Rotational quantum state distribution

Dixon et al. [75] use a simple quantum mechanical model to predict the rotational quantum state distribution of OH. As discussed by Clary [78], the component of the molecular wave function that describes dissociation to a particular OH rotational state N is approximated as... 

Magnesium. Excited Mg atoms (3s 3p P ) and PH3 give MgH (v = 0,1) Its nascent rotational quantum state distribution was determined [75]. 

Recent work (161) with a tunable VUV flash lamp has shown that the CN(A2II) can be detected directly using the LIF technique. Thus one is able, in principle, to determine the vibrational and rotational population of each of the fragments (CN(X2E), (A2n)). The tunable UV flash lamp allows one to measure these quantum state distributions as a function of the vibrational frequency of the upper electronic state. The results from these studies thus far are summarized in Table 8. 

The photochemical dynamics of H2S has been studied in its first absorption band between 180 and 260 nm (2) using LIF measurements to determine the quantum state distribution of the SH fragment (169-171), as well as TOF measurements of the velocity distribution of H atom fragment (172). In the former case, the vibrational and rotational distribution of the SH fragment was only measured in the v" = 0 level because fewer radicals with v" > 0 are produced and the LIF technique does not efficiently detect these excited radicals. 

The OH radical is produced in a particular vibrational and rotational quantum state specified by the quantum numbers n and j. The corresponding energies are denoted by tnj. The probabilities with which the individual quantum states are populated are determined by the forces between the translational mode (the dissociation coordinate) and the internal degrees of freedom of the product molecule along the reaction path. Final vibrational and rotational state distributions essentially reflect the dynamics in the fragment channel. They are one major source of information about the dissociation process. 

For reactants in complete thermal equilibrium, the probability of finding a BC molecule in a specific quantum state, n, is given by the Boltzmann distribution (see Appendix A.l). Thus, in the special case of non-interacting molecules the probability PBC(n)y °f finding a BC molecule in the internal (electronic, vibrational, and rotational) quantum states with energy En is... 

The Gaussian width b of the angular distributions of NO detected in different rotational quantum states (J = 6.5 and 15.5) exhibits comparable values and the same dependence on the desorption velocity,... 

Extending the theory to interpret or predict the rovibrational state distribution of the products of the unimolecular dissociation, requires some postulate about the nature of the motion after the unimolecularly dissociating system leaves the TS on its way to form products. For systems with no potential energy maximum in the exit channel, the higher frequency vibrations will tend to remain in the same vibrational quantum state after leaving the TS. That is, the reaction is expected to be vibrationally adiabatic for those coordinates in the exit channel (we return to vibrational adiabaticity in Section 1.2.9). The hindered rotations and the translation along the reaction coordinate were assumed to be in statistical equilibrium in the exit channel after leaving the TS until an outer TS, the PST TS , is reached. With these assumptions, the products quantum state distribution was calculated. (After the system leaves the PST TS, there can be no further dynamical interactions, by definition.)... 

The large Einstein radiative coefficients [225] and the widely spaced vibration-rotation quantum states make HF peculiarly prone to stimulated emission, and a large proportion of the chemical lasers which have been reported operate on lines in the infrared bands of this molecule [224], H-atom abstraction reactions by F and F-atom abstraction by H are both normally exothermic, and HF is quite generally produced in a vibrational distribution giving rise to oscillation. However, the systems are complex frequently both types of reaction occur, and the details of the vibrational distribution resulting from chemical reaction are difficult to evaluate. 

Chemical dynamics experiments in which OH product quantum state distributions and an absolute reaction cross section for reaction (1) could be measured were reported in 1984. Subsequent experiments revealed additional details about the reaction dynamics, including nascent OH( H) spin-orbit and A-doublet rotational fine structure state distributions, Oi P) product fine structure state distributions, and OH angular momentum polarization distributions,as well as differential cross sections. The experimental results indicate that depending on the reagent collision energy... 

In this chapter we elucidate the state-specific perspective of unimolec-ular decomposition of real polyatomic molecules. We will emphasize the quantum mechanical approach and the interpretation of the results of state-of-the-art experiments and calculations in terms of the quantum dynamics of the dissociating molecule. The basis of our discussion is the resonance formulation of unimolecular decay (Sect. 2). Summaries of experimental and numerical methods appropriate for investigating resonances and their decay are the subjects of Sects. 3 and 4, respectively. Sections 5 and 6 are the main parts of the chapter here, the dissociation rates for several prototype systems are contrasted. In Sect. 5 we shall discuss the mode-specific dissociation of HCO and HOCl, while Sect. 6 concentrates on statistical state-specific dissociation represented by D2CO and NO2. Vibrational and rotational product state distributions and the information they carry about the fragmentation step will be discussed in Sect. 7. Our description would be incomplete without alluding to the dissociation dynamics of larger molecules. For them, the only available dynamical method is the use of classical trajectories (Sect. 8). The conclusions and outlook are summarized in Sect. 9. 

