Dissociation of van der Waals

Gerber, R.B., Buch, V., Ratner, M.A. Time-dependent self-consistent field approximation for intramolecular energy transfer. I. Formulation and application to dissociation of van der Waals molecules. J. Chem. Phys. 77 (1982) 3022-3030. 

Figure 12.9 depicts a comparison between classical trajectory results and exact close-coupling calculations for He--Cl2 and Ne- -Cl2, respectively. In both cases, the classical procedure reproduces the overall behavior of the final state distributions satisfactorily. Subtle details such as the weak undulations particularly for He are not reproduced, however. As shown by Gray and Wozny (1991), who treated the dissociation of van der Waals molecules in the time-dependent framework, the bimodality for He CI2 is the result of a quantum mechanical interference between two branches of the evolving wavepacket and therefore cannot be obtained in purely classical calculations. 

The general theory for the absorption of light and its extension to photodissociation is outlined in Chapter 2. Chapters 3-5 summarize the basic theoretical tools, namely the time-independent and the time-dependent quantum mechanical theories as well as the classical trajectory picture of photodissociation. The two fundamental types of photofragmentation — direct and indirect photodissociation — will be elucidated in Chapters 6 and 7, and in Chapter 8 I will focus attention on some intermediate cases, which are neither truly direct nor indirect. Chapters 9-11 consider in detail the internal quantum state distributions of the fragment molecules which contain a wealth of information on the dissociation dynamics. Some related and more advanced topics such as the dissociation of van der Waals molecules, dissociation of vibrationally excited molecules, emission during dissociation, and nonadiabatic effects are discussed in Chapters 12-15. Finally, we consider briefly in Chapter 16 the most recent class of experiments, i.e., the photodissociation with laser pulses in the femtosecond range, which allows the study of the evolution of the molecular system in real time. 

R.B. Gerber, V. Buch and M.A. Ratner, Time-dependent self-consistent field approximation for intramolecular energy transfer. I. Formulation and application to dissociation of van der Waals molecules, J. Chem. Phys., 77 (1982), 3022 M.A. Ratner and R.B. Gerber, Excited vibrational states of polyatomic molcecules the semiclassical self-consistent field approach, J. Phys. Chem., 90 (1986) 20 R.B. Gerber and M.A. Ratner, Mean-field models for molecular states and dynamics new developments, J. Phys. Chem., 92 (1988) 3252 ... 

Unimolecular dissociation of van der Waals clusters Dissociation of van der Waals clusters provides a nice illustration of several of the ideas that were just discussed in connection with mode selectivity. Van der... 

The normal substances, however, really exhibit small deviations which are all the greater the more complex is the molecule of the substance. The theory of van der Waals, or in fact any hypothesis from which a theorem of corresponding states could be derived, assumes however that the transition from the gaseous to the liquid state, as well as the changes of density in either state, result from alterations in the propinquity of molecules which otherwise remain unaltered. Any association or dissociation of the substance would therefore give rise to abnormalities, and in fact the substances which deviate most from the normal relations (e.g.l water, acetic acid) are those which appear, on other grounds, to be associated in the liquid state. In the case of acetic acid the commencement of polymerisation, even in the state of vapour, is evident from the abnormal densities. 

In fact, the measured dissociation energies of appropriate examples of homo-nuclear diatomic molecules and molecular ions are H, 2.648 e.v. H2, 4.476 e.v. He, 3.1 e.v. He2, only slight attraction in the ground electronic state (binding of van der Waals type, at internuclear separations large compared with typical chemical binding energies.)... 

In hydrate equilibrium, it may seem slightly unusual to apply it to binary systems (water and one guest component) of three-phase (Lw-H-V or I-H-V) equilibrium to obtain the heats of dissociation. As van der Waals and Platteeuw (1959b) point out, however, the application of the Clapeyron equation is thermodynamically correct, as long as the system is univariant, as is the case for simple hydrates. 

The extremely wide range of possible dissociation energies necessitates the use of different kinds of light source to break molecular bonds. Van der Waals molecules can be fragmented with single infrared (IR) photons whereas the fission of a chemical bond requires either a single ultraviolet (UV) or many IR photons. The photofragmentation of van der Waals molecules has become a very active field in the last decade and deserves a book in itself (Beswick and Halberstadt 1993). It is a special case of UV photodissociation and can be described by the same theoretical means. In Chapter 12 we will briefly discuss some simple aspects of IR photodissociation in order to elucidate the similarities and the differences to UV photodissociation. 

Predissociation of van der Waals molecules is ideally suited for the application of the general expressions for the decay of resonance states derived in Section 7.2, especially Equation (7.12) for the dissociation rate. The reason is that the coupling is so small that we can rigorously define accurate zero-order states... 

In conclusion, the quantum-state dependence of the dissociation rate reveals a lot of detailed information on the decay of van der Waals complexes and allows to accurately ascertain parts of the multi-dimensional PES. 

In summary, the overall behavior of final state distributions in the decay of van der Waals complexes may be well described by direct dissociation mechanisms and classical mechanics, despite the exceedingly large lifetime. 

The data presented show features of the IVR/VP process which any theory of van der Waals molecule dissociation must be able to reproduce. First, only the bare molecule ethyl torsion mode and 0° are populated and emit following IVR and VP of 4EA/polyatomic solvent clusters. Second, specific product state distributions in the torsional mode manifold are observed which depend on the cluster and the excitation energy. Third, the rate of dissociation depends on the excitation energy. Fourth, the emission behavior of the three clusters studied is... 

The RRKM theory of unimolecular reactions predicts that the rate constant for dissociation will be given by eq. (5-3). The probability of populating a state with energy Ev restricted into the chromophore vibrations is proportional to the ratio of the density of van der Waals states at E — Ev to that at ... 

The dissociation of weakly bound van der Waals complexes is a special case of unimolecular dissociation [20]. Because of the exceedingly weak coupling between the dissociation coordinate and the mode (or modes) initially excited, and the very low density of states of the energized complex, narrow resonances are the dominant features of van der Waals spectra. There are, of course, many similarities between the dynamics of physically bound and chemically bound molecules. The dissociation dynamics of these special molecules (or clusters) has been studied in great detail, both experimentally and theoretically. Exhaustive review articles are available [85-89] and therefore van der Waals molecules will not be particularly considered in this chapter. However, one must keep in mind that, as the density of states of van der Waals molecules increases, their dynamics becomes more and more comparable with the dynamics of strongly bound molecules [90,91]. 

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