Position-Specific and Clumped Stable Isotope Studies: Comparison of the Urey and Path-Integral Approaches for Carbon Dioxide, Nitrous Oxide, Methane, and Propane

Cold seep formation from salt diapir-controlled deep biosphere oases

Deep sea cold seeps are sites where hydrogen sulfide, methane, and other hydrocarbon-rich fluids vent from the ocean floor. They are an important component of Earth's carbon cycle in which subsurface hydrocarbons form the energy source for highly diverse benthic micro- and macro-fauna in what is otherwise vast and spartan sea scape. Passive continental margin cold seeps are typically attributed to the migration of hydrocarbons generated from deeply buried source rocks. Many of these seeps occur over salt tectonic provinces, where the movement of salt generates complex fault systems that can enable fluid migration or create seals and traps associated with reservoir formation. The elevated advective heat transport of the salt also produces a chimney effect directly over these structures. Here, we provide geophysical and geochemical evidence that the salt chimney effect in conjunction with diapiric faulting drives a subsurface groundwater circulation system that brings dissolved inorganic carbon, nutrient-rich deep basinal fluids, and potentially overlying seawater onto the crests of deeply buried salt diapirs. The mobilized fluids fuel methanogenic archaea locally enhancing the deep biosphere. The resulting elevated biogenic methane production, alongside the upward heat-driven fluid transport, represents a previously unrecognized mechanism of cold seep formation and regulation.

A Spectroscopic Description of Asymmetric Isotopologues of CO2

A polyad-conserving algebraic model applied to vibrational excitations of asymmetric isotopologues of CO2 is presented. First, the problem of vibrational excitations is studied by taking into account only the minimum subspace of states to characterize the Fermi interaction. This analysis allows an estimation of the force constants as well as the feasibility of describing the system in a local mode scheme, in terms of SU(2) operators associated with Morse ladder operators for the stretches. This description together with the algebraic U(3) for the bends establishes the dynamical group SU1(2) × U(3) × SU2(2) for a series of isotopologues. Six isotopologues are considered, namely, 16O12C18O, 16O12C17O, 16O13C18O, 16O13C17O, 17O13C18O, and 17O12C18O in their electronic ground states. For isotopologues 16O12C18O, 16O12C17O, 17O12C18O, and 16O13C18O, the vibrational description was carried out using a Hamiltonian involving 14 parameters. For this series of isotopologues with a number of energy terms 90, 57, 42, and 40, the deviations obtained were rms = 0.15, 0.10, 0.06, and 0.07 cm-1, respectively. For 16O13C17O, with 28 experimental energies and involving 13 parameters, the deviation was rms = 0.05 cm-1, while for 17O13C18O, a different strategy was proposed since only 12 experimental energy levels. In all cases, the polyad scheme P212 = 2(ν1 + ν3) + ν2 was considered. In addition, a new criterion of locality/normality degree is proposed, embracing the case of molecules with normal mode behavior, in particular, the isotopologues of CO2.

Temperature dependence of isotopic fractionation in the CO2 -O2 isotope exchange reaction

RATIONALE

Oxygen isotope exchange between O₂ and CO₂ in the presence of heated platinum (Pt) is an established technique for determining the δ¹⁷ O value of CO₂ . However, there is not yet a consensus on the associated fractionation factors at the steady state.

METHODS

We determined experimentally the steady-state α¹⁷ and α¹⁸ fractionation factors for Pt-catalyzed CO₂ -O₂ oxygen isotope exchange at temperatures ranging from 500 to 1200°C. For comparison, the theoretical α¹⁸ equilibrium exchange values reported by Richet et al. (1997) have been updated using the direct sum method for CO₂ and the corresponding α¹⁷ values were determined. Finally, we examined whether the steady-state fractionation factors depend on the isotopic composition of the reactants, by using CO₂ and O₂ differing in δ¹⁸ O value from -66 ‰ to +4 ‰.

RESULTS

The experimentally determined steady-state fractionation factors α¹⁷ and α¹⁸ are lower than those obtained from the updated theoretical calculations (of CO₂ -O₂ isotope exchange under equilibrium conditions) by 0.0024 ± 0.0001 and 0.0048 ± 0.0002, respectively. The offset is not due to scale incompatibilities between isotope measurements of O₂ and CO₂ nor to the neglect of non-Born-Oppenheimer effects in the calculations. There is a crossover temperature at which enrichment in the minor isotopes switches from CO₂ to O₂ . The direct sum evaluation yields a θ value of ~0.54, i.e. higher than the canonical range maximum for a mass-dependent fractionation process.

