Orbital Interaction Model

It is easy to show that A very likely is increased if there is an orbital contact between two electron exchanging systems. As pointed out in Section 1.4, A may be calculated at the top of the activation barrier in a symmetric system. In the case of an asymmetric system, the transition state should occur when the relevant MOs are localized half on the donor and half on the acceptor. In principle, one may find the activated geometry by modifying relevant bond lengths on the donor and/or acceptor ( relevant means consistent with the physical meaning of the reaction path). 

The most important orbitals of the pyrazine bridge for mediating the interactions between the metal ions are the HOMO and LUMO, shown on the left. The k orbital is occupied by two electrons, and the % orbital is empty. 

FIGURE 10.14 Illustration of electronic coupling via an aromatic bridge. Aj is coupling through space. Ag is coupling through bonds. 

If the larger dipyridine molecule is used as a bridge, the symmetric and antisymmetric bridge orbitals are much closer in energy. The final energy gap is thus much less. 

The discussion may be formalized using the partitioning technique of Appendix 4. The transition state may be found by inspection of the LUMO and LUMO -E 1 in the electron case and the HOMO and HOMO - 1 in the hole case. According to Equation 10.20 MOs have the character c )i + ( )2 and c )i - (f)2 at the transition state. This form is easily checked out by inspection. For this geometry, the Fock matrix may be written as (see Appendix 4) 

---

Although sophisticated electronic structure methods may be able to accurately predict a molecular structure or the outcome of a chemical reaction, the results are often hard to rationalize. Generalizing the results to other similar systems therefore becomes difficult. Qualitative theories, on the other hand, are unable to provide accurate results but they may be useful for gaining insight, for example why a certain reaction is favoured over another. They also provide a link to many concepts used by experimentalists. Frontier molecular orbital theory considers the interaction of the orbitals of the reactants and attempts to predict relative reactivities by second-order perturbation theory. It may also be considered as a simplified version of the Fukui function, which considered how easily the total electron density can be distorted. The Woodward-Hoffmann rules allow a rationalization of the stereochemistry of certain types of reactions, while the more general qualitative orbital interaction model can often rationalize the preference for certain molecular structures over other possible arrangements. 

R. A. Albright, Orbital Interactions in Chemistry John Wiley Sons, New York (1998). A. R. Leach, Molecular Modelling Principles and Applications Longman, Essex (1996). J. B. Foresman, JE. Frisch, Exploring Chemistry with Electronic Structure Methods Gaussian, Pittsburgh (1996). 

MO calculations were performed rarely for thiopyrans except for an MNDO study of 2 [84ZN(A)267], Charge distribution and orbital interaction concepts were explored in an interpretation of model reactions of thiopyrylium ions with azides giving 68 and the corresponding 3,5-unsub-stituted thiopyrans (84T3549) as well as for the equilibria between 1 and 2 or 167 and 168, respectively (92JOC4431). 

Butadiene has two n bonds. The interaction between the two n bonds is one of the simplest models to derive molecular orbitals from bond orbitals. A n bond in butadiene is similar to that in ethylene. The n bond is represented by the bonding and antibonding orbitals. The interactions occur between the n bonds in butadiene. The bond interactions are represented by the bond orbital interactions. 

The electron delocalizations in the linear and cross-conjugated hexatrienes serve as good models to show cyclic orbital interaction in non-cyclic conjugation (Schemes 2 and 3), to derive the orbital phase continuity conditions (Scheme 4), and to understand the relative stabilities (Scheme 5) [15]. 

Interactions polarize bonds. Trimethylenemethane (TMM) and 2-buten-l,4-diyl (BD) dianions (Scheme 6a, b) are chosen as models for hnear and cross-conjngated dianions. The bond polarization (Scheme 7) is shown to contain cyclic orbital interaction (Scheme 6c) even in non-cyclic conjugation [15]. The orbital phase continnity-discon-tinnity properties (Scheme 6d, e) control the relative thermodynamic stabihties. 

Benzene (Scheme 11) serves as a simple model to illnstrate the cyclic orbital interaction in the cyclic systems. 

There are assnmed to be three n bonds. A, B, and C, in benzene. Here we consider the electron delocalization from A to C. The electron delocalization via B is the same as that in the linear conjngate hexatriene (Schemes 2 and 3) used as a model of non-cyclic conjngate systems. The cyclic orbital interaction has been shown to be favored by the phase continnity (Scheme 5a). There is an additional path for the delocalization in cyclic geometry, which is the direct path from A to C or from a to c. The path gives rise to the cyclic a-b-c and a-b -c interactions. The cyclic orbital interactions satisfy the orbital phase continnity conditions... 

The n orbitals on the two CO molecules interact with the same lobe of a vacant 3p orbital on a metal atom in the model for the acute angle coordination, and with different lobes for the obtuse angle coordination (Scheme 29b). Cychc orbital interaction occurs between the occupied 3s orbital and the vacant 3p orbitals on M and the n orbitals, n, and n, of the CO molecules (Scheme 29c). The phase is continuous for the same lobe interaction and discontinuous for the different lobe interaction (Scheme 29d, cf. Scheme 4). The acute-angle coordination is favored. 

Because electrons have wave-like properties, orbital interactions involve similar addition or subtraction of wave functions. When two orbitals are superimposed, one result is a new orbital that is a composite of the originals, as shown for molecular hydrogen in Figure 10-2. This interaction is called orbital overlap, and it is the foundation of the bonding models described in this chapter. 

FIGURE 7.13 Molecular model of the pyrrolo [ 1,2-<2] i ndol e showing the site of nucleophile attack that provides a favorable stereoelectronic effect. The inset shows expected orbital interactions. 

The charge transfer model suggested to rationalize the correlati on between i oni zati on potenti al and reacti vi ti es of i ron, vanadium, and niobium with dihydrogen fails for other systems. However a model that takes into account the frontier orbital interactions, although highly simplistic, does account for a variety of observations. This model suggests extensions that include... 

As a simple model for the cr-metathesis pathway, let us examine the key orbital interactions for reaction of H2 with Hfl-FMe to produce HfH4 and methane ... 

In the present model, a maximum of two localized states arises, which depends on the initial assumptions that only one adatom orbital interacts... 

We shall first consider how nonbonded interactions influence bond angles in molecules. Our approach will be illustrated by reference to the model systems difluoro-methane and 1,1-difluoroethylene. In these problems, we shall consider not only stabilizing orbital interactions but also overlap repulsion in order to demonstrate some interesting trends which obtain in these angle problems. 

As we have already discussed in Section 1.2, there are several cases which may obtain in comparing two orbital interactions. Since all of them cannot be incorporated in any single simple framework, we have chosen to develop a model which leads to correct predictions whenever AS (A,B) < 0 and AHjj (A,B) > 0 or AS ey (A, B) < 0 and AHy (A, B) 0 (see Section 1.2). Accordingly, interactions, which are matrix element controlled should be anticipated and treated separately. 

---