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the calibration gas, an uncalibrated working reference is sufficient and usage of international calibration standards is obsolete.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.

Mass spectrometry of multiply substituted isotopologues or clumped isotopes has become an extremely powerful tool in the natural sciences. Demonstrated applications which investigated carbon dioxide, methane, nitrous oxide, molecular hydrogen and oxygen range from tectonic history and evolution, geobiology and atmospheric chemistry over the investigation of non-equilibrium processes with correction procedures, diagenesis studies, the investigation of mineral formation conditions, the assessment of hydrothermal flow systems and paleo-evolution to paleothermometry; and there are many more potential applications 1,2 . The most prominent uses are linked to the oxygen isotope exchange reaction between the main isotopologue and the 13 C- 18 O containing species of CO 2 12 2 16 13 16 18 13 2 16 12 16 18 Reaction (R1) involves only a single chemical compound, but could not be exploited scientifically until recently. This is because their very low natural abundance hampers the study of multi-substituted isotopic molecules, such as 13 C 16 O 18 O, containing two or more rare isotopes (e.g. 13 C and 18 O) simultaneously. When compared to the main isotopologue 12 C 16 O 2 , these are well below 10 −4 (see Table 1). At the same time, the measurement techniques needed to attain extremely high accuracy levels of a few 0.01‰ (~tens of ppm) in order to trace the natural variability of the corresponding isotopologue and a dynamic range on the order of about 10 9 or better is therefore required. So far, only mass spectrometer instruments are capable of fulfilling these criteria and clumped CO 2 has not yet been measured by optical methods 1,2 . Doubly substituted 13 CH 3 D methane, which shows higher fractionation values, however, has been investigated using laser-based instruments. The first laser spectrometer setup 3 for clumped methane isotopologues based on difference frequency generation (DFG) still suffered from uncertainties in the 20‰ range which exceeds natural 13 CH 3 D variability of about 8‰ 4 . Nevertheless, a more recent diode laser study on doubly substituted methane 5 has successfully demonstrated that optical systems can well approach the necessary requirements. The achieved precision level of 200 ppm, however, remains still well above the commonly accepted threshold of 100 ppm (or 0.1‰) required for the study of clumped isotope fractionation in non-hydrogenated molecules.
www.nature.com/scientificreports www.nature.com/scientificreports/ While mass spectrometers excel in the achieved precision of about 10 to 20 ppm 6,7 , the instruments have to cope with inherent drawbacks. Not only are they relatively costly and heavy, thus not permitting in-field operation; they also require time consuming measurements and careful sample preparation in order to avoid contamination of the measurement signal. With current mass spectrometric procedures, preparation and analysis of a carbonate sample take about 3 to 6 h 8 . Importantly, only the largest and most sophisticated instruments can reach the mass resolution required to resolve isobaric interferences in CO 2 9 . Typical operation conditions are around M/ΔM ~ 40000 or lower, which is insufficient to separate 13 18 O at m/z = 47, for example. In order to resolve these masses, a resolving power of above 52000 is needed -so far only accessible for large radius instruments in 'non-normal operation' mode 9 . This makes multiply substituted isotopologue analysis by mass spectrometry a very exclusive technology that will remain limited to only a handful of highly specialised laboratories worldwide, likely also constraining industrial or commercial use. Note that only two ( 12 C 16 O 2 and 13 C 18 O 2 ) out of twelve stable CO 2 isotopologues can be detected entirely free from isobaric interference using a mass spectrometer (see Table 1). The four isotopologues 13 [10][11][12] must be employed at the cost of prolonged measurement time and reduced precision.
