Diatomic molecules, dissociation

Figure 4.25. Side and top views of the calculated transition state structures for different diatomic molecules dissociating on different close-packed (top) and stepped (bottom) metal surfaces. Adapted from Ref. [80].

For more on the determination of diatomic-molecule dissociation energies, see A. G. Gaydon, Dissociation Energies and Spectra of Diatomic Molecules, Third Edition, Chapman and Hall, London, 1968. 

When a diatomic molecule dissociates photochemically it yields atoms either in their ground or in excited states. When the optical transition leading to dissociation is not forbidden, and does not arise from predissociation, one of the two atoms formed will not be in its ground state. 

The preceding treatment is, undoubtedly, an oversimplification. For example, many diatomic molecules dissociate upon adsorption (e.g., H2, SiH, GeH). Each atom from the dissociated molecule then occupies its own distinct surface site and this naturally changes the rate law expression. When these types of details are accounted for, the Langmuir-Hinshelwood mechanism has been very successful at explaining the growth rates of a number of thin-film chemical vapor deposition (CVD) processes. However, more important, our treatment served to illustrate how crystal growth from the vapor phase can be related to macroscopic observables namely, the partial pressures of the reacting species. 

So far we have summarized some basic reactions starting with the cosmic ray ionization of Hj. However cosmic ray ionization of He, which is considerably less abundant in dense clouds than H2 (about V4) seems to be important for two reasons firstly, an activation energy barrier (Johnsen and Biondi, 1974) is likely to keep the reaction rates of H with H and Hj anomalously small (reaction rate 8 x 10 cm sec Sando et al. 1972), and therefore He remains available for the ionization of neutral molecules. Secondly, in most cases, the charge transfer from He to diatomic molecules dissociates them, producing essentially ionized heavy elements, such as C, N , O". The reaction sequence has the general form (see note added in proof). 

If the diatomic molecule dissociates upon adsorption, the heat of adsorption for this purpose is defined as... 

For the simplest case of a diatomic molecule dissociating instantaneously to products of high translational energy, the factor c — 2, but if the molecule has a finite average lifetime, r, then... 

For each of the following processes, indicate whether the signs of As and AH are expected to be positive, n ative, or about zero, (a) A solid sublimes, (b) The temperature of a sample of Co(s) is lowered from 60 °C to 25 C. (c) Ethyl alcohol evaporates from a beaker, (d) A diatomic molecule dissociates into atoms, (e) A piece of charcoal is combusted to form C02(g) and H20(g). 

Fig. 66. Influence of rotation on an energy curve V (p) of a diatomic molecule. Dissociation by rotation.

For a reaction in which a diatomic molecule dissociates into atoms, what are the signs of AS and AHl Explain your answer. You may use the reaction 2(g) —2N(g) as an example of such a reaction. 

The direct dissociation of diatomic molecules is the most well studied process in gas-surface dynamics, the one for which the combination of surface science and molecular beam teclmiques allied to the computation of total energies and detailed and painstaking solution of the molecular dynamics has been most successful. The result is a substantial body of knowledge concerning the importance of the various degrees of freedom (e.g. molecular rotation) to the reaction dynamics, the details of which are contained in a number of review articles [2, 36, 37, 38, 39, 40 and 41]. 

Darling G R and Holloway S 1995 Tlie dissociation of diatomic molecules Prog. Phys.. 58 1595... 

Kaye J A and Kuppermann A 1988 Mass effect in quantum-mechanical collision-induced dissociation in collinear reactive atom diatomic molecule collisions Chem. Phys. 125 279-91... 

A simple example would be in a study of a diatomic molecule that in a Hartree-Fock calculation has a bonded cr orbital as the highest occupied MO (HOMO) and a a lowest unoccupied MO (LUMO). A CASSCF calculation would then use the two a electrons and set up four CSFs with single and double excitations from the HOMO into the a orbital. This allows the bond dissociation to be described correctly, with different amounts of the neutral atoms, ion pair, and bonded pair controlled by the Cl coefficients, with the optimal shapes of the orbitals also being found. For more complicated systems... 

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. 

