Transition state angular momentum conservation

Polyatomic molecules differ from diatoms in that the departing fragments can themselves rotate so that the angular momentum can be conserved in many different ways. Secondly, the dissociation of polyatomic species may involve a complex series of rearrangements in which the transition state may have a structure that is very different from the molecule so that its rotational constants may differ as well. If the transition state has a real barrier and is described solely in terms of vibrational oscillators (plus perhaps one or two internal rotors), that is, a vibrator transition state, angular momentum conservation results in a much larger rotational barrier than the previously discussed centrifugal barrier in the diatom dissociation. 

B. Loose Transition State and Angular Momentum Conservation (PST)... 

We consider next phase-space theory (PST), which was designed principally to calculate energy distributions of the reaction products.12 In PST a loose transition state is assumed and, rather than using the approximation of l J,l is chosen so as to satisfy angular momentum conservation, namely, the triangle inequality,... 

Transitions between states are subject to certain restrictions called selection rules. The conservation of angular momentum and the parity of the spherical harmonics limit transitions for hydrogen-like atoms to those for which A/ = 1 and for which Am = 0, 1. Thus, an observed spectral line vq in the absence of the magnetic field, given by equation (6.83), is split into three lines with wave numbers vq + (/ bB/he), vq, and vq — (HbB/he). 

The desorption flux is so low under these conditions that no gas phase collisions occurred between molecular desorption and LIF probing. Phase space treatments " of final-state distributions for dissociation processes where exit channel barriers do not complicate the ensuing dynamics often result in nominally thermal distributions. In the phase space treatment a loose transition state is assumed (e.g. one resembling the products) and the conserved quantities are total energy and angular momentum the probability of forming a particular flnal state of ( , J) is obtained by analyzing the number of ways to statistically distribute the available (E, J). 

In any allowed electronic energy transfer process, the overall spin angular momentum of the system should not change. This statement is known as Wigner s spin conservation rule. The rule is applicable whether the transfer occurs between an excited atom or a molecule and another molecule in its ground state or in the excited state. In an electronic transition between the energy states of the same molecule also, spin is necessarily conserved. But the phenomenon is governed by rules for dipole-dipole interaction. 

We have seen that transitions between electronic states of different spin quantum numbers are in principle forbidden by the law of conservation of angular momentum. In practice these transitions take place only through the compensation of two simultaneous changes in angular momentum represented by the orbital quantum number L and the spin quantum number S their sum J=L + S remains constant while L and S vary in opposite directions. 

Assuming that the ion is formed with equal probability in states of different mt, the population of the different m, sublevels of 2Ds/2 is in the ratios 0 1 2 3 4 5, which gives rise to polarization of the observed light emitted in the 2D5/2—>2DJ/2 transition.72 It may be noted that the exchange mechanism of Pgl" implies the conservation of a component of spin angular momentum. 

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