Mode specificity

For some systems qiiasiperiodic (or nearly qiiasiperiodic) motion exists above the unimoleciilar tlireshold, and intrinsic non-RRKM lifetime distributions result. This type of behaviour has been found for Hamiltonians with low uninioleciilar tliresholds, widely separated frequencies and/or disparate masses [12,, ]. Thus, classical trajectory simulations perfomied for realistic Hamiltonians predict that, for some molecules, the uninioleciilar rate constant may be strongly sensitive to the modes excited in the molecule, in agreement with the Slater theory. This property is called mode specificity and is discussed in the next section. 

A3.12.7.1 ISOLATED REACTANT RESONANCE STATES MODE SPECIFICITY... 

The ability to assign a group of resonance states, as required for mode-specific decomposition, implies that the complete Hamiltonian for these states is well approxmiated by a zero-order Hamiltonian with eigenfunctions [M]. The ( ). are product fiinctions of a zero-order orthogonal basis for the reactant molecule and the quantity m. represents the quantum numbers defining ( ).. The wavefimctions / for the compound state resonances are given by... 

Mode specificity has been widely observed in the unimolecular decomposition of van der Waals molecules [82], e.g. 

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]. 

There are fewer experimental examples of mode specificity for the unimolecular decomposition of covalently bound molecules. One example is the decomposition of the fomiyl radical HCO, namely... 

Mode specificity has also been observed for HOCl—>Cl+OH dissociation [92, 93 and 94]- For this system, many of the states are highly mixed and unassignable (see below). However, resonance states with most of the energy in the OH bond, e.g. = 6, are assignable and have nnimolecnlar rate constants orders of magnitude smaller than the RRKM prediction [92, 93 and 94]- The lifetimes of these resonances have a very strong dependence on the J and K quantum numbers of HOCl. 

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]. 

Waite B A and Miller W H 1980 Model studies of mode specificity in unimolecular reaction dynamics J. Chem. Phys. 73 3713-21... 

Figure B2.5.23. Mode-specific stereomiitation tunnelling in hydrogen peroxide time-dependent probability...

Wang D and Bowman J M 1992 Reduced dimensionality quantum calculations of mode specificity in OH + H2 H2O + HJ. Chem. Phys. 96 8906... 

Both vibrational spectroscopies are valuable tools in the characterization of crystalline polymers. The degree of crystallinity is calculated from the ratio of isolated vibrational modes, specific to the crystalline regions, and a mode whose intensity is not influenced by degree of crystallinity and serves as internal standard. A significant number of studies have used both types of spectroscopy for quantitative crystallinity determination in the polyethylenes [38,74-82] and other semi-crystalline polymers such as polyfethylene terephthalate) [83-85], isotactic poly(propylene) [86,87], polyfaryl ether ether ketone) [88], polyftetra-fluoroethylene) [89,90] and bisphenol A polycarbonate [91]. 

The basic assumption behind the sequential dissolution methods is that a particular extractant is phase or retention mode specific in its chemical attachment on a mixture of forms (D Amore et al., 2005). The procedure... 

Table XI presents the results of tests on the same materials in the NBS smoke chamber. It is immediately clear that these results do not correlate well with those measured on the RHR apparatuses. Furthermore, an attempt at a linear correlation between the flaming mode specific maximum optical density and the Cone calorimeter SmkPar at 20 kW/m2 yielded a correlation coefficient of ca. 1%, a coefficient of variation of 217% and statistically invalid correlations. A comparison between a Cone and OSU calorimeter correlation and one with the NBS smoke chamber is shown in Figure 4. This suggests that unrelated properties are being measured.

PHOTOINDUCED BOND CLEAVAGE AS A PROBE OF MODE SPECIFICITY AND INTRAMOLECULAR DYNAMICS IN ROVIBRATIONALLY EXCITED TRIATOMIC TO 10 ATOM MOLECULES... 

RESONANCES IN UNIMOLECULAR DISSOCIATION FROM MODE-SPECIFIC TO STATISTICAL BEHAVIOR... 

The purpose of this chapter is a detailed comparison of these systems and the elucidation of the transition from regular to irregular dynamics or from mode-specific to statistical behavior. The main focus will be the intimate relationship between the multidimensional PES on one hand and observables like dissociation rate and final-state distributions on the other. Another important question is the rigorous test of statistical methods for these systems, in comparison to quantum mechanical as well as classical calculations. The chapter is organized in the following way The three potential-energy surfaces and the quantum mechanical dynamics calculations are briefly described in Sections II and III, respectively. The results for HCO, DCO, HNO, and H02 are discussed in Sections IV-VII, and the overview ends with a short summary in Section VIII. 

There are many interesting facets of this elementary fragmentation process. In this presentation we emphasize primarily the mode specificity, that is, the more or less sytematic dependence of the resonance widths and the final-state distributions on the excited mode and the number of quanta in each mode. (For more complete analyses the reader is referred to Refs. 32 and 33 and some future publications.)... 

---