Simple counting statistics prevent using current mass spectrometer technology for the analysis of CO 2 isotopologues below the relative abundance level of 10 −5 , even if these provide the main contribution to a cardinal mass. Assuming the measurement uncertainty being limited by Poisson statistics, the 10 ppm precision is reached after about 3 or 4 h of measurement on m/z = 47 ( 13 C 16 O 18 O) 13 . In order to obtain the same precision for the 12 C 18 O 2 isotopologue on m/z = 48, a (n( 16 13 C 16 O 18 O)/n( 12 C 18 O 2 )) 2 ~ 100 times longer analysis time would be required, thus about two weeks. Even measurement times of two days are impractical and contrary to common practice. Demonstrations of ppm level instrument stabilities over such long time periods are lacking too. The m/z = 48 and 49 signals can therefore only be used as an indicator for sample contamination (hydrocarbons, halocarbons, sulphur monoxide) 1,14,15 and must remain useless in exploiting 12 C 18 O 2 or 13 C 18 O 2 as isotopic tracers with mass spectrometry.
Despite the pioneering achievements of mass spectrometry in rare multi-isotope research, it is evident that alternative technologies are needed to overcome several of the aforementioned limitations. In this paper, we will present the first optical multi-isotopologue analyser for CO 2 that is not influenced by most of these limitations, most notably the isobaric interference problem. The instrument achieves a measurement accuracy well below the 100 ppm level in the measurement of 13 C 16 O 18 O and the technique has the capacity of assessing new tracers such as 12 C 18 O 2 that likely provide new and complementary information. In principle the developed method is calibration free and has strong potential of becoming a breakthrough technology, because it provides great isotopologue selectivity at reduced time, size and cost factors, which makes it well suited for widespread scientific, laboratory and commercial applications. The paper focusses on the measurement of carbon dioxide and the isotope exchange in the gas phase and we present the analysis of CO 2 from thermal sources in the Upper Rhine Valley. The results will be compared to duplicate mass spectrometer measurements of CO 2 from the same source. Apart from direct studies of gaseous carbon dioxide, current applications are concerned with multiply-substituted isotopologues in carbonates. Because carbonate isotopologues are obtained from measurements of gaseous CO 2 released during the acid digestion of the carbonates, they can be investigated using the same analysis systems. The direct application of carbon dioxide isotopologue analysis to carbonates is further facilitated by the fact that the carbonate clumped isotope scale has been directly tied into the equilibrium CO 2 gas scale 6 . www.nature.com/scientificreports www.nature.com/scientificreports/ operating principles and Instrumental Approach Isotopologue absorption spectroscopy. The optical measurement of CO 2 isotopologues is based on absorption of isotopologue dependent ro-vibrational transitions in the ν 3 fundamental band around 4 µm ( Fig. 1), where infra-red absorption of carbon dioxide is strongest. With respect to the 12 C containing species, the vibrational bands of 13 C containing isotopologues are shifted towards lower energies. Using simultaneously two tuneable inter-band cascade lasers (ICLs) at 4.3 and 4.4 µm and absorption-balanced light paths of 9.2 cm and 10 m length, respectively, absorption signals of several ten percent of the five most abundant isotopologues can be obtained when a few mbar of pure CO 2 are analysed in a cylindrical 0.8 L thermostated stainless steel absorption cell. A Herriott cell configuration made out of two concave mirrors at a distance of about 17.6 cm has been realised in order to achieve the long light path with 58 reflections. The short path traverses the cell just once in the perpendicular direction. More information on the absorption lines and a more detailed description of the set up displayed in Fig. 2 are given elsewhere 16 .
