set of n A—B o bonds in AB molecules are often thought of as independent entities, and no doubt this point of view is pragmatically useful. It... 

With the case of tetrahedral AB4 molecules now fully explained, the principles required to deal with a bonding in any AB molecule should be clear. We take first the important case of an octahedral AB6 molecule. It can easily be shown that the set of six a bonding orbitals gives rise to the following representation ... 

Figure 8.6 A schematic MO diagram for an octahedral AB molecule in which only a bonding occurs. Lower case letters are used for MOs as for AOs, and the denotes an antibonding orbital.

The MO approach to a bonding in AB molecules is widely regarded as the most generally useful one for two reasons. First, it is rigorous with regard to the symmetry properties of both the basis orbitals and MOs. Second, within this symmetry-based framework, the numerical accuracy of the results can then be taken to any level desired if sufficiently elaborate computations are done. 

Long before it was. possible to perform MO calculations on even the simplest molecules, the equivalence of the bonds led to the development of a different conception of the bonding in AB molecules, in which nonequivalent AOs on the central atom are combined into hybrid orbitals. These hybrid orbitals provide a set of equivalent lobes directed at the set (or subset) of symmetry equivalent B atoms. It is therefore obvious that all A—B bonds to all equivalent B atoms will be equivalent. 

There are several other symmetries of AB molecules for which hybrid orbitals on atom A are often wanted. The results for these are summarized below. 

Figure 8.12 Coordinate system for an octahedral AB molecule or complex ion.

Figure 9.11 Two of the normal vibrations of an octahedral AB molecule in which the displacements of the atoms destroy the center of symmetry. Another type of Tlu vibration, not shown here, has the same property.

Now, it is important to remember that the activated state of AB is identical with the activated state of A + B) in collision, the reactant and the products being probably indistinguishable in the condition corresponding to activation. Hence if activated AB molecules are capable of being attached to C molecules, the colliding complex of A + B is also capable of being so held. Moreover, the activated systems have equal chances of meeting molecules of C, whether they are formed from AB molecules or by the collision of A and B. 

Fig. 6.16 Molecular Orbital pictures and qnalilalive energies of linear and bent AB molecules. Open and shaded areas represent differences in sign (+ or ) of the wave functions. Changes in shape which increase in-phase overlap lower the molecular orbital energy- From Gimarc.

Heterogeneous reactions of the type A+B = AB can, in principle, occur in two ways. 1) The product molecule AB is formed from A and B in the surrounding solvent or immediately at the surface of the AB crystal. These AB molecules are then added to the crystal on its external surface. This is additive crystal growth. 2) The solid product AB forms between A and B and separates the reactants spatially. Further reaction is possible only via (diffusional) transport across the reaction layer AB. This is reactive crystal growth [H. Schmalzried (1993)]. The moving AB interfaces in additive crystal growth are inherently unstable morphologically (see Chapter 11). 

---