MO-energy diagram

Fig. 12. MO energy diagram of [2,2]paracyclophanes bridged by Group 14 E-E bonds.

Textbook discussions of homonuclear diatomic molecules are commonly based on the familiar type of MO energy diagram shown in Fig. 3.28, which underlies the standard MO Aufbau procedure for constructing many-electron molecular configurations (which is analogous to the well-known procedure for atoms). Figure 3.28 purports to represent the energies and compositions of available MOs, which are... 

The general protocol for the derivation of the MO energy diagram for any molecule is outlined in this section. It is applied to the 90° water molecule as follows. 

The above interactions are made obvious in the pictorial representation of the a, and b2 orbital combination diagrams shown in Figure 5.9, and the MO energy diagram for the 90° water molecule is shown in Figure 5.10. 

The right to exist of the H2 molecule should be apparent from a glance at the MO energy diagram the molecule should be more stable than the separated atoms (disregarding interelectron repulsion, which, of course, is not allowed for in one-electron calculations). We now address the question of the nonexistence and instability of the He2 molecule. 

Fig. 7.5. MO energy diagram for homonuclear diatomic molecule X2 (where X is an atom in the Period Li—>Ne), (a) with neglect of 2s-2p overlap and (b) with 2s-2p overlap included.

This brings us to the question of how far MO theory accounts for the existence/nonexistence of diatomic molecules. The likes of He2 and BeNe are expected to be unstable in the sense that the molecules are likely to fly apart they are thermodynamically unstable with respect to the free atoms. Other molecules whose MO energy diagrams indicate stability may be collectively unstable as molecular substances, because the molecules react with each other to give more stable products, usually via dimerisation, polymerisation or disproportionation. It is not immediately obvious from a qualitative MO treatment that both NO(g) and... 

More complex polyatomic molecules AB are tackled in essentially the same way as H20. In a qualitative treatment, the most difficult part is working out the group orbitals. In the simple case of HzO, this was done by inspection. Group-theoretical techniques are available in cases where this would not be practicable. The resulting MO energy diagram, after feeding in the appropriate number of electrons, will usually confirm or... 

Fig. 8.2. MO energy diagram for octahedral ML6, considering only o bonding.

The effect upon the relevant part of the MO energy diagram is shown below ... 

Does the MO energy diagram of cyclooctatetraene (Figure 16-8) appear to be a particularly stable or unstable configuration Explain. 

The polygon rule predicts that the MO energy diagrams for these annulenes will resemble the polygonal shapes of the annulenes. 

Figure 41. Qualitative MO energy diagram for [MoO(bdt)2]1. Here, (b) represents a bonding MO and (nb) represents a non-bonding MO. [Adapted from (106).]...

Figure 3.1 shows the usual MO energy diagrams for several molecules. This is a convenient way of assessing a chemical species in cases where I and A are known. The direction of spontaneous electron flow will be from (CH3)2O to Mg, and from Mg, or (CH3)2O, to CI2. The ether is a hard molecule, which limits the amount of electron transfer, whereas Mg and CI2 are soft. The amount of initial transfer is given by the equation... 

Figure 4.1 MO energy diagram for methane in its stable tetrahedral form and in the unstable planar form.

Figure 4.7 MO energy diagrams for a ground-state molecule, M , an excited state, M, and...

Figure 19-9. MO energy diagram for the d-based orbitals of Coacacen as determined by LFDFT (see color plate section)...

Figure 19-11. MO energy diagram for complex I (Figure 19-10) calculated with LFDFT the energies of LFDFT orbitals are compared with those resulting from the average-of-configuration KS calculation. Orbital contours (pertaining to values of the density of 0.05 a.u.) are plotted, but atoms are omitted for clarity (see color plate section)...

Figure 4. MO energy diagram for O2. Eight electrons from each oxygen atom add up to 16 electrons in the O2 molecule. They combine to form the molecular orbitals indicated above.

The >S 0(0)C- species touches on another aspect of general interest, namely, the establishment of a three-electron bond between two elements of very different electronegativity. Any sulfur-oxygen interaction, in principle, constitutes an extreme situation with respect to an asymmetry in the MO energy diagram. One of the most relevant examples is probably the association of a water molecule to an oxidized sulfur radical cation, as formulated in eq. 58.56... 

The MO energy diagram of the cycloheptatrienyl cation, shown at the right, has completely filled HOMOs. Therefore it is aromatic. The anion has two more electrons, so it has half-filled HOMOs and is antiaromatic. 

As an example of a rr system involving a disulfide unit we briefly consider naphthalene-1,8-disulfide (55). Also this species belongs to a series of rr donors with remarkable electric properties The tt MO energy diagram can be constructed... 

Plan We will use the MO description of O2 to determine the desired properties. We must first determine the number of electrons in 02 and then draw its MO energy diagram. The unpaired electrons are those without a partner of opposite spin. The bond order is one-half the difference between the number of bonding and antibonding electrons. After calculating the bond order, we can use Figure 9.43 to estimate the bond enthalpy and bond length. 

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