H2 clumped isotope measurements at natural isotopic abundances

Rationale Molecular hydrogen (H2) is an important gas for atmospheric chemistry, and an indirect greenhouse gas due to its reaction with OH. The isotopic composition of H2 (δD) has been used to investigate its atmospheric budget; here we add a new observable, the clumped isotopic signature ΔDD, to the tools that can be used to study the global cycle of H2. Methods A method for determining ΔDD in H2 was developed using the high‐resolution MAT 253‐Ultra isotope ratio mass spectrometer (Thermo Fisher). The HH, HD and DD abundances are quantified at medium resolution (M/ΔM ≈ 6000), which is sufficient for HD+ and DD+ to be distinguished from H3 + and H2D+, respectively. The method involves sequential measurement of isotopologues, and DD is measured using an ion counter. For verification, catalytic ΔDD equilibration experiments were performed at temperatures of up to 850°C. Results The typical precision obtained for ΔDD is 2–6‰, close to the theoretical counting statistics limit, and adequate for detecting the expected natural variations. Compatibility and medium‐term reproducibility are consistent with the precision values. The method was validated using temperature equilibration experiments, which showed a dependence of ΔDD on temperature as expected form theoretical calculations. Conclusions We have established a method for determining ΔDD in H2 at natural isotopic abundances, with a precision that is adequate for observing the expected variations in atmospheric and other natural H2. This method opens the road to new research on the natural H2 cycle.

H 2 has a strong link with microbial life; for example, it is produced in soils and in the ocean in the process of bacterial N 2 fixation, and in microbial fermentation processes. It is an important subsistence source of energy for soil microbes, which makes soil uptake the most important sink for atmospheric H 2 ; 2,6,7 it is also an important source of energy for other (chemoautotrophs, extremophiles) microbes. [8][9][10] It is involved in anoxic methane formation, for example in wetlands. H 2 is also produced by bacteria in the digestive tract of living animals, including humans, and anomalous H 2 production is used in medicine for diagnosis. 11,12 Furthermore, H 2 can be produced by geologic processes. Studying the abundance and isotopic composition of H 2 emitted from seeps and volcanoes can provide information about underground processes and temperatures. [13][14][15][16] In addition to its natural relevance, H 2 is also important economically as a clean energy carrier, and its use is expected to increase in the future. 3,17,18 Hydrogen has two stable isotopes, protium ( 1 H) and deuterium ( 2 H or D). The protium nucleus has only one proton and no neutrons (atomic mass 1) and it accounts for about 99.984% of all hydrogen atoms in water on Earth. Deuterium has one proton and one neutron (atomic mass 2) and its natural relative abundance on Earth is 0.0156%. The molecules of H 2 can consist of any combination of these two atoms, i.e. HH, HD or DD; the DD molecules are the socalled "clumped isotope" variants. If the atoms combine in a purely stochastic way, the abundance of HD molecules will be 0.03%, i.e. double the abundance of D atoms (because both HD and DH molecules are formed, each with a probability of 0.015%). The relative abundance of the DD molecules will be 2.4E-8, calculated as (D/H) 2 .
The different H 2 isotopologues have different masses and, because of this, slightly different physical and chemical behavior; this leads to discrimination during physical or chemical processes and thus to isotopic fractionation. Based on this, analyzing the isotopic composition of H 2 can help understand various aspects of the natural H 2 cycle. Recently, it became possible to analyze the D content of H 2 (δD) in small atmospheric samples at natural isotopic abundances. 19,20 These measurements enabled the study of different components of the H 2 cycle [21][22][23][24] and helped constrain the atmospheric H 2 budget, which as a consequence is currently relatively well understood on the large scale. 6,25,26 Although H 2 isotope measurements have proven useful, they are difficult to perform, and only few labs had or have this capability.
The δD value quantifies the abundance of D atoms in the sample and it is estimated from the measurements of HD/H 2 molecular ratio.
DD molecules are also present in natural H 2 , but at such a low abundance that they do not contribute significantly to the total D quantity. However, the DD content in H 2 is a potentially interesting and independent tracer. At stochastic distribution of isotopes among molecules, the DD content is related to the HD content, and thus to the δD value. However, at ambient temperatures formation of DD molecules is thermodynamically favored over HD, because the zero-point energy is lower for the left-hand side of the exchange reaction below: At thermodynamic equilibrium, DD will be enriched compared with the amount corresponding to a stochastic distribution. Thus, while the total D proportion stays constant, at different temperatures the D atoms are distributed between HD and DD in different fractions. At high temperatures (>1000°C) the thermodynamic equilibrium tends towards the stochastic distribution HD 2 /HHxDD = 4.
It is interesting to note that the equilibrium has been used as a prime example for illustrating the principle of clumped isotope fractionation in the past, 27 although multiply substituted isotopologues have never been measured at natural abundance before, only when enriched mixtures were used. [28][29][30] The distribution of the D atoms between the HD and DD molecules is quantified by the ΔDD value (see section 2 for definition).
For H 2 in thermodynamic equilibrium, according to classical isotope theory, ΔDD is expected to be strongly temperature dependent, with a temperature coefficient of about −1‰ per°C at ambient temperatures 5 (see also Figure 6). Thus, when the sample can be assumed to be in thermodynamic equilibrium, ΔDD can be used to derive the temperature of equilibration (or formation). Such situations occur, for example, in geological or combustion processes. It is also possible that H 2 is not in thermodynamic equilibrium; in such situations, if the formation temperature is known, the departure from equilibrium may provide information on the underlying processes occurring during H 2 formation. Examples of potential applications are (micro)biological and chemical (kinetic) processes, when the temperatures are known.
The expected ΔDD variations in natural H 2 are of tens or hundreds of ‰, due to the large mass and energy difference of the isotopologues and to the large variation in ΔDD with temperature. 5 Large ΔDD signals can also occur from mixing H 2 gases with different isotopic compositions, even if, for each of these gases, the ΔDD = 0. 31 Finally, when forming H 2 from two atom pools with different isotope ratios, a negative ΔDD value can result. 32,33 The clumped isotope ratio of molecular hydrogen at natural abundances has never been measured. That is partly because of the very low abundance of the DD molecules. Furthermore, the DD molecule and the 4 He molecule interfere at the same nominal mass 4 and are not distinguishable using conventional isotope ratio mass spectrometry (IRMS) instruments. However, instruments with much higher mass resolution have become available in recent years. This has opened up the possibility to measure new isotopic signatures, including the very rare clumped isotopes.
In this paper we report the first high-precision (‰ level) measurements of the abundance of DD in H 2 at natural isotopic composition, using the new high-resolution, high-sensitivity MAT 253-Ultra IRMS. We describe the measurement method, which is based on rapid sequential measurement of HH, HD and DD, and evaluate the performance. We also present isotope equilibration experiments at different temperatures that we performed for validation, and compare them with the temperature dependence expected from theoretical calculations.