CONCLUSIONS

Updated theoretical values of α¹⁸ for equilibrium isotope exchange are lower than those derived from previous work by Richet et al. (1997). The direct sum evaluation for CO₂ yields θ values higher than the canonical range maximum for mass-dependent fractionation processes. This demonstrates the need to include anharmonic effects in the calculation and definition of mass-dependent fractionation processes for poly-atomic molecules. The discrepancy between the theory and the experimental α¹⁷ and α¹⁸ values may be due to thermal diffusion associated with the temperature gradient in the reactor.

Standardization for 13 C-13 C clumped isotope analysis by the fluorination method

RATIONALE

The ¹³ C-¹³ C isotopologues of C₂ molecules have recently been measured using a fluorination method. The C₂ compound is first fluorinated into hexafluoroethane (C₂ F₆ ), and its ¹³ C-isotopologues are subsequently measured using a conventional isotope ratio mass spectrometer. Here, we present an approach for standardizing the fluorination method on an absolute reference scale by using isotopically enriched C₂ F₆ .

METHODS

We prepared physical mixtures of ¹³ C-¹³ C-labeled ethanol and natural ethanol. The enriched ethanol samples were measured using the recently developed fluorination method. Based on the difference between the calculated and measured ∆¹³ C¹³ C values, we quantified the extent to which isotopologues were scrambled during dehydration, fluorination, and ionization in the ion source.

RESULTS

The measured ∆¹³ C¹³ C value was approximately 20% lower than that expected from the amount of ¹³ C-¹³ C ethanol. The potential scrambling in the ion source was estimated to be 0.5-2%, which is lower than the observed isotopic reordering. Therefore, isotopic reordering may have occurred during either dehydration or fluorination.

CONCLUSIONS

For typical analysis of natural samples, scrambling in the ion source can only change the ∆¹³ C¹³ C value by less than 0.04‰, which is lower than the current analytical precision (±0.07‰). Therefore, the observed isotopic reordering may have occurred during the fluorination of ethene through the scrambling of isotopologues of ethene but not in the ion source of the mass spectrometer or during the dehydration of ethanol, given the small amount of C₁ and C₃₊ molecules. Thus, we obtained the empirical transfer function ∆¹³ C¹³ C_CSC  = λ × ∆¹³ C¹³ C with a λ value of 1.25 ± 0.01 for ethanol/ethene and 1.00 for ethane. Using the empirical transfer function, the developed fluorination method can provide actual differences in ∆ values.

A fluorination method for measuring the 13 C-13 C isotopologue of C2 molecules

RATIONALE

Doubly substituted isotope species ("clumped" isotopes) can provide insights into the biogeochemical history of a molecule, including its temperature of formation and/or its (bio)synthetic pathway. Here, we propose a new fluorination method for the measurement of ¹³ C-¹³ C species in C₂ molecules using a conventional isotope ratio mass spectrometer. Target molecules include ethane, ethene and ethanol.

METHODS

¹³ C-¹³ C isotope species in C₂ molecules were measured as C₂ F₆ using a conventional isotope ratio mass spectrometer. Ethane and ethene are directly fluorinated to C₂ F₆ . Ethanol is measured after dehydration to ethene and subsequent fluorination of the latter. The method enables the measurement of the Δ¹³ C¹³ C values normalized against a reference working standard.

RESULTS

The reproducibility of the whole protocol, including chemical modification steps and measurement of C₂ F₆ isotopologues, is better than ±0.14‰ for all the compounds. Ethane from natural gas samples and biologically derived ethanol show a narrow range of Δ¹³ C¹³ C values, varying from 0.72‰ to 0.90‰. In contrast, synthetic ethanol as well as putative abiotic ethane show Δ¹³ C¹³ C values significantly different from this range with values of 1.14‰ and 0.25‰, respectively.

CONCLUSIONS

The method presented here provides alternative means of measuring ¹³ C-¹³ C species to that using high-resolution mass spectrometry. Preliminary data from natural and synthetic molecules re-emphasizes the potential of ¹³ C clumped isotope species as a (bio)marker.

A combined on-the-fly/interpolation procedure for evaluating energy values needed in molecular simulations

We propose an algorithm for molecular dynamics or Monte Carlo simulations that uses an interpolation procedure to estimate potential energy values from energies and gradients evaluated previously at points of a simplicial mesh. We chose an interpolation procedure that is exact for harmonic systems and considered two possible mesh types: Delaunay triangulation and an alternative anisotropic triangulation designed to improve performance in anharmonic systems. The mesh is generated and updated on the fly during the simulation. The procedure is tested on two-dimensional quartic oscillators and on the path integral Monte Carlo evaluation of the HCN/DCN equilibrium isotope effect.

