The Isotopic Anatomies of Molecules and Minerals

EA41CH16-Eiler ARI 30 April 2013 16:38

John M. Eiler

Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, California 91125; email: [email protected]

Annu. Rev. Earth Planet. Sci. 2013. 41:411–41 Keywords The Annual Review of Earth and Planetary Sciences is stable isotope, isotopologue, isotopomer, clumped isotope, online at earth.annualreviews.org position-specific isotope This article’s doi: 10.1146/annurev-earth-042711-105348 Abstract Copyright c 2013 by Annual Reviews. Most natural compounds are composed of diverse isotopologues that dif- All rights reserved fer in the number and/or symmetrically unique atomic locations of isotopic substitutions. Little of this isotopic diversity is observed by conventional Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org methods of stable isotope geochemistry, which generally measure concentrations of rare isotopes without constraining differences in isotopic composition between different atomic sites or nonrandom probabilities of multiple isotopic substitutions in the same molecule. Recent advances in analytical instrumentation and methodology have created a set of geochemical tools— geothermometers, biosynthetic signatures, forensic fingerprints—based on these position-specific isotope effects and multiply substituted isotopologues. This progress suggests we are entering a period in which many new geochemical tools of this type will be created. This review describes the principles, background, analytical methods, existing applied tools, and likely future progress of this emerging field.

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1. INTRODUCTION Fractionations of stable isotopes by natural processes are the basis of geochemical tools used to study climate (e.g., Zachos et al. 2001), biogeochemical cycles (e.g., Hedges 1991), and hydrology (e.g., Dansgaard 1964); the origin and evolution of igneous, metamorphic, and sedimentary rocks (e.g., Eiler 2001); the sources of meteorites and other extraterrestrial materials (e.g., Clayton 2007); as well as many other subjects. The precise and accurate methods developed by earth scientists to study subtle natural isotopic variations (McKinney et al. 1950) have led to advances in the use of isotopes in forensics, biomedical science, chemistry, and other disciplines beyond the earth sciences (e.g., Ehleringer et al. 2008). Nevertheless, most of stable isotope geochemistry is based on relatively simple measurements of bulk isotopic composition—an inventory of the proportions of isotopes in a sample, irrespective of their positions within molecular structures or the spatial relationships of rare isotopes with respect to each other. In principle, measurements of the distributions of isotopes in natural materials should provide a diverse, complex, and speciﬁc record of their origins, sources, and histories. Consider a familiar

organic compound: table sugar (sucrose; C12H22O11)(Figure 1). The substitution of rare for common isotopes (e.g., 13Cfor12C) can take a variety of forms: Approximately 10% of natural sucrose contains a single 13C in one of its 12 carbon positions, and because all the C sites are symmetrically nonequivalent, each of the 12 possible singly 13C-substituted species is unique. Approximately 0.3% of natural sucrose contains at least one deuterium and ∼2% contains at least one 18O. Roughly 0.03% contains both a 13C and a D, and there are 264 geometrically different ways in which this double substitution can be accomplished. When one adds up all possible combinations and spatial conﬁgurations of stable isotopes in sucrose, there are ∼3 × 1015 isotopic versions (“isotopologues”) of this molecule—10,000 times the number of stars in our galaxy. Even though many of these combinations are exceedingly rare (some may not even exist in nature), a very large number of singly, doubly, and triply substituted versions have measurable concentrations in the range of parts per million or more—within the reach of modern methods of stable isotopic analysis (e.g., Eiler & Schauble 2004). A full accounting of the isotopic composition of a sample of table sugar, with consideration of only those one-to-severally substituted species that seem potentially analyzable, could involve the most complex isotopic measurement ever attempted.

Single substitutions D or 18O or 13C Carbon Oxygen Position-specific Hydrogen 13C differences or Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org

18O Nonadjacent D and multiple and D D substitution Adjacent multiple substitution Figure 1

Examples of possible isotopic substitutions in sucrose (C12H22O11). Note not all bonds and atoms are clearly visible in this projection. “Adjacent” multiple substitutions share a bond between the rare isotopes; “nonadjacent” multiple substitutions contain two or more rare isotopes that do not share a bond.

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Every one of the symmetrically nonequivalent isotopic variants of a molecular structure is unique with respect to its chemical and physical properties (e.g., mass, intramolecular vibration frequencies, moment of inertia, polarizability). Therefore, all such species must generally exhibit variations in relative concentration due to physical, chemical, and biochemical fractionations. Thus, patterns of isotopic substitution—the mix of singly and multiply substituted isotopologues that make up a sample’s comprehensive molecular isotopic composition (here referred to as the sample’s isotopic “anatomy”)—could provide a distinctive forensic fingerprint (Benson et al. 2006), constraints on the sources of substrates from which the molecule was synthesized (Hattori et al. 2011), information regarding the reaction pathways of synthesis (e.g., Monson & Hayes 1982b), the temperature of formation (e.g., Wang et al. 2004), the geographic location of synthesis (e.g., Ehleringer et al. 2008), and perhaps other information. Virtually none of the isotopic diversity we imagine must exist in natural molecular structures has ever been observed through conventional measurements of bulk isotope abundance ratios: A conventional measurement of the isotopic stable composition of sucrose yields only 13C/12C, D/H, 18O/16O ratios, and, possibly, 17O/16O ratios (the latter is presently made in a small number of laboratories). But this situation is changing: An emerging group of novel analytical instruments and methods promises to transform stable isotope geochemistry into a more complete study of isotopic anatomies of molecules and minerals. This emerging discipline has its roots in papers on the chemical physics of isotopes published during the 1930s, and several efforts have examined parts of the problem over subsequent decades. In the past decade, however, the pace of advancement has increased rapidly. This shift has been enabled by technical innovations in isotopic analysis; novel conceptual tools for the geochemical uses of isotopologues; and the emergence of tools with clear value in applied geochemical, geological, and forensic studies. This review examines the history, state of the art, and anticipated future development of the study of position-specific and multiply substituted isotopic compositions of natural materials. Pieces of this subject matter have been addressed in previous reviews (Brenna 2001; Eiler 2007, 2011), but I am not aware of any source that encompasses advances in the various relevant fields— biochemistry, paleoclimate research, atmospheric science, among others. Here, the focus is on a

few applied tools that are the leading edge of this discipline: “clumped” isotope analysis of CO2 15 13 and O2; position-specific analysis of NinN2O; and position-specific analysis of CandDin natural sugars, cellulose, vanillin, and other complex organics. However, these are considered to be the earliest proven examples of what is emerging as a frontier of isotope chemistry that will soon reach into other kinds of chemical compounds and impact a wide range of scientific disciplines.

2. MULTIPLY SUBSTITUTED ISOTOPOLOGUES Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org In the early 1930s, Harold Urey contributed to several papers on a quantum mechanical theory for

isotope effects on the vibrational energies of molecules, starting with H2 (Urey et al. 1932, Urey & Rittenberg 1933, Rittenberg et al. 1934, Urey & Greiff 1935). This work was fundamental to the experimental discovery of D and served as the basis for our understanding of chemical isotopic fractionations generally. This set of short papers (though now rarely cited) is arguably among the most important in all of geochemistry. Several reviews of this theory and its relevance for thermodynamic control of abundances of multiply substituted isotopologues have been presented (Urey 1947, Richet et al. 1977, Wang et al. 2004, Eiler 2007). Brieﬂy, heavy isotope (e.g., D, 13C, 18O) substitution generally reduces vibration frequencies and thus lowers vibrational energies of molecules; this phenomenon is sometimes referred to as the “zero-point energy” effect and is the dominant factor controlling equilibrium stable isotope fractionations. In addition, though less widely understood, double heavy isotope substitution generally leads to a reduction in frequency

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and lowering of vibrational energy somewhat greater than twice that of single substitution. Ac- cordingly, grouping heavy isotopes into bonds with each other is usually energetically favorable to distributing them as singly substituted molecules. This effect is relatively strong at low temperatures and diminishes with increasing temperature, where the greater conﬁgurational entropy of random isotopic distributions is more greatly favored. Although the chemical physics community has extensively studied the energetics of multiple heavy isotope substitutions through theoretical calculations and experiments on highly enriched synthetic materials (e.g., Pyper et al. 1967, Richet et al. 1977, Polyakov et al. 2005), only recently has anyone attempted to quantitatively measure equilibrium constants for such reactions in natural materials.

2.1. Measurements of Multiply Substituted Isotopologues at Their Natural Abundances Carbon dioxide is the ﬁrst compound to be studied for its temperature-dependent thermodynamic enrichment in multiply substituted isotopologues at natural isotope abundances (Eiler & Schauble

2004). Equilibrated CO2 gases should have proportions of the 18 (or 12, if only stable isotopes 12 16 13 18 16 14 17 are considered) possible isotopologues (e.g., C O2, C O O, C O2) controlled by the thermodynamics of homogeneous isotope exchange reactions such as the following:

12 18 16 13 16 12 16 13 18 16 C O O + C O2 = C O2 + C O O. (1) Wang et al. (2004) presented a theoretical prediction of the temperature dependence of this reaction (and many related reactions for other di- and triatomic molecules) on the basis of spectro-

scopic constraints on the vibrational properties of CO2 and the theories of quantum mechanics and statistical thermodynamics (i.e., Urey-Bigeleisen theory for partition function ratios) (Bigeleisen & Goeppert Mayer 1947, Urey 1947). Using a modiﬁed gas source isotope ratio mass spectrometer (the Thermo IRMS-253), Eiler & Schauble (2004) presented the ﬁrst measurements of the

equilibrium constant for this reaction in CO2 with natural abundances of C and O isotopes. The key enabling technology used in this instrument is a relatively simple modiﬁcation to the detector array: positioning of faraday cups read through 1012 ampliﬁers in the appropriate portion of the

detector array image plane to collect the mass 47, 48, and 49 isotopologues of CO2. Wang et al. (2004) and Eiler & Schauble (2004) are effectively the starting point of the discipline that has come to be called “clumped isotope geochemistry”—the study of variations in abundance of multiply substituted isotopologues in natural materials (Eiler 2007). One of the ﬁrst issues addressed in these papers concerns the nomenclature of clumped isotope geochemistry: What is the best method to describe the proportions of isotopologues in a sample? Investigators suggested that the reference frame should be a random, or stochastic, distribution of isotopes among all Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org possible isotopologues, i.e., the proportions of isotopologues that arise through sampling statistics,

given the sample’s bulk abundances of isotopes. For example, if a sample of H2 is known to have abundances of H and D of 0.9999 and 0.0001 (as a fraction of all hydrogen atoms), respectively, 2 then the expected stochastic abundances of isotopologues for that sample are [H2] = (0.9999) = −4 2 −8 0.9998, [HD] = (2 × 0.0001 × 0.9999) = 1.9998 × 10 ,and[D2] = (0.0001) = 10 . These predicted proportions can be described as the “stochastic composition” for that sample, and normalization of the measured composition of a sample to this predicted composition is described as a normalization to the “stochastic reference frame.”

Figure 2 illustrates the relationship between the concentration of D2 among all possible isotopologues of molecular hydrogen and the concentration of D among all H atoms in the molecular hydrogen population. In Figure 2, the line in composition space that deﬁnes the stochastic refer-

ence frame (the set of compositions shared by all samples of H2 that have a stochastic distribution)

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1.0 n o ti u ib tr 0.8 is d )

]) m o 2 d n a (r 0.6 c ti ] as 2 h oc

[D t + ΔD2 S 0.4 ] + [HD] + [D ] + [HD] 2 ([H

0.2 – ΔD2

0 0 0.20.4 0.6 0.8 1.0 [D] ([H] + [D]) Figure 2 The stochastic reference frame for the stable isotopologues of molecular hydrogen. Any sample of molecular hydrogen having a random distribution of H and D among all possible stable isotopologues (H2,HD,and D2) must fall on the curved trend, the composition of which follows sampling statistics. The D2 variable (deﬁned in the text) describes enrichments (for positive values) and depletions (for negative values) in D2 with respect to the amount expected for the random distribution for a given sample of molecular hydrogen (i.e., based on its proportion of D among all H atoms).

is strongly curved because abundances of singly substituted species are in linear proportion to the overall abundance of the rare isotope, whereas doubly substituted species vary as the square of rare isotope abundance. By this same reasoning, the stochastic reference frame for highly substituted versions of larger molecules must be very sharply curved (e.g., quadruply 13C substituted alkanes must scale as the fourth power of overall 13C abundance). This may be an important feature of any future studies of multiply substituted isotopologues of organics.

Measured deviations from a stochastic reference frame are generally reported as i values, which are differences between a measured ratio of isotopologues and an expected

stochastic ratio of isotopologues for that sample, in units of per mil (). Thus, D2 = [(D2/H2)measured/(D2/H2)stochastic − 1] × 1,000 (see Figure 2 for a graphical representation of the vector in composition space corresponding to a change in D2). Alternatively, for CO2, 13C18O16O 13 18 16 12 16 13 18 16 12 16 = [( C O O/ C O2)measured/( C O O/ C O2)stochastic − 1] × 1,000. Because conventional gas source isotope ratio mass spectrometers lack the mass resolution to distinguish between iso- 13 18 16 12 18 17 Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org topologues that share a common cardinal mass (e.g., C O O versus C O Oat47amu),

i nomenclature is also used to describe departures from a stochastic distribution for all species having the same cardinal mass. For example, 47 for CO2 = [{(mass 47 isotopologues)/(mass 44)}measured/{(mass 47 isotopologues)/(mass 44)}stochastic − 1] × 1,000. In this case, the i value reﬂects the combined effects of enrichments and/or depletions in 13C18O16O, 12C17O18O, and 13 17 C O2. These conventions of the stochastic reference frame and i values emphasize distinctive fractionations that change the state of isotopic ordering of a sample, i.e., the relative probabilities that rare isotopes will be in singly versus multiply substituted isotopologues. A key practical question for all measurements of multiply substituted isotopologues arises: How can the stochastic reference frame for a sample be established? In other words, how can researchers determine which ion intensity ratio measured on a mass spectrometer corresponds to the random distribution of isotopologues? Eiler & Schauble (2004) proposed an approach that

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has been the basis of most subsequent work. First, to force a standard gas to take on a nearly stochastic distribution, it is heated to ∼1,000◦C, a temperature at which the kinetics of isotopic exchange are relatively rapid. Then, these heated gases are measured for their bulk isotopic compositions (e.g., δ13C, δ18O, δD), based on comparison with conventional interlaboratory standards via conventional techniques. A gas with known bulk isotopic composition and, a priori, a random (or nearly random) distribution of isotopes also has known abundances of multiply substituted isotopologues and thus can serve as a standard for calibrating the instrumental mass fractionation of abundance ratios of all measured isotopologues. Several other secondary details must be considered to make this approach accurate: Instrument backgrounds, linearity, abundance sensitivity and/or fragmentation/recombination reactions in the source must be corrected for (for details, see Huntington et al. 2009). Nevertheless, this approach is expected to remain central to the calibration of measurements of multiply substituted isotopologues in simple molecular gases that can be heated without spontaneously decomposing (e.g., see the recent work of Yeung et al. 2012). It is less clear how standardization will be addressed with compounds that lack high-temperature stability (e.g., a stochastic distribution for sucrose cannot be standardized in this way). More recently, researchers have recognized that precise and accurate interlaboratory calibration of measurements of multiply substituted isotopologues requires a reference frame that includes two or more materials that have absolutely known (and different) isotopic distributions

(i.e., differing in i values) (Dennis et al. 2011). This is because fragmentation/recombination reactions in the ion sources of gas source isotope ratio mass spectrometers artiﬁcially compress the

scale of natural variations in i values by driving all measured gases toward a random distribution

(i = 0). The resultant “scrambling” effect is small (∼0–10%, relative) and appears to be relatively stable through time in any one laboratory, but it differs from instrument to instrument as a result of pumping conditions in the source, source tuning, and perhaps other less understood variables.

Dennis et al. (2011) proposed that in the case of CO2 this issue can be addressed by assuming that CO2 equilibrated at known temperature will take on a 13C18O16O (or, equivalently, 47) value consistent with the predicted temperature-dependent equilibrium constant for Reaction 2 (e.g.,

Wang et al. 2004). If these predictions are considered strictly accurate, measured differences in 47 between CO2 gases equilibrated at two or more different and known temperatures can be used to

correct for the compression of the 47 scale by fragmentation/recombination in the ion source, in a way that can be repeated self-consistently in multiple laboratories. This approach must engender

some small inaccuracy because the spectroscopy of CO2 and the theory of the quantum mechanics of molecular vibrations are not perfect. Nevertheless, it provides a reasonably well-understood reference frame that all laboratories can (potentially) agree on and experimentally reproduce using

common methods of CO2-water equilibration. Multiply substituted isotopologues are exceptionally rare in natural materials (typically parts to Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org tens of parts per million), must be measured with high precision to be useful in applied studies, and are typically analyzed on mass spectrometers that are incapable of distinguishing between species that share a common cardinal mass. For this reason, much of the methodological development in this ﬁeld has focused on puriﬁcation of samples and recognition of gases that contain hydrocarbons, chlorocarbons, and other contaminants that interfere with isotopic analyses. To illustrate

this point, Figure 3 shows a mass spectrum near 48 amu for a sample of natural CO2 gas, which was measured with a new prototype high-resolution gas source isotope ratio mass spectrometer. The Thermo Fisher IRMS 253 Ultra is the ﬁrst spectrometer suitable for isotopic analyses of molecular gases that is capable of both precisely analyzing isotope ratios and mass-resolving isobaric interferences. This instrument and its applications to isotopic anatomy are detailed below, but for now, note that high-resolution analysis of molecular gases often reveals that the rare multiply substituted species can be surrounded by contaminant isobaric interferences. Here, mass 48 of even

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102

12 18 C O2 (+ 13C17O18O)

101

16 O3 48Ti Relative intensity (%) intensity Relative

100 Mass (amu) Figure 3

Mass spectrum of CO2 near 48 amu, measured with a high-resolution gas source isotope ratio mass spectrometer (the Thermo IRMS 253 Ultra) (described in text). The doubly substituted (“clumped”) 12 18 48 isotopologue, C O2, is the dominant species, but contributions from Ti (presumably evaporated from 16 the electron filament in the ion source) and O3 (perhaps a recombination product formed from the ion 13 17 18 fragments O2 and O, or dissociation of unstable CO3) are visible. The trace species, C O O, is presumed to be present but not visible. The slope of the top of the largest peak reflects both pressure loss from the sample bellows over the time frame of the mass scan and the loss of the 48Ti ion beam halfway across the peak width (a step obscured by the logarithmic scale of the figure). All these species contribute to the measured mass-48 signal in lower resolution gas source mass spectrometers and presumably contribute to nonlinearities and other empirical artifacts in conventional clumped isotope analyses (Huntington et al. 2009).

a relatively pure sample of CO2 (i.e., free of organic compounds responsible for most recognized isobaric interferences in clumped isotope measurements) clearly suffers from interferences by 48Ti 16 (presumably evolved from the W filament in the mass spectrometer source) and O3 (perhaps a product of ion chemistry in the ion source). The past decade of research on clumped isotope geochemistry has contended with these problems through sample purification, data filtering, and empirical standardization schemes. The direct evidence of high-resolution mass spectra such as that shown in Figure 3 may improve data quality and our understanding of past analytical artifacts in conventional clumped isotope data. Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org

2.2. Atmospheric CO2

The study of multiply substituted isotopologues of natural CO2 (Eiler & Schauble 2004, Affek & Eiler 2006, Affek et al. 2007, Yeung et al. 2009) initially focused on 13C18O16Oinairandthe

various end-member sources and sinks that inﬂuence the atmospheric CO2 budget (Figure 4). Despite the current rudimentary understanding of this subject, several noteworthy discoveries have been made: 13 18 16 1. CO2 in air is characterized by a positive 47 value (i.e., enrichment in C O O, which makes up ∼97% of the mass-47 isotopologues of CO2, relative to the stochastic distribution) of slightly less than 1. This is on the same order as the value expected for equilibrium with respect to Reaction 2 at Earth surface temperatures. Such similarity may

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2.0 Free troposphere Urban air 1.6 Polar stratosphere Nonpolar stratosphere Car exhaust Human respiration 1.2 Combustion in air (‰) 47 Δ 0.8

0.4

0 20 25 30 35 40 45 50 δ18 OVSMOW (‰) Figure 4

Isotopic systematics of CO2 in air and representative sources to air. The 47 value represents the 13 18 16 enrichment, in units of per mil (), of mass-47 amu isotopologues of CO2 (mostly C O O) relative to a stochastic, or random, distribution of isotopes among all isotopologues. A 47 value of ∼0.95 would be consistent with thermodynamic equilibrium at Earth surface temperatures; lower values are consistent with equilibrium at higher temperatures and higher values with equilibrium at lower temperatures (though other processes also lead to systematic variations in i values) (see Figures 5 and 6). Measurements of 47 can 18 13 distinguish respiration from combustion sources of CO2 having similar δ Oandδ C values and can 18 17 distinguish between polar and nonpolar stratospheric CO2 having similar δ Oand O. Data from Eiler & Schauble (2004), Affek & Eiler (2006), Affek et al. (2007), and Yeung et al. (2009).

be a coincidence but is consistent with the interpretation that abundances of the multiply

substituted isotopologues of CO2 in air are strongly inﬂuenced by equilibration when air is exposed to water at the sea surface and in leaves.

2. The 47 value of CO2 varies seasonally (at least in the limited range of locations and times examined to date): Values lie near equilibrium in summer but are somewhat lower than

equilibrium in winter. This implies that one or more of the major sources of CO2 to air may be somewhat lower in 47 than equilibrium at ambient temperatures. Consideration of the relative sizes and isotopic signatures of the various atmospheric sources suggests respiration may be responsible for this effect (Figure 4).

3. Anthropogenic CO2 sources—car exhaust, emissions from gas-ﬁred power plants, or car- Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org bonate decrepitation—are clearly distinguishable from each other and from both ambient

air and CO2 generated by respiration (Figure 4). CO2 generated by natural gas combustion and thermal decomposition of carbonate have very nearly random distributions of isotopes

(47 ∼ 0) (Figure 4); CO2 in car exhaust has a somewhat higher 47 of a few tenths per mil (Figure 4), implying that it undergoes exchange with coevolved water vapor down to temperatures of ∼200◦C (perhaps quenched when the exhaust enters the relatively cool portion of the tailpipe). These signatures provide a ﬁngerprint for recognizing and characterizing anthropogenic emissions, particularly in urban environments.

