Molecular dissociation threshold

The coupling between the angle y and the dissociation coordinate R is always large if Jacobi coordinates are used. At low energies deep inside the well, this coupling is linear and normal coordinates are usually better suited for interpretation and assignment than are Jacobi coordinates. However, if the molecular dynamics above the dissociation threshold is studied, the normal-mode picture breaks down and scattering coordinates have to be employed. 

For energies below the dissociation threshold we can use various coordinate systems to solve the nuclear Schrodinger equation (2.32). If the displacement from equilibrium is small, normal coordinates are most appropriate (Wilson, Decius, and, Cross 1955 ch.2 Weissbluth 1978 ch.27 Daudel et al. 1983 ch.7 Atkins 1983 ch.ll). However, if the vibrational amplitudes increase so-called local coordinates become more advantageous (Child and Halonen 1984 Child 1985 Halonen 1989). Eventually, the molecular vibration becomes unbound and the molecule dissociates. Under such circumstances, Jacobi or so-called scattering coordinates are the most suitable coordinates they facilitate the definition of the boundary conditions of the continuum wavefunctions at infinite distances which we need to determine scattering or dissociation cross sections (Child 1991 ch.l0). Normal coordinates become less and less appropriate if the vibrational amplitudes increase they are completely impractical for the description of unbound motion in the continuum. 

If the photon excites states with energies above the dissociation threshold, i.e., in the continuum of the molecular Hamiltonian, the absorption spectrum becomes a continuous function of the energy Ef = Ei+hu> as illustrated in the upper part of Figure 2.2. There are two major differences between bound-bound and bound-continuum transitions ... 

The form of the potential hypersurface for a molecular species changes drastically upon ionization. As an example, whereas azacyclohexatriene-2-ylidene 7 is largely destabilized (by ca 50 kcal mol ) relative to isomeric pyridine, it has been calculated that the difference is reduced to a few kcal mol for the corresponding radical cation 7 (see Scheme 7) [40]. Isomerization of the ions is prohibited by an energy barrier, evaluated at 40-60 kcal mol , which is lower, however, than the dissociation threshold, so interconversion does occur under mass spectrometric conditions. The effect of aromaticity even at the radical cation stage can, on the other hand, be evaluated because the furan radical cation is the main fragment formed (along with a minor amount of vinylketene) from the decarbonylation of the 2- and 4-pyrone radical cation (8+ , see Scheme 8) [41]. 

This model stresses the view of the hydrogen atom as a quantum particle acting independently of the heavy atoms and playing a role somewhat like the electrons in a molecular orbital. Systems containing formally symmetric hydrogen bonds could, in this model, have similar dissociation thresholds, and overall potential functions, almost independently of their chemical nature. 

A possible absorption spectrum for a molecule near its unimolecular dissociation threshold is shown in figure 8.1. Below the absorption lines for the molecular eigenstates are very narrow and are only broadened by interaction of the excited molecule with the radiation field. However, above the excited states leak toward product space, which gives rise to characteristic widths for the resonances in the spectrum. Since the line widths do not overlap, the resonances are isolated. Each... 

Notes. Key parameters for consideration of the photolysis of iodine-containing gases in the air (data taken from the International Union of Pure and Applied Chemistry (lUPAC) Subcommittee for Gas Kinetic Data Evaluation online database http //www.iupac-kinetic.ch.cam.ac.uk/). a Photo-dissociation threshold wavelength, b Bond dissociation energy (298 K). c Wavelength of maximum absorption, d Peak molecular absorption cross-section (298 K). 

