Homonuclear diatomic molecules defined

Covalent bonds may be either polar or nonpolar. In a nonpolar bond such as that in the hydrogen molecule, H2, (H H or H—H) the electron pair is shared equally between the two hydrogen nuclei. We defined electronegativity as the tendency of an atom to attract electrons to itself in a chemical bond (see Section 6-6). Both H atoms have the same electronegativity. This means that the shared electrons are equally attracted to both hydrogen nuclei and therefore spend equal amounts of time near each nucleus. In this nonpolar covalent bond, the electron density is s)mimetrical about a plane that is perpendicular to a line between the two nuclei. This is true for all homonuclear diatomic molecules, such as H2, O2, N2, F2, and CI2, because the two identical atoms have identical electronegativities. We can generalize ... 

For homonuclear molecules, the g or u symmetry is almost always conserved. Only external electric fields, hyperfine effects (Pique, et al., 1984), and collisions can induce perturbations between g and u states. See Reinhold, et al., (1998) who discuss how several terms that are neglected in the Born-Oppenheimer approximation can give rise to interactions between g and u states in hetero-isotopomers, as in the HD molecule. An additional symmetry will be discussed in Section 3.2.2 parity or, more usefully, the e and / symmetry character of the rotational levels remains well defined for both hetero- and homonuclear diatomic molecules. The matrix elements of Table 3.2 describe direct interactions between basis states. Indirect interactions can also occur and are discussed in Sections 4.2, 4.4.2 and 4.5.1. Even for indirect interactions the A J = 0 and e / perturbation selection rules remain valid (see Section 3.2.2). 

In Fig. 4.1 we present a plot of the dissociation energies of the homonuclear diatomic molecules H2, X2 and M2 as a function of the bond distances. The bond distances reflect the sizes of the atoms involved. Indeed, one might define the bonding radius of the atom A as half the single bond distance A-A. It is seen that - except for the rule-breaker F2 - the bond energy decreases with increasing bond distance large atoms form weak bonds. 

In Section 22.3, we found that only half of the values of the rotational quantum number J occurred for a homonuclear diatomic molecule because of the indistinguishability of the nuclei. In the case of polyatomic molecules the effect of the indistinguishability of identical nuclei is more complicated. We assert without proof that the fraction of the conceivable rotational states that can occur is 1 /a, where a is called the symmetry number of the molecule. The symmetry number is defined as the number of equivalent orientations of the molecule in its equilibrium conformation, which means the number of orientations in which the molecule can be placed and have each nuclear location occupied by a nucleus of the same kind as in the first orientation. 

The formula given in Eq. (25.4-11) applies to heteronuclear diatomic molecules, but must be modified for homonuclear diatomic molecules, for which either odd values of J or even values of J do not occur, as discussed in Chapter 22. This restriction corresponds to omitting half of the rectangles in Figure 25.4, approximately cutting the value of the sum in half. For diatomic molecules the symmetry number a is defined in Section 22.5. 

In a molecular compound, covalent bonding happens when two nonmetals share electrons. Covalent bonds are defined not only by the number of electrons shared but also by their length and strength. Covalent bonds have a specific bond length and bond energy. In a homonuclear diatomic molecule where both atoms are identical, the pair or pairs of electrons is/are shared equally between the two atoms. However, in a heteronuclear diatomic molecule, one shared pair(s) will be more attracted to one atom than the other. 

Interchanging the nuclear coordinates does not affect R, but it does affect the electronic spatial coordinates since they are defined with respect to the molecule-fixed xyz axes, which are rigidly attached to the nuclei. To find the effect on el of interchanging the nuclear coordinates, we will first invert the space-fixed coordinates of the nuclei and the electrons, and then carry out a second inversion of the space-fixed electronic coordinates only the net effect will be the interchange of the space-fixed coordinates of the two nuclei. We found in the last section that inversion of the space-fixed coordinates of all particles left //e, unchanged for 2+,n+,... electronic states, but multiplied it by —1 for 2, II ,... states. Consider now the effect of the second step, reinversion of the electronic space-fixed coordinates. Since the nuclei are unaffected by this step, the molecule-fixed axes remain fixed for this inversion, so that inversion of the space-fixed coordinates of the electrons also inverts their molecule-fixed coordinates. But we noted in Section 1.19 that the electronic wave functions of homonuclear diatomics could be classified as g or m, according to whether inversion of molecule-fixed electronic coordinates multiplies ptl by + 1 or -1. We conclude that for 2+,2,7,11, IV,... electronic states, i//el is symmetric with respect to interchange of nuclear coordinates, whereas for... 

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