4. Polar stratospheric CO2 is characterized by (so far) uniquely elevated 47 values up to 1.6, or ∼0.7 higher than typical tropospheric CO2. Isotopic exchange between CO2 and O(1D) is the most important of the known stratospheric reactions inﬂuencing the oxygen isotope

budget of CO2, but it reduces, not increases, 47. Thus, the measurements of stratospheric

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air indicate that some unrecognized reaction inﬂuences the isotopic budget of CO2 in the polar stratosphere. This may be an unrecognized mesospheric gas phase reaction that is sampled by downwelling into the polar stratosphere or perhaps a heterogeneous reaction or exchange on the surfaces of polar stratospheric cloud particles. The most attractive targets for future study are records of latitudinal and temporal variations

in 47 of free air, which could reveal the balance of major sources and sinks driving the secular variations observed by Affek et al. 2007, and detailed study of polar stratospheric air, which could reveal the currently mysterious chemical mechanisms responsible for its marked enrichment in 13C18O16O. Measurements of multiply substituted isotopologues also hold promise as a new win-

dow into the chemical and physical kinetics of processes important to the CO2 cycle, such as air-sea exchange or air-leaf interactions. All these applications could be leveraged even further by adding 12 18 13 18 data for C O2 and C O2, which may be enabled by new high-resolution and high-sensitivity gas source mass spectrometers.

2.3. Multiply Substituted Isotopologues in Carbonate and the “Clumped Isotope” Paleothermometer The largest body of work examining the natural distributions of multiply substituted isotopologues 13 18 16 −2 focuses on the C O O2 ion group in carbonate minerals and the aqueous solutions from which they precipitate. This research is an outgrowth of the studies on CO2 gas described above because they share a common analytical methodology: Reaction of carbonates with anhydrous

phosphoric acid releases CO2 that contains all the carbonate’s C atoms and two-thirds of the original O atoms. This reaction is accompanied by a signiﬁcant (∼10) but controllable O isotope

fractionation and, importantly, no O isotopic exchange between released CO2 and the acid or 18 other product compounds (McCrea 1950). Therefore, even though CO2 is fractioned in δ O with respect to reactant carbonate, the fractionation is reproducible provided the temperature of reaction is controlled and, thus, can be experimentally calibrated and corrected. Similarly,

Ghosh et al. (2006a) and Guo et al. (2009) demonstrated that CO2 produced by phosphoric acid 13 18 16 digestion of carbonate has a proportion of C O O (reﬂected in its 47 value) that is offset

from the 13C18O16O2 value of reactant carbonate by an amount that is generally reproducible so long as reaction temperature is controlled. Thus, 13C18O16O2 of carbonates can be constrained via

analysis of 47 in CO2 released by acid digestion. At equilibrium, the 13C18O16O2 of carbonate ion groups is predicted to vary as a function of temperature through homogeneous isotope exchange reactions such as (Schauble et al. 2006)

13 16 12 18 16 13 18 16 12 16 Ca C O3 + Ca C O O2 = Ca C O O2 + Ca C O3. (2) Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org The equilibrium constant for this reaction is greater than 1 at ﬁnite temperature and generally increases with decreasing temperature, for much the same reason that Reaction 1 (and similar gas phase isotopic “clumping” reactions) are driven to the right, strongly at low temperature

and more weakly at high temperature. Thus, the 47 value of CO2 extracted from carbonates by phosphoric acid digestion should be proportional to the equilibrium constant of Reaction 2 and therefore a function of the temperature of isotopic equilibrium of carbonate. This method of paleotemperature measurement has been referred to as “carbonate clumped isotope thermometry” (Eiler 2011 and references therein). Carbonate clumped isotope thermometry has several attractive properties (assuming it can be made to work in practice). First, as Urey (1947) noted when the carbonate-water thermometer was ﬁrst proposed, carbonate minerals are unusually well suited to stable isotope paleothermometry: They are widespread components of the geological record, often grow at or near equilibrium with

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the aqueous solutions from which they precipitate, and are more refractory to postdepositional change than some other components of the surface environment (e.g., pore waters, clays, opaline oozes, and organic matter) (see below). Here, I add a new strength of carbonate clumped isotope thermometry in particular: This method is based on a homogeneous isotope exchange reaction (Reaction 2), meaning all reactant and product species are preserved in the carbonate mineral. In this respect, the method differs from carbonate-water O isotope thermometry (Urey 1947, McCrea 1950), which is based on the heterogeneous reaction between two coexisting phases:

1 1 CaC16O + H 18O = CaC18O + H 16O. (3) 3 3 2 3 3 2 One can rigorously reconstruct paleotemperature by constraining proportions of the carbonate isotopologues in Reaction 2. By contrast, Reaction 3 can be used as a temperature constraint only if the isotopic composition of water from which the carbonate grew is also known. This is challenging for most of geologic time and terrestrial deposits of all ages. Furthermore, all

measurements of the clumped isotope compositions of carbonates (i.e., 47 values) are accompanied by measurements of δ18O. Therefore, they constrain both temperature and, through the known temperature dependence of Reaction 3, the δ18O of waters, which are often of interest to paleoenvironmental, paleoaltitude, and paleohydrologic studies. That is, whereas attempts at conventional carbonate O isotope thermometry often fail to produce unique solutions for either temperature or the δ18O of water, combining it with carbonate clumped isotope thermometry permits one to constrain both rigorously. Calibration and paleoclimatic applications of the carbonate clumped isotope thermometer were recently reviewed in detail (Eiler 2011). Therefore, only a broad overview of this subject and a few comments on the most recent developments are offered here. Perhaps the most noticeable feature of most of the published data calibrating the carbonate clumped isotope thermometer (Figure 5) ◦ is its simplicity: Most results between 40 and 0 C define a single trend of increasing 47 of CO2 extracted by acid digestion with decreasing temperature, despite the combination of samples from a wide range of biological and abiological sources (data from Ghosh et al. 2006a, 2007; Came et al. 2007; Eagle et al. 2010; Tripati et al. 2010; Thiagarajan et al. 2011). This review focuses on studies of materials with well-known growth temperatures that have been studied at Caltech (see Eiler 2011 for a more comprehensive discussion of all calibrations). In this respect, the method appears to be relatively little influenced by vital effects and other nonequilibrium phenomena that complicate conventional O isotope thermometry (e.g., Adkins et al. 2003), Mg/Ca thermometry (Elderfield et al. 2006), and other common methods. Nevertheless, exceptions to this trend are known, and much of the ongoing research on carbonate clumped isotope thermometry is focused on understanding them. The best explored are Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org speleothems and synthetic carbonates grown by rapidly degassing CO2 from carbonate solutions (Affek et al. 2008, Daeron et al. 2011, Kluge & Affek 2012). These processes lead to 47 values systematically lower than expected for their growth temperatures, assuming the common calibration trend in Figure 5, which reflects a kinetic isotope effect associated with irreversible dehydroxyla- tion of bicarbonate and dehydration of carbonic acid (Guo et al. 2009, Daeron et al. 2011). This nonequilibrium fractionation is surprisingly regular in its amplitude, such that natural speleothems

grown at known temperatures and laboratory analogues exhibit a correlation between 47 and temperature that differs from the canonical calibration in Figure 5 but is statistically significant and may be suitable for paleoclimatic studies (Affek et al. 2008, Kluge & Affek 2012). A second nonequilibrium effect was hinted at in the first study to calibrate the carbonate clumped isotope thermometer (Ghosh et al. 2006a) and recently confirmed and explored in greater

detail (Saenger et al. 2012). Some surface corals exhibit 47 values greater than expected for their

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T (˚C) 40 30 20 10 0 0.80 Ghosh et al. 2006a synthetic Foraminifera 0.75 Corals 3 CO H 2

2 Fast-growing + H surface corals 0.70 2 CO (‰) 47 Δ 0.65 O 2 + H 2 CO Speleothems 3 CO Mollusks 0.60 2 H Brachiopods Bioapatite Otoliths 0.55 Canonical calibration 10.07 10.57 11.07 11.57 12.07 12.57 13.07 13.57 106 (K) T 2

Figure 5 Empirical calibrations of the carbonate clumped isotope thermometer, which is based on the relationship between the growth temperatures of carbonate minerals and the 47 values of CO2 extracted from those carbonates by phosphoric acid digestion. The data are a subset of those summarized by Eiler (2011) and represent all published calibrations determined in the Caltech labs. The solid line represents the “canonical” ◦ calibration of Ghosh et al. (2006a). All values are normalized to an acid digestion temperature of 25 Cand assume the Caltech intralab reference frame for 47 values; see Dennis et al. (2011) for the methods needed to convert these data and the canonical calibration to the absolute reference frame. Note that diverse biogenic carbonates are similar to the canonical inorganic calibration of Ghosh et al. (2006a), but that speleothems and fast-growing surface corals are known exceptions—presumably due to kinetic isotope effects associated with rapid CO2 degassing or rapid hydration of CO2, respectively.

growth temperatures, by an amount that appears to increase with increasing growth rate. Such values may reﬂect a kinetic isotope effect associated with rapid hydration and hydroxylation of

CO2(aq) in organisms that biologically pump CO2 into ﬂuids at the site of biomineralization as a way of increasing local supersaturation (Saenger et al. 2012). If correct, this hypothesis suggests this vital effect is the mirror image of the nonequilibrium effects observed in speleothems (Figure 5). Conﬂicting reports of vital effects in mollusks will likely be published in the near future. Further- more, carbonates grown below ∼10◦C are generally more irregular in their calibrations, perhaps Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org owing to the slow kinetics of exchange between water and dissolved inorganic C species at these conditions (Dennis & Schrag 2010). Nevertheless, these discoveries do not undo the relatively

simple observation that many carbonates exhibit a simple, shared relationship between 47 and growth temperature. No published work extends calibrations to high temperatures and noncal- cium carbonates. However, data disseminated through abstracts or still in preparation suggest that this simplicity generally holds for calcite, dolomite, and magnesite above 50◦C (Ferry et al. 2011). One of the potential uses of carbonate clumped isotope thermometry is reconstruction of past climates in terrestrial environments, where the large variability in isotopic composition of meteoritic water largely precludes conventional O isotope paleothermometry (Ghosh et al. 2006b; Quade et al. 2007, 2013; Huntington et al. 2010; Passey et al. 2010; Snell et al. 2013). Therefore, signiﬁcant work has been put into understanding the carbonate clumped isotope records of soil and lake carbonates (Huntington et al. 2010, Passey et al. 2010, Quade et al. 2013)

