Second-Row Homonuclear Diatomic Molecules

2-9 SECOND-ROW HOMONUCLEAR DIATOMIC MOLECULES Let US proceed now to the atoms in the second row of the periodic table, namely, Li, Be, B, C, N, O, F, and Ne. These atoms have 2s, Ipx, 2py, and Ip valence orbitals. We first need to specify a coordinate system for the general homonuclear diatomic molecule A2, since the Ip orbitals have directional properties. The z axis is customarily assigned to be the unique molecular axis, as shown in Fig. 2-10. The molecular orbitals are obtained by adding and subtracting those atomic orbitals that overlap. 

The Is and Ipz orbitals combine to give cr molecular orbitals, as illustrated in Fig. 2-11. The normalized wave functions are  

Notice that the cr molecular orbitals are symmetric for rotation about the z axis. 

The Ipx and Ify orbitals are not symmetric for rotation about the z axis. The two Ipx orbitals overlap to give the molecular orbital shown in Fig. 2-12. This molecular orbital has a plus lobe on one side of the z axis and a minus lobe on the other side. So if we rotate the molecular orbital by 180°, it simply changes sign. Multiplication by — 1 restores the original orbital. In other words, there is a node in th.eyz plane as shown in Fig. 2-13. A molecular orbital of this type is called a tt molecular orbital. It is clear that the two Ipy orbitals can also overlap to give tt molecular orbitals, which have a node in the xz plane. There will be tt bonding (tt ) and ir antibonding (j ) molecular orbitals the more stable orbitals will have a 

The relative positioning of the ffj level is uncertain. When the Is-lp energy difference is large, r is probably more stable than fl-, /, as shown in Fig. 2-15. We should emphasize here that it is a good approximation to consider the r, molecular orbitals as com- 

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O Albert Haim, "The Relative Energies of Molecular Orbitals for Second-Row Homonuclear Diatomic Molecules The Effect of s-p Mixing," /. Chem. Educ., Vol. 68, 1991,737-738. 

Table 3.3.2 summarizes the various properties of second-row homonuclear diatomic molecules. In the last column of the table, we list the bond order between atoms A and B in the molecule AB. Simply put, the bond order is a number that gives an indication of its strength relative to that of a two-electron single bond. Thus the bond order ofHf (cr ) is 1/2, while that of H2 (afs) is 1. For a system with antibonding electrons, we take the simplistic view that one antibonding electron cancels out one bonding electron. Thus the bond orders in lief (ofs o-j 1) and He2 (ofs aj s2) are 1 /2 and 0, respectively, and helium is not expected to form a diatomic molecule. 

Table 1 Bond orders of second-row homonuclear diatomic molecules with bond lengths and energies...

A. HAIM, The relative energies of molecular orbitals for second-row homonuclear diatomic molecules. J. Chem. Educ., 68, Til (1991). 

Figure 9.38 Energy-level diagram for MOs of second-row homonuclear diatomic molecules. The diagram assumes no interaction between the 2s atomic orbital on one atom and the 2p atomic orbitals on the other atom and experiment shows that it fits only for O2, F2, and Ne2-... 

Give the term symbol for the ground-state electron configuration of each of the second-row homonuclear diatomic molecules (Li2 through F2). 

A large number of strongly bound molecules have been studied with the correlation consistent basis sets, including the first- and second-row diatomic hydrides, the first-and second-row homonuclear diatomics, mixed first- and second-row heteronuclear diatomics, etc. As archetypes of strongly bound molecules, we will focus here on the CH, HF, N2, and CO molecules and the CH and C2H (n = 1-4) series. It is unlikely that these molecules will be fully representative of the class of strongly bound molecules. However, they display a range of behaviors that provide important insights into the selection of basis sets for molecular calculations. 

Table 6.1 shows the bond energies, the bond lengths and the magnetic features of homonuclear diatomic molecules and ions involving second row elements. 

Which of the homonuclear diatomic molecules of the second row of the periodic table (Li2 to Nc2) are predicted by MO theory to be paramagnetic Which ones are predicted to have a bond order of one Which ones are predicted to have a bond order of two Which one is predicted to have the highest bond order ... 

Studies on molecular charge distributions and chemical binding due to Bader and co-workers include the first-row homonuclear diatomics (Bader et al., 1967a), the first-row diatomic hydrides (Bader et al., 1976b), the first-row 12- and 14-electron diatomic series (Bader and Bandrauk, 1968a), the second-row diatomic hydrides (Cade et al., 1969), and the excited, ionized, and electron-attached states of several diatomic molecules (Cade et al., 1971). Bader (1970, 1975,1981), Deb (1973), and Mulli-ken and Ermler (1977) review their works in some detail. 

A homonuclear diatomic molecule is one in which both nuclei are the same, for example H2 and N2. In the first row of the Periodic Table, H2 is the only example. From the second row we have N2, 02 and F2, which are stable under normal conditions of temperature and pressure. We looked at N2 in the previous Section. Here we shall consider the molecular orbital description of 02, and use it as an example of how we can use the theory to explain and/or predict properties of molecules. 

Just as we treated the bonding in H2 by using molecular orbital theory, we can consider the MO description of otiier diatomic molecules. Initially we will restrict our discussion to homonuclear diatomic molecules (those composed of two identical atoms) of elements in flie second row of the periodic table. As we will see, die procedure for determining the distribution of electrons in these molecules closely follows the one we used for H2. 

Figure 10.34 shows the relative energies of the molecular orbitals obtained from 2s and 2p atomic orbitals. This order of molecular orbitals reproduces the known electron configurations of homonuclear diatomic molecules composed of elements in the second row of the periodic table. The order of filling is... 

A FIGURE 10.15 Molecular Orbital Energy Diagrams for Second-Row p-block Homonuclear Diatomic Molecules... 

All the molecules considered so far have had H as one of the participants in the bonding scheme. In this section we will start to consider the MOs produced for interactions between heavier atoms, beginning with homonuclear diatomics, A2, of second-row elements. General MO diagrams for these diatomics will be constructed and then used to discuss the relative stability of those that are observed experimentally N2, O2 and F2 and those that are not found under normal circumstances, Li2, Be2, B2 and C2. In common with H2, these molecules all belong to the Dooh point group and so the 2s valence orbitals will be linked together as <7g+ and SALCs ... 

The next homonuclear molecule composed of second row elements is B2, which has six total valence electrons to accommodate. We can approximate the next higher energy molecular orbitals for B2 and the rest of the period 2 diatomic molecules as linear... 

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