Frontier orbital model

The basis of electrocyclic reactions can be considered in terms of the molecular orbitals involved. By considering the phasing of the molecular orbitals it is possible to say whether a reaction can proceed (only orbitals of the same phase can overlap and bond) and to predict the stereochemistry of the reaction. This approach is called the frontier orbital model. 

The relative rates of reaction of the singlet TMM derivative 14b with a series of alkenes (32) parallel those of a conjugated diene with the same alkenes in Diels-Alder reactions. These relative rates also are well correlated by the frontier orbital model for a concerted reaction. The absolute rates of the biradical cycloadditions are many orders of magnitude greater than those of the model dienes. The relative rates of the alkenes in the cycloadditions of the triplet biradical 14b, on the other hand, follow the reactivity order of their addition reactions with monoradicals. 

The description of the bonding of unsaturated hydrocarbons to metals was originally developed by Dewar, Chatt and Duncanson and is now known as the well-established DCD model based on a frontier-orbital concept [82]. In this model, the interaction is viewed in terms of a donation of charge from the highest occupied -orbital into the metal and a subsequent backdonation from filled metal-states into the lowest unoccupied -orbital, see Figure 2.33. Contrary to the case of the standard Blyholder model for CO and N2 the DCD frontier-orbital model is supported by experimental XES measurements [83]. In the present section, we will show how we can experimentally identify and quantify the contributions of the different -orbitals involved in the interaction with the surface. The DCD model will be shown to very well describe the chemical bonding of ethylene on Cu and Ni surfaces. Furthermore, the differences in bonding of benzene to Cu and Ni will be discussed. 

The frontier orbital model predicts regioselectivity by determining the relative magnitudes of the coefficients in the HOMO and LUMO of the 1,3-dipole and dipolarophile.65,66 The favored cycloadduct will be that formed by the privileged union of the atoms with the largest coefficients.51,54,58 If the energy of interaction is very small for both possible orientations, addition occurs in both directions and two isomeric triazolines will be obtained.54,67... 

Topological control of the position of the carbonyl groups on the properties of 4-azaazulenones 4-8 has been studied by self-consistent field (SCF) calculations and a frontier orbital model was proposed based on dipolar structures of oxo derivatives, such as 4a and 6a (85MI2, 85UP1). 

The LDOS-based frontier orbital model is different from the simpler collective-electron model, in which all local information is averaged out. In the context of alloys. Ponec and Bond (23. p. 451). stated that it must be clear to the reader that (the collective electron model of catalytic activity of alloys] has now been consigned to the trash can of science. . . [because of] the discovery that, more in tune with chemists intuition, the atoms in an alloy retain their identity more or less completely. Such local properties disappear from the collective-electron model in which it was supposed that the available electrons were equally shared by aU the atoms present, and that. .. the density of states at the Fermi surface or some related... 

LDOS of different symmetries (cr, n, and 8). This is not due to a failure of the frontier orbital model but simply to the fact that the NMR experiment yields just two numbers, a shift and a relaxation rate. 

Further evidence for the validity of the frontier orbital approach derives from its success in predicting the shift (increase or decrease) in naked cluster IP upon the chemisorption of small reactant molecules. For all metal clusters examined thus far, H2 chemisorption induces an increase in cluster IP. ° This follows directly from interactions (1) and (2), since the creation of the two new metal-hydride bonding orbitals effectively removes two electrons from the cluster valence orbital manifold. Thus with resjiect to the metal cluster, H2 chemisorption can be viewed as an oxidative addition process. If a one-electron (Aufbau filling) approximation is assumed as above, the Fermi level of the cluster is shifted toward lower energy, that is, there is an increase in IP. As the cluster grows larger, the shift in IP diminishes. This is simply a manifestation of cluster-size-dependent variations in the valence orbital density of states, and is again consistent with the frontier orbital model. 

It is important to note that the Laplace concentration reflects the effects of all occupied MOs and, therefore, provides a more reliable description than the frontier MOs that often must be supplemented by the next lower (higher) orbital to the HOMO (LUMO) to reproduce experimental findings. However, it must be born in mind that the analysis of the Laplace concentration as well as the frontier orbital model are both not sufficient to distinguish between bonding and nonbonding situations and to draw a border line between electrostatic and covalent Ng,X bonding. 

All excited states of HeX" " listed in Table 7 possess a He,X bond with covalent character according to the properties of the calculated electron and energy distribution [4], The pg and Hg data in Table 7 suggest that the He,B bond is the weakest Ng, X bond, actually more electrostatic than covalent. The strongest covalent bond is found for HeN ( n), which is in line with the frontier orbital model (Sect. 4.3) and the Laplace description of He,X interactions. 

The a orbital of a C-X bond, is, like the p-type lone pair on oxygen, composed of two approximately equal lobes. The overlap between the p-type lone pair and the ct orbital of an axial C-X bond in a pyranose ring is relatively efficient [the dihedral angle about C1-05 bond described by the axis of the p-type lone pair and the a orbital will be about 30° p-p overlap of this type varies approximately as the square of the cosine of the dihedral angle and cos (30°) = 0.75]. While the overlap of the sp lone pair with an equatorial C-X bond is geometrically optimal, the electrons in an sp orbital are held very much closer to the nucleus than those of a p orbital and are much less readily available for donation. The anomeric effect, on the frontier orbital model, thus corresponds to no bond resonance in the sense shown, but only in the axial position (Figure 2.12). 

R. Cohen et al.. Frontier Orbital Model of Semiconductor Surface Passivation Dicar-boxylic Acids on n- and p-GaAs, Adv. Mater. 

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