One possible source of mass-independent fractionation of sulfur isotopes in the Archean atmosphere of Earth

Abstract

Energy transfer mechanism for recombination of two sulfur atoms into a diatomic molecule, S2, is studied theoretically and computationally to determine whether the rate coefficient of this process can be significantly affected by isotopic substitutions, and whether the resultant isotope effect is expected to be mass-dependent or mass-independent. This is one of sulfur polymerization processes thought to be important in the anoxic atmosphere of the Archean Earth and, potentially, relevant to mass-independent fractionation of sulfur isotopes. A simplified theoretical approach is employed, in which all properties of S2 molecule are characterized rather accurately, whereas the process of stabilization of metastable S2∗ by bath gas collisions is described approximately. Properties of individual scattering resonances in S2 are studied in detail, and it is found that most important contributions to the recombination process come from ro-vibrational states formed near the top of centrifugal barrier, and that the number of such states is about 50 (in 32S32S). Absolute value of recombination rate coefficient is computed to be 1.22×10−33cm6/s (for 32S32S at room temperature and atmospheric pressure), close to experimental result. Two distinct isotope effects are identified. One is a classical mass-dependent effect due to translational partition function, which leads to a weak, smooth, and negative mass-dependence of rate coefficient (4% decrease when the mass is raised from 32S32S to 34S34S). Second effect, due to quantized resonances, is two orders of magnitude stronger, but is local. In practice, due to presence of multiple individual resonances, this phenomenon leads to irregular mass-independent variations of rate coefficients in the ranges ±5%. It is also demonstrated that in real molecules this irregular behavior is expected to be somewhat smoother, and the isotope effect is somewhat smaller, due to dependence of stabilization cross section on properties of individual resonances (not described by present model). Thus, additional calculations of stabilization cross sections are needed in order to give quantitative prediction of this mass-independent isotope effect, and to determine its relevance to mass-independent fractionation of sulfur isotopes in the Archean rock record.