Despite a decade of intense experimental research the molecular mechanism of mass independent fractionation of sulfur isotopes (S-MIF, observed in the Archean rock record) remains unclear. Since the discovery of S-MIF in 2001, the focus of geological community has been on photolytic origin of the effect. While the photolysis of sulfur dioxide by UV radiation, or the subsequent photochemistry, indeed, carry potential for revealing the nature of S-MIF, other sources of S-MIF can't be ruled out and should also be explored. In particular, the gas phase chemical reactions that produce sulfur allotropes or other sulfur-containing small molecules may hold the key to this mystery. Our major idea is that S-MIF occurred in recombination reactions that produced small sulfur allotropes, such as S2 and S3, in the anoxic Archean atmosphere. This initial fractionation was then transferred to larger allotropes, up to S8, and, finally, was preserved in the Archean deposits. In order to test this hypothesis we will carry out theoretical and computational studies of the isotope effects in the recombination reactions relevant to sulfur chemistry in the Archean atmosphere. Using the tools of electronic structure theory and quantum dynamics, we will calculate the rates of formation for different isotopologues of the most relevant sulfur-containing molecules. This information will permit us to estimate the values of enrichments and fractionations of sulfur isotopes in the Archean atmosphere. It will also provide critical input data to the kinetics modelers trying to test, by sensitivity studies, the possible mechanisms of S-MIF accumulation and preservation in the Archean deposits. We will collaborate with experimentalists and will suggest new laboratory experiments that should help to confirm our predictions.