Homonuclear diatomic molecules molecular orbitals

The energies of The energies of the molecular orbitals of atomic orbitals homonuclear diatomic molecules of free atoms... 

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

Hurley, A. C., Proc. Roy. Soc. [London) A216, 424, The molecular orbital theory of chemical valency. XIII. Orbital wave functions for excited states of a homonuclear diatomic molecule."... 

In the molecular orbital description of homonuclear diatomic molecules, we first build all possible molecular orbitals from the available valence-shell atomic orbitals. Then we accommodate the valence electrons in molecular orbitals by using the same procedure we used in the building-up principle for atoms (Section 1.13). That is,... 

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. 

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. 

Hiroshima, 721 histidine, 443, 774 hole, 195 homeostasis, 386 HOMO, 126, 580 homogeneous alloy, 202 homogeneous catalyst, 565 homogeneous equilibria, 362 homogeneous mixture, F53 homolytic dissociation, 80 homonuclear diatomic molecule, 103 Hooke s law, 92 hormone, 670 horsepower, A4, 791 hour, A4 HPLC, 354 HRF products, 723 HTSC, 192 Humphreys series, 51 Hund, F 35 Hund s rule, 35, 37 Hurricane Rita, 144 hyaluronic acid, 344 hybrid orbital, 109 hybridization bond angle, 131 molecular shape, 111 hydrangea color, 463 hydrate, F32 hydrate isomer, 676 hydration, 178 hydrazine, 627... 

The limitation of the above analysis to the case of homonuclear diatomic molecules was made by imposing the relation Haa = Hbb> as in this case the two nuclei are identical. More generally, Haa and for heteronuclear diatomic molecules Eq. (134) cannot be simplified (see problem 25). However, the polarity of the bond can be estimated in this case. The reader is referred to specialized texts on molecular orbital theory for a development of this application. 

Valence bond theory does agree fairly well with molecular orbital (MO) theory for homonuclear diatomic molecules that can obey the octet rule H2 (single bond, bond order = 1), Li2 (single bond, bond order = 1), N2 (triple bond, bond order = 3), 02 (double bond, bond order = 2), F2 (single bond, bond order = 1). However, for those molecules that don t, it is more difficult to know if they exist or not and what bond orders they have. MO theory allows us to predict that He2, Be2 and Ne2 do not exist since they have bond orders = 0, and that B2 has bond order = 1 and C2 has bond order = 2. 

As can be seen from its ground-state molecular orbital diagram in Figure 4.11, dioxygen has a paramagnetic ground state. It is the only stable homonuclear diatomic molecule with this property. 

There exists no uniformity as regards the relation between localized orbitals and canonical orbitals. For example, if one considers an atom with two electrons in a (Is) atomic orbital and two electrons in a (2s) atomic orbital, then one finds that the localized atomic orbitals are rather close to the canonical atomic orbitals, which indicates that the canonical orbitals themselves are already highly, though not maximally, localized.18) (In this case, localization essentially diminishes the (Is) character of the (2s) orbital.) The opposite situation is found, on the other hand, if one considers the two inner shells in a homonuclear diatomic molecule. Here, the canonical orbitals are the molecular orbitals (lo ) and (1 ou), i.e. the bonding and the antibonding combinations of the (Is) orbitals from the two atoms, which are completely delocalized. In contrast, the localization procedure yields two localized orbitals which are essentially the inner shell orbital on the first atom and that on the second atom.19 It is thus apparent that the canonical orbitals may be identical with the localized orbitals, that they may be close to the localized orbitals, that they may be identical with the completely delocalized orbitals, or that they may be intermediate in character. 

The construction of the molecular orbitals of the homonuclear diatomic molecules of the second period using group theory... 

This section consists of the formal molecular orbital treatment of homonuclear diatomic molecules of the second short period. The molec-... 

Figure 4.2 The molecular orbital diagrams for homonuclear diatomic molecules of the second short period, Li. to Ne2. Diagram (a) is appropriate for 02, F2 and Ne2, diagram (b) for the molecules Li2 to N2...

The molecular orbital diagram for the nitrogen monoxide molecule is shown in Figure 4.6. The orbitals are produced from the same pairs of atomic orbitals as in the cases of the homonuclear diatomic molecules of Section 4.2. 

Homogeneous catalysts, 705 Homonuclear diatomic molecules. molecular orbitals in, 160-166... 

Figure 2-11 Bonding and antibonding molecular orbitals composed of the p orbitals in a homonuclear diatomic molecule.

Figure 2-12 Energy diagrams for a homonuclear diatomic molecule. Note that the differences in the energy levels of the atoms are larger than the energy differences between the molecular orbitals. Diagram (a) is appropriate for no interaction between 2s and 2p levels, and diagram (b) is appropriate for substantial interaction between 2s and 2p levels. Refer to pp. 36-38.

In general, it is advantageous to use the symmetry elements of a molecule in dealing with the molecular orbitals. For example, consider the symmetry properties of a homonuclear diatomic molecule... 

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. 

The shapes and energy ordering of the molecular orbitals for homonuclear diatomic molecules. The scheme on the left is applicable to 02 and F2, while that on the right is applicable to other diatomics of the same period. 

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