Dissociation of van der Waals molecules

1) The small dissociation energy ranging from a few cm-1 to about 1000 

3) The retention of the properties of the individual entities within the van der Waals complex. 

4) Relatively weak coupling between the van der Waals mode and the internal coordinates of the molecular entity. 

Owing to the small dissociation energy, van der Waals molecules exist mainly at very low temperatures as they prevail in the interstellar medium or in supersonic jets. 

Potential energy surfaces of van der Waals molecules have — in comparison to the PESs of excited states of chemically bound molecules like H2O, H2S, or CH3ONO — a relatively simple general appearance. There are no barriers due to avoided crossings and no saddle points etc. Moreover, the coupling between R, on one hand, and r and 7, on the other hand, is usually weak so that a representation of the form 

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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 ... 

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... 

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 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]. 

The infrared and UV spectra of van der Waals molecules do, however display many sharp lines.This indicates that the excited states often have sufficiently long lifetimes to display sharp spectral features, despite the fact that they have more than enough energy to dissociate. In principle every observed spectral line corresponds to a photodissociation process. If the line is sharp the dissociation proceeds through a long lived intermediate resonance state and, in spectroscopic parlance, is termed a predissociation process. In the present brief overview I will discuss the spectra of van der Waals molecules from this view point. The main objective of the chapter will be to outline the different possible treatments of the process and their relationship to each other as well as to collect together a few key references on the theory of these processes. 

The study of van der Waals molecules is often made difficult (but interesting) by the multitude of energy transfer processes possible. If these weakly bound complexes are studied under equilibrium conditions near the normal condensation point of the gas then kT = D. This means that the kinetic energy of most collisions is sufficient to dissociate the van der Waals molecules. Energy transfer by destructive collisions can be reduced if the complexes are generated by a supersonic nozzle since temperatures can be effectively lowered to 10 K or below. 

A covalent bond (or particular nomial mode) in the van der Waals molecule (e.g. the I2 bond in l2-He) can be selectively excited, and what is usually observed experimentally is that the unimolecular dissociation rate constant is orders of magnitude smaller than the RRKM prediction. This is thought to result from weak coupling between the excited high-frequency intramolecular mode and the low-frequency van der Waals intemiolecular modes [83]. This coupling may be highly mode specific. Exciting the two different HE stretch modes in the (HF)2 dimer with one quantum results in lifetimes which differ by a factor of 24 [84]. Other van der Waals molecules studied include (NO)2 [85], NO-HF [ ], and (C2i J )2 [87]. 

As discussed in section A3.12.2. intrinsic non-RRKM behaviour occurs when there is at least one bottleneck for transitions between the reactant molecule s vibrational states, so drat IVR is slow and a microcanonical ensemble over the reactant s phase space is not maintained during the unimolecular reaction. The above discussion of mode-specific decomposition illustrates that there are unimolecular reactions which are intrinsically non-RRKM. Many van der Waals molecules behave in this maimer [4,82]. For example, in an initial microcanonical ensemble for the ( 211 )2 van der Waals molecule both the C2H4—C2H4 intennolecular modes and C2H4 intramolecular modes are excited with equal probabilities. However, this microcanonical ensemble is not maintained as the dimer dissociates. States with energy in the intermolecular modes react more rapidly than do those with the C2H4 intramolecular modes excited [85]. 

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.)... 

Apparently there are no experimental data on BeNe. If we fit a Morse function to the parameters we obtain for the dissociation curve, it is estimated that there would be 14-15 bound vibrational states for this Van der Waals molecule. Thus, VB theory predicts the existence of stable gaseous BeNe, if it is cold enough, since Dg is only 2kT for room temperature. 

Dissociation energies vary from a few thousandths of an eV for physically bound van der Waals molecules to several eV for chemically bound molecules. Van der Waals molecules are bound by the weak long-range forces and exist only at very low temperatures, either in a supersonic beam or in the interstellar space (Buckingham, Fowler, and Hutson 1988). Typical examples are t... 

It is worthwhile, however, pointing out that the existence of a long-lived intermediate state and the absence of a barrier in the exit channel do not necessarily imply statistical product state distributions. The fragment distributions in the dissociation of weakly bound van der Waals molecules are usually neither thermal nor statistical, despite the extremely long lifetime of the complex. We will come back to this in Chapter 12. 

In equation (63) we must insist, however, that the potential have only one set of atomic and molecular fragments as the dissociation limit. Hence, the electronic states of those fragments (which are established by the spin-spatial Wigner-Witmer correlation rules116) are supposed to be independent of the way the dissociation occurs. This is a typical situation in van der Waals molecules, e.g., RgX2 (Rg = rare gas, X = H, Li,...),... 

The recent study by Hilpert (18)of the van der Waals molecule Hg2, illustrated in Table III (3,4,18,19). is an exan ile of the high sensitivity attainable with the method. The investigation also showed that the equilibria involving a very weakly bonded molecule could be reliably studied although the molecule had been ionized by electrons with an energy of approximately two hundred times that of its dissociation energy. At the same time this study confirmed a recent reevaluation by Huber and Herzberg ( ) of thermal spectroscopic literature data. 

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