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and land snails (Zaarur et al. 2011). The ﬁrst two of these materials appear to have 47 values that reﬂect the temperatures of their growth (i.e., they appear to conform to the canonical calibration trend in Figure 5) but also reveal that seasonality and, in the case of soils, radiant ground heating strongly bias the record of past temperatures. If one is attempting to reconstruct mean annual temperature, these complications must be addressed. However, this behavior also provides a useful window into the physical processes responsible for creating the terrestrial carbonate record and, when combined with other temperature proxies, can be used to reconstruct seasonality in temperature—an important and much debated climatic variable (Snell et al. 2013). The meaning of land-snail records is less clear. Some work to date suggests they preserve average growth season air temperatures (Eagle et al. 2012); other work suggests they either exhibit nonequilibrium vital

effects in their 47 values and/or are so idiosyncratic in their timing and microenvironments of growth that they will be challenging to use as paleoclimate archives (Zaarur et al. 2011). Additional study, preferably of cultured organisms with well-known growth temperatures and rates, will be required to better understand these materials. Perhaps the most rapidly growing group of applications of carbonate clumped isotope thermometry pertains to diagenesis, metamorphism, and faulting (Dennis & Schrag 2010, Bristow et al. 2011, Ferry et al. 2011, Huntington et al. 2011, Passey & Henkes 2012, Swanson et al. 2012). As veins, cements, concretions, and recrystallized components of limestones and carbonate or bioapatite fossils, carbonate is widespread in shallow crustal rocks. Clumped isotope analyses of these materials have been used to reconstruct temperature variations and diagenetic reaction histories in basins and fault zones (Bergmann et al. 2011, Ferry et al. 2011, Huntington et al. 2011, Swanson et al. 2012), and this approach may be easily extended to study anchimetamorphic terrains, ore bodies, and uplift histories of diverse rocks (Passey & Henkes 2012). The central issue associated with using carbonate clumped isotope thermometry in deeply buried materials is the blocking temperature for isotopic redistribution by lattice diffusion. Below this temperature, the method can record temperatures of discrete events of mineral growth; above it, the state of isotopic ordering can freely change with changing environmental temperature, and interpreting a ﬁnal measured apparent temperature as a constraint on heating or cooling history becomes a challenge. Studies of natural marbles and carbonatites have provided empirical constraints suggesting this blocking temperature is on the order of ∼200◦C for calcite, perhaps 50–100◦C higher for dolomite (Eiler 2007, 2011; Dennis & Schrag 2010; Ferry et al. 2011) and somewhat lower for carbonate apatite (Stolper & Eiler 2011). Subsequent controlled experiments generally support these conclusions but also reveal a complex time dependence to the evolution

of 47 values during heating—rapid partial re-equilibration followed by slower change (Stolper & Eiler 2011, Passey & Henkes 2012). These violations of first-order kinetics may reflect annealing of defects (which may or may not be present during cooling of high-temperature rocks) (Passey Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org & Henkes 2012). However, no evidence directly connects this behavior to any specific defect population, so alternate explanations may be possible. Two factors suggest applications of carbonate clumped isotope thermometry to shallow crustal problems could expand significantly in coming years. First, making quantitative, precise deter- minations of burial and metamorphic temperatures in the range ∼0–200◦C is difficult because most paleothermometers developed for this range (e.g., vitrinite reflectance, illite crystallinity) involve indirect temperature proxies and kinetic phenomena that can be influenced by substrate grain size and other properties, heating and cooling rate, and other complications. As a result, clumped isotope analyses of carbonates could add relatively straightforward measures of temperature. Second, carbonate clumped isotope measurements directly constrain the δ18O of waters from which carbonates grew, meaning they can be used to reconstruct pore water compositions. This has already proven useful in documenting the irrigation of faults with meteoric waters (Swanson

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et al. 2012) and in distinguishing buried sedimentary strata that evolve in isolated hydrologic seals versus those that are conduits for ﬂuid ﬂow (Ferry et al. 2011, Bergmann et al. 2011).

36 35 36 2.4. O2 and O OinAir The ﬁrst study to make a precise measurement of a multiply substituted isotopologue other than 13 18 16 17 18 C O O in a natural material examined two doubly substituted species of O2— O Oand 18 O2—in the atmosphere (Yeung et al. 2012). Using estimates of the fundamental stretching frequency of O2 and Urey-Bigeleisen theory of isotope effects on vibrational energies, Wang et al. (2004) predicted the temperature-dependent enrichments of these species relative to a stochastic

distribution for O2 in thermodynamic equilibrium. The methods of analysis and standardization used by Yeung et al. (2012) are similar to those previously developed for study of CO2: Puriﬁed O2 is analyzed by gas source isotope ratio mass spectrometry on a Thermo MAT-253, using faraday cups read through 1012 ampliﬁers to detect the weak ion beams corresponding to doubly substituted

species and standardizing values of 35 and 36 by comparison with intralaboratory reference gases that are equilibrated at known, controlled temperatures. The mass spectrometer used for this work 36 18 to date is unable to mass resolve Ar from O2. In addition, the chromatographic methods of gas puriﬁcation used by Yeung et al. (2012) are not perfectly efﬁcient, so all sample gases contain some amount of argon. This interference has been dealt with by peak-stripping the inferred 36Ar contamination on the basis of measured 40Ar, thereby resolving the true “clumped isotope”

anomalies of natural O2 samples. However, as with prior measurements of mass-47 anomalies of

CO2, this method should be conﬁrmed by high-resolution mass spectrometry. Initial measurements of air from the Los Angeles Basin suggest that atmospheric O2 is characterized by 18O2 and 18O17O values of ∼2 and 1, respectively. These enrichments may

reﬂect thermodynamic equilibrium promoted by rapid photochemical exchange between O2 and 18 the radical species O(1D) and/or O(3P). This interpretation is supported by the fact that the O2 and 17O18O excesses are consistent with thermodynamic equilibrium at a common temperature 18 16 18 16 (i.e., through the two independent homogeneous equilibria: 2 × O O = O2 + O2 and 17 16 18 16 17 18 16 O O + O O = O O + O2). If so, the measured enrichments in these species suggest a mean temperature of ∼250 K. This is signiﬁcantly warmer than the temperatures of the lower

stratosphere where O2 undergoes rapid isotopic exchange associated with ozone chemistry, but it is cooler than the boundary layer air masses where rapid exchange associated with NOx chemistry takes place. Yeung et al. (2012) suggest that the observed enrichment reﬂects the weighted average of equilibration in cold stratospheric air and warm boundary layer air. If so, variations in these

anomalies with time and location may provide a tracer for the vigor of NOx chemistry, which is strongly inﬂuenced by urban pollution. Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org

2.5. Fractionations of Multiply Substituted Isotopologues in Nonequilibrium Processes Most of the recent progress in understanding multiple isotopic substitutions in natural materials has focused on the temperature-dependent “preferences” for clumped isotopic species that manifest in systems in or near thermodynamic equilibrium. Such isotope effects are relatively easy to understand because they are grounded in well-known principles of statistical thermodynamics and quantum mechanics. And, they are useful in the earth sciences because they may provide constraints on the temperatures of past natural events and processes. Nevertheless, such equilibrium thermodynamic effects represent just one of many mechanisms of isotopic fractionation that lead to distinctive proportions of multiply substituted isotopologues.

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Previous applied studies and reviews of multiply substituted isotopologues discuss general expectations regarding the clumped isotope systematics of diffusion, gravitational fractionation,

and mixing, and emphasize CO2 in response to the relatively large proportion of applied work in this ﬁeld that focuses on 13C18O16O (Eiler 2007, 2011). Here we examine the principles behind

such effects for the simpler and more easily illustrated system: H2-HD-D2. Figure 6 reproduces a portion of the isotopic composition space introduced in Figure 2 but focuses on plausible natural ranges of composition. All samples having an equilibrium constant of

0.25 for the reaction: 2 × HD = H2 + D2 will lie along this curve, at a position determined by the sample’s bulk D/H ratio (i.e., δD value). The equilibrium processes described in the preceding

section promote production of D2 at the expense of HD, displacing samples to positions above the stochastic line—more at low temperatures, less at high temperatures (e.g., compositions of molecular hydrogen gases equilibrated at 700 K are indicated with a second black line in each panel, based on models of Urey & Rittenberg 1933). The isotopic signatures of nonequilibrium fractionations depend on the geometric relationships between the vectors describing those fractionations and the curvature of the stochastic reference frame. For example, Knudsen diffusion is characterized by isotopic fractionation that scales as the square root of mass (i.e., Graham’s law). Therefore, a population of molecular hydrogen gas

molecules that diffusively fractionates from a reservoir of vapor is lower in HD/H2 and D2/H2 ratios than that source vapor by factors of (2.016/3.022)0.5 = 0.8167 and (2.016/4.028)0.5 = 0.7074, respectively. The slope of the resulting vector in the composition space of Figure 6a is “ﬂatter” than the tangent to the curve representing the stochastic distribution, meaning the

population of diffused molecules will be lower in HD/H2 and D2/H2 than its vapor source but greater in D2/H2 than predicted by the stochastic distribution at its HD/H2. Thus, the diffused gas is isotopically “lighter” but “clumpier” than its source. When translated into the dimensions

of Figure 6b, the vector followed by diffusing gas has a negative slope: D2 increases while δD decreases. Conversely, gas that is residual to Knudsen diffusion is isotopically “heavy” (enriched

in HD and D2 relative to its initial composition) but relatively poor in D2 for its new HD content (i.e., it is poorer in “clumps” than expected given the stochastic distribution). This somewhat counterintuitive result is common to the isotopic systematics of Knudsen diffusion and gas phase

interdiffusion for CO2,O2,N2, and other small molecules (Eiler & Schauble 2004, Eiler 2007, Yeung et al. 2012). Gravitational fractionations (and the related phenomenon of separation of isotopes in a gas centrifuge) follow a mass law in which the fractionation factor, α, for isotopes i and j between two different points (1 and 2) in a gravitational ﬁeld at equilibrium scales with the strength of −2 the gravitational ﬁeld (g, in m s ), height difference between the two samples of interest (Z2−1, in m), the temperature of the system (T, in K), and the absolute difference in mass between the

Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org isotopic species of interest ( Mi−j, in grams per mol), following the relationship ( Mi−j)g( Z2−1) RT α1−2 = e , (4) where R is the gas constant. This expression is often approximated as

1,000 · (Mi−j)g(Z2−1) − ∼ , (5) 1 2 RT

which assumes 1,000 × lnαi−j ∼ i−j = δi−δj. This approximation in the relationship between α and values is not exact. A previous discussion of the “clumped” isotope systematics of gravitational fractionations (Eiler 2007) used the approximate form of the gravitational fractionation law (Equation 7), leading to the erroneous conclusion that gravitational fractionations create very subtle but possibly measurable clumped isotope anomalies (i.e., movements relative to the stochastic

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a 4 –8 700 K equilibrium Mixtures × 10 Random ]) 2 3 ]

2 Settled

[D Diffused 2 ] + [HD] + [D ] + [HD] 2 ([H

1 1.0 1.2 1.4 1.6 1.8 2.0 2.2 [D] × 10–4 ([H] + [D])

120 b 700 K equilibrium 100 Mixtures Random 80

60 (‰) D2

Δ 40 Diffused 20 Settled 0

–300 –200 –100 0 100 200 300 δ DVSMOW (‰) Figure 6 “Clumped isotope” systematics of various processes that can inﬂuence the isotopic composition of molecular hydrogen. (a) Composition space from Figure 2 but with focus on the range of compositions close to the natural sources of H. Solid curves indicate compositions of molecular hydrogen that have a random distribution or are consistent with the enrichment in D2 expected for thermodynamic equilibrium at 700 K (based on models of Urey & Rittenberg 1933). The dashed purple line indicates compositions produced by mixing two gases that have random isotopic distributions but differ markedly in total D content. The mixing line is straight, whereas the random and equilibrium lines are curved. Red and dark blue arrows indicate vectors of compositional change due to diffusional and gravitational fractionation: The isotopically “light” diffused gas and isotopically heavy “settled” gas are shown; both assume a complementary source that has the Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org isotopic composition of SMOW and a random distribution of isotopes. (b) Coordinates have been transformed into the dimensions of δDVSMOW and D2, presenting vectors in this composition space followed by various mechanisms of isotopic fractionation. This composition space has the advantage of more clearly visually separating various fractionation mechanisms, but nonlinearities in the conversions of concentrations to these isotopic indices mean some trends are counterintuitive in shape.

