Bond homonuclear diatomics

Interactivity Energy Levels of Bonding— Homonuclear Diatomic Molecules (10.6)... 

Energy Levels oi Bonding— Homonuclear Diatomic Molecules ARIS, Interactives... 

Infrared spectroscopy has broad appHcations for sensitive molecular speciation. Infrared frequencies depend on the masses of the atoms iavolved ia 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 iaertia. The rovibrational spectmm of a gas thus provides direct molecular stmctural information, resulting ia very high specificity. The vibrational spectmm of any molecule is unique, except for those of optical isomers. Every molecule, except homonuclear diatomics such as O2, N2, and the halogens, has at least one vibrational absorption ia the iafrared. Several texts treat iafrared iastmmentation and techniques (22,36—38) and thek appHcations (39—42). 

Figure 13.18 Bond dissociation energies for gaseous, homonuclear diatomic molecules (from J. A. Kerr in Handbook of Chemistry and Physics, 73rd edn., 1992-3, CRC Press, Boca Raton, Florida), pp. 9.129-9.137.

In Section 2.12, we saw that a polar covalent bond in which electrons are not evenly distributed has a nonzero dipole moment. A polar molecule is a molecule with a nonzero dipole moment. All diatomic molecules are polar if their bonds are polar. An HC1 molecule, with its polar covalent bond (8+H—Clfi ), is a polar molecule. Its dipole moment of 1.1 D is typical of polar diatomic molecules (Table 3.1). All diatomic molecules that are composed of atoms of different elements are at least slightly polar. A nonpolar molecule is a molecule that has no electric dipole moment. All homonuclear diatomic molecules, diatomic molecules containing atoms of only one element, such as 02, N2, and Cl2, are nonpolar, because their bonds are nonpolar. 

HOWTO DETERMINE THE ELECTRON CONFIGURATION AND BOND ORDER OF A HOMONUCLEAR DIATOMIC SPECIES... 

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... 

To describe the band structure of metals, we use the approach employed above to describe the bonding in molecules. First, we consider a chain of two atoms. The result is the same as that obtained for a homonuclear diatomic molecule we find two energy levels, the lower one bonding and the upper one antibonding. Upon adding additional atoms, we obtain an additional energy level per added electron, until a continuous band arises (Fig. 6.9). To describe the electron band of a metal in a... 

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. 

Atoms do not all have the same ability to attract electrons. When two different types of atoms form a covalent bond by sharing a pair of electrons, the shared pair of electrons will spend more time in the vicinity of the atom that has the greater ability to attract them. In other words, the electron pair is shared, but it is not shared equally. The ability of an atom in a molecule to attract electrons to it is expressed as the electronegativity of the atom. Earlier, for a homonuclear diatomic molecule we wrote the combination of two atomic wave functions as... 

A homonuclear diatomic molecule contains a nonpolar bond, since the electron pair between the two atoms is shared equally. Cl2 is an example of a homonuclear diatomic molecule. 

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. 

The first-row homonuclear diatomic molecules A2 of main-group elements (A = B, C, N, O, F) exhibit a well-known diversity of ground-state multiplicities, bond lengths, and bond energies. Calculated potential-energy curves for low-lying singlet and triplet states of these species are pictured in Fig. 3.27 and summarized in Table 3.13 (with comparison experimental values). Because these homonuclear... 

Table 3.13. Calculated spin multiplicity, bond length Re, and dissociation energy De of first-row homonuclear diatomic molecules, with comparison experimental valued1 in parentheses...

Although the most naive form of valence-bond and Lewis-structure theory would not predict the paramagnetism of O2, the VB-like NBO donor-acceptor perspective allows us to develop an alternative localized picture of general wavefunctions, including those of MO type. Let us therefore seek to develop a general NBO-based configurational picture of homonuclear diatomics to complement the usual MO description. 

The first three entries of Table 3.14 correspond to formation of conventional pi and sigma NBOs. The fourth (hn— hCT, occurring in complementary pairs) corresponds to formation of asymmetric nu bonds Cv, y), as previously discussed in Section 3.2.6 for N2+. (The fifth [hn — hn 1 ] cannot occur in the present series, because hn is never an unfilled acceptor orbital [if hn is occupied] in neutral homonuclear diatomics.)... 

Let us also briefly examine the corresponding behavior in second- and third-row homonuclear diatomics. Figures 3.31(a) and (b) display the calculated potential-energy curves for these species (ground-state multiplicities only) and Table 3.16 summarizes the equilibrium bond lengths and bond energies. 

Table 3.18. Parameters e and (cf. Eqs. (3.93a)-(3.93c)) for describing hybridization k of sigma bonds in homonuclear diatomics...

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. 

For this case, the primary change that is observable in the IR spectrum is due to changes in the vibrahonal frequencies of the probe molecule due to modificahons in bond energies. This can lead to changes in bond force constants and the normal mode frequencies of the probe molecule. In some cases, where the symmetry of the molecule is perturbed, un-allowed vibrational modes in the unperturbed molecule can be come allowed and therefore observed. A good example of this effect is with the adsorption of homonuclear diatomic molecules, such as N2 and H2 (see Section 4.5.6.8). 

Table 11.1. Bond distances and De for some second row homonuclear diatomics.

---