Ab initio Quantum Chemical Studies on Kinetic Fractionation during the analysis of Carbonates for the Clumped Isotope Thermometry
Stable and clumped isotopic compositions of molecules and minerals carry the signatures of temperatures and other physical and chemical conditions of the time of their formation. Isotopic compositions of such precipitate are preserved in carbonate that provides information about the climate through geological time. The carbonates formed in the aquatic environment serve as an archive for past climate and temperature reconstruction. In nature, sedimentary carbonate rocks are primarily composed of minerals calcite (CaCO3) and dolomite (CaMg(CO3)2). They comprise ~20% of the surface sedimentary rocks on Earth and are also found in other planets, with the oldest being ~3.5 Ga, almost as primitive as the Earth itself. The majority of them form in the aquatic environments that ranged from the warm, sunlit shallow seafloor to the cold, perpetually dark, deep ocean. Carbonate rocks are also traced in the terrestrial and extraterrestrial environment, which includes terrestrial spring waters, rivers and lakes, caves, soils, and meteorites from outer space. Ab initio quantum chemical simulations are used to calculate the extent of equilibrium and kinetic isotope fractionations, which provided additional theoretical references in clumped isotope paleothermometry. Ab initio quantum chemical simulations provide the inputs in terms of vibration frequencies and thermal energies of the optimized stable molecules and the transition state structures for the partition function calculations of equilibrium and kinetic fractionations. Ab initio calculations using density functional theory (DFT) are performed using 'Gaussian09' computational chemistry packages. Equilibrium constant and partition function calculations are performed using scripts in Matlab and Python. Though the clumped isotope proxy is based on the temperature dependence of 13C-18O bonding preference in the mineral lattice, which is captured in the product CO2, there is limited information on the phosphoric acid reaction mechanism and the magnitude of clumped isotopic fractionation (mass 63 in CO32- to mass 47 in CO2) during the acid digestion. We explored the reaction mechanism for phosphoric acid digestion of calcite using first-principles density functional theory. We identified the transition state structures for each protonation reaction involving different isotopologues and used the corresponding vibrational frequencies in reduced partition function theory to estimate Δ47 acid fractionation. We showed that the acid digestion reaction, which results in the formation of CO2 enriched with 13C-18O bonds, commences with the protonation of calcium carbonate in the presence of water. Our simulations yielded a relationship between Δ47 acid fractionation for calcite and reaction temperature as Δ47 acid fractionation in calcite = -0.30175 + 0.57700*105/ T2 - 0.10791* (105/ T2)2, with T varying between 298.15 K and 383.15 K. This relationship shows a higher slope (Δ47 acid fractionation vs. 1/T2 curve) than previous studies based on the H2CO3 model. The theoretical estimates from the present and earlier studies encapsulate experimental observations from both 'sealed vessel' and 'common acid bath' acid digestion methods from literature. Previous theoretical models for determining clumped isotopic fractionation in product CO2 during acid digestion of carbonates are independent of the cations present in the carbonate lattice. Hence further study is required to understand the cationic effect. We studied the acid reaction mechanism and calculated the acid fractionation factor for dolomite using partition functions and vibrational frequencies obtained for the transition state structure, and determined the effect of cations on the acid fractionation factor. Theoretically obtained acid fractionation factor for dolomite can be expressed as Δ47 acid fractionation in dolomite = -0.28563 + 0.49508*(105/ T2) - 0.08231* (105/ T2)2 for a temperature range between 278.15 K and 383.15 K. The theoretical slope of the dolomite-acid digestion curve is lower than that of the calcite-acid digestion curve obtained using the identical reaction mechanism. Our theoretical slope is consistent with the result from the common acid bath experiments but higher than the slope obtained in the experimental study using the sealed vessel and modified sealed vessel method and previous theoretical study using the H2CO3 model. Transition state structure, obtained in our study, includes the cations present in the carbonate minerals and provides distinct acid fractionation factors for calcite and dolomite. The observed gentler slope of theoretically calculated dolomite-acid digestion curve compared to calcite is expected considering the stronger Mg-O bond. In the present theoretical study, we provided the acid digestion reaction mechanism based on the protonation and determined a quantitative acid digestion correction factor for a range of reaction temperature for the experimental protocols where the product CO2 is immediately removed from the system, and there is not enough chance of post-digestion isotope exchanges. We suggest using appropriate acid digestion correction factors depending on the experimental techniques used for acid digestion of carbonates.