The MO Model

Molecular orbitals can be thought to be generated by the overlap of atomic orbitals, which are wave functions that may reinforce the composite wave function (in-phase overlap) or may destructively interfere with it (out-of-phase overlap). In-phase overlap of s atomic orbitals or of end-on p orbitals is particularly effective 

We observe that as the -C=C- chromophore accumulates, the required transition energy decreases such that we would expect that a transition in the visible region would eventually become possible. Nature has actually given us such a molecule, containing 11 such chromophores jS-carotene, known to all for its orange color due to absorption in the blue region of the visible spectrum its absorption maximum is 470 nm (about 2.5 eV) (Fig. 3.4). 

An example of the effect of the presence of heteroatoms, especially those containing lone pairs of electrons, can be seen in comparing stilbene, which is colorless, with azobenzene, which is orange. The presence of the non-bonded electrons on the nitrogens in the azo compound allow for n tt transitions, which occur for the most part in the visible region of the spectrum (Fig. 3.5). 

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The foregoing discussion indicates that while there are difficulties in the way of a bonding role for 3d orbitals, for certain situations at least it is possible to conceive of ways in which these difficulties may be overcome. However, it is necessary to say that even for hypervalent molecules such as SF6 which seem to require the use of d orbitals, there are molecular orbital treatments not involving the use of d orbitals. In fact, as shown by Bent in an elegant exposition12, the MO model of SF6 involving the use of d orbitals is only one of several possibilities. The octahedral stereochemistry of SF6, traditionally explained in... 

The second of these four consequences has proved to be the most unfortunate. Even when a set of parameters has been consciously optimised within the MO model (and there can be no objection of principle to the conscious use of the MO framework as a numerical interpolation device), the temptation to improve on the MO results has proved irresistable. We can therefore And Cl and VB calculations using molecular integrals which have been constrained by the invariance requirement to be meaningful only in the MO framework. 

The most widely used qualitative model for the explanation of the shapes of molecules is the Valence Shell Electron Pair Repulsion (VSEPR) model of Gillespie and Nyholm (25). The orbital correlation diagrams of Walsh (26) are also used for simple systems for which the qualitative form of the MOs may be deduced from symmetry considerations. Attempts have been made to prove that these two approaches are equivalent (27). But this is impossible since Walsh s Rules refer explicitly to (and only have meaning within) the MO model while the VSEPR method does not refer to (is not confined by) any explicitly-stated model of molecular electronic structure. Thus, any proof that the two approaches are equivalent can only prove, at best, that the two are equivalent at the MO level i.e. that Walsh s Rules are contained in the VSEPR model. Of course, the transformation to localised orbitals of an MO determinant provides a convenient picture of VSEPR rules but the VSEPR method itself depends not on the independent-particle model but on the possibility of separating the total electronic structure of a molecule into more or less autonomous electron pairs which interact as separate entities (28). The localised MO description is merely the simplest such separation the general case is our Eq. (6)... 

These latter considerations clarify our position on the use of particular models of molecular electronic structure. The electron-pair model is not absolutely preferable to the MO model in all respects, that is the electron-pair model is not to be recommended per se, but is to be preferred in most systems consisting of ground states of saturated bonds. 

Several other molecular orbital models have been applied to the analysis of VCD spectra, primarily using CNDO wave functions. The nonlocalized molecular orbital model (NMO) is the MO analog of the charge flow models, based on atomic contributions to the dipole moment derivative (38). Currents are restricted to lie along bonds. An additional electronic term is introduced in the MO model that corresponds to s-p rehybridization effects during vibrational motion. 

In Table 13, calculated and measured geometry data of substituted cyclopropanes are compared with predictions of the MO model of Clark andcoworkers (Table 14)33 and those of the electron density model by Cremer and Kraka (Table 15)97. From the comparison, it becomes clear that both models lead to similar predictions, but differ with regard to some... 

