Molecular Orbital Energy Level Diagrams

The combination of atomic orbitals and the relative energies of the molecular orbitals are shown by an energy-level (or molecular orbital) diagram. When the appropriate number of electrons are put into the MOs, we can calculate the bond order of a bond, which is half the difference between the number of electrons in bonding MOs and the number of electrons in antibonding MOs. A bond order of 1 corresponds to a single bond, and so forth. Bond orders can be fiactional numbers. 

Fig. 10.26 A molecular orbital energy level diagram for orbitals constructed from (Is,Is) overlap, the separation of the levels corresponding to the equilibrium bond length.

These absorptions are ascribed to n-n transitions, that is, transitions of an electron from the highest occupied n molecular orbital (HOMO) to the lowest unoccupied n molecular orbital (LUMO). One can decide which orbitals are the HOMO and LUMO by filling electrons into the molecular energy level diagram from the bottom up, two electrons to each molecular orbital. The number of electrons is the number of sp carbon atoms contributing to the n system of a neuhal polyalkene, two for each double bond. In ethylene, there is only one occupied MO and one unoccupied MO. The occupied orbital in ethylene is p below the energy level represented by ot, and the unoccupied orbital is p above it. The separation between the only possibilities for the HOMO and LUMO is 2.00p. 

Once you have calculated an ab initio or a semi-empirical wave function via a single point calculation, geometry optimization, molecular dynamics or vibrations, you can plot the electrostatic potential surrounding the molecule, the total electronic density, the spin density, one or more molecular orbitals /i, and the electron densities of individual orbitals You can examine orbital energies and select orbitals for plotting from an orbital energy level diagram. 

Figure 7.14 Molecular orbital energy level diagram for first-row homonuclear diatomic molecules. The 2p, 2py, 2p atomic orbitals are degenerate in an atom and have been separated for convenience. (In O2 and F2 the order of

Figure 14.1 Schematic molecular-orbital energy level diagram for the molecule O2 in its ground state,. The intemuclear vector is along the z-axis.

Figure 19.17 Schematic molecular energy level diagram for CO. The Is orbitals have been omitted as they contribute nothing to the bonding. A more sophisticated treatment would allow some mixing of the 2s and 2p, orbitals in the bonding direction (z) as implied by the orbital diagram in Fig. 19.18.

FIGURE 3.31 Atypical molecular orbital energy-level diagram for the homonuclear diatomic molecules Li2 through N2. Each box represents one molecular orbital and can accommodate up to two electrons. 

Step 2 Use matching valence-shell atomic orbitals to build bonding and antibonding molecular orbitals and draw the resulting molecular orbital energy-level diagram (Figs. 3.31 and 3.32). 

FIGURE 3.33 A typical d molecular orbital energy-level diagram for a heteronuclear diatomic molecule AB the relative contributions of the atomic orbitals to the molecular orbitals are represented by the relative sizes of the spheres and the horizontal position of the boxes. In this case, A is the more electronegative of the two elements. 

The molecular orbital energy-level diagrams of heteronuclear diatomic molecules are much harder to predict qualitatitvely and we have to calculate each one explicitly because the atomic orbitals contribute differently to each one. Figure 3.35 shows the calculated scheme typically found for CO and NO. We can use this diagram to state the electron configuration by using the same procedure as for homonuclear diatomic molecules. 

Sei f-Test 3.1 IB Write the configuration of the ground state of the cyanide ion, CN, assuming that its molecular orbital energy-level diagram is the same as that for CO. 

FIGURE 3.37 The molecular orbital energy-level diagram for methane and the occupation of the orbitals by the eight valence electrons of the atoms. 

FIGURE 3.39 The molecular orbital energy-level diagram for the ir-orbitals of benzene. In the ground state of the molecule, only the net bonding orbitals are occupied. 

FIGURE 3.40 The molecular orbital energy-level diagram for SFf, and the occupation of the orbitals by the 12 valence electrons of the atoms. Note that no antibonding orbitals are occupied and that there is a net bonding interaction even though no d-orbitals are involved. 

Construct and interpret a molecular orbital energy-level diagram for a homonuclear diatomic species (Sections 3.9 and 3.10). 

Draw simple molecular orbital energy-level diagrams to indicate how the bonding in the saline hydrides, such as NaH or KH, differs from that between hydrogen and a light p-block element such as carbon or nitrogen. 

For each of the following, draw a molecular orbital energy level diagram and give the bond order. Tell whether the species would be more or less stable after gaining an electron, (a) 02+ (b) CN (c) S2 (d) NO (e) Be2+. 

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