Spectra of pure CO 2 at 297 K and 3 to 4 mbar are recorded at a rate of 1.56 kHz by driving laser currents at the same pace. A non-linear current ramp has been chosen for minimising the non-linearity of the laser frequency response over time 17 . Individual spectra were then averaged over 1 s time interval and analysed using a home-built fitting routine employing Rautian line profiles 18 . Required line parameters have been taken either from the HITRAN database (position) or were determined in separate experiments (self broadening coefficient and frequency of velocity changing collisions) 16 . The particle number density n of an isotopologue is obtained from applying the Beer-Lambert law to one of its transitions (see insets in Fig. 1), located at the centre wavenumber ν = ν c . For a spectrally narrow laser the CO 2 gas number density (n(CO 2 ) = [CO 2 ]) is linked to the optical measurement via 19 where L is the path length, Tr(ν) the transmittance, S the line strength and g(ν − ν c ) the molecular line shape function of the particular transition. Isotopologue concentrations can thus be obtained from the extinction coefficient α = −ln(Tr(ν c )) and the absorption cross section σ = S ⋅ g(0) at peak centre, which remain constant under fixed experimental conditions. The path length cancels in the measurement of an isotopologue ratio when both isotopologues are detected using the same path, e.g. 20 .
[CO 2 ] 1 /[CO 2 ] 2 = α 1 /α 2 ⋅(σ 1 /σ 2 ) −1 , making the method immune against eventual slight path length changes. Note that in spite of using the simplifying notation on the right hand side of Eq. (1) spectra are fitted over a whole frequency window and therefore include information from entire absorption lines and not just from peak absorption values. Duplicate isotope ratio mass spectrometer (IRMS) measurements have been performed using the ThermoFischer MAT253Plus instrument at IUP Heidelberg, that has been equipped with an additional m/z = 47.5 www.nature.com/scientificreports www.nature.com/scientificreports/ cup and 10 13 Ω resistors on m/z = 47−49 mass cups 16 . The m/z = 47.5 is used for continuous baseline monitoring. The mass spectrometric analysis follows accepted procedures 6,14 , as does the sample processing and cleaning 8 .
Equilibrium constant, thermodynamics and Δ 47 . The equilibrium constant K 1 of the isotope exchange reaction (R1) is strictly proportional to the product of absorption signals 1   13  2  16  12 16 18  12  2  16 13 16 18 , which therefore allows for the optical measurement via where the scaling factor 1   12  2  16  13 16 18  13  2  16 12 16 18 depends on the involved molecular line strengths. Lacking the required accuracy, current database values cannot be used for determining Σ, which best is determined experimentally by exploiting the temperature dependence of K 1 or its logarithm (see Fig. 3). The latter is widely used, because deviations from the statistical value = , where the *-symbol indicates the high temperature limit) are small and it can be expressed by three individual logarithmic terms, which can be  Figure 2. Scheme of the dual-laser system. Lasers are connected to the absorption cell via optical fibres. An off-axis parabolic mirror focusses the exiting light from the multi-pass cell on a photo-detector. The light of the single pass is projected on a second detector without further focussing. The cell is filled with sample and reference gases via a custom-built inlet system and can be evacuated using a second gas connection. www.nature.com/scientificreports www.nature.com/scientificreports/ identified with the isotopologue specific enrichment or fractionation values (CO 2 denoting any particular isotopologue in the following equation) commonly used for the quantification of isotopomers 21 or multiply substituted isotopologues 22,23 : The right hand side expression is applicable to the optical measurement, which provides the two particular isotopologue ratios as independent observables. As evident from Eq. (4), the temperature information contained in the equilibrium constant does only depend on two concentration ratios, that may be regrouped differently. ln (K 1 ) is completely independent of the bulk isotope composition. Consequently, the 17  13 16 18 and keeping only the leading terms in the Taylor series expansion on both sides, one obtains , where isotopologues are replaced by m/z signals, because they cannot be measured individually. Comparison of Eqs (5) and (6)  with the relative deviation of the equilibrium constant K 1 from its statistical value. It has been argued that the last two terms on the right hand side are zero 24 , but this premise is not completely consistent with the definition of Δ in Eq. (3) and thermodynamic calculations 22 that respectively yield −4 and −11 ppm for Δ( 45 CO 2 ) and Δ( 46 CO 2 ) for CO 2 equilibrated at 300 K. The reason for the conflicting results is that in the one case approximate but precisely measurable and in the other case exact but only approximatively accessible atomic isotope ratios are used in the calculations of the statistical abundances. Nonetheless, the so defined Δ 47 is overwhelmingly influenced by the first of the three terms, which in turn is to a large extent (97%, see Table 1) dominated by the 13 Unlike the direct measurement of ln (K 1 ) according to Eq. (4), mass spectrometer determinations of Δ 47 not only require measurement of heavy isotopologue abundances. The 'absolute' or bulk isotope composition must also be known in order to determine the statistical abundance of the m/z = 47 signal. This implies determining atomic 13 C/ 12 C, 18 24 . Equally important, mass spectrometers can only approximately access the clumped 13 C 16 O 18 O isotopologue (also due to an ion-source dependent scrambling effect) using the m/z = 47 signal and a corresponding scaling factor must be applied 1,14 .
