Comparison of Experimental vs Theoretical Abundances of ¹³CH₃D and ¹²CH₂D₂ for Isotopically Equilibrated Systems from 1 to 500 °c

Methane is produced and consumed via numerous microbial and chemical reactions in atmospheric, hydrothermal, and magmatic reactions. The stable isotopic composition of methane has been used extensively for decades to constrain the source of methane in the environment. A recently introduced isotopic parameter used to study the formation temperature and formational conditions of methane is the measurement of molecules of methane with multiple rare, heavy isotopes ("clumped") such as ¹³CH₃D and ¹²CH₂D₂. In order to place methane-clumped isotope measurements into a thermodynamic reference frame that allows calculations of clumped isotope-based temperatures (geothermometry) and comparison between laboratories, all past studies have calibrated their measurements using a combination of experiment and theory based on the temperature dependence of clumped isotopologue distributions for isotopically equilibrated systems. These have previously been performed at relatively high temperatures (>150 °C). Given that many natural occurrences of methane form below these temperatures, previous calibrations require extrapolation when calculating clumped isotope-based temperatures outside of this calibration range. We provide a new experimental calibration of the relative equilibrium abundances of ¹³CH₃D and ¹²CH₂D₂ from 1 to 500 °C using a combination of γ-Al₂O₃- and Ni-based catalysts and compare them to new theoretical computations using Path Integral Monte Carlo (PIMC) methods and find 1:1 agreement (within ±1 standard error) for the observed temperature dependence of clumping between experiment and theory over this range. This demonstrates that measurements, experiments, and theory agree from 1 to 500 °C, providing confidence in the overall approaches. Polynomial fits to PIMC computations, which are considered the most rigorous theoretical approach available, are given as follows (valid T ≥ 270 K): Δ _¹³CH3D ≅ 1000 × ln(K _{¹³ CH3D}) = (1.47348 × 10¹⁹)/T⁷ - (2.08648 × 10¹⁷)/T⁶ + (1.19810 × 10¹⁵)/T⁵ - (3.54757 × 10¹²)/T⁴ + (5.54476 × 10⁹)/T³ - (3.49294 × 10⁶)/T² + (8.89370 × 10²)/T and Δ _¹²CH2D2 ≅ 1000 × ln(8/3K _{¹² CH2D2} ) = -(9.67634 × 10¹⁵)/T⁶ + (1.71917 × 10¹⁴)/T⁵ - (1.24819 × 10¹²)/T⁴ + (4.30283 × 10⁹)/T³ - (4.48660 × 10⁶)/T² + (1.86258 × 10³)/T. We additionally compare PIMC computations to those performed utilizing traditional approaches that are the basis of most previous calibrations (Bigeleisen, Mayer, and Urey model, BMU) and discuss the potential sources of error in the BMU model relative to PIMC computations.