The continuous spectrum is also present, both in physical processes and in the quantum mechanical formalism, when an atomic (molecular) state is made to interact with an external electromagnetic field of appropriate frequency and strength. In conjunction with energy shifts, the normal processes involve ionization, or electron detachment, or molecular dissociation by absorption of one or more photons, or electron tunneling. Treated as stationary systems with time-independent atom - - field Hamiltonians, these problems are equivalent to the CESE scheme of a decaying state with a complex eigenvalue. For the treatment of the related MEPs, the implementation of the CESE approach has led to the state-specific, nonperturbative many-electron, many-photon (MEMP) theory [179-190] which was presented in Section 11. Its various applications include the ab initio calculation of properties from the interaction with electric and magnetic fields, of multiphoton above threshold ionization and detachment, of analysis of path interference in the ionization by di- and tri-chromatic ac-fields, of cross-sections for double electron photoionization and photodetachment, etc. 

The electron interaction with molecules takes place in the same way as described for atoms. The only difference is that the excitation can result in molecular dissociation. Let us give a few examples First for CF, which has the exdtation threshold 12.5 eV (18,19] ... 

Figure 3 Scheme of a two laser pump-pump experiment for the production of internal energy-selected molecular ions in a reflectron time-of-flight mass spectrometer (from ref. /15/). Laser 1 produces state-selected molecular ions and 200 ns later laser 2 excites these ions to a well defined internal energy level above dissociation threshold. The dissociation rate constants of the energy-selected ions are measured by the technique of detection and energy analysis of metastable ions. 

We note in passing that for dissociation of many gases the adsorption of molecules from the gas phase directly upon the surface of catalyst nanoparticles is not necessary. Tsu and Boudart (1961) and others (Henry et al. 1991 Bowker 1996) showed that the molecules can first adsorb onto the oxide support and diffuse to a catalyst particle. This means that the effective capture radius of a catalyst nanoparticle (Pd, Pt, etc.) can be much greater than the nanoparticle s physical radius. As with the spillover zones, the molecule-collection zones (Tsu and Boudart 1961) overlap when the coverage of catalyst nanoparticles exceeds some threshold value, effectively converting the entire surface of the nanostructure into a molecular delivery system for the metal catalyst nanoparticles. This so-called back-spillover effect further increases the likelihood of molecular dissociation and ionosorption on the metal oxide surface. 

An experiment of this kind was performed (Bagratashvili et al. 1983) with anthracene (C14H10) molecules (5 = 66, Dq = 4.8 eV), for which the estimate in eqn (10.1) gives — Eg c 3Eg. With so strong an overexcitation, ionization of the molecule (I = 7.4 eV) is quite possible. In fact, the formation of anthracene molecular ions was observed when the molecules were irradiated by sufficiently powerful (about 10 W/cm ) short (70 ns) C02-laser pulses under collisionless conditions (pressure 4 X 10 Torr) in a time-of-flight mass spectrometer. These ions can be believed to appear as a result of the IR multiphoton ionization of molecules in accordance with the scheme of Fig. 10.5(b). Of course, such a multiphoton ionization technique is applicable only to large polyatomic molecules, since for polyatomic molecules with a small number of atoms the maximum possible degree of overexcitation above the dissociation threshold is comparatively low. 

Thus, if any two of the three heats of formation are known, the third can be calculated from the measured dissociation energy, DE. Many heats of formation derived using this approach have been reported. However, the validity of this method depends upon a rapid dissociation of the molecular ion. What is actually measured is the appearance energy, AE, of the product ions which is always greater than DE. Ions prepared just above their dissociation threshold often fragment very slowly (e.g. <10" s ) so that no A" ions will be observed since ions are collected in just a few microseconds after their formation. It is not until the ion energy reaches a level at which the dissociation rate constant, k, exceeds lO s- that A+ ions are observed. An effective means for circumventing this problem is to measure the dissociation... 

Here at least nine dissociative channels are theoretically accessible below the ionization threshold. The dissociation products are NH2 -NH + H2, NH2 + H, or NH + 2H (final state), of which NH and NH2 may exist either in the ground or an excited state. Production of molecular hydrogen is negligible at low excitation energies, but it can account for 15% or more of the dissociation processes when the excitation exceeds -7 eV Note that the lowest excited state of NH3 ( 4 eV) does dissociate into NH and H2 but is spin forbidden. 

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