Nuclear spin selection rules for reactive collision systems by the spin-modification probability method

Abstract

The spin-modification probability (SMP) method, which provides fundamental and detailed quantitative information on the nuclear spin selection rules, is discussed more systematically and generalized for reactive collision systems involving more than one configuration of reactant and product molecules, explicitly taking account of the conservation of the overall nuclear spin symmetry as well as the conservation of the total nuclear spin angular momentum, under the assumption of no nuclear hyperfine interaction. The values of SMP once calculated can be used for any system of identical nuclei of any spin as long as the system has the corresponding nuclear spin symmetry. The values of SMP calculated for simple systems can also be used for more complex systems containing several kinds of identical nuclei or various isotopomers. The generalized formulation of statistical scattering theory which can easily represent various rearrangement mechanisms is also presented.

Spin-state chemistry of deuterated ammonia

“…The method is described in Quack (1977) and in Park & Light (2007b). The collision partners are classified, or labeled, according to the irreducible representations of an appropriate permutation group.…”

“…This implies that for the doubly deuterated ammonium ion, NH 2 D + 2 , for example, we keep track of four different forms depending on the two possible spin symmetries, "ortho" (A) and "para" (B), of the pairs of the H and D nuclei. In reactions involving multiple H or D nuclei, the branching ratios between different nuclear spin channels are assumed to be determined by their pure nuclear spin statistical weights, that is, the number of nuclear spin functions belonging to each channel, which are calculated using permutation symmetry algebra (Quack 1977;Park & Light 2007b;Hugo 2009;Hugo et al 2009). This method uses the assumptions of nuclear spin conservation and full scrambling of nuclei in reactive collisions.…”

Dynamically biased statistical model for the ortho/para conversion in the ${\rm H}_2 + {\rm H}_3^+$H2+H3+ → ${\rm H}_3^{+} +$H3++ H2 reaction

“…In the last years several PES's, of increasing accuracy, have appeared in the literature. [29][30][31][32][33][34][35] The exchange reaction barrier is rather low, below the zero-point energy, so that all identical nuclei can permute, subject to the symmetry constraints imposed by nuclear spin angular momenta, 23,24,26 as experimentally confirmed by measurements in plasmas at 300-500 K. 12,13 All this makes extremely difficult to perform complete quantum calculations including the 12 degrees of freedom (9 vibrational and 3 rotational), considering the whole permutation group of symmetry. For this aim, proper coordinates should be designed, as the democratic hyperspherical coordinates developed recently by Kuppermann.…”

“…ticular interest is the spin-statistics of these species, which determines selection rules for the ortho/para conversion of H + 3 . 12,16,[23][24][25][26][27] The most detailed theoretical studies performed until now are based on the statistical approach, including nuclear spin symmetry constraints. 16,17,28 The applicability of these methods relies on the formation of long-lived H + 5 complexes, in which a complete randomization of energy among all degrees of freedom is produced.…”

Editorial: Remembering John C. Light. II. Scientific contributions

“…[25][26][27][28][29][30][31] He continued in this vein until his retirement, his final two papers in the journal being on ortho-para hydrogen conversion in the H 3 + + H 2 reaction at collision energies of relevance to the chemistry of the interstellar medium. 32,33 Interestingly, these papers hark back (albeit in a more sophisticated way) to the statistical picture of complex-forming reactions with which he began his career.…”