Molecular-Orbital Picture

The picture of benzene as a planar framework of ct bonds with six electrons m a delo cahzed rr orbital is a useful but superficial one Six elecfrons cannof simulfaneously occupy any one orbifal be if an afomic orbifal or a molecular orbifal We can fix fhis wifh the more accurate molecular orbital picture shown m Figure 114 We learned m Section 2 4 that when atomic orbitals (AOs) combine to give molecular orbitals (MOs) the final number of MOs musf equal fhe original number of AOs Thus fhe six 2p AOs of SIX sp hybridized carbons combine fo give six tt MOs of benzene... 

The first step in constructing a molecular orbital picture of a chemical reaction is to decide which orbitals are most likely to serve as the electron donor and electron acceptor orbitals. It should be obvious that the electron donor orbital must be drawn from the set of occupied orbitals, and the electron acceptor orbital must be an unoccupied orbital, but there are many orbitals in each set to choose from. 

Draw the structure of 1,3-pentadiene. Use valence-bond and molecular orbital pictures to describe the bonding for the (T-framework and -n-orhitals, respectively. 

A simple molecular orbital picture (using, e.g., an species for... 

Fukui functions and other response properties can also be derived from the one-electron Kohn-Sham orbitals of the unperturbed system [14]. Following Equation 12.9, Fukui functions can be connected and estimated within the molecular orbital picture as well. Under frozen orbital approximation (FOA of Fukui) and neglecting the second-order variations in the electron density, the Fukui function can be approximated as follows [15] ... 

In particular the last observation is easily understood by the molecular orbital picture given above. The 7z>orbitals of the monomers are required for a stabilization of the otherwise anti-bonding cluster orbitals of t2 symmetry which must accept six electrons. If this mixing is prevented because these orbitals adopt the electron density of the ligands, e.g., 7z>electrons of the side-on coordinated cyclopentadienyl groups, their contribution to the cluster stability is minimized or in particular cases the formation of clusters does not occur at all. Thus, the substituents attached terminally to the clusters strongly influence their stability by the different donor or acceptor capabilities. A further effect may result from the different steric demand of the substituents which will be discussed below. 

As can be seen from the energy level structure diagram, the relative position of the HOMO and LUMO levels are not less important than the energy gap between them, since they control the possibility of charge injection. At this point, however, note, that a MO scheme is often used for illustration, but more properly the total energy states of the molecules and their radical cations and anions that may be subjected to electronic rearrangement have to be considered. Bearing this in mind, the measured values of redox potentials can be translated into the molecular orbital picture. 

Corresponding to this valence bond view is a molecular orbital picture. The three cr-orbitals of a CH3 group are regarded as a basis from which three group orbitals may be constructed. One of the possible combinations of the tr-orbitals has the same local symmetry as the vacant p-orbital on the cationic centre, and hence may overlap with it. Therefore, a withdrawal of electrons from the methyl group can take place. The orbital from which electron density... 

Stabilized allyl radical will be stabilized further if substituents are introduced. This stabilization occurs to different degrees in the ground state and the transition structure for rotation. In the ground state the substituent acts on a delocalized radical. Its influence on this state should be smaller than in the transition structure, where it acts on a localized radical. In the transition state the double bond and the atom with the unpaired electron are decoupled, i.e. in the simple Hiickel molecular orbital picture, the electron is localized in an orbital perpendicular to the jt(- c bond. 

The molecular orbital picture of benzene proposes that the six jt electrons are no longer associated with particular bonds, but are effectively delocalized over the whole molecule, spread out via orbitals that span all six carbons. This picture allows us to appreciate the enhanced stability of an aromatic ring, and also, in due course, to understand the reactivity of aromatic systems. There is an alternative approach based on Lewis structures that is also of particular value in helping us to understand chemical behaviour. Because this method is simple and easy to apply, it is an approach we shall use frequently. This approach is based on what we term resonance structures. 

These simple molecular orbital pictures provide useful descriptions of the structures and spectroscopic properties of planar conjugated molecules such as benzene and naphthalene, and heterocychc species such as pyridine. Heats of combustion or hydrogenation reflect the resonance stabilization of the ground states of these systems. Spectroscopic properties in the visible and near-ultraviolet depend on the nature and distribution of low-lying excited electronic states. The success of the simple molecular orbital description in rationalizing these experimental data speaks for the importance of symmetry in determining the basic characteristics of the molecular energy levels. 

It is essential to have tools that allow studies of the electronic structure of adsorbates in a molecular orbital picture. In the following, we will demonstrate how we can use X-ray and electron spectroscopies together with Density Functional Theory (DFT) calculations to obtain an understanding of the local electronic structure and chemical bonding of adsorbates on metal surfaces. The goal is to use molecular orbital theory and relate the chemical bond formation to perturbations of the orbital structure of the free molecule. This chapter is complementary to Chapter 4, which... 

Quantum chemical methods may be divided into two classes wave function-based techniques and functionals of the density and its derivatives. In the former, a simple Hamiltonian describes the interactions while a hierarchy of wave functions of increasing complexity is used to improve the calculation. With this approach it is in principle possible to come arbitrarily close to the correct solution, but at the expense of interpretability of the wave function the molecular orbital concept loses meaning for correlated wave functions. In DFT on the other hand, the complexity is built into the energy expression, rather than in the wave function which can still be written similar to a simple single-determinant Hartree-Fock wave function. We can thus still interpret our results in terms of a simple molecular orbital picture when using a cluster model of the metal substrate, i.e., the surface represented by a suitable number of metal atoms. 

Figure 2 Zeroth-order molecular orbital picture of the bonding in MoSi.

It needs to be stressed that this simple molecular orbital picture is not appropriate for all purposes, but it is convenient for visualizing the changes brought about by light absorption in organic molecules, and as a qualitative basis for describing the mechanisms of organic photochemical reactions. 

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.

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