Unimolecular resonance

Table 8.1. Quantum Mechanical Studies of Positions and Widths of Isolated Unimolecular Resonances. ...

The optical model " of unimolecular resonances uses the partitioning of Hilbert space into Q and P subspaces, where Q and P represent the projection of the Hilbert space onto bound states and dissociative continua, respectively ... 

These experiments stimulated theoretical work by us (9-14), independently by Schinke and co-workers (15-17), and recently both groups (18) to rigorously model this unimolecular dissociation. Ab /wiYio-based potential energy surfaces were constructed by these groups, and used in quantum dynamics calculations to obtain the real energies and widths of the HOCl resonances for OH-overtones. The results of our calculations and their interpretation will be reviewed below. However, before describing that work, we present a short overview of the theory and calculation of unimolecular resonances. 

In a time-dependent picture, resonances can be viewed as localized wavepackets composed of a superposition of continuum wavefimctions, which qualitatively resemble bound states for a period of time. The unimolecular reactant in a resonance state moves within the potential energy well for a considerable period of time, leaving it only when a fairly long time interval r has elapsed r may be called the lifetime of the almost stationary resonance state. 

Figure A3.12.8. Possible absorption spectrum for a molecule which dissociates via isolated compound-state resonances. Eq is the unimolecular threshold. (Adapted from [4].)...

The theory of isolated resonances is well understood and is discussed below. Mies and Krauss [79, ] and Rice [ ] were pioneers m treating unimolecular rate theory in temis of the decomposition of isolated Feshbach resonances. 

Figure A3.12.9. Comparison of the unimolecular dissociation rates for HO2—>H+02 as obtained from the quantum mechanical resonances open circles) and from variational transition state RRKM step...

Mies F H 1969 Resonant scattering theory of association reactions and unimolecular decomposition. Comparison of the collision theory and the absolute rate theory J. Cham. Phys. 51 798-807... 

Tobiason J D, Dunlap J R and Rohifing E A 1995 The unimolecular dissociation of HCO a spectroscopic study of resonance energies and widths J. Cham. Phys. 103 1448-69... 

Stock C, Li X, Keller H-M, Schinke R and Temps F 1997 Unimolecular dissociation dynamics of highly vibrationally excited DCO x-A t- I- Investigation of dissociative resonance states by stimulated emission pumping spectroscopy J. Cham. Phys. 106 5333-58... 

Dobbyn A J, Stumpf M, Keller H-M and Schinke R 1996 Theoretical study of the unimolecular dissociation HO2—>H+02. II. Calculation of resonant states, dissociation rates, and O2 product state distributions J. Chem. Phys. 104 8357-81... 

A) During the luultiphoton excitation of molecular vibrations witli IR lasers, many (typically 10-50) photons are absorbed in a quasi-resonant stepwise process until the absorbed energy is suflFicient to initiate a unimolecular reaction, dissociation, or isomerization, usually in the electronic ground state. 

The problem of unimolecular decomposition into one or several continua via simultaneous direct and resonance-mediated routes is conveniently formulated within Feshbach s partitioning framework [56]. Following Refs. 29 and 31, we partition the scattering eigenstate into its bound and continuum projections as... 

Reactants AB+ + CD are considered to associate to form a weakly bonded intermediate complex, AB+ CD, the ground vibrational state of which has a barrier to the formation of the more strongly bound form, ABCD+. The reactants, of course, have access to both of these isomeric forms, although the presence of the barrier will affect the rate of unimolecular isomerization between them. Note that the minimum energy barrier may not be accessed in a particular interaction of AB+ with CD since the dynamics, i.e. initial trajectories and the detailed nature of the potential surface, control the reaction coordinate followed. Even in the absence (left hand dashed line in Figure 1) of a formal barrier (i.e. of a local potential maximum), the intermediate will resonate between the conformations having AB+ CD or ABCD+ character. These complexes only have the possibilities of unimolecular decomposition back to AB+ + CD or collisional stabilization. In the stabilization process,... 

