deficits in abiotic methane
The Δ12CH2D2 values here exhibit pronounced disequilibrium, in sharp contrast with those of Δ13CH3D. The Δ12CH2D2 values are exclusively of negative sign, ranging from −3.0 ± 2.5‰ (1σ) at 210 °C to −32.0 ± 1.6‰ at 183 °C. These values are substantially lower than the expected equilibrium values of 9.2‰ and 4.3‰ at 130 and 250 °C, respectively. We argue that the Δ12CH2D2 deficits are apparent disequilibrium signatures resulting from combinatorial effects. In general, combinatorial effects arise when a molecule contains indistinguishable atoms of the same element, and that these atoms come from pools with distinct isotope ratios, as has been predicted and shown for methane previously both from theory and in the laboratory (Röckmann et al., 2016; Taenzer et al., 2020; Yeung, 2016). Among the two mass-18 isotopologues of methane, only Δ12CH2D2 can be affected by combinatorial effects, because it is the isotopologue with two indistinguishable deuterium substitutions for hydrogen.
The root of the combinatorial effect comes from the notation convention used with clumped isotopes. As an example, consider a sample of methane gas with δD = –100 ‰ relative to SMOW and δ13C = -10 ‰ relative to PDB, corresponding to a measured bulk D/H ratio of 1.40184⋅10-4 and a13C/12C ratio of 0.01112483. In this example we will use a measured12CH2D2/12CH4ratio of 1.11600×10-7. To calculate the value for Δ12CH2D2, we compute the stochastic ratio from the measured bulk carbon and hydrogen isotope ratios. Isotope-specific mole fractions for singly-substituted isotopologues are closely approximated as: