Stable isotope equilibria in the dihydrogen-water-methane-ethane-propane system. Part 1: Path-integral calculations with CCSD(T) quality potentials

Isotopic compositions of alkanes are typically assumed to be kinetically controlled, but recently it has been proposed that alkanes can isotopically equilibrate for both C and H isotopes during natural gas generation. Evaluation of this requires knowledge of the isotopic equilibrium between alkanes and other common hydrogen and carbon bearing species. Here we calculate isotopic equilibria within and between gaseous dihydrogen (H2), water (H2O), methane (CH4), ethane (C2H6) and propane (C3H8), including isotope fractionation among molecules, clumped isotope effects, as well as among sites of propane (i.e., the site-specific isotope effects) from 0°C to 500°C using a path-integral method paired with high-level descriptions of molecular potentials and the diagonal correction to the Born–Oppenheimer approximation. While path-integral calculations with high-level CCSD(T) potentials are available for the isotopic equilibria involving methane, the path-integral calculations for ethane and propane have only been performed based on lower-level descriptions of the molecular potentials. We analyze the relative importance of various approximations that are commonly employed when isotopic equilibria are evaluated. We find that clumped isotope effects can be calculated to the same accuracy using computationally inexpensive combination of the Bigeleisen-Mayer-Urey model with the molecular potential from density functional theory. In contrast, fractionation and site preferences of both deuterium and carbon-13 benefit from the use of the higher level CCSD(T) potentials and accounting for anharmonic effects. Additionally, for fractionation and site preference of deuterium, corrections to Born–Oppenheimer approximation can also be important.

烷烃（alkanes）的同位素组成通常被认为受动力学控制，但近期已有研究提出，在天然气生成过程中，烷烃的碳（C）和氢（H）同位素均可实现同位素平衡。要验证该论点，需明确烷烃与其他常见含氢、含碳物种间的同位素平衡关系。本研究采用路径积分法（path-integral method），结合高精度分子势能描述与玻恩-奥本海默近似（Born–Oppenheimer approximation）的对角校正，在0℃至500℃温度范围内，计算气态氢（H₂）、水（H₂O）、甲烷（CH₄）、乙烷（C₂H₆）与丙烷（C₃H₈）分子内部及彼此间的同位素平衡，涵盖分子间同位素分馏、团簇同位素效应（clumped isotope effects）以及丙烷分子内不同位点的位专一性同位素效应（site-specific isotope effects）。尽管针对涉及甲烷的同位素平衡，已有采用高精度CCSD(T)势能的路径积分计算研究，但针对乙烷与丙烷的同类计算仅基于低精度分子势能描述完成。本研究分析了同位素平衡评估中常用的各类近似方法的相对重要性。研究发现，采用计算成本较低的比格莱森-迈耶-尤里模型（Bigeleisen-Mayer-Urey model）与密度泛函理论（density functional theory）分子势能的组合方案，即可达到与高精度计算相当的团簇同位素效应计算精度。与之相反，氘（deuterium）与碳-13（¹³C）的同位素分馏及位点偏好性分析，需借助高精度CCSD(T)势能并考虑非简谐效应（anharmonic effects）方可获得可靠结果。此外，针对氘的同位素分馏与位点偏好性，玻恩-奥本海默近似的校正同样至关重要。