Diatomic dissociation energy

The curves of Figures 5.4 and 5.5 show remarkable dependence on the golden ratio. The attractive and repulsive curves intersect where d = r, at which point the diatomic dissociation energy D = 2r. Again, the limiting curves (marked 1.0 and 0.25(H) in Figure 5.5) are maximally separated at d = 2r,... 

The symbols D0 and Dc are mainly used for diatomic dissociation energies. 

Metals of the second and third transition series are well known to be characterized by multiple dimetal interactions of orders 3, 3f, and 4 [29]. The large reported errors in the measured diatomic dissociation energies for some of these metals are interpreted as due to spectroscopic activation, producing equiUbrium mixtures of compounds of poorly resolved bond order. It is noted that in all such cases, an average over two bond orders reproduces the experimental data rather well. 

A more useful quantity for comparison with experiment is the heat of formation, which is defined as the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states. The heat of formation can thus be calculated by subtracting the heats of atomisation of the elements and the atomic ionisation energies from the total energy. Unfortunately, ab initio calculations that do not include electron correlation (which we will discuss in Chapter 3) provide uniformly poor estimates of heats of formation w ith errors in bond dissociation energies of 25-40 kcal/mol, even at the Hartree-Fock limit for diatomic molecules. 

Figure S-1. Form of a potential energy curve for diatomic molecule AB. VfrAa) is the potential energy, Tab is the intemuclear distance, is the equilibrium intemuclear distance, and D is the bond dissociation energy. (The zero point energy is neglected in the figure.)...

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.

The same ideas may be applied to the other processes of Fig. 1. The work required to dissociate a diatomic molecule into two electricallt/ neutral atoms may he quite small the dissociation energy of the bromine molecule Br2 in a vacuum, for example, is only 1.915 electron-volts. On the other hand, the work to dissociate a molecule into two atomic ions in a vacuum cannot be as small as this, since work must be done to set up the full electrostatic field of the positive ion, and the full electrostatic field of the negative ion and this must amount to at least a few electron-volts.1 In addition, the non-electrostatic forces may make a small or large contribution. 

The name dissociation energy is given to the work required to break up a diatomic molecule which is in its lowest rotation-vibrational state, and to leave the two particles (either atoms or ions) at rest in a vacuum. This quantity, which will be denoted by D , corresponds to the length of the arrow in Fig. 7 or Fig. 8a, where the length is the vertical distance between the lowest level of the molecule and the horizontal line which... 

Figure 4.10 Calculated relativistic bond contractions ARte in A (circles and solid line, axis on the left-hand side) and relativistic change in the dissociation energy contractions (triangles and dashed line, axis on the right-hand side) for various diatomic compounds as a function ofthe electronegativity of the ligand.

We can use Pauling s empirical formula, which defines the Pauling electronegativity scale, for dissociation energies of a diatomic gold molecule. 

Within the framework of the Bom-Oppenheimer approximation, a diatomic molecule consists of two nuclei that are more-or-less attached by the surrounding electron cloud. Often the specific form of the resulting potential function is not known. However, if a chemical bond is formed between the two nuclei, the potential function displays a minimum at a distance that corresponds to the equilibrium bond length. Furthermore, the energy necessary to break the chemical bond, the dissociation energy, is often evaluated by spectroscopic measurements. It can be concluded, then, that the potential fiinction has the general form shown in Fig. 6. A simple derivation of the Born- Qppenheimer approximation is presented in Section 12.1. 

The relationships between bond length, stretching force constant, and bond dissociation energy are made clear by the potential energy curve for a diatomic molecule, the plot of the change in the internal energy AU of the molecule A2 as the internuclear separation is increased until the molecule dissociates into two A atoms ... 

We saw in Figure 2.1 that the energy needed to rupture the bond in a diatomic molecule, the bond dissociation energy is the energy Af/e. This is the energy that can be cal-... 

Figure 4. Comparison of theoretical and experimental bond dissociation energies for first row diatomic metal hydride ions. Data from reference 27.

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...

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