Homonudear Diatomic Molecules

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. )... 

FIGURE 3.8 Molecular orbital diagrams for second-row homonudear diatomic molecules. 

Ortho and Para Modifications of Homonudear Diatomic Molecules... 

For any homonudear diatomic molecule whose nuclei have nonzero spin, it should, in principle, be possible to isolate a modified form with only even-numbered rotational levels populated. (For /=0, half the rotational levels do not exist.) However, only for H2 and D2 has this been achieved. The small moments of inertia of these light molecules give a relatively large spacing between 7 = 0 and 7= 1 rotational levels, so that we can get nearly all the molecules into the 7 = 0 level at a temperature above the freezing point of the substance. 

Molecular orbitals in heteronudear diatomic molecules. 167-175 in homonudear diatomic molecules, 160-166 of metallocenes. 670-673 in octahedral complexes, 414-418... 

Chapter 1 Homonudear diatomic molecules molecular orbital (MO) theory 31... 

Molecular orbital theory can be applied to any homonudear diatomic molecule, but as more valence atomic orbitals become available, the MO diagram becomes more complex. Treatments of the bonding in He2, Li2 and Be2 are similar to that for H2. In practice. He does not form He2, and the construction of an MO diagram for He2 is a useful exercise because it rationalizes this observation. Figure 1.19a shows that when the two H atomic orbitals of two He atoms interact, a and a MOs are formed as in H2. However, each He atom contributes two electrons, meaning that in He2, both the bonding and antibonding MOs are fully occupied. The bond order (equation 1.31) is zero and so the MO picture of He2 is consistent with its non-existence. 

Fig. 1.23 Changes in the energy levels of the MOs and the ground state electronic configurations of homonudear diatomic molecules involving first-row / -block elements.

Table 1.6 Experimental data and bond orders for homonudear diatomic molecules X2 in which X is an atom in the period Li to F.

The various methods to calculate the vibrational frequencies and force constants from ab-initio data on diatomic molecules is represented in Sections 5 A to K. It is seen that the various approximations yield results which fluctuate from molecule to molecule, although the order of magnitude is mostly correct. It is clear, however, that it is not at the present moment possible to calculate co and ke of molecules to such a d ee of accuracy that the factors which contribute to the intemudear forces in molecules can be pinpointed and compared. This is perhaps the reason why semi-empirical models continue to be exploited, e.g. the simple bond-charge model (electrostatic) model for P.E.-curves of homonudear diatomic molecules of Parr and Borckmann (114) based upon the Fues potential from which the famous Birge-Mecke relation is derived ... 

Almost simultaneously and independently, two research groups started systematic IR spectroscopic work on the adsorption of homonudear diatomic molecules in zeolites, viz. the groups of Foerster [587,588] and Cohen de Lara [216, 589-593]. Their studies provided valuable information both about the properties of the sorbents, e.g., the internal electric fields the sorbate molecules, e.g., their modes of motion and mobility and the interaction between adsorbate and zeolite, e.g.,the effect of adsorption on the molecular bonds. Mostly, A-type zeolites were employed as hosts. In fact, some early studies were also carried out with X-andY-typezeolites [594,595]. 

In a simple LCAO MO treatment of a homonuclear diatomic molecule the two solutions for the energy are E = —When the two atoms are infinitely apart, the total energy of the system will be 2Hn, the energy of the two separated atoms. Using this as the reference state, the potential energy of a two-electron homonudear diatomic molecule is... 

For a homonudear diatomic molecule, there are additional concerns because we now have identical nuclei. These concerns have to do with the Pauli principle, which was introduced in Chapter 12. Recall that the strict form of the Pauli principle required that a wavefunction of fermions must be antisymmetric with respect... 

Student Annotation Recall that a homonudear diatomic molecule is one in which both atoms are the same element [ H Section 2.6]. 

In addition to the homonudear molecules, the elements of the second period form numerous important and interesting heteronudear species, both neutral molecules and diatomic ions. The molecular orbital diagrams for several of these species are shown in Figure 3.9. Keep in mind that the energies of the molecular orbitals having the same designations are not equal for these species. The diagrams are only qualitatively correct. 

Infrared spectroscopy has broad appHcations for sensitive molecular speciation. Infrared frequencies depend on the masses of the atoms involved in the various vibrational motions, and on the force constants and geometry of the bonds connecting them band shapes are determined by the rotational stmcture and hence by the molecular symmetry and moments of inertia. The rovibrational spectmm of a gas thus provides direct molecular stmctural information, resulting in very high specificity. The vibrational spectrum of any molecule is unique, except for those of optical isomers. Every molecule, except homonudear diatomics such as O2, N2, and the halogens, has at least one vibrational absorption in the infrared. Several texts treat infrared instrumentation and techniques (22,36—38) and their appHcations (39—42). 

Finally, we have to undostand the reason for the opposite behaviour of diatomic homonudear molecules. In this case, we have seen that the first non-zero non-central term (13.5.Q is more important than for tetrahedra s. When one calculates the average contribution of such a term, one sees it is attractive. It tends therefore to lower the potential... 

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