Cost-effective density functional theory (DFT) calculations of equilibrium isotopic fractionation in large organic molecules

The application of stable isotopes to address a wide range of biochemical, microbiological and environmental problems is hindered by the experimental difficulty and the computational cost of determining equilibrium isotopic fractionations (EIF) of large organic molecules. Here, we evaluate the factors that impact the accuracy of computed EIFs and develop a framework for cost-effective and accurate computation of EIFs by density functional theory (DFT). We generated two benchmark databases of experimentally determined EIFs, one for H isotopes and another for the isotopes of the heavy atoms C, N and O. The accuracy of several DFT exchange-correlation functionals in calculating EIFs was then evaluated by comparing the computational results to these experimental datasets. We find that with the def2-TZVP basis set, O3LYP had the lowest mean absolute deviation (21‰ and 3.9‰ for the isotopic fractionation of H and the heavier atoms, respectively), but the GGA/meta-GGA functionals τHCTH_D3BJ, τHCTH and HCTH have similar performances (22‰ and 4.1‰, respectively, for τHCTH_D3BJ). Leveraging the good performance of computationally efficient functionals, we provide a robust, practical, experimentally validated framework for using DFT to accurately predict EIFs of large organic molecules, including uncertainty estimates.

Optical clumped isotope thermometry of carbon dioxide

Simultaneous analysis of carbon dioxide isotopologues involved in the isotope exchange between the doubly substituted ¹³C¹⁶O¹⁸O molecule and ¹²C¹⁶O₂ has become an exciting new tool for geochemical, atmospheric and paleoclimatic research with applications ranging from stratospheric chemistry to carbonate-based geothermometry studies. Full exploitation of this isotope proxy and thermometer is limited due to time consuming and costly analysis using mass spectrometric instrumentation. Here, we present an all optical clumped CO₂ isotopologue thermometer with capability for rapid analysis and simplified sample preparation. The current development also provides the option for analysis of additional multiply-substituted isotopologues, such as ¹²C¹⁸O₂. Since the instrument unambiguously measures all isotopologues of the ¹²C¹⁶O₂ + ¹³C¹⁶O¹⁸O \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rightleftharpoons $$\end{document}⇌ ¹³C¹⁶O₂ + ¹²C¹⁶O¹⁸O exchange, its equilibrium constant and the corresponding temperature are measured directly. Being essentially independent of the isotope composition of the calibration gas, an uncalibrated working reference is sufficient and usage of international calibration standards is obsolete. Other isotopologues and molecules can be accessed using the methodology, opening up new avenues in isotope research. Here we demonstrate the high-precision performance of the instrument with first gas temperature measurements of carbon dioxide samples from geothermal sources.

Identifying apparent local stable isotope equilibrium in a complex non-equilibrium system

RATIONALE

Although being out of equilibrium, biomolecules in organisms have the potential to approach isotope equilibrium locally because enzymatic reactions are intrinsically reversible. A rigorous approach that can describe isotope distribution among biomolecules and their apparent deviation from equilibrium state is lacking, however.

METHODS

Applying the concept of distance matrix in graph theory, we propose that apparent local isotope equilibrium among a subset of biomolecules can be assessed using an apparent fractionation difference (|Δα|) matrix, in which the differences between the observed isotope composition (δ') and the calculated equilibrium fractionation factor (1000lnβ) can be more rigorously evaluated than by using a previous approach for multiple biomolecules. We tested our |Δα| matrix approach by re-analyzing published data of different amino acids (AAs) in potato and in green alga.

RESULTS

Our re-analysis shows that biosynthesis pathways could be the reason for an apparently close-to-equilibrium relationship inside AA families in potato leaves. Different biosynthesis/degradation pathways in tubers may have led to the observed isotope distribution difference between potato leaves and tubers. The analysis of data from green algae does not support the conclusion that AAs are further from equilibrium in glucose-cultured green algae than in the autotrophic ones.

CONCLUSIONS

Application of the |Δα| matrix can help us to locate potential reversible reactions or reaction networks in a complex system such as a metabolic system. The same approach can be broadly applied to all complex systems that have multiple components, e.g. geochemical or atmospheric systems of early Earth or other planets.