Next, we discuss the J = 0 calculations of bound and pseudobound vibrational states reported elsewhere [12] for Li3 in its first-excited electronic doublet state. A total of 1944 (1675), 1787 (1732), and 2349 (2387) vibrational states of A, Ai, and E symmetries have been computed without (with) consideration of the GP effect up to the Li2(63 X)u) +Li dissociation threshold of 0.0422 eV. Figure 9 shows the energy levels that have been calculated without consideration of the GP effect up to the dissociation threshold of the lower surface, 1.0560eV, in a total of 41, 16, and 51 levels of A], A2, and E symmetries. Note that they are genuine bound states. On the other hand, the cone states above the dissociation energy of the lower surface are embedded in a continuum, and hence appear as resonances in scattering experiments or long-lived complexes in unimolecular decay experiments. They are therefore pseudobound states or resonance states if the full two-state nonadiabatic problem is considered. The lowest levels of A, A2, and E symmetries lie at —1.4282,... 

Many bimolecular and unimolecular reactions are dominated by long-lived resonances. As a result, having knowledge about the positions and lifetimes of such resonance states is highly desired. Recursive calculations of resonance states have been reported for many molecular systems, including... 

Describe the principal unimolecular and bimolecular reactions of free radicals and explain the usefulness of electron spin resonance in detecting radical species. 

The mechanism of acid hydrolysis is also different in acyclic amides and /1-lactams acid catalysis of acyclic amides proceeds via O-protonation (see Chapt. 4), whereas that of /1-lactams appears to be a unimolecular A1 type process, involving V-protonation (Fig. 5.6,b) [76], A-Protonation is not the result of reduced amide resonance but an intrinsic property of the /1-lactam structure, since bicyclic /1-lactams and monocyclic /1-lactams exhibit similar reactivity and behavior [76],... 

Prior to 1967 acetal hydrolysis had been found to be a specific-acid catalysed reaction with the accepted mechanism [equation (46)] involving fast pre-equilibrium protonation of the acetal by hydronium ion, followed by unimolecular rate-determining decomposition of the protonated intermediate to an alcohol and a resonance stabilized carbonium ion (Cordes, 1967). An A-1 mechanism was supported by an extremely large body of evidence, but it appeared unlikely that such a mechanism could expledn the... 

In the present review, a new variation on an existing experimental method will be used to show how accurate unimolecular dissociation rate constants can be derived for thermal systems. For example, thermal bimolecular reactions are amenable to study by use of several, now well-known, techniques such as (Fourier transform) ion cyclotron resonance spectrometry (FTICR), flowing afterglow (FA), and high-pressure mass spectrometry (HPMS). In systems where a bimolecular reaction leads to products other than a simple association adduct, the bimolecular reaction can always be thought of as containing a unimolecular... 

More recently, Audier and McMahon have shown that the unimolecular dissociation spectrum of transient ions can be directly obtained from a simple manipulation of a series of FTICR spectra. The data arising from this approach very closely resemble those obtained from metastable dissociations in conventional sector spectrometers (MIKES), and it has been consequently dubbed metastable ion cyclotron resonance (MICR) spectrometry. Very briefly, the method functions as follows ... 

Figure 16. Metastable ion cyclotron resonance (MICR) spectra for the unimolecular dissociation of the chemically activated adduct ion derived from association of the methoxymethyl cation with pivaldehyde during a 2-s reaction delay at a pressure of pivaldehyde of 1.0 x 10 torr. The three spectra correspond to values of rf amplitude appropriate to eject transient intermediates with lifetimes longer than (a) 60 ps, (b) 80 ps, and (c) 1 70 ps. A partial pressure of CH4 of 1.0 x 10 torr was also present to thermalize ions. The peak at m/z 125 is a secondary reaction product of m/z 85.

---