Using the equilibrium constant of an isotope exchange (or isomerisation) reaction with a particular working gas as a thermometer, temperature is directly measured as a thermodynamic variable. The equilibrium constant of an isotope exchange reaction is linked to the reaction free enthalpy ΔF of that reaction K = exp(−ΔF/(kT)) [25][26][27] , where k is the Boltzmann constant and where we have adopted a per molecule rather than a per mole definition of energies. The free energy of the gas is linked to the gas' molecular partition function, which sums over all energy states ε i taking degeneracies d i into account and counting internal energy states from the lowest or zero-point energy (ZPE) ε 0 state of the molecule i levels i kT trans int kT i 0 In the Eq. (7) we have made the usual separation of the centre of mass motion (trans) from the molecular internal degrees of freedom (int). Since the equilibrium constant is given as a product of partition functions of reactant (react) and product (prod) molecules 26,27  it is amenable to quantum statistical mechanics and computational chemistry methods. Here we have followed the usual simplification to evaluate the ratio of translational partition functions to ratios of molecular masses M 26 . The only non-trivial factors are the total internal partition functions that need to be evaluated separately. If one is mainly interested in isotope fractionation effects, it is convenient to normalise the equilibrium constant by dividing through its classical high temperature limiting value K*, which is given as the product of the classical symmetry numbers of product and reactant molecules: www.nature.com/scientificreports www.nature.com/scientificreports/ , one obtains the ZPE change of the reaction in terms of measurable quantities: The different terms in Eq. (9) can be identified with the reaction enthalpy or energy ΔH = ΔU = Δε 0 , the reaction free enthalpy (Δ = − F kT K ln ), and the free enthalpy change associated to the reaction entropy (TΔS), which is given by the two remaining terms on the right hand side. Eq. (9) takes into account the energy change associated with the translational and internal molecular motion. In the following we adopt spectroscopic conventions and use term energies in wavenumber units Δν = Δε/hc, where h and c are the Planck constant and the speed of light, respectively. Different methods have been proposed to calculate the internal partition functions in Eq. (7). The traditional method based on work of Urey, Bigeleisen and Goeppert-Mayer (BMU) [25][26][27] is to consider molecules as rigid rotor -harmonic oscillators and use corresponding spectroscopic constants. Combination of this approach with the Teller-Redlich rule 28 , usually attributed to Urey 29 , leads to a very simple description. For better accuracy, anharmonic corrections to vibrational energies and rotation-vibration interactions can be taken into account 25,30,31 , but for reasons of convenience or lack of parameters mostly only the anharmonic corrections to the ZPE are applied 22,29 . This can lead to significant uncertainties and more elaborate methods have been proposed, such as calculating the direct sum as a path integral using Monte-Carlo (PIMC) methods 32,33 . If highly accurate potential surfaces with spectroscopic quality are available or global effective Hamiltonians have been determined, such as for CO 2 34 , the total internal partition function in Eq. (7) might also be calculated very accurately by summing directly over all terms. In any case, the standard BMU approach must fail at low temperatures and masses (e.g. H 2 ) due to neglecting the quantisation of rotational states, which is only taken into account approximately. In such a case the sum in Eq. (7) must be evaluated directly 25 . Conversely, the computational cost associated with numerical methods, such as PIMC and direct summation will increase when the temperature augments, because the number of thermally accessible states increases strongly. In addition the potential energy surface properties far from the equilibrium configuration become important when temperatures raise, leading to numerical convergence problems and artefacts 22,35 . In this limiting case, where isotope fractionation must vanish and a high precision is required, the BMU approach in combination with the Teller-Redlich rule might serve as a particularly useful guide, because its convergence towards the statistical limit is always assured. Implementation of the spectroscopic measurement. Unlike mass spectrometry, a laser absorption