A VRRKM/ECC model for product vibrational and rotational distributions was introduced by Wardlaw and Marcus (1988). Subsequently, Marcus (1988) constructed a refined version which successfully describes rotational quantum number distributions of products arising from the decomposition of NCNO (Klippenstein et al., 1988) and CH2CO (Klippenstein and Marcus, 1989). In the latter model, the conserved modes are assumed vibrationally adiabatic (as in SACM) after passage through the transition state and, consequently, the distribution of vibrational quantum numbers for the products is the same as it is at the transition state. The transitional modes are assumed nonadiabatic between the variationally determined TS and a loose TS located at the centrifugal barrier. [These are the same two transition states associated with the TS switching... 

Figure 9.19 The product rotational quantum number distributions, P(j), of FNO obtained by mapping the transition state wave function onto the rotational excitation... 

This book presents a detailed exposition of angular momentum theory in quantum mechanics, with numerous applications and problems in chemical physics. Of particular relevance to the present section is an elegant and clear discussion of molecular wavefiinctions and the detennination of populations and moments of the rotational state distributions from polarized laser fluorescence excitation experiments. 

In Figure 1, we see that there are relative shifts of the peak of the rotational distribution toward the left from f = 12 to / = 8 in the presence of the geometiic phase. Thus, for the D + Ha (v = 1, DH (v, f) - - H reaction with the same total energy 1.8 eV, we find qualitatively the same effect as found quantum mechanically. Kuppermann and Wu [46] showed that the peak of the rotational state distribution moves toward the left in the presence of a geometric phase for the process D + H2 (v = 1, J = 1) DH (v = 1,/)- -H. It is important to note the effect of the position of the conical intersection (0o) on the rotational distribution for the D + H2 reaction. Although the absolute position of the peak (from / = 10 to / = 8) obtained from the quantum mechanical calculation is different from our results, it is worthwhile to see that the peak... 

The H2O molecules are cooled in a supersonic expansion to a rotational temperature of 10K before photodissociation. The evidence for pathway competition is an odd-even intensity alteration in the OH product state distribution for rotational quantum numbers V = 33 45. This intensity alternation is attributed to quantum mechanical interference due to the N-dependent phase shifts that arise as the population passes through the two different conical intersections. 

Gray and Wozny [101, 102] later disclosed the role of quantum interference in the vibrational predissociation of He Cl2(B, v, n = 0) and Ne Cl2(B, v, = 0) using three-dimensional wave packet calculations. Their results revealed that the high / tail for the VP product distribution of Ne Cl2(B, v ) was consistent with the final-state interactions during predissociation of the complex, while the node at in the He Cl2(B, v )Av = — 1 rotational distribution could only be accounted for through interference effects. They also implemented this model in calculations of the VP from the T-shaped He I C1(B, v = 3, n = 0) intermolecular level forming He+ I C1(B, v = 2) products [101]. The calculated I C1(B, v = 2,/) product state distribution remarkably resembles the distribution obtained by our group, open circles in Fig. 12(b). 

Fig. 12. Partitionings of hydrogen fragment translational energy distribution into three components. The solid line denotes the contribution from H2S — 8H(,4 "S+ ) + H which yields a resolved structure with a rovibrational state assignment on the top. The dotted line denotes the contribution of hydrogen from the SH(442 +) —> S(3P) + H reaction, which is a reflection of the solid curve but the structure is smeared out. The corresponding rotational quantum numbers of the parent molecule SI I (A 2>l 1 ) l =0 is marked on the bottom. The remaining part of the P(E) spectrum is represented by the square-like dashed curve.

The time-of-flight spectrum of the H-atom product from the H20 photodissociation at 157 nm was measured using the HRTOF technique described above. The experimental TOF spectrum is then converted into the total product translational distribution of the photodissociation products. Figure 5 shows the total product translational energy spectrum of H20 photodissociation at 157.6 nm in the molecular beam condition (with rotational temperature 10 K or less). Five vibrational features have been observed in each of this spectrum, which can be easily assigned to the vibrationally excited OH (v = 0 to 4) products from the photodissociation of H20 at 157.6 nm. In the experiment under the molecular beam condition, rotational structures with larger N quantum numbers are partially resolved. By integrating the whole area of each vibrational manifold, the OH vibrational state distribution from the H2O sample at 10 K can be obtained. In... 

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