MO Configurations of Homonuclear Diatomic Molecules

TTu2p energy level, we can use the pair of real MOs (13.80) and (13.82), or the pair of complex MOs (13.73) and (13.75), or any two linearly independent linear combinations of these functions. 

We have shown the correlation of the MOs with the separated-atoms AOs. We can also show how they correlate with the united-atom AOs. As R goes to zero, the o- li MO (Fig. 13.9) increasingly resembles the 2p AO, with which it correlates. Similarly, the TTu2p MOs correlate with p united-atom states, while the TT g2p MOs correlate with d united-atom states. 

An online simulation of Hj MOs is at www.falstad.com/qmmo you can vary the internuclear distance. 

We now use the U2 MOs developed in the last section to discuss many-electron homonuclear diatomic molecules. (Homonuclear means the two nuclei are the same heteronuclear means they are different.) If we ignore the interelectronic repulsions, the zeroth-order wave function is a Slater determinant of H -like one-electron spin-orbitals. We approximate the spatial part of the spin-orbitals by the LCAO-MOs of the last section. Treatments that go beyond this crude first approximation will be discussed later. 

The sizes and energies of the MOs vary with varying internuclear distance for each molecule and vary as we go from one molecule to another. Thus we saw how the orbital exponent k in the trial function (13.54) varied with R. As we go to molecules with higher 

Each bonding orbital fills before the corresponding antibonding orbital. The orbitals are close in energy to the ag2p orbital, and it was formerly believed that the cTg2p MO filled first. 

Besides the separated-atoms designation, there are other ways of referring to these MOs see Table 13.1. The second colmnn of this table gives the united-atom designations. The nomenclature of the third column uses ICg for the lowest Cg MO, 20-g for the second lowest Tg MO, and so on. 

A useful principle in drawing orbital correlation diagrams is the noncrossing rule, which states that for MO correlation diagrams of many-electron diatomic molecules. 

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Fig. 2.9 Changes in the energy levels of the MOs and the ground state electronic configurations of homonuclear diatomic molecules involving first-row p-block elements.

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 electron configuration of simple diatomic molecules can be discussed quite simply in terms of the MO s described on p. 84. It is only necessary, in the aufbau approach, to know the energy order of the various orbitals, and for most homonuclear molecules (taking the bond as the z axis) this is ... 

Some heteronuclear diatomic molecules, such as nitric oxide (NO), carbon monoxide (CO) and the short-lived CN molecule, contain atoms which are sufficiently similar that the MOs resemble quite closely those of homonuclear diatomics. In nitric oxide the 15 electrons can be fed into MOs, in the order relevant to O2 and F2, to give the ground configuration... 

In this section we consider homonuclear diatomic molecules (those composed of two identical atoms) formed by elements in Period 2 of the periodic table. The lithium atom has a 1 s22s electron configuration, and from our discussion in the previous section, it would seem logical to use the Li Is and 2s orbitals to form the MOs of the Li2 molecule. However, the Is orbitals on the lithium atoms are much smaller than the 2s orbitals and therefore do not overlap in space to any appreciable extent (see Fig. 14.33). Thus the two electrons... 

We have restricted all of this to homonuclear diatomic molecules. These are obviously a very small subset of the possible diatomic molecules. It is time to move on to heteronuclear molecules. We already know what needs to be considered. Let s write some configurations first, then look at the MOs in detail. 

Figure 11.20 MO occupancy and molecular properties for B2 through Ne2- The sequence of MOs and their electron populations are shown for the homonuclear diatomic molecules in the p block of Period 2 [Groups 3A(13) to 8A(18)]. The bond energy, bond length, bond order, magnetic properties, and outer (valence) electron configuration appear below the orbital diagrams. Note the correlation between bond order and bond energy, both of which are inversely related to bond length.

Transitions between electronic states of the same MO configuration are always forbidden in a homonuclear diatomic molecule. Explain why this must be true. 

For the homonuclear diatomic molecule Be2, give the MO configuration and bond order for the ground state and first excited state, based on the correlation diagram as the values of R approach (a) the separated atom limit and... 

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