instrument can unambiguously measure all four (or three) required isotopologues of a homogenous CO 2 isotope exchange reaction. The measurement is conceptually straight forward and does not depend on additional determinations and hypotheses on the bulk isotopic composition, as it directly determines ln K or ⁎ K K ln( / ) and its temperature dependence, disregarding the ln Σ term (see Eqs (2) and (4)), which needs to be determined experimentally using a reference measurement: Here, A(T) and A ref indicate the measured product of absorbances in Eq. (2) for CO 2 , once for the sample and once for a reference gas with known equilibrium constant K 1 that has been equilibrated at the reference temperature T ref . Consequently, the method makes the quantification of the statistical distribution of isotopes obsolete (as indicated by Eq. (4)). Since absolute abundances of C and O isotopes don't need to be known, the absorption measurement dispenses in principle the use and measurement of international standard substances. It only requires the comparison with a working gas whose value of ln K is known and remains stable over time. The extremely slow gas phase isotope exchange at ambient temperatures assures that any equilibrated CO 2 gas with an isotopic composition close to natural sample gas composition in principle suffices for determining ln Σ (see Eq. (10)). This should make laser-based clumped isotopologue analysis much easier applicable than mass spectrometer investigations. In our setup, however, a slight cross-sensitivity of ln K on the difference in δ 13 C between the sample and the working reference gas of −4 ppm/‰ has been observed. This entails the determination of δ 13 C in our samples such that the interference can be corrected empirically 16 . The correction requires only one extra measurement and evaluation step relative to the sophisticated and error-prone mass spectrometric procedure. On the contrary, a cross correlation between ln K and δ 18 O has not been observed. The δ 13 C interference is much stronger than the isotope dependence of the thermodynamic equilibrium composition of about −0.01 ppm/‰. The effect is likely due to an insufficient modelling of the baseline originating from strong nearby absorption features of 13 CO 2 . An improved fitting algorithm and a better choice of the spectral micro-window for the absorption lines should eliminate the effect, but this hypothesis requires further examination. A natural candidate for the calibration of the optical method using Eq. (10) are measurements of the equilibrium constant at the high temperature limit > =  ⁎ K T K (ln ( 2000 K) ln 0) 1 1 . As these conditions are difficult to realise experimentally, we use a two step calibration, involving a heated working reference gas at a lower temperature and an ambient temperature working reference gas. The hot CO 2 serves as calibration point, that determines the origin of the optical ln K 1 measurements. The gas has been equilibrated at 1000 °C for about 5 h. We use the calculated value of = − K ln 2 6 1 ppm at that temperature (see Table 2) to determine A ref in Eq. (10). The uncer-www.nature.com/scientificreports www.nature.com/scientificreports/ tainty of this calibration is very small: different calculations at 1000 K are given in the literature 22,36 and our calculation based on partition functions evaluated as direct sums of energy levels provided by ab initio calculations that were refined by spectroscopic measurements 34 , indicate that the error at that temperature is about 5 ppm. This deviates by only 2 ppm from the BMU method using the molecular constants of Wang et al. 22 . If we assume that the relative uncertainty remains the same, the systematic bias of the calibration should only be about 2 to 3 ppm at 1000 °C. Calculated room temperature (300 K) values of ln (K 1 ) show a larger spread between −951 and −968 ppm, giving an order of ±10 ppm agreement (see Table 2). This uncertainty span is significantly larger than the spread in the high temperature values, rendering high temperature measurement preferable for calibration. As does the temperature gradient, which is 82 times smaller than the room temperature gradient of = . d K dT ln / 57 1 ppm/K and makes the high temperature calibration less sensitive to instabilities in the temperature than its room temperature counterpart. This first calibration led us assign a value of = − ± K ln ( 954 20) If not noted otherwise, we indicate measurement uncertainties as combined standard uncertainties at the 68% level of confidence.