reference frame). Re-examination of this problem with the exact form of the gravitational frac- tional law (Equation 6) reveals that gravitational fractionations generally parallel the trend of the stochastic distribution and thus lead to changes in bulk isotopic composition without changes in clumped isotope anomalies. The ﬁrst-order conclusion of Eiler (2007) is unchanged: Gravitational

fractionations are distinctive for their relative lack of change in clumped isotope signature (i values) as compared with other fractionating mechanisms (see also Yeung et al. 2012). However,

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even the subtle variations in i values discussed there should not actually occur (at least in the doubly substituted species of simple molecular gases considered to date). Note that gravitational fractionations are an equilibrium thermodynamic effect, but for the sake of convenience they are here considered along with other less-well-understood fractionations. Chemical kinetics presents perhaps the most diverse and complex family of nonequilibrium fractionation behaviors because of the great diversity of chemical physics phenomena involved, e.g., photolysis, transition state energetics, solvation and desolvation, or any fractionation arising from motion of species through a reaction coordinate. Although a rich body of experimental data and theory constrains isotope effects in chemical kinetics, little of it is directly relevant to the isotope geochemistry of multiply substituted compounds. A large proportion of uses of isotopes in studies of chemical kinetics simply use them as tracers for reaction mechanisms and pathways and do not constrain isotope effects on reaction rate. In addition, studies of chemical kinetic isotope effects are rarely performed with sufﬁcient precision to interpret geochemical data and examine

an adequately broad set of singly and multiply substituted compounds to permit calculation of i values (i.e., clumped isotope anomalies) resulting from reactions. Much remains to be done in this subdiscipline of clumped isotope geochemistry. The photochemistry of methane is the first known example in which a chemical kinetic phenomenon was recognized to have potential effects on natural abundances of multiply substituted 13 12 isotopologues. Mroz et al. (1989) detected quadruply substituted methanes ( CHD3 + CD4) in Antarctic air, finding very large (∼500,000) enrichments relative to a random distribution of isotopes among all methane isotopologues. Soon thereafter, Kaye & Jackman (1990) demonstrated that this enrichment is equal in sign but much larger in amplitude than that expected on the basis of experimental studies of the isotope effects on rates of methane photo-oxidation and our understanding of the atmospheric methane budget, which predict enrichments in these species of “only” ∼10,000. More recent experimental constraints on isotope effects on methane photo-oxidation (Saueressig et al. 2001) are generally consistent with this argument and do not fundamentally change the conclusion by Kaye & Jackman (1990) that Mroz et al. (1989) observed an inexplicably large clumped isotope anomaly. The two most obvious remaining explanations of 12 this finding are that (a) Mroz et al. (1989) detected an anthropogenic spike of CD4 that had been previously released to track Antarctic circulation or that (b) it was an analytical artifact. The only chemical-kinetic isotope effect to be subjected to detailed study in the modern era of high-precision clumped isotope geochemistry is that associated with decomposition of carbonate

ion groups to release CO2 either during acid digestion of carbonate (Guo et al. 2009) or during degassing of oversaturated aqueous carbonate solutions (Daeron et al. 2011). Both cases involve

disproportionation of carbonate ion groups to liberate CO2, yielding a kinetic isotope effect that 13 18 causes the lost CO2 to be lower in δ Candδ O than reactant carbonate but with a higher 13 18 13 18 Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org proportion of C– O bonds. Residual carbonate is correspondingly enriched in δ Candδ O but depleted in 13C–18O bonds. If such reactions are driven by outgassing from an aqueous carbonate solution, solid carbonate may precipitate from this residual dissolved carbonate pool faster than it can re-equilibrate through exchange with water. In this case, the product solid carbonate will be

lower in 47 than expected for carbonate grown at equilibrium at the growth temperature (i.e., the apparent temperature will be too high). This effect is believed to be responsible for the fact

that speleothems are often lower in 47 than inorganic calcite grown at equilibrium at the same temperature (Figure 5). There are a number of outstanding problems in carbonate clumped isotope thermometry that may be resolved through a better understanding of kinetic isotope effects related to those described above: e.g., vital effects for fast-growing surface corals and mollusks and controversies regarding the experimental calibration of the technique at temperatures near the freezing point of water (e.g.,

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Ghosh et al. 2006a, Dennis & Schrag 2010, Saenger et al. 2012). However, the diversity of chemical physics phenomena involved in chemical kinetic isotope effects likely precludes any generalizations from the examples above. Useful general predictions regarding the clumped isotope systematics of kinetically controlled chemical reactions do not seem possible, and each instance will likely require detailed study.

3. POSITION-SPECIFIC ISOTOPE EFFECTS Position-specific (sometimes called site-specific) isotopic fractionations describe fractionations between isotopologues that share a bulk isotopic content but differ in the isotopic content of nonequivalent sites in a molecular or mineral structure. Equivalently, the term may be used to describe differences between the isotopic composition of a site in a molecule and the composition it would have if that molecule had randomly distributed isotopes of an element among all relevant sites in that molecule. For example, any process that distinguishes between 15N14N16O 14 15 16 12 13 12 13 and N N O (isotopologues of nitrous oxide) or between CH3– CH2– CH3 and CH3– 12 12 CH2– CH3 (isotopologues of propane) could be described as a position-specific isotopic fractionation. A difference in δ13C between carboxyl and methyl ends of the acetate molecule may also be described with the same term. Some of the earliest studies of chemical isotope effects examined position-specific thermodynamic isotopic fractionations, such as vapor pressure isotope effects associated with deuteration of specific sites in organic acids and other low-symmetry compounds (Yankwich & Promislow 1954).

A large amount of research was done on such effects in N2O, alkanes, and a host of other relatively volatile compounds through the 1960s and 1970s (e.g., Bigeleisen & Ribnikar 1961; see Jansco & Van Hook 1974 for a summary). Perhaps the most influential body of work on position-specific isotope effects in natural materials has focused on biosynthetic products, particularly amino acids and lipids. Abelson & Hoering (1961) isolated natural amino acids from cultured photosynthetic organisms and analyzed separately the δ13C values of whole amino acids and C liberated by decarboxylation. The first-order finding was that the terminal carboxyl groups on most amino acids are generally significantly (from several to tens of per mil) higher in δ13C than other C positions. This is consistent with the notion that relatively reduced C sites inherit, directly or indirectly, the low δ13C value characteristic of photosynthetically fixed C, whereas the citric acid cycle promotes 13 exchange of carboxyl groups with the pool of dissolved CO2, which is generally higher in δ C than biomass. This phenomenon is partially responsible for systematic differences in δ13C between amino acids (Macko et al. 1987). Several studies have examined the position-specific isotopic fractionations associated with synthesis of lipids and fatty acids. DeNiro & Epstein (1977) conducted in vitro experiments to Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org constrain the C isotope effects associated with enzymatic decarboxylation of pyruvate to produce acetyl groups, which were extracted as the volatile compound acetaldehyde. Although this abiological, in vitro experiment is several steps removed from natural lipid synthesis, the results provide some insight into the isotopic compositions of acetyl groups incorporated into acetyl coenzyme-A (acetyl-coA, a fundamental building block in lipid synthesis as well as a participant in the citric acid cycle) (Figure 7). Decarboxylation attacks the bond between C2 and C3 in pyruvate, with a kinetic isotope effect that leaves the carbonyl position of product acetyl groups significantly (∼10–20) depleted in 13C relative to the adjacent methyl group. The size of this isotope effect depends on temperature of reaction and proportion of pyruvate consumed (and in natural systems likely depends on the branching ratio of pyruvate consumption through this versus other metabolic pathways). Nevertheless, the resulting difference in δ13C between the carbonyl and methyl positions in acetyl-CoA should lead to an even/odd ordering of C isotope

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Pyruvate 40 Extrapolation 30

Carbon

(˚C) 20

Oxygen T Hydrogen 10

C1 C2 CO2 0 0 5 10 15 20 25 Acetyl group δ13C (C2) – δ13C (C1) (‰)

Acetyl-CoA O OH Acetate Lipids Amino acids

Figure 7 Schematic illustration of biosynthetic reactions resulting in position-specific carbon isotope fractionations in lipids. Pyruvate undergoes decarboxylation, producing acetyl groups. In vitro experiments conducted to study the isotope effects of this reaction (DeNiro & Epstein 1977) evolve these groups as acetaldehyde, but in vivo they are incorporated into acetyl-CoA, a fraction of which contributes C2 groups to lipids (e.g., palmitoleic acid). Decarboxylation of pyruvate is associated with a kinetic isotope effect, resulting in a ∼10–20 contrast between the methyl and carbonyl sites of the product acetyl group. In vitro, this isotope effect has an unexplained and somewhat peculiar temperature dependence (becoming stronger with increasing temperature). Regardless, this site-specific isotope effect in acetyl groups is inherited by product lipids as an even/odd ordering of C isotope compositions in backbones of lipid structures. This even/odd ordering is further modified by advanced lipid synthesis, particularly for terminal carboxyl groups and C=C double bonds (see Monson & Hayes 1982a,b; Hayes 2001).

compositions in lipids because acetyl groups are assembled “head to tail” in lipid synthesis. 13C depletion of carbonyl positions relative to reactant pyruvate may also contribute to the depletion of lipids in 13C relative to original C sources (and bulk biomass generally) (Hayes 2001). In a series of papers published from 1980 to 1982, Monson & Hayes (1980, 1982a,b) directly examined the C isotope anatomies of lipids by subjecting isolated fatty acids to ozonolysis, which cleaves and oxidizes C=C double bonds in the middle of lipid chains, and then by decarboxylating Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org the products to liberate the oxidized C positions for isotopic analysis as CO2. This work examined just a few positions of a few compounds but revealed two “themes” controlling isotopic anatomies of lipids: (a) Their findings confirmed the first-order findings of DeNiro & Epstein (1977), i.e., natural lipids do have an even/odd ordering in C isotope composition, inherited from the contrast between methyl and carbonyl ends of acetyl-CoA. However, Monson & Hayes also found that natural decarboxylation of pyruvate appears to have a stronger isotope effect than suggested by the in vitro experiments of DeNiro & Epstein (∼23 versus ∼15). (b) Additionally, the carboxyl groups of fatty acids are subjected to additional, more complex isotopic fractionations in the final stages of lipid biosynthesis. Chain lengthening involves hydrolysis reactions that proceed more rapidly for substrates that have isotopically light carboxyl groups, promoting their incorporation into complex lipids. This can be thought of as a secondary modification of the “head to tail” C isotope ordering inherited from acetyl-CoA that particularly influences relatively long fatty acids.

