Bond order, in diatomic molecules

This case study shows that CO molecules do not have significant vibrational energy unless the temperature is quite high. This happens because CO has a triple bond and, therefore, a large force constant k = 1902 N m ). The correlation between force constant and bond order in diatomic molecules is explained by molecular orbital theory, and is summarized in Figure 6.20. Other diatomic molecules will behave differently, as determined by their structure and the Boltzmann distribution. 

Find the bond order in diatomic molecules and ions... 

These results can be interpreted successfully in terms of Pauling s valence bond order concept. In the framework of this model, a chemical bond between X and H in diatomic molecule XH or between H and B in a HB molecule can be characterized by empirical valence bond orders Pxh and Phb decreasing exponentially with bond distance ... 

The bond order in a diatomic molecule is defined as one-half the difference between the number of electrons in bonding orbitals and the number of antibonding orbitals. The factor one-half preserves the concept of the electron pair and makes the bond order correspond to the multiplicity in the valence-bond formulation one for a single bond, two for a double bond, and three for a triple bond. Fractional bond orders are allowed, but are not within the scope of this discussion. 

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. 

Provocative experimental evidence, at variance with conventional theory, is provided by the estimates of molecular diameters for diatomic molecules. Bonding theory requires the concentration of valence densities between the nuclei to increase as a function of bond order, in agreement with observed bond lengths (1.097, 1.208, 0.741 A) and force constants (22.95, 11.77, 5.75 Ncm-1) of the species N=N, 0=0 and H-H respectively. Molecular diameters can be measured by a variety of techniques based on gas viscosity, heat conductivity, diffusion and van der Waals equation of state. The results are in excellent agreement at values of 3.75, 3.61 and 2.72 A, for N2, O2 and H2, respectively. Conventional bonding theory cannot account for these results. 

If we combine the splitting schemes for the 2s and 2p orbitals, we can predict bond order in all of the diatomic molecules and ions composed of elements in the first complete row of the periodic table. Remember that only the valence orbitals of the atoms need be considered as we saw in the cases of lithium hydride and dilithium, the inner orbitals remain tightly bound and retain their localized atomic character. 

In the example of H2, the bond order = (2 - 0) = 1 (a single bond). In diatomic molecules, a bond order of 1 corresponds to a single bond, a bond order of 2 to a double bond, and so forth. 

The bond order in N2, O2, and F2 is the same whether or not mixing is taken into account, but the order of the (Tg(2p) and TT (2p) orbitals is different in N2 than in O2 and F2. As stated previously and further described in Section 5.3.1, the energy difference between the 2s and 2p orbitals of the second row main group elements increases with increasing Z, from 5.7 eV in boron to 21.5 eV in fluorine. As this difference increases, the s-p interaction (mixing) decreases, and the normal order of molecular orbitals returns in O2 and F2. The higher a-g(2p) orbital (relative to 7T (2p)) occurs in many heteronuclear diatomic molecules, such as CO, described in Section 5.3.1. 

The molecular orbital description of period 2 diatomic molecules leads to bond orders in accord with the Lewis structures of these molecules. Further, the model predicts correctly that O2 should exhibit paramagnetism, which leads to attraction of a molecule into a magnetic field due to the influence of unpaired electrons. Molecules in which all the electrons are paired exhibit diamagnetism, which leads to weak repulsion from a magnetic field. 

The metal-metal bond order in transition metal M2-type molecules and in transition metal complexes may be higher than in the case of the main group elements because of the participation of the d orbitals. The diatomic molecule M02 has a quintuple bond, with an electronic configuration of (the Mo-Mo... 

Bond lengths in homo-diatomic molecules (A2) [36-52] are compiled in Table 3.1. For Groups 1 and 17 they correspond to single covalent bonds, for Group 16 to double bonds and for Group 15 to triple bonds. To find out the bond order in other... 

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