In the second step, individual samples are measured by alternating acquisition sequences of sample and working gas. Each sequence starts by filling the spectrometer with the working reference gas and acquiring spectra for about 30 s with 1 s integration time. Then fast (~2 min) removal of the working reference occurs and the sample gas is analysed following the same acquisition procedure. Pressures of sample and reference gases are matched to agree within 0.01%. For repeated analysis, the sample is recovered using cryogenic trapping for about 5 minutes. At the end of the evacuation period the optical base line is determined. These repeated sample-reference comparisons, where Eq. (10) is applied each time, allow to take into account slow instrumental drifts that may have an impact on the determination of ln Σ.

Results and Discussion
Co 2 thermometry with 13 C 16 o 18 o and case application. The newly developed laser instrument has first been employed to demonstrate its capacity as CO 2 isotopologue thermometer using ln K 1 as directly observable temperature proxy. Four different samples of equilibrated CO 2 have been prepared, with equilibration temperatures at 1 °C, 21 °C, 131 °C, and 1000 °C. For measurements at 1000 °C, pure CO 2 gas was filled into quartz vials and kept in a lab oven for about 5 h. For the lower temperatures, droplets of liquid water were added to facilitate isotope exchange between isotopologues of CO 2 . At 1 °C equilibration times were about one month, and they were about a week for the intermediate temperature at 131 °C. Figure 4 shows the results of the measurements in comparison to the theoretically calculated curve. As a reference we use our evaluations of K 1 from partition functions determined as direct sums and from the BMU method with harmonic frequencies and ZPE values given by Wang et al. 22 (see Table 2). The maximum deviation of 59 ppm between either of the theoretical calculations in Fig. 4 and the measurements has been observed at 274 K. It is within twice the combined standard uncertainty (61 ppm) of the laser spectroscopic measurements at that temperature. At room temperature or above, the observed agreement is well within one standard uncertainty, which is 25 and 33 ppm, respectively.
Clumped isotope thermometry of gas phase CO 2 originating from hydrothermal systems might provide a new and unique tracer for hydrothermal reservoir temperatures. The application is particularly relevant for studying the feasibility of the construction of hydrothermal power plants and estimating the associated risks, because the isotope thermometer may provide additional information on the related geological system and involved aquifers.   Table 2. Temperature dependence of the isotope equilibrium constant K 1 . Different theories are employed: BMU approach using harmonic frequencies for application of the Teller-Redlich 28 rule and anharmonic correction to the ZPEs -WSE2004 22 . The same approach using harmonic frequencies from another level of theory -CL2012 54 . Path-Integral Monte Carlo (PIMC) evaluation of partition sums -WM2014 33 . Approximate direct sum partition functions from a refined potential surface -CBRZ2014 36 . Direct sum calculation of partition functions (this work) using state energies from new spectroscopic data generated from experimentally refined ab initio calculations 34 . a Values at temperatures other than 200, 300 and 1000 K were recalculated from molecular constants in Table 3 of Wang et al. 22 .