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Recent experimental studies of H isotope fractionations between organic compounds and water suggest that they must also be characterized by dramatic position-speciﬁc isotope effects (Wang & Sessions 2009a,b). These studies constructed density functional theory (DFT) models of the isotope effects of deuteration of speciﬁc sites in organic molecules and then calibrated those models by comparing them with experiments in which H in sites that undergo keto-enol tautomerism (i.e., equilibration of a ketone and an alcohol) were equilibrated with water of known isotopic composition at known temperature. Extension of these results to entire molecules assumes that calibration of DFT model predictions for an exchangeable site results in accurate predictions for unobserved, nonexchangeable sites. Nevertheless, if one takes this working hypothesis at face value, it predicts equilibrium intramolecular variations in δDofupto∼200 at Earth surface temperatures. The primary controls of these differences are electron density of neighboring C–H bonds and the presence and identity of nearby functional groups, such as carbonyl and ketone. For example, at equilibrium, methyl groups at the ends of n-alkanes are systematically ∼70 lower

in δD than neighboring CH2. Wang & Sessions (2009a,b) calibrated these fractionations to understand H isotope compositions of components of natural oils that had been exposed to water at elevated temperatures for many millions of years and, thus, plausibly had reached equilibrium, both with respect to the heterogeneous isotope exchange equilibrium with coexisting water and with respect to intramolecular position-speciﬁc isotope effects. What relevance these equilibrium fractionations have for understanding biosynthetic fractionations is less clear. Galimov (1973, 1974) argued that equilibrium fractionation factors for various components of organic compounds control (or at least predict) the isotopic variations among biomolecules and natural oils and gasses. Several observations loosely 13 support this notion: CO2 is generally tens of per mil higher in δ C than methane in systems with active biogeochemical cycles—the same sign and order of magnitude as the low-temperature equilibrium fractionation between these gases (Chacko et al. 2001, Freeman 2001). Similarly, the

C isotope effect associated with CO2 ﬁxation by the RuBisCO enzyme (the key chemical step in photosynthesis) has the same sign and order of magnitude as the equilibrium fractionation be-

tween CO2 and graphite or other reduced forms of C at low temperatures (Guy et al. 1993, Chacko et al. 2001). Rustad (2009) presented a relatively sophisticated theoretical study in which DFT and related methods were used to predict position-specific isotope effects in amino acids, some of which compare favorably (at least in order of magnitude and direction) with the observations of Abelson & Hoering (1961). Nevertheless, compelling reasons indicate that the similarities between biosynthetic and equilibrium fractionations are coincidental or otherwise misleading. Where metabolic and other biosynthetic isotopic fractionations have been studied in detail, they generally do not represent chemical systems with nearly balanced rates of forward and back reaction, which is a prereq- Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org uisite for equilibrium. Instead, such reactions are irreversible (often complex and multistepped) and better understood through transition state theory and other concepts of chemical kinetics (e.g., McNevin et al. 2007). If a general physical insight is to be drawn from equilibrium models of isotope effects in biosynthetic compounds, it may be that such models describe the extent to which heavy isotope substitution lowers vibrational energies of bonds, which can slow the rates at which bonds are broken in irreversible reactions. Furthermore, vibrational effects on energies of transition states may influence chemical kinetic isotope effects in a way that broadly resembles “equilibrium” fractionations between reactants and products. Some of the most detailed information describing the nature of position-specific isotope effects that accompany irreversible reactions comes from a novel set of organic chemistry experiments by Singleton and colleagues (e.g., Singleton & Thomas 1995, Singleton & Szymanski 1999). These experiments examine strictly irreversible reactions that closely satisfy the conditions of

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C5H8 + C4H2O3 e.g., C9H12O3 Isoprene Maleic anhydride Cyclohexene products

NMR analysis of residual isoprene after extensive distillation

Fractionations (ε, ‰) Assumed D 13C 0‰ –10‰

1‰ 0‰ –32‰ Carbon Hydrogen 17‰ –44‰ 22‰ –62‰ –92‰ Figure 8 Experimental study of the position-specific isotope effects associated with a Diels-Alder reaction: synthesis of cyclohexenes from isoprene and maleic anhydride. The reaction is strictly irreversible and so can be run to high extents of Rayleigh distillation, resulting in isotopic fractionations in residual isoprene so large that they can be quantified by conventional nuclear magnetic resonance techniques. This measurement is intrinsically site specific and reveals the pattern of kinetic isotope effects causing enrichments and depletions for every carbon and hydrogen site in isoprene. Listed fractionations are ε values, calculated as (α − 1) × 1,000. The resulting pattern of fractionations constrains the mechanism of reaction (in this case indicating a concerted reaction, i.e., both terminal C sites in isoprene participate in the rate-limiting step). The analysis is internally standardized and assumes that the methyl group is unfractionated—a reasonable approximation that is likely untrue in detail (particularly for H) (based on Singleton & Thomas 1995). The illustrated results are for a ◦ reaction at 25 C.

Rayleigh distillation. Investigators ran such reactions to high extents of completion and then examined the isotopic compositions of the residues using nuclear magnetic resonance (NMR) techniques. NMR signals are intrinsically site specific and capable of constraining δ13CandδD values. Conventional NMR methods generally lack the sensitivity to precisely measure natural variations in stable isotope abundance at meaningful precision. However, as reactions approach completion, the residues of high extents of irreversible reactions can take on exceptional isotopic enrichments and depletions as a result of the amplifying effects of Rayleigh distillation. An early example of this approach demonstrates that the Diels-Alder reaction (Figure 8) is accompanied by strong isotope effects in both H and C isotopes at the C1 and C4 positions of isoprene and Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org more subtle, likely secondary, isotope effects in other C and H positions, thereby supporting a concerted mechanism of simultaneous reaction of the terminal C sites—one of several imaginable models of this reaction. These studies examine simultaneous fractionations on a large number and diversity of molecular sites during chemical reactions. As such, they provide a model for ways in which earth scientists will interpret similar data once they are available for natural systems. It is easy to envision studies in which the “fingerprint” of a constellation of position-specific isotope effects could serve as a highly diagnostic marker for particular reaction pathways in the synthesis or consumption of metabolites or other molecules of moderate size and complexity. The studies of intramolecular isotopic variations of biomolecules summarized above have greatly influenced the interpretation of intermolecular variations in isotopic compositions among lipids, amino acids, and other organic compounds as well as their geological derivatives in oils and gases. A full discussion of this subject is beyond the scope of this review; readers are directed to

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reviews by Hayes (2001) and Freeman (2001). However, there has been surprisingly little subsequent direct study of intramolecular isotopic variations in natural organics. In fact, when one considers the likely universality of position-specific isotope effects in structurally complex molecules and the potential richness of the information they record, it is surprising how few examples there are of such effects being used in applied fields of stable isotope geochemistry (e.g., paleoclimate research, environmental chemistry, forensics). The dearth of applied work in this field likely reflects the specialized and difficult nature of experiments required to extract mi-

cromole quantities of molecules suitable for isotopic analysis (e.g., CO2) of natural biomolecules (Ivlev 1991, Brenna 2001). For much of the history of isotope geochemistry, this problem has been as intractable as it is attractive. Nevertheless, several methods of position-speciﬁc isotopic analysis based on selective chemical or thermal degradation are sufﬁciently simple to enable routine applied study to natural samples. One of the most successful is chemical decomposition or pyrolysis of acetate or acetic acid fol-

lowed by isotopic analysis of product CO2 (Blair & Carter 1992). By combining such data with conventional analyses of the δ13C of the whole molecule, researchers can calculate the position- specific C isotope composition through mass balance arguments. Innovations of this method (chromatographic concentration of analyte coupled with on-line pyrolysis) make it applicable to even acetate-poor aqueous solutions with little preparation. Accordingly, this method is one of the only position-specific analyses that can be conducted on nearly “raw” environmental samples (Thomas et al. 2008). Such data have been particularly useful for understanding the biogeochemical cycles of acetate and acetic acid in environmental samples because their carboxyl groups are relatively easily exchanged with dissolved inorganic C, and thus one must isolate the δ13Cofthe methyl group to confidently use C isotope variations to track the sources and sinks of acetate (e.g., Thomas et al. 2008, Hattori et al. 2011). In a series of papers, Brenna and colleagues (Corso & Brenna 1997, 1999; Corso et al. 1998; Brenna 2001) presented a more sophisticated variation on this theme. Their approach involved online pyrolysis of diverse volatile organics, gas chromatographic separation of the product fragment

compounds, and, finally, on-line combustion of individual fragments to CO2 and isotopic analysis of that CO2 (see also the related, more recent development by Gauchotte et al. 2009). This method is applicable to a wide range of volatile and semivolatile organic compounds (fatty acids, sugars, amino acids, among others) (Corso & Brenna 1997, 1999; Corso et al. 1998), raising the possibility of a wide range of applications to forensics, food science, and biomedical research (Brenna 2001, Gauchotte et al. 2009, Tobias et al. 2011) as well as to the earth sciences and meteoritics (e.g., Seph- ton 2005). However, this approach has limitations: It is likely inappropriate for position-specific H isotope analysis because H is relatively mobile, exchangeable, and easily fractionated during pyrolysis. This approach is also intrinsically unsuited to any form of “clumped isotope” analysis Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org because all analyzed C atoms are ultimately separated from their original molecular sites during combustion. Finally, few published applications of this method have involved geochemistry, which suggests that technical barriers to application to natural samples may have held back its advance. Perhaps the fastest growing approach to position-specific isotopic analyses is emerging from the food science and forensics communities: SNIF-NMR (site-specific natural isotope fractionation– nuclear magnetic resonance) is an innovation of conventional NMR analysis that permits resolution of natural isotopic variations (Martin & Martin 1981; Caer et al. 1991; Tenailleau et al. 2004; Betson et al. 2006; Gilbert et al. 2009, 2012). This technique has existed in some form for ∼30 years but has only recently emerged as a practical applied tool in the natural and forensic sciences. NMR analysis is based on the absorption of electromagnetic energy by nuclei with nuclear spin (e.g., the spin-1/2 species, 13C and H, or the spin-1 species, D; note D can also be detected indirectly by its effects on adjacent H or 13C in the same molecular structure). The principle limitation to

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SNIF-NMR is sensitivity owing to the low natural abundances of rare isotopes: To date, all studies have considered only single substitutions (i.e., very rare multiply substituted isotopologues have not been analyzed at their natural abundances, though this could be possible), sample sizes are typically hundreds of milligrams to grams, and integration times are on the order of many hours per sample. Nevertheless, the method may be uniquely well suited to quantitative analysis of position- specific C and H isotope fractionations in large, structurally complex organic molecules, which can be only partially reconstructed by chemical and pyrolytic degradations. Moreover, the technique is applicable to both C and H isotope variations. Although the details of the methods differ for isotopes of these two elements, nothing prevents both from being applied to a single sample. Within food science and forensics, this method has been applied to source vanillin (Tenailleau et al. 2004) and characterize isotopic distributions in fatty acids (Billault et al. 2001) and glucose (though the latter requires a chemical preparation prior to analysis) (Gilbert et al. 2009, 2012). Of greatest potential interest to earth and environmental sciences, this technique has also been used to generate records of position-specific H isotope variations in natural samples of cellulose from wood (Betson et al. 2006, Augusti et al. 2008). As with glucose, this measurement also requires significant chemical preparation and derivatization prior to NMR analysis. Discriminating site-specific H isotope compositions of cellulose appears to disentangle climatic versus metabolic influences on the overall D content of cellulose, which may lead to improved uses of woody plants as records of climate variability. Nevertheless, with the possible exception of acetate, the methods of position- specific isotopic analyses described above—chemical, pyrolytic or NMR—have remained tools for laboratory studies of isotope effects or proof-of-concept studies of potential applications, but they have not yet greatly influenced debates in the applied studies of climate, biogeochemical cycles, or other major branches of stable isotope geochemistry. Arguably the greatest impact of position-specific isotopic analysis in a natural material has come from studies of the environmental biogeochemistry of nitrous oxide. Such studies are motivated by

the facts that N2O is a metabolic intermediate in nitrification and denitrification (Yamagishi et al. 2007, Galloway et al. 2008), a participant in important photochemical reactions (Ravishankara et al. 2009), and a greenhouse gas (IPCC 2007). Position-specific N isotope fractionation discriminates between 15N located in the central position of nitrous oxide and 15N located in the terminal N position (i.e., 14N–15N–16O versus 15N–14N–16O; Yoshida & Toyoda 2000). Nitrifying bacteria

