Diatomic molecules antibonding orbitals

The three 2p orbitals from each atom can be combined to give o bonding and antibonding orbitals and n bonding and antibonding orbitals. In heteronuclear diatomic molecules, these orbitals are simply labelled c or n and do not have subscripts. The subscripts g and u refer to behaviour under inversion through the... 

Figure 6.6 shows the molecular orbital energy diagrams for a few homonudear diatomic molecules. The stability of the molecules can be estimated from the number of electrons occupying bonding orbitals compared with the number of electrons in the antibonding orbitals. (Antibonding orbitals are sometimes denoted with the subscript, as in 2jt. )... 

In diatomic molecules such as N2, O2, and CO the valence electrons are located on the 5cr, Ijt and 2jt orbitals, as shown by Fig. 6.6. [Note that the 5cr level is below the Ijt level due to interaction with the 4cr level, which was not included in the figure.] In general, the Ijt level is filled and sufficiently low in energy that the interaction with a metal surface is primarily though the 5cr and 2jt orbitals. Note that the former is bonding and the latter antibonding for the molecule. We discuss the adsorption of CO on d metals. CO is the favorite test molecule of surface scientists, as it is stable and shows a rich chemistry upon adsorption that is conveniently tracked by vibrational spectroscopy. 

Figure A.15 Energy diagram for the adsorption of a simple diatomic molecule on a d-metal. Chemisorption orbitals are constructed from both the bonding and the antibonding levels of the molecule. As the latter becomes partially occupied, the intramolecular bond of the adsorbate has been activated.

It is not difficult to draw a qualitative picture for the chemisorption of a molecule on a d-metal (see Fig. A. 15). We use again the diatomic molecule A2 with a filled bonding c-orbital as the HOMO and an empty antibonding c -orbital as the LUMO. These are the necessary steps ... 

There exists no uniformity as regards the relation between localized orbitals and canonical orbitals. For example, if one considers an atom with two electrons in a (Is) atomic orbital and two electrons in a (2s) atomic orbital, then one finds that the localized atomic orbitals are rather close to the canonical atomic orbitals, which indicates that the canonical orbitals themselves are already highly, though not maximally, localized.18) (In this case, localization essentially diminishes the (Is) character of the (2s) orbital.) The opposite situation is found, on the other hand, if one considers the two inner shells in a homonuclear diatomic molecule. Here, the canonical orbitals are the molecular orbitals (lo ) and (1 ou), i.e. the bonding and the antibonding combinations of the (Is) orbitals from the two atoms, which are completely delocalized. In contrast, the localization procedure yields two localized orbitals which are essentially the inner shell orbital on the first atom and that on the second atom.19 It is thus apparent that the canonical orbitals may be identical with the localized orbitals, that they may be close to the localized orbitals, that they may be identical with the completely delocalized orbitals, or that they may be intermediate in character. 

The diagram suggests, albeit in a crude way, that the Isa + Isb molecular orbital should be bonding, and the Isa — Isb should be antibonding. This leads to the prediction that diatomic molecules containing 2 electrons should be more tightly bound than those containing 1 or 3 electrons, and that examples such as He—He should not be stably bound. 

Problem 9-1. The bond order of a diatomic molecule is defined as [number of electrons in binding orbitals - number of electrons in antibonding orbitals]. Show that the following values are correct ... 

In a structural formula the bonds are of course localized between pairs of atoms, so that the corresponding bonding and antibonding orbitals are by implication localized in the same way. This picture of localized orbitals is adequate in general for the a orbitals of single bonds, and also for the tt orbitals of isolated double bonds such as the one in formaldehyde. The important difference between diatomic and polyatomic molecules, which was alluded to above, arises when the molecule contains alternating single and... 

Figure 2-11 Bonding and antibonding molecular orbitals composed of the p orbitals in a homonuclear diatomic molecule.

The bond order in a diatomic molecule is defined as one-half the difference between the number of electrons in bonding orbitals and the number of antibonding orbitals. The factor one-half preserves the concept of the electron pair and makes the bond order correspond to the multiplicity in the valence-bond formulation one for a single bond, two for a double bond, and three for a triple bond. Fractional bond orders are allowed, but are not within the scope of this discussion. 

If we wish to understand the conditions under which a diatomic molecule such as H2, N2, or CO dissociates on a surface, we need to take two orbitals of the molecule into account - the highest occupied and the lowest unoccupied molecular orbital (the HOMO and LUMO of the so-called frontier orbital concept). Let us take a simple case to start with the molecule A2 with occupied bonding level a and unoccupied antibonding level a. We use jellium as the substrate metal and discuss the chemisorption of A2 in the resonant level model. What happens is that the two levels broaden due to the rather weak interaction with the free electron cloud of the metal. 

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