Summary. The electron density model of substituent-ring interactions functions better than the MO model, which is not surprising since the electron density covers all MO effects while any MO model will simplify orbital interactions by selecting just a few important... 

Construct a complete orbital model for HN3, showing both a and tt molecular orbitals, and giving an approximate energy-level diagram showing electron occupancy. Compare the MO model with the resonance model. 

Tungsten is hard and has a very high melting point (3422°C), and gold is soft and has a relatively low melting point (1064°C). Are these facts in better agreement with the electron-sea model or the MO model (band theory) Explain. 

In the valence-bond (VB) model, this effect results from the fact that radicals of this type can be stabilized by resonance (Table 1.1, right). In the MO model, the stabilization of radical centers of this type is due to the overlap of the n system of the unsaturated substituent with the 2pz AO at the radical center (Figure 1.5). This overlap is called conjugation. 

Alkynyl substituents stabilize a radical center by the same 12 kcal/mol that on average is achieved by alkenyl and aryl substituents. From the point of view of the VB model this is due to the fact that propargyl radicals exhibit the same type of resonance stabilization as formulated for allyl and benzyl radicals in the right column of Table 1.1. In the MO model, the stability of propargyl radicals rests on the overlap between the one correctly oriented n system of the C=C triple bond and the 2 pz AO of the radical center, just as outlined for allyl and benzyl radicals in Figure 1.5 (the other 7t system of the C=C triple bond is orthogonal to the 2pz AO of the radical center, thus excluding an overlap that is associated with stabilization). 

In the MO picture, there will be a bonding MO (and an antibonding MO) for each bond in die Lewis structure. Furthermore, the MO model must be in accord with experimental observations. Experiments have shown that the bonds in methane are all identical, with tetrahedral geometry. Therefore, methane must have four equivalent bonding MOs, with a tetrahedral arrangement. 

Benzene has two major resonance structures that contribute equally to the resonance hybrid. These are sometimes called Kekule structures because they were originally postulated by Kekule in 1866. You may also encounter benzene written with a circle inside the six-membered ring rather than the three double bonds. This representation is meant to show that the bonds in benzene are neither double nor single. However, the circle structure makes it difficult to count electrons. This text uses a single Kekule structure to represent benzene or its derivatives. You must recognize that this does not represent the true structure and picture the other resonance structure or call upon the MO model presented in Section 16.3 when needed. 

Ionization of H2 can be described as removing an electron from the bonding MO and Koopmans theorem states that the ionization energy IE = — eMo- The MO model suggests that IE(H2) should be larger than IE(H) = 13.6 eV. As shown by its photoelectron spectrum, IE(H2) = 15.4eV. The photoelectron spectrum gives us additional information about the nature of the occupied molecular orbital from the fine structure observed in the photoelectron band. This fine structure corresponds to vibrational excitation of the molecular ion H2+ and reports on the role of the electron... 

To test your understanding of the MO model for a typical octahedral coordination complex, construct an appropriate, qualitative MO diagram for Oh SHg (a model for known SF6). Hint first calculate the total number of MOs you should end up with from the number of available basis functions (AOs). Second, compare the valence AO functions of S with those of a transition metal (refer to Figure 1.9 and realize that, for a coordinate system with the H atoms on the x, y and z axes, the AO functions of the central atom and the symmetry-adapted linear combinations of ligand functions transform as s, aig p, tiu djey d dy, t2g dx2-y2 dz2, eg in the Oh point group). Now count the number of filled MOs and the number of S-H bonding interactions. 

Halocyclopropanes. According to Clark and coworkers,F acts predominantly as cr-acceptor. If 71-donor ability is invoked for F, then controversial geometry effects are predicted by the MO model. Predictions by the electron density model of Cremer and Kraka are consistent, no matter whether cr-attractor or 7r-repeller ability of F is considered (Table 13). The other halogens are also cr-attractors/7r-repellers but their effects on the geometry of 1 decrease in the order... 

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