The isotopic structures of geological organic compounds

Organic compounds are ubiquitous in the Earth's surface, sediments and many rocks, and preserve records of geological, geochemical and biological history; they are also critical natural resources and major environmental pollutants. The naturally occurring stable isotopes of volatile elements (D, 13C, 15N, 17,18O, 33,34,36S) provide one way of studying the origin, evolution and migration of geological organic compounds. The study of bulk stable isotope compositions (i.e. averaged across all possible molecular isotopic forms) is well established and widely practised, but frequently results in non-unique interpretations. Increasingly, researchers are reading the organic isotopic record with greater depth and specificity by characterizing stable isotope ‘structures’ – the proportions of site-specific and multiply substituted isotopologues that contribute to the total rare-isotope inventory of each compound. Most of the technologies for measuring stable isotope structures of organic molecules have been only recently developed and to date have been applied only in an exploratory way. Nevertheless, recent advances have demonstrated that molecular isotopic structures provide distinctive records of biosynthetic origins, conditions and mechanisms of chemical transformation during burial, and forensic fingerprints of exceptional specificity. This paper provides a review of this young field, which is organized to follow the evolution of molecular isotopic structure from biosynthesis, through diagenesis, catagenesis and metamorphism.

Importance of a Fully Anharmonic Treatment of Equilibrium Isotope Fractionation Properties of Dissolved Ionic Species As Evidenced by Li+(aq)

Equilibrium fractionation of stable isotopes is critically important in fields ranging from chemistry, including medicinal chemistry, electrochemistry, geochemistry, and nuclear chemistry, to environmental science. The dearth of reliable estimates of equilibrium fractionation factors, from experiment or from natural observations, has created a need for accurate computational approaches. Because isotope fractionation is a purely quantum mechanical phenomenon, exact calculation of fractionation factors is nontrivial. Consequently, a severe approximation is often made, in which it is assumed that the system can be decomposed into a set of independent harmonic oscillators. Reliance on this often crude approximation is one of the primary reasons that theoretical prediction of isotope fractionation has lagged behind experiment. A class of problems for which one might expect the harmonic approximation to perform most poorly is the isotopic fractionation between solid and solution phases. In order to illustrate the errors associated with the harmonic approximation, we have considered the fractionation of Li isotopes between aqueous solution and phyllosilicate minerals, where we find that the harmonic approximation overestimates isotope fractionation factors by as much as 30% at 25 °C. Lithium is a particularly interesting species to examine, as natural lithium isotope signatures provide information about hydrothermal processes, carbon cycle, and regulation of the Earth's climate by continental alteration. Further, separation of lithium isotopes is of growing interest in the nuclear industry due to a need for pure ⁶Li and ⁷Li isotopes. Moving beyond the harmonic approximation entails performing exact quantum calculations, which can be achieved using the Feynman path integral formulation of quantum statistical mechanics. In the path integral approach, a system of quantum particles is represented as a set of classical-like ring-polymer chains, whose interparticle interactions are determined by the rules of quantum mechanics. Because a classical isomorphism exists between the true quantum system and the system of ring-polymers, classical-like methods can be applied. Recent developments of efficient path integral approaches for the exact calculation of isotope fractionation now allow the case of the aforementioned dissolved Li fractionation properties to be studied in detail. Applying this technique, we find that the calculations yield results that are in good agreement with both experimental data and natural observations. Importantly, path integral methods, being fully atomistic, allow us to identify the origins of anharmonic effects and to make reliable predictions at temperatures that are experimentally inaccessible yet are, nevertheless, relevant for natural phenomena.

Measurement of rare isotopologues of nitrous oxide by high-resolution multi-collector mass spectrometry

RATIONALE

Bulk and position-specific stable isotope characterization of nitrous oxide represents one of the most powerful tools for identifying its environmental sources and sinks. Constraining (14) N(15) N(18) O and (15) N(14) N(18) O will add two new dimensions to our ability to uniquely fingerprint N2 O sources.

METHODS

We describe a technique to measure six singly and doubly substituted isotopic variants of N2 O, constraining the values of δ(15) N, δ(18) O, ∆(17) O, (15) N site preference, and the clumped isotopomers (14) N(15) N(18) O and (15) N(14) N(18) O. The technique uses a Thermo MAT 253 Ultra, a high-resolution multi-collector gas source isotope ratio mass spectrometer. It requires 8-10 hours per sample and ~10 micromoles or more of pure N2 O.

RESULTS

We demonstrate the precision and accuracy of these measurements by analyzing N2 O brought to equilibrium in its position-specific and clumped isotopic composition by heating in the presence of a catalyst. Finally, an illustrative analysis of biogenic N2 O from a denitrifying bacterium suggests that its clumped isotopic composition is controlled by kinetic isotope effects in N2 O production.

CONCLUSIONS

We developed a method for measuring six isotopic variants of N2 O and tested it with analyses of biogenic N2 O. The added isotopic constraints provided by these measurements will enhance our ability to apportion N2 O sources.