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 Delta(i) ("i" refers to a specific isotopologue) and Delta(mass) ("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., (NNO)-N-14-N-15-O-16 vs. (NNO)-N-15-N-14-O-16) and can estimate Delta(mass) of any kind of molecule, whether the Delta(i) 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 Delta(i) have been studied carefully. Our results suggest that such corrections are significant, especially for isotopologues involving hydrogen atoms. To obtain the most precise Delta(i) or Delta(mass) value, including those higher-order anharmonic corrections into the calculation is recommended. Such corrections to Delta(i) are on the order of percent and are similar to anharmonic corrections for the beta factor. The difference is that higher-order anharmonic corrections usually reduce beta values, but would either reduce or increase Delta(i) values. For example, the corrections can reduce Delta(13CDH3) by five percent but increase Delta(18O13C16O) by two percent at 300 K. The choice of the frequency scaling factor in the Delta(i) calculation is also found similar to the calculation of beta factors. The scaled Delta(i) value will approximately equal the un-scaled Delta(i) 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 Delta(i). 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 Delta(47) of CO2 is found to be roughly independent of delta C-13 and delta O-18 for most geologic samples, suggesting the effects of bulk isotope compositions on Delta(47) are negligible. We find that the sum of Delta(i) for all of the singly substituted isotopologues will be equal to zero approximately, enabling us to determine the stochastic concentrations of isotopologues from experiments. (C) 2011 Elsevier Ltd. All rights reserved.

Publication name	GEOCHIMICA ET COSMOCHIMICA ACTA　Volume: 77 　Pages: 292-303　 Published: JAN 15 2012
Author(s)	Cao, Xiaobin; Liu, Yun
Corresponding author	LIU Yun  liuyun@vip.gyig.ac.cn  Chinese Acad Sci, Inst Geochem, State Key Lab Ore Deposit Geochem, Guiyang 550002, Peoples R China

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