Theoretical estimation of the equilibrium distribution of clumped isotopes in nature

Details Theoretical estimation of the equilibrium distribution of clumped isotopes in nature Theoretical estimation of the equilibrium distribution of clumped isotopes in nature

Jan 2012

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2012gecoa..77..292c&link_type=abstract

Geochimica et Cosmochimica Acta, Volume 77, p. 292-303.

Mathematics

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Scientific paper

Clumped (or multiply substituted) isotope geochemistry, as an emerging field, has displayed an array of unique and effective geological and atmospheric applications. In this study, we introduce a new method to facilitate the calculation of concentrations of multiply substituted isotopologues at equilibrium conditions, especially for the calculation of Δi ("i" refers to a specific isotopologue) and Δmass ("mass" refers to isotopologues with the same mass number). The proposed exact method has equivalent accuracy and can be solved by similar level of effort compared to that of Wang et al. (2004). However, the approximate method proposed here can handle molecules with isotopomers (e.g., 14N15N16O vs. 15N14N16O) and can estimate Δmass of any kind of molecule, whether the Δi values of singly-substituted isotopologues are small or large. The accuracy and convenience of the proposed method are illustrated through several examples (i.e., CO2, N2O and CH4).Higher-order anharmonic corrections to Δi have been studied carefully. Our results suggest that such corrections are significant, especially for isotopologues involving hydrogen atoms. To obtain the most precise Δi or Δmass value, including those higher-order anharmonic corrections into the calculation is recommended. Such corrections to Δi are on the order of percent and are similar to anharmonic corrections for the β factor. The difference is that higher-order anharmonic corrections usually reduce β values, but would either reduce or increase Δi values. For example, the corrections can reduce Δ by five percent but increase Δ by two percent at 300 K. The choice of the frequency scaling factor in the Δi calculation is also found similar to the calculation of β factors. The scaled Δi value will approximately equal the un-scaled Δi times the scaling factor, suggesting that the uncertainty in the frequency scaling factor (usually on the order of percent) could possibly cause large errors in the calculation of Δi. The best way to reduce such errors is to use high-level theoretical methods to reduce the uncertainty of the scaling factor, or to choose frequency scaling factors carefully.Using the method proposed, the equilibrium Δ47 of CO2 is found to be roughly independent of δ13C and δ18O for most geologic samples, suggesting the effects of bulk isotope compositions on Δ47 are negligible. We find that the sum of Δi for all of the singly substituted isotopologues will be equal to zero approximately, enabling us to determine the stochastic concentrations of isotopologues from experiments.

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