www.nature.com/scientificreports www.nature.com/scientificreports/ For this case study we compare tuneable laser direct absorption spectroscopy (TLDAS) and IRMS measurements of the 13 C 16 O 18 O isotopologue in a case study of natural carbon dioxide extracted from an operating hydrothermal power plant (Soultz) and two shallow wells (Landgrafenbrunnen and Stahlbrunnen), all located in the Upper Rhine Valley. The geothermal reservoir in Soultz (Alsace, France) has a temperature of about 200 °C at a depth of 5000 m 37 . During power plant operation, the water cools down to ~150 °C at the surface. Carbon dioxide for the analysis has been sampled from a separate sampling line, where the water has been rapidly cooled down to 38.5 °C. The mass spectrometric and laser measurements show clumped isotope temperatures between 92 and 108 °C and the two methods agree well within the respective uncertainties of 8 °C for the mass spectrometer determinations and 11 °C for the laser measurements (Fig. 5). Stahlbrunnen and Landgrafenbrunnen are two hydrothermal wells in Bad Homburg, Germany. The CO 2 from the first one has been sampled directly from the well in the gas phase, whereas sampling of the carbon dioxide dissolved in water has been performed for the latter. The preparation of the gas samples for laser spectroscopic analysis follows a simplified procedure. It involves cryogenic separation from water and removal of non-condensable species through vacuum pumping. Compared to preparation for IRMS analysis, which requires additional cleaning by passage through a Porapak column 38 , the total preparation time is reduced by a factor of two. Laser spectroscopy and IRMS analysis of Landgrafenbrunnen CO 2 apparent equilibrium temperatures show values of (10 ± 4) °C and (15 ± 6) °C, respectively, which is in good agreement with the temperature of the well's water, T w = 13.5 °C. A slight deviation from the expected water-CO 2 equilibrium towards higher temperature has been observed for Stahlbrunnen, T w = 12.4 °C versus T IRMS = (20 ± 5) °C and T TLDAS = (28 ± 7) °C. The interpretation of eventual discrepancies between measured apparent equilibration temperatures and parent water temperatures requires further investigation and is beyond the scope of this paper. Future developments. The standard uncertainty of the laser measurements in the 50 ppm range is obtained with samples of about 100 µmol and about 10 sample reference comparisons, which take between 1.5 and 2 h. This is still slightly larger than what can be obtained by mass spectrometry. However, this type of optical measurements is still in its infancy and is expected to improve soon. Already, our 0.8 L Herriott cell can be replaced with a very compact 40 to 140 mL multi-pass cell 39,40 that provides a similar absorption length. Such small volumes imply reduced sample sizes on the order of 10 μmol or below and lead to faster evacuation times due to much simpler geometry without dead volumes. This shortens the time lapse between sample and reference measurement, thus limiting the impact of instrument drift and reducing the overall measurement uncertainty. We further anticipate that the introduction of an automated pressure balance system will allow for more reproducible conditions that further improve the measurement uncertainty.
It is also worth noting that optical measurements in the ν 3 fundamental region of CO 2 around 4.4 µm are not exclusively limited to the detection of the 13   temperature range. ln (K 1 ) is determined directly for samples of different isotopic composition that were equilibrated in quartz (T > 1000 K) or in pyrex tubes to which drops of liquid water were added (T = 274, 294 and 404 K). Data are given with combined standard uncertainties that include the uncertainty of the calibration procedure based on the working gas measurement. Solid and dashed lines indicate two different theoretical temperature dependencies (see text and caption Fig. 3 for more details). The high temperature value (practically error free) has been used to determine the isotopic composition of the room temperature working gas, with respect to which values at 274, 294 and 404 K have been determined.
