Stable Isotopes – Terminology 1 2

Outline

Key questions to answer after this lecture: Stable Isotopes – Terminology 1) Definitions and terminology Roland A. Werner What is an isotope ? Institut für Agrarwissenschaften, ETH Zürich 2) Properties and isotope fractionation What properties differ between isotopic variants ? How does this influence reaction rates ?

3) Calculating and describing isotope fractionation How can I calculate and describe isotope fractionation ? What pitfalls and approximation should I be aware of ?

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Part 1 Definition Isotope

. Greek isos = "equal", tópos = "site, place" Isotopes occupy the same position in the periodic table of elements . Isotopes of an element have nuclei with the same number of protons (atomic number) but different numbers of neutrons . Therefore, isotopes have different masses and different nuclear properties

Mass number m Element Atomic number n E

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1 Definition Isotope Definition Isotope

. Same position in periodic table Atom Core Mass number . Same number of protons (atomic number) but 6- 6- Hull different numbers of neutrons 6+ 6+ . Therefore, isotopes have different masses (mass 6n 7n number) and different nuclear properties

6 protons and 6 protons and Atomic number 7 neutrons 6 neutrons 12 13 Atoms with a (higher) number of neutrons C C 13 6 6 C can be used (one or more) than protons for NMR Different atomic weight 6 protons

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Definition Isotope Definition Stable / Radioactive Isotope

Atom Core Stable isotope or radioactive isotope ? Mass number 6- 6- Hull If the ratio of protons to neutrons in the nuclide of an atom is unbalanced, the atom is instable and decays 6+ 6+ under emission of radiation. This phenomenon is 6n 7n called radioactivity or radioactive decay.

Protium Stable isotope Atomic number Calotte model Deuterium Stable isotope Electronic structure of an atom determines its chemical behaviour Nucleus is responsible for physical properties of the atom Tritium Radioactive isotope

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2 Chart of Nuclides 13C natural abundance: Rough calculation

Stable Isotopes

Monoisotopic Relative atomic mass in u element 12 13 p+: 1.007276466583 u n : 1.00866491588 u C C e- : 5.48579909070 x 10−4 u "Valley of nuclear 6 6 stability" 12C: 12 u per definition 12C: 12 u  ~ 98.9 % 13 C: 13.003355 u 13C: 13.003… u  ~ 1.1 %

12 u x 0.989 + 13.003… u x 0.011 = 12.011 u Data from wikipedia

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Average abundances of the stable isotopes Definition Isotopologue / Isotopomer

Element Isotope Atomic Mass [u] Abundance . Isotopologues are molecules that differ only in their isotopic Hydrogen 1H 1.007 825 0319(6) 99.98 85(70) composition: 2H 2.014 101 7779(6) 0.01 15 (70) 12C is used to define Carbon 12C 12 (exactly) 98.93(8) Different mass atomic mass units 13C 13.003 354 838(5) 1.07(8) . Isotopomers are molecules with the same number of each Nitrogen 14N 14.003 074 0074(18) 99.63 6(20) Heavier isotopes of isotopic atom but differing in their positions: 15N 15.000 108 973(12) 0.36 4(20) bioelements have lower natural abundance Oxygen 16O 15.994 914 6223(25) 99.75 7(16) 17O 16.999 131 50(22) 0.03 8(1) 17O, 33S, 36S interesting for specific 18O 17.999 160 4(9) 0.20 5(14) applications Same mass Sulfur 32S 31.972 070 73(15) 94.99(26) after NE Holden in Handbook of 33 S 32.971 458 54(15) 0.75(2) Chemistry and Physics 92nd Edition, 2011-2012 34S 33.967 866 87(14) 4.25(24) http://www.hbcpnetbase.com/ . What can we call all four