(which oxidize ammonia or ammonium to nitrite or nitrate) emit N2O that has a large (≥30) enrichment of the central N position relative to the terminal N position, whereas N2O emitted

from denitrifying bacteria (which reduce nitrate to N2 gas) and other major sources of N2O exhibit no significant position-specific isotope effect (Sutka et al. 2006). The position-specific isotopic

composition of N2O can be reconstructed by introducing N2O into an electron impact gas ion + source, where a fraction of the N2O molecules are ionized to N2O and a fraction are fragmented + + Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org and ionized to NO (Yoshida & Toyoda 2000). Roughly 90% of the NO ions inherit N from the

central N position from the parent N2O (the remaining ∼10% samples the terminal N position and presumably forms by recombination of N and O in the ion source). With precise calibration of the + 15 + + proportion of N in NO coming from each site, comparison of the δ NofN2O and NO permits one to calculate the position-specific N isotope fractionation through mass balance arguments. This measurement has been adopted by several laboratories and is arguably more fully developed as a tool of environmental geochemistry than any other position-specific isotopic measurement (e.g., Park et al. 2012). It is also the only such measurement that can be performed relatively quickly and precisely as a direct mass spectrometric analysis, with no preparatory stage of chemical or pyrolytic degradation. It also has both smaller sample sizes and shorter measurement times than NMR-based techniques. Finally, recent innovation has demonstrated that position-specific N isotope analysis of

N2O can be accomplished by infrared absorption spectroscopy (using instruments and techniques

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resembling those of increasingly common commercial devices for spectroscopic analysis of the

conventional stable isotope composition of H2O, CO2,andCH4) (Waechter et al. 2008). This innovation promises to lower the technical barriers to such measurement and will likely lead to even further expansion of its use in applied environmental geochemistry.

4. THE EMERGENCE OF HIGH-RESOLUTION ISOTOPE RATIO GAS SOURCE MASS SPECTROMETRY The preceding sections have treated multiple isotopic substitutions (“clumping”) and position- specific isotope effects as separate phenomena. This approach reflects the fact that analytical technologies used to date are generally suitable for measurements of either isotopic clumping or position-specific fractionations but not both. Nevertheless, this separation of clumped from position-specific isotope geochemistry is an artificial division that limits the scope of both fields. Most isotopic diversity in molecular structures involves multiply substituted isotopologues (e.g., of the 45 possible isotopologues of methane—considering species containing H, D, T, 12C, 13C, and/or 14C—40 are multiply substituted). And, for all but the simplest molecular structures, most of the “clumped” isotopic species also possess unique position-specific isotopic properties (e.g., 13 13 12 C-D clumping in propane can manifest as any of the five nonequivalent species: CDH2– CH2– 12 13 12 12 13 12 12 12 13 12 12 CH3, CH3– CHD– CH3, CH3– CH2– CH2D, CH3– CHD– CH3,or CDH2– 13 12 CH2– CH3). Many of the chemical and physical processes that drive clumped isotope fractionations simultaneously drive position-specific fractionations and vice versa. That is, if we could study all isotopic diversity in nature, most isotopic geochemistry would be both clumped and position specific. Researchers are developing an approach with the potential to explore the coupled clumped and position-specific isotopic compositions of volatile and semivolatile molecules: high-resolution gas source isotope ratio mass spectrometry. The first realization of this approach was a prototype mass spectrometer called the Thermo IRMS-253 Ultra (or Ultra). The Ultra is described in detail in Eiler et al. (2012, 2013); briefly, it is a normal-geometry, double-focusing sector mass spectrometer with an electron impact gas source, both dual-inlet and carrier gas sample inlets, and an array of moveable detectors, each of which can register ion currents using either a faraday cup or secondary electron multiplier. This instrument achieves mass resolution up to 27,000 (M/M, 5/95% definition)—sufficient for separating isobaric interferences from many contaminants (e.g., 13 H2Oon CH3D), isotopologues of the same compound that share a cardinal mass but differ 13 12 13 in isotopic content (e.g., CH3Dand CH2D2), and adducts or fragments (e.g., CH3Dand 13 CH4)(Figure 9). Because analytes are molecular ions, the association of rare isotopes with each other is preserved, enabling clumped isotope analysis. In addition, because molecular species Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org generate distinctive families of molecular and fragment ion populations, position-specific isotope effects can be reconstructed, much in the way mass spectrometry is currently used to compare the + + 15 isotopic composition of NO and N2O to constrain position-specific N abundance in nitrous oxide. Initial work on methane, ethane, propane, and N2O provides examples of these capabilities (Eiler et al. 2012, 2013; Magyar et al. 2012; Piasecki & Eiler 2012; Stolper et al. 2012). There are several obvious targets for analysis with the Ultra (or related instruments that may be built): The low-molecular-weight alkanes (up through hexane) have high vapor pressures and relatively well-understood fragmentation spectra that should permit reconstruction of position- specific isotope effects through isotopic analysis of fragment ions (e.g., distinguishing 13C substitution in the terminal versus central position of propane) (Piasecki & Eiler 2012). The isobaric interferences follow simple patterns and include a large number of species that can be resolved from neighbors at resolutions of 10,000–20,000 (e.g., in general, the 13C-substituted version of any

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10–1 16 OH2

10–3 13CH = 1) = Δ 5 + 4 M/ M ≈ 12,000 12 13 CH D –5 CH D 2 2 10 3 12 CH4D 17OH 16OD Δ 10–7 M/ M ≈ 6,000

13 Ion intensity (CH Ion intensity CHD 10–9 2

M/ΔM ≈ 600 10–11

18.01 18.02 18.03 18.04

Mass (amu) 12 CD3

Figure 9 Illustration of the mass resolution problems encountered in mass spectrometric analyses of hydrocarbons and their common contaminants; mass-18 isotopologues (and fragments and adducts) of methane and water are shown. Contaminants that differ in chemical stoichiometry from analytes can often be resolved at mass resolutions of 1,000 or less. Isotopic isobars generally require resolutions of several thousand (e.g., ∼6,000 is 13 12 required to separate the two doubly substituted species of methane, CH3Dand CH2D2). When one considers fragments and adducts, even greater resolutions may be required (e.g., 12,000 is required to 13 13 12 13 separate CH5 from CH3D; the triply deuterated fragment, CD3, is unresolvable from CH5). “Clean” separation of the major isotopic isobars requires mass resolutions (5/95% deﬁnition) up to 20,000–25,000 (depending on relative intensities). The calculated ion intensities assume natural isotopic abundances; random distributions among isotopologues; and commonly observed proportions of fragments, adducts, and background water.

species can be resolved from deuterated or H-adduct species of the same cardinal mass). Further- more, the geochemistry of natural gases, biogeochemistry of reducing environments, and budgets and photochemical reactions of light alkanes all present well-deﬁned and important applications (e.g., geothermometry based on 13C-D clumping) (Stolper et al. 2012).

The isotopologues of N2O and SO2 include several species that can be mass resolved with the Ultra (or, presumably, other instruments of similar design) and should permit precise determination of singly substituted isotopic composition (i.e., δ15N, δ34S, δ18O, δ17O) as well as clumped Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org and/or (in the case of N2O) position-speciﬁc composition (Yoshida & Toyoda 2000, Magyar et al. 2012). Given the importance of biogeochemical and photochemical cycles of these species, a variety of useful new proxies will likely emerge from a study of previously unanalyzed isotopologues (e.g., 15N14N18Oand14N15N18O) (Magyar et al. 2012). Similarly, the clumped isotopologues of

O2,H2, and other simple molecular gases are generally analyzable with high precision and well resolved from relevant isobaric interferences. Additionally, the Ultra (or other similar instruments that may be built) could be used to study the isotopic anatomy of organic compounds other than alkanes (e.g., sugars, alcohols, lipids, hopanes). These species or their derivatives can be introduced into a Nier-type gas source through a carrier-gas inlet, and despite limited experience with their analysis on the Ultra, their known ion fragmentation patterns suggest they present a rich territory to explore position-speciﬁc and

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clumped isotope fractionations. Such measurements would complement existing NMR and pyrolysis techniques for measuring intramolecular isotopic distributions, possibly resulting in isotopic analyses with many independent compositional dimensions.

5. CONCLUSION: TOWARD THE SYSTEMATIC STUDY OF ISOTOPIC ANATOMIES OF NATURAL MOLECULAR STRUCTURES Recent advances in the analytical techniques of stable isotope geochemistry have added greatly to the number and complexity of isotopic properties that can be measured in natural compounds. Problems that for decades have been approached through relatively simple measurements of bulk isotopic composition (i.e., δ13CorδD values) can now be addressed through a combination of position-speciﬁc and clumped isotope analyses that have the potential to reveal a large fraction of the isotopic “anatomies” of molecular structures. The usefulness of isotopic clumping for

thermometry of CO2 and carbonate (Affek et al. 2007; Eiler 2007, 2011) and the insights position-specific isotopic data have provided into lipid and sugar biosynthesis (Monson & Hayes 1982a,b) suggest many useful tools for applied research in paleoclimate, environmental chemistry, and forensics will emerge from such work. For example, clumping of 13C and/or D in components of organic compounds may be able to record the temperatures of synthesis and/or storage of natural gases and oils (Stolper et al. 2012), the environmental conditions of plant growth, or the substrates and reaction pathways responsible for creating organic molecules of forensic interest. Conventional isotopic data commonly define low-dimensionality composition spaces (e.g., δ13C versus δD of natural gas or δ18O versus δD of waters), in which many questions cannot be answered without additional independent constraints. The emergence of position-specific and clumped isotope measurements creates the possibility of isotopic composition spaces that have a very large number of dimensions, possibly letting us retrieve enough information from a sample’s isotopic anatomy to constrain its forensic uniqueness, conditions of formation, or other properties of interest. A challenge will be to figure out how we can most efficiently navigate these large composition spaces, measuring only those properties that are most useful for our purposes. Another will be to describe or visually represent large composition spaces and the positions of samples within them. These are problems common to disciplines that study compositional diversity of biomolecules with great structural diversity—genes, proteins, and metabolites, which constitute a collection of disciplines sometimes referred to collectively as “omics” (e.g., Goodacre et al. 2004). An “omics” of isotopic geochemistry (“isotomics”?) is not upon us but is in sight. Several hurdles must be overcome before it is a reality: At present, gas source mass spectrometry provides the only known method for usefully precise measurements of multiply substituted isotopologues, which represent most of the Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org isotopic diversity of molecular structures. The first high-resolution instrument of this kind was just recently constructed, and the techniques for using it are still in the earliest stages of evolution. We know these instruments can precisely measure clumped isotope and position-specific compositions of gaseous n-alkanes (Eiler et al. 2012, 2013; Piasecki & Eiler 2012; Stolper et al. 2012), but much remains to be explored before it is possible to use these techniques on biomolecules and their derivatives. The full potential of these methods will not be realized until we solve the logistical problem of simultaneously studying materials using a combination of methods having complementary strengths: e.g., NMR (which seems uniquely well suited to position-specific analysis of low-volatility, abundant analytes) with gas source mass spectrometry (which is, at present, uniquely capable of analyzing multiply substituted isotopologues).