This difference is shown in the next illustration which presents the qualitative form of a potential curve for a diatomic molecule for both a molecular mechanics method (like AMBER) or a semi-empirical method (like AMI). At large internuclear distances, the differences between the two methods are obvious. With AMI, the molecule properly dissociates into atoms, while the AMBERpoten-tial continues to rise. However, in explorations of the potential curve only around the minimum, results from the two methods might be rather similar. Indeed, it is quite possible that AMBER will give more accurate structural results than AMI. This is due to the closer link between experimental data and computed results of molecular mechanics calculations. 

Equation (6.8), to (d /dx)g. Figure 6.1 shows how the magnitude /r of the dipole moment varies with intemuclear distance in a typical heteronuclear diatomic molecule. Obviously, /r 0 when r 0 and the nuclei coalesce. For neutral diatomics, /r 0 when r qg because the molecule dissociates into neutral atoms. Therefore, between r = 0 and r = oo there must be a maximum value of /r. Figure 6.1 has been drawn with this maximum at r < Tg, giving a negative slope d/r/dr at r. If the maximum were at r > Tg there would be a positive slope at r. It is possible that the maximum is at r, in which case d/r/dr = 0 at Tg and the Av = transitions, although allowed, would have zero intensity. 

In a diatomic molecule one of the main effects of mechanical anharmonicity, the only type that concerns us in detail, is to cause the vibrational energy levels to close up smoothly with increasing v, as shown in Figure 6.4. The separation of the levels becomes zero at the limit of dissociation. 

An Xc2 excimer laser has been made to operate in this way, but of much greater importance are the noble gas halide lasers. These halides also have repulsive ground states and bound excited states they are examples of exciplexes. An exciplex is a complex consisting, in a diatomic molecule, of two different atoms, which is stable in an excited electronic state but dissociates readily in the ground state. In spite of this clear distinction between an excimer and an exciplex it is now common for all such lasers to be called excimer lasers. 

All heteronuclear diatomic molecules, in their ground electronic state, dissociate into neutral atoms, however strongly polar they may be. The simple explanation for this is that dissociation into a positive and a negative ion is much less likely because of the attractive force between the ions even at a relatively large separation. The highly polar Nal molecule is no exception. The lowest energy dissociation process is... 

Iodine vapor is characterized by the familiar violet color and by its unusually high specific gravity, approximately nine times that of air. The vapor is made up of diatomic molecules at low temperatures at moderately elevated temperatures, dissociation becomes appreciable. The concentration of monoatomic molecules, for example, is 1.4% at 600°C and 101.3 kPa (1 atm) total pressure. Iodine is fluorescent at low pressures and rotates the plane of polarized light when placed in a magnetic field. It is also thermoluminescent, emitting visible light when heated at 500°C or higher. 

D is the chemical energy of dissociation which cair be obtained from thermodynamic data, aird is the reduced mass of the diatomic molecule... 

Chain reactions such as those described above, in which atomic species or radicals play a rate-determining part in a series of sequential reactions, are nearly always present in processes for the preparation of thin films by die decomposition of gaseous molecules. This may be achieved by thermal dissociation, by radiation decomposition (photochemical decomposition), or by electron bombardment, either by beams of elecuons or in plasmas. The molecules involved cover a wide range from simple diatomic molecules which dissociate to atoms, to organometallic species with complex dissociation patterns. The... 

In these examples tire entropy change does not vaty widely, and the value of the equilibrium constant is mainly determined by the heat of dissociation. It can be concluded, tlrerefore, that niuogen is one of the most stable diatomic molecules, and tlrat chlorine is tire most stable diatomic halogen molecule. 

Table 2.5 Dissociation quanta of some diatomic molecules...

If we were to calculate the potential energy V of the diatomic molecule AB as a function of the distance tab between the centers of the atoms, the result would be a curve having a shape like that seen in Fig. 5-1. This is a bond dissociation curve, the path from the minimum (the equilibrium intemuclear distance in the diatomic molecule) to increasing values of tab describing the dissociation of the molecule. It is conventional to take as the zero of energy the infinitely separated species. 

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.)...

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