| Definitions and units
D/H and DD/HH ratios are reported using the δ values, defined as follows: The international reference is Vienna Standard Mean Ocean Water (VSMOW), with a D/H ratio of (155.76 ± 0.8) × 10 −6 .
The clumped isotope value ΔDD is calculated as the relative difference between the actual DD/HH ratio and the stochastic DD/HH ratio; the stochastic ratio is calculated from the D/H content, assuming stochastic distribution of H and D atoms in HH, HD and DD molecules.
The δD and δDD values represent the relative abundances of D atoms and DD molecules, respectively. ΔDD refers instead to the distribution of the D atoms among HD and DD molecules, and it is independent of the abundance of D in the sample. Note that the stochastic HD/HH ratio is twice the D/H ratio, because there are two different sites where a D can replace an H in the H₂ molecule, each with a D/H chance of occurrence.
Therefore, when relating the abundances of DD and HD molecules,

| Instrument
The high-resolution isotope ratio mass spectrometer MAT253-Ultra allowing the instrument to be configured for measuring different species. In addition, the Faraday cups can be configured with any of the available amplifiers (3 × 10 8 Ω, 1 × 10 9 Ω, 1 × 10 10 Ω, 1 × 10 11 Ω, 1 × 10 12 Ω and 1 × 10 13 Ω), depending on the intensity of the measured ion beam. The instrument can be used in low, medium or high mass resolution; the resolution is controlled by the size of the entrance slit used (250, 16, and 5 μm for low, medium and high resolution, respectively), and higher mass resolution is associated with lower signal intensity. For this work we used the medium resolution setting, which gives for H 2 a mass resolving power of around 6000. Here we use the M/ΔM definition of mass resolving power, where ΔM corresponds to the mass width of the rising/falling edge of a peak, between 5% and 95% of the maximum peak intensity. 34 There are two dual-inlet systems, each with two adjustable-volume (max. 40 mL) metal bellows.
Qtegra (Thermo Fisher Scientific) is the software that controls the instrument and makes a preliminary data analysis; during the time of this work it was still under development. The prototype of the MAT 253-Ultra has previously been described by Eiler et al. 34