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It is imaginable that absorption spectroscopy will provide the preferred method for analysis of exceptionally rare, doubly deuterated, or triply substituted compounds. There are reasons to believe such methods could work, but even the first-order technical exploration of their limits remains to be done. It is not obvious how we will standardize many measurements of position-specific and, particularly, multiply substituted isotopic composition. Prior standardization of multiply substituted isotopologues has driven molecules to a known thermodynamic state of isotopic ordering. This likely cannot be done for many structurally complex organic molecules. The only real solutions for many compounds may be standard-additions experiments using mixtures of pure, labeled compounds—an arduous undertaking when one is interested in a large number of isotopic properties for each targeted analyte. Measurements of even a fraction of the unique singly and doubly substituted isotopologues of moderately complex molecules (e.g., hexanes) could result in data sets with dozens of isotopic dimensions. At present, no tools for visualizing such high-dimensionality isotopic composition spaces are known. The existing “omic” disciplines (genomics, metabolomics, proteomics) have their own solutions to these problems, but it is not clear how they can be translated to “isotomics,” where measurements not only show the presence or absence of a compositional dimension, but also define proportions of components with (sometimes) exceptional precision. Given the pace of recent developments in analytical techniques (NMR and high-resolution mass spectrometry), data sets of high complexity may be generated before researchers understand how they can be visually illustrated for convenient presentation and interpretation. Finally, historical precedence suggests that no emerging analytical capability grows to its full potential unless it meets a serious need in the applied sciences—solving a forensic dilemma, constraining a little-understood paleoclimatic property, recognizing a cryptic ancient metabolism. Clumped isotope geochemistry has emerged as a significant new field because it permits reconstruction of carbonate paleotemperatures in times and geographic locations that have been hard to address with other techniques. Mass independent isotope geochemistry has high impact because the early Solar System was characterized by highly distinctive O isotope variations and Earth’s Archean eon by distinctive sulfur isotope anomalies. What will measurements of isotopic anatomies of complex molecular structures teach us that may be so important as to demand the attention of a broad community of applied scientists? Recent work provides some possible suggestions—geothermometry of natural gases (Stolper et al. 2012), paleoclimate studies of ancient cellulose (Betson et al. 2006), or forensics of sugars (Gilbert et al. 2009)—but a real answer to this question still lies in the future. Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org

DISCLOSURE STATEMENT The author is not aware of any afﬁliations, memberships, funding, or ﬁnancial holdings that might be perceived as affecting the objectivity of this review.

ACKNOWLEDGMENTS This review beneﬁted from discussions with many current and former members of the Caltech laboratories for geochemistry, particularly Alex Sessions, Jess Adkins, Matthieu Clog, Daniel Stolper, Alison Piasecki, and Paul Magyar, and the engineering staff of Thermo’s Bremen mass

spectrometry group. Matthieu Clog performed the mass scan of CO2 illustrated in Figure 3 of

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this paper. Thanks also go to Nathaniel David for suggesting the term “isotomics” as a catch-all phrase describing the information content of molecular isotopic diversity. This work beneﬁted from funding from the National Science Foundation, Caltech, and Petrobras.

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Annual Review of Earth and Planetary Sciences Volume 41, 2013 Contents

On Escalation Geerat J. Vermeij pppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp1 The Meaning of Stromatolites Tanja Bosak, Andrew H. Knoll, and Alexander P. Petroff ppppppppppppppppppppppppppppppppp21 The Anthropocene William F. Ruddiman pppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp45 Global Cooling by Grassland Soils of the Geological Past and Near Future Gregory J. Retallack pppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp69 Psychrophiles Khawar S. Siddiqui, Timothy J. Williams, David Wilkins, Sheree Yau, Michelle A. Allen, Mark V. Brown, Federico M. Lauro, and Ricardo Cavicchioli pppppp87 Initiation and Evolution of Plate Tectonics on Earth: Theories and Observations Jun Korenaga ppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp117 Experimental Dynamos and the Dynamics of Planetary Cores Peter Olson pppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp153 Extracting Earth’s Elastic Wave Response from Noise Measurements Roel Snieder and Eric Larose ppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp183 Miller-Urey and Beyond: What Have We Learned About Prebiotic Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org Organic Synthesis Reactions in the Past 60 Years? Thomas M. McCollom pppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp207 The Science of Geoengineering Ken Caldeira, Govindasamy Bala, and Long Cao ppppppppppppppppppppppppppppppppppppppppp231 Shock Events in the Solar System: The Message from Minerals in Terrestrial Planets and Asteroids Philippe Gillet and Ahmed El Goresy pppppppppppppppppppppppppppppppppppppppppppppppppppppp257 The Fossil Record of Plant-Insect Dynamics Conrad C. Labandeira and Ellen D. Currano pppppppppppppppppppppppppppppppppppppppppppp287

viii EA41-FrontMatter ARI 7 May 2013 7:19

The Betic-Rif Arc and Its Orogenic Hinterland: A Review John P. Platt, Whitney M. Behr, Katherine Johanesen, and Jason R. Williams ppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp313 Assessing the Use of Archaeal Lipids as Marine Environmental Proxies Ann Pearson and Anitra E. Ingalls pppppppppppppppppppppppppppppppppppppppppppppppppppppppp359 Heat Flow, Heat Generation, and the Thermal State of the Lithosphere Kevin P. Furlong and David S. Chapman pppppppppppppppppppppppppppppppppppppppppppppppp385 The Isotopic Anatomies of Molecules and Minerals John M. Eiler ppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp411 The Behavior of the Lithosphere on Seismic to Geologic Timescales A.B. Watts, S.J. Zhong, and J. Hunter ppppppppppppppppppppppppppppppppppppppppppppppppppp443 The Formation and Dynamics of Super-Earth Planets Nader Haghighipour ppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp469 Kimberlite Volcanism R.S.J. Sparks pppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp497 Differentiated Planetesimals and the Parent Bodies of Chondrites Benjamin P. Weiss and Linda T. Elkins-Tanton ppppppppppppppppppppppppppppppppppppppppp529 Splendid and Seldom Isolated: The Paleobiogeography of Patagonia Peter Wilf, N. Rubén Cúneo, Ignacio H. Escapa, Diego Pol, and Michael O. Woodburne pppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp561 Electrical Conductivity of Mantle Minerals: Role of Water in Conductivity Anomalies Takashi Yoshino and Tomoo Katsura pppppppppppppppppppppppppppppppppppppppppppppppppppppp605 The Late Paleozoic Ice Age: An Evolving Paradigm Isabel P. Montañez and Christopher J. Poulsen ppppppppppppppppppppppppppppppppppppppppppp629 Composition and State of the Core Kei Hirose, Stéphane Labrosse, and John Hernlund pppppppppppppppppppppppppppppppppppppp657 Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org Enceladus: An Active Ice World in the Saturn System John R. Spencer and Francis Nimmo pppppppppppppppppppppppppppppppppppppppppppppppppppppp693 Earth’s Background Free Oscillations Kiwamu Nishida pppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp719 Global Warming and Neotropical Rainforests: A Historical Perspective Carlos Jaramillo and Andrés Cárdenas pppppppppppppppppppppppppppppppppppppppppppppppppppp741 The Scotia Arc: Genesis, Evolution, Global Significance Ian W.D. Dalziel, Lawrence A. Lawver, Ian O. Norton, and Lisa M. Gahagan pppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp767

Contents ix Annual Reviews It’s about time. Your time. It’s time well spent.

New From Annual Reviews: Annual Review of Statistics and Its Application Volume 1 • Online January 2014 • http://statistics.annualreviews.org Editor: Stephen E. Fienberg, Carnegie Mellon University Associate Editors: Nancy Reid, University of Toronto Stephen M. Stigler, University of Chicago The Annual Review of Statistics and Its Application aims to inform statisticians and quantitative methodologists, as well as all scientists and users of statistics about major methodological advances and the computational tools that allow for their implementation. It will include developments in the field of statistics, including theoretical statistical underpinnings of new methodology, as well as developments in specific application domains such as biostatistics and bioinformatics, economics, machine learning, psychology, sociology, and aspects of the physical sciences. Complimentary online access to the first volume will be available until January 2015.

table of contents: • What Is Statistics? Stephen E. Fienberg • High-Dimensional Statistics with a View Toward Applications • A Systematic Statistical Approach to Evaluating Evidence in Biology, Peter Bühlmann, Markus Kalisch, Lukas Meier from Observational Studies, David Madigan, Paul E. Stang, • Next-Generation Statistical Genetics: Modeling, Penalization, Jesse A. Berlin, Martijn Schuemie, J. Marc Overhage, and Optimization in High-Dimensional Data, Kenneth Lange, Marc A. Suchard, Bill Dumouchel, Abraham G. Hartzema, Jeanette C. Papp, Janet S. Sinsheimer, Eric M. Sobel Patrick B. Ryan • Breaking Bad: Two Decades of Life-Course Data Analysis • The Role of Statistics in the Discovery of a Higgs Boson, in Criminology, Developmental Psychology, and Beyond, David A. van Dyk Elena A. Erosheva, Ross L. Matsueda, Donatello Telesca • Brain Imaging Analysis, F. DuBois Bowman • Event History Analysis, Niels Keiding • Statistics and Climate, Peter Guttorp • Statistical Evaluation of Forensic DNA Profile Evidence, • Climate Simulators and Climate Projections, Christopher D. Steele, David J. Balding Jonathan Rougier, Michael Goldstein • Using League Table Rankings in Public Policy Formation: • Probabilistic Forecasting, Tilmann Gneiting, Statistical Issues, Harvey Goldstein Matthias Katzfuss • Statistical Ecology, Ruth King • Bayesian Computational Tools, Christian P. Robert • Estimating the Number of Species in Microbial Diversity Access provided by California Institute of Technology on 01/20/15. For personal use only. Annu. Rev. Earth Planet. Sci. 2013.41:411-441. Downloaded from www.annualreviews.org • Bayesian Computation Via Markov Chain Monte Carlo, Studies, John Bunge, Amy Willis, Fiona Walsh Radu V. Craiu, Jeffrey S. Rosenthal • Dynamic Treatment Regimes, Bibhas Chakraborty, • Build, Compute, Critique, Repeat: Data Analysis with Latent Susan A. Murphy Variable Models, David M. Blei • Statistics and Related Topics in Single-Molecule Biophysics, • Structured Regularizers for High-Dimensional Problems: Hong Qian, S.C. Kou Statistical and Computational Issues, Martin J. Wainwright • Statistics and Quantitative Risk Management for Banking and Insurance, Paul Embrechts, Marius Hofert

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