『Abstract
　Phosphoric acid digestion has been used for oxygen- and carbon-isotope analysis of carbonate minerals since 1950, and was recently established as a method for carbonate ‘clumped isotope’ analysis. The CO2 recovered from this reaction has an oxygen isotope composition substantially different from reactant carbonate, by an amount that varies with temperature of reaction and carbonate chemistry. Here, we present a theoretical model of the kinetic isotope effects associated with phosphoric acid digestion of carbonates, based on structural arguments that the key step in the reaction is disproportionation of H2CO3 reaction intermediary. We test that model against previous experimental constraints on the magnitudes and temperature dependences of these oxygen isotope fractionations, and against new experimental determinations of the fractionation of ¹³C-¹⁸O-containing isotopologues (‘clumped’ isotopic species). Our model predicts that the isotope fractionations associated with phosphoric acid digestion of carbonates at 25℃ are 10.72‰, 0.220‰, 0.137‰, 0.593‰ for, respectively, ¹⁸O/¹⁶O ratios (1000 lnα^*) and three indices that measure proportions of multiply-substituted isotopologues (Δ47^*, Δ48^*, Δ49^*). We also predict that oxygen isotope fractionations follow the mass dependence exponent, λ of 0.5281 (where α17o＝α18o^λ). These predictions compare favorably to independent experimental constraints for phosphoric acid digestion of calcite, including our new data for fractionations of ¹³C-¹⁸O bonds (the measured change in Δ47=0.23‰) during phosphoric acid digestion of calcite at 25℃.
　We have also attempted to evaluate the effect of carbonate cation compositions on phosphoric acid digestion fractionations using cluster models in which disproportionating H2CO3 interacts with adjacent cations. These models underestimate the magnitude of isotope fractionations and so must be regarded as unsuccessful, but do reproduce the general trend of variations and temperature dependences of oxygen isotope acid digestion fractionations among different carbonate minerals. We suggest these results present a useful starting point for future, more sophisticated models of the reacting carbonate/acid interface. Examinations of these theoretical predictions and available experimental data suggest cation radius is the most important factor governing the variations of isotope fractionation among different carbonate minerals. We predict a negative correlation between acid digestion fractionation of oxygen isotopes and of ¹³C-¹⁸O doubly-substituted isotopologues, and use this relationship to estimate the acid digestion fractionation of Δ47^* for different carbonate minerals. Combined with previous theoretical evaluations of ¹³C-¹⁸O clumping effects in carbonate minerals, this enables us to predict the temperature calibration relationship for different carbonate clumped isotope thermometers (witherite, calcite, aragonite, dolomite and magnesite), and to compare these predictions with available experimental determinations. The success of our models in capturing several of the features of isotope fractionation during acid digestion supports our hypothesis that phosphoric acid digestion of carbonate minerals involves disproportionation of transition state structures containing H2CO3.』

1. Introduction
2. Theoretical and computational methods
　2.1. Transition state theory of reaction rates
　2.2. Application of transition state theory to phosphoric acid digestion of carbonate minerals
　　2.2.1. Proposed reaction mechanism and transition state structure during phosphoric acid digestion of carbonate minerals
　　2.2.2. Fractionation of CO3^2- isotopologues during dissociation of carbonic acid
　　2.2.3. Exploration of cation effects during phosphoric acid digestion through cluster models
　2.3. Computational methods
3. Experimental methods
4. Results and discussion
　4.1. Experimentally determined acid-digestion fractionation of Δ47
　4.2. Model results for the oxygen-isotope and clumped-isotope fractionations associated with phosphoric acid digestion
　4.3. Dependence of acid digestion fractionations on the isotopic compositions of reactant carbonate minerals?
　4.4. Cation effects on acid digestion fractionations
　　4.4.1. Cluster model results on the oxygen isotope fractionation among different carbonate minerals
　　4.4.2. Controls on the variations of acid digestion isotope fractionations among different carbonate minerals
　　4.4.3. Cluster model results on the fractionation of ¹³C-¹⁸O doubly substituted isotopologues during phosphoric acid digestion
5. Summary
Acknowledgments
Appendix A
　A.1. Estimation on the equilibrium distributions of multiply-substituted isotopologues inside reactant carbonate mineral for assumed temperatures and bulk isotopic compositions
　A.2. Predicted dependence of the fractionations of multiply-substituted isotopologues on proportions of multiply substituted isotopologues of reactant carbonates
References