www.nature.com/scientificreports www.nature.com/scientificreports/ )   12  2  18  12  2  16 12 16 18 exchange reaction, whose equilibrium constant has a temperature coefficient ( = . d K dT ln( /4)/ 35 2 ppm/K) of the same magnitude than K 1 at 300 K (see Fig. 3). The advantage of using this clumped CO 2 thermometer along with 13 C 16 O 18 O thermometry is its independence from 13 C. The presence of kinetic fractionation effects that possibly compromise equilibrium thermometer readings would thus likely be different in the 13 C containing and in the 13 C free clumped isotope systems [43][44][45][46] . These effects could thus potentially be identified and corrected for. Therefore, optical measurements could provide an entirely new level of temperature information in the future. As an aside, we mention that clumped isotopes are often discussed in terms of bond ordering 4,47 , i.e. whether two rare isotopes form a common bond, such as 13 C- 18 O in 13 C 16 O 18 O. Reaction R2 is an example of indirect isotope clumping, where the two rare isotopes do not share the same bond 1 . In larger molecules, such as propane, ethane etc. this will be the predominant clumping mechanism. By definition, statistical combination of two different isotopic reservoirs leads to position-independent (anti-)clumping 48,49 . The similar magnitude of isotope fractionation in both reactions R2 and R1 (Fig. 3) demonstrates that thermodynamic clumping effects should also be considered as concentrating two (or more) rare isotopes in the same molecule, leading to a molecular configuration which is thermodynamically more stable than when these isotopes are redistributed over two (or more) different molecules -irrespective whether these isotopes share the same chemical bond or not.
Finally, the direct measurement of the equilibrium constant of an homogeneous exchange reaction at ppm accuracy may provide an interesting benchmark for molecular quantum calculations and potential energy surfaces. At low temperatures, different models are particularly sensitive to ZPE differences (Δν 0 and the energies of the lowest states (see Eqs (8) or (9)). At 300 K the ZPE difference factor ν − Δ c T exp( / ) 2 0 deviates from unity by 5 parts in 10 6 if Δν 0 = 0.001 cm −1 . This implies that an uncertainty of a few ppm -a range that will be amenable to measurements in the near future -is sufficient to determine ZPE differences at the 0.001 cm −1 uncertainty level, irrespective whether the ZPE differences are large, as in the case of the H 2 + D 2  2 HD reaction where Δν 0 = 54.867 cm −1 50,51 , or small -as in reaction R1, where calculated values 22,33,34 range from 0.433 to 0.435 cm −1 .

summary and Conclusion
We provide the first optical measurement of multiply-substituted isotopologues of CO 2 at the accuracy level of better than 100 ppm. New advances in laser absorption spectroscopy, such as evidenced by the recent measurement of 12 C 16 O 17 O at the precision level of 10 ppm within a time frame of 10 min 52 , indicate that laser instruments will favourably compete with mass spectrometer technology very soon. The comparatively high selectivity of laser-based instruments and their large potential of assessing new tracers, such as 12 C 18 O 2 for the homogeneous isotope exchange with 12 C 16 O 2 , will open up new horizons in clumped isotope science and thermometry. The most important advantage of the technology is that the temperature can be obtained easily and directly via an unambiguous measurement of the equilibrium constant of the isotope exchange reaction. The optical CO 2 Figure 5. Comparison of optical (y-axis) and mass spectrometer (x-axis) measurements using natural samples from three sources in Germany and France. Two low temperature sources Landgrafenbrunnen (water temperature T w = 13.5 °C) and Stahlbrunnen (water temperature T w = 12.4 °C) are situated in Bad Homburg (50°13′26″ N, 8′37′21″ W) and are compared to a thermal source (sampling water temperature T w = 38.5 °C) in Soultz (47°53′12″ N, 7°13′47″ W), France. Note that both clumped isotope equilibrium methods are consistent in magnitude and relative to each other. Uncertainties as well as combined preparation plus analysis times are similar for both, mass spectrometer and laser measurements.
www.nature.com/scientificreports www.nature.com/scientificreports/ isotopologue thermometer is a strong example showcasing the full potential for this and other molecules in the future. We have shown how the technology can be used for the thermometry of gaseous CO 2 and that new areas related to molecular chemistry and physics are opened up for clumped isotope research. The relatively low cost and size factors of the technology will be additional parameters for developing and easing the spread of this exciting frontier science technology to more laboratories and technological applications.