| Isotopologues and peak shapes
The isotopologues of interest are HH, HD and DD, and their average natural abundances are shown in Table 1 Figure 1 is less than 30 cpsthese scans were made using a different gas from the one shown in Table 1, and a different source pressure.

| Measurement method
The measurement of the three molecules of interest (HH, HD, DD) cannot be performed at the same time, because the large relative difference between the three isotopologue masses results in a dispersion of the three ion beams that is larger than the collector plane of the instrument (dispersion of~15%). Thus for H 2 we developed a method in which the different isotopologues are measured sequentially.
In this measurement method, we define a separate collector configuration for each isotopologue, and the measurement sequence cycles through these three configurations. Each step involves adjusting the magnetic fieldthis will be referred to as "peak hopping"  short "dummy" measurement series for the CDD stabilization. This is followed by 5 long (33 s) analyses, which are averaged, resulting in one data point. The HD/HH ratio is determined for each gas before and after the DD measurement, as a check for memory effects when switching between the sample and reference gas.
The final δ values are calculated from the isotope ratios of the sample and the bracketing reference gas.
This method poses particular challenges to the stability and performance of the instrument, which are conceptually different from conventional isotope ratio measurements that use multiple collector arrays where the different isotopologues are recorded simultaneously.
i) After measurement of each individual isotopologue, the magnetic field has to be changed in order to record the following isotopologue. The mass jumps have to be reproducible at thẽ 0.1 mu level for HD and DD because these isotopologues are measured on a narrow peak shoulder ( Figure 1). In the MAT 253-Ultra instrument this is facilitated using a high-precision magnetic field probe.
ii) Both the source and the bellow pressure decrease continuously, because the gas is being consumed. Since the isotopologues are measured successively and not simultaneously as in conventional IRMS measurements, the pressure changes from one isotopologue measurement to the next. The isotope ratios and the δ values have to be determined from these dynamically changing signals. This is taken into account by referencing the ratios of gas B to the average of the surrounding ratios of gas A, which mostly cancels the systematic error in ratios due to the pressure decrease.

| Gases
For setting up and testing the measurement method, we used a number of H 2 gases and mixtures with different isotopic composition.
The δD scale is maintained using two small calibration H 2 cylinders A summary of the gases used is given in Supplement 1 (supporting information).

| Experiments
In order to optimize and test the H 2 measurement method, about 150 experiments were performed, mostly between July and September 2017. Most experiments involved analyzing two gases (different or not), from two bellows, against each other.
The experiments were carried out to establish: • instrumental precision under different conditions (e.g. at different source pressures).
• medium-term reproducibility for the same sample (weeks to months).
• consistency of results between different samples.
An overview of all experiments is given in Supplement 2 (supporting information). For these experiments we used two "heating tubes" which have

| Theoretical calculation of thermodynamic DD equilibration
The thermodynamic equilibrium constant for the three hydrogen isotopologues was calculated from molecular masses and internal partition sums, 40  The ΔDD of a gas can in principle be estimated from the abundances of DD, HD and HH, using Equation 4 from section 2.1.
However, application of Equation 4 requires knowledge of the absolute abundances of the three isotopologues but, as mentioned above, a calibrated standard for DD is not available. Therefore, we used as a reference for the ΔDD calculation one of the gases that were heated to 850°C. We chose (somewhat arbitrarily) the gas analyzed during Experiment 576, which had been heated to 850°C for 8 h, and we assigned it a ΔDD value of 19‰, which is the theoretically calculated value corresponding to this temperature. The sample ΔDD value was then calculated using the formula: The standard error of ΔDD was calculated by error propagation, from the errors of the δD and δDD values, considering the individual errors to be not correlated. In general, instrument stability is one of the main factors limiting the measurement precision, with the peak position often drifting during the measurement. In addition, the decrease in pressure during a measurement cycle between two pressure adjust steps, which gradually becomes larger, starts to affect the results significantly at high bellow compression. Because of these effects, the precision of the average result does not increase any more after a relatively short number of measurements (compared with typical dual-inlet measurements), as shown in the Allan variance plots in Figure S2 (Supplement 3, supporting information).

| Precision of one sample measurement
We tested measuring at lower source pressure, in order to assess the capability of measuring smaller samples. We observed as expected a small decrease in precision with pressure, but no systematic differences in the ΔDD resultssee Figure S2 (Supplement 3, supporting information). A normal measurement (source pressure of 2.5e-7 mbar) requires about 5 mL of H 2 , which is a pressure of 125 mbar in the 40-mL bellow (all gas volumes are at standard laboratory conditions unless specified differently). We obtained good measurements even with a sample size of about 1.5 mL H 2 . In these measurements the source pressure was about half the normal pressure and measurements were started with the bellows partly compressed.

| Sample inter-compatibility
Several gases were analyzed using two different gases (B4 and B6) as "reference". The relative δD and δDD values were then calculated for the pairs of gases, using each of the different references. The results are shown in Table 3

| Heating experiments
An overview of the heating experiments is given in The results of the temperature equilibration experiments are shown in Figure 6, with different colors for different gases. Only heating times longer than 30 min are considered here. As already mentioned, we used four gases with different isotopic composition; one of these has an extreme enrichment in DD, with an initial ΔDD value of about +26000‰. We included this gas in order to verify that starting with a very anomalous composition does not influence the final ΔDD value after equilibration, and the results prove that this is the case. Indeed, the results of all four gases are similar. Gas 4 seems to have generally higher ΔDD valuesthe cause is presently unknown, but this was the last tested gas, during a period when a contamination with N 2 was also observed, indicating possible air leakage into the sample.
The theoretical temperature dependence curve, calculated as described in section 2.7, is also shown in Figure 6. The experimental results fall well around this line, except for Gas 4 as mentioned above.
The scatter around the calculated temperature curve has been estimated as the standard deviation of the residuals. The observed scatter is between 4 and 12‰ for the different gases, which is comparable with the scatter of repeated measurements as shown in Table 2.
As explained above, one of the experimental results where H 2 was heated to 850°C was used as reference for the calculation of the ΔDD value. The results would be slightly different if we chose the gas from another experiment as a reference; however, changing the reference would mainly introduce a "vertical" shift of all values in Figure 6, but would not change the shape of the curve. Therefore, we can confidently state that the experimental evolution of ΔDD with temperature is as expected.
The fact that the experimental results reproduce the theoretical dependence of ΔDD on equilibration temperature: (1) provides a convincing validation of our measurement method; (2) demonstrates that no significant re-equilibration occurs inside the instrument; and (3) implies that this method holds potential for producing a calibration scale.

| Mass stability
The peak position stability is essential for the H 2 measurements, because the flat shoulder part of the HD and DD peaks next to the interfering adduct peaks is very narrow (Figure 1). Moreover, the peak position has to be precisely reproduced after each peak hopping, i.e.
for each individual determination of an ion signal. At the low field strengths required for analysis of the light isotopologues of H 2 , the MAT 253-Ultra is in principle able to find the narrow plateaus (peak shoulders) after each peak jump. However, at the sub-mu level needed for the measurements presented here, the peak stability was somewhat unpredictable, with stable time periods followed by unstable ones or even large jumps that we could not explain. Figure S1 (Supplement 3, supporting information) shows the peak position registered at the beginning of each experiment, over the several months of experiments presented here.

| Storage in bellows and containers
The stability of the sample (see section 3.2) shows that the containers that we used are stable for H 2 traditional and clumped isotope measurements over the time range of a few months, and thus suitable for storage of pure H 2 samples.
In several tests we stored H 2 in bellows overnight, and we measured δD and δDD values before and after. We also tested the storage volumes between bellows and the valve to the source, storing the H 2 for about 1 day and measuring before and after (tests 499 and 500). No significant difference was observed in any of these, which suggests that no re-equilibration takes place inside the instrument over time intervals of several hours.

| Precision
The ΔDD precision of 2-6‰ obtained for a sample of 5 mL is sufficient to detect the expected differences between environmental samples, and also temporal and spatial variations in atmospheric H 2 .
The precision depends on the number of usable data points that can be obtained for one sample, which is limited by the peak position stability, and by the larger pressure decrease between two pressureadjust events at low bellow volume (high compression).
It is evident that instrument stability is the key requirement when attempting isotope ratio measurements sequentially and under dynamically changing intensities rather than simultaneously. The results demonstrate that the MAT 253-Ultra instrument is generally sufficiently stable to allow measurements of a signal of merely 30 cps for DD over several hours and under dynamic conditions near the counting statistics level. The system is generally able to repeatedly position the ion beams into the collectors in a reproducible manner at a precision of 0.1 mu at the extremely low magnetic field strengths that are required for these light molecules.

| Sample size
The H 2 sample size needed for a measurement is decisive for the types of samples that will be possible to analyze. So far, we have demonstrated that we can achieve systematically good results with a sample size of 5 mL H 2 ; although the precision decreases somewhat, acceptable results were obtained when the sample size was reduced to 1.5 mL H 2 .
Considering atmospheric air with a H 2 mole fraction of 500 ppb, an air volume of 10 m 3 is needed to obtain a volume of H 2 of 5 mL. Geologic and microbial gas samples can have up to percent levels of H 2 ; thus, much smaller quantities of gas would be needed in such cases.

| Reproducibility and stability
As shown in section 3.2, repeated measurements over several weeks to months of the same sample give stable results, consistent with the measurement precision. This fulfills an essential validity condition for our measurements. In addition, this shows that pure H 2 samples can be stored for months in containers without significantly altering their ΔDD signature.

| Instrumental improvements
Some of the current limitations in precision and sample size needed could be overcome with relatively simple changes in the instrument software. Implementing a procedure of peak position correction transfer in the software (i.e. scan a peak, define a correction, and apply it to other peaks), and/or a peak centering based on a shoulder scan, would allow the peak positions to be adjusted during a measurement, which would result in longer usable measurement sequences. A continuous pressure adjustment would improve/allow measurements at lower bellow sizes, and thus with lower sample size. With these improvements we estimate that the measurements on a sample size lower than 1 mL should be possible, with a precision of a few per mill. In the case of atmospheric samples, for a quantity of 1 mL H 2 , one needs 2 m 3 air (2000 L) at the normal atmospheric H 2 mole fraction of 500 ppb.

| Calibration
Currently, there are no available standards with known δDD (or ΔDD) values in H 2 at natural levels; however, such standards will be needed if we aim to analyze H 2 in natural samples. We intend to use the heating method presented here for producing, in the near future, calibration gases with known ΔDD anomaly. The experiments so far prove that the method works in principle. To define a calibration scale, we need to improve the reproducibility of this method, and to validate it by independent methods, e.g. producing H 2 by electrolysis from waters with different δD values, and/or mixing gases with different δD and δDD compositions.

| Extraction of H 2 from air (gas) samples and its potential utility
In order to analyze natural samples, it is necessary to extract pure H 2 from a variety of gases or air. Extracting H 2 is more difficult than for most other common gases, because H 2 has a very low condensation point. The method foreseen includes a combination of cryogenic and gas chromatographic separation steps. The use of He as a carrier gas is not possible for this application because it is very difficult to separate from H 2 afterwards. If significant amounts of He remain in the H 2 sample, the DD peak would be located on the He peak tail.
One of our main interests is measuring ΔDD of atmospheric H 2 , but very interesting applications are related to other fields like geology and (micro)biology. For H 2 formed in thermodynamic equilibrium, the ΔDD anomaly will be linked to the temperature of formation. We expect this to be the case for some geologic samples, for example, in gas emitted from H 2 -rich seeps and volcanoes. On the other hand, the H 2 of microbiological origin (e.g. fermentation or N 2 fixation) is not necessarily at thermodynamic equilibrium; such a phenomenon has been observed for CH 4 . 47,48 In that case, it is likely that the ΔDD anomaly (when the formation temperature is known) will inform us about processes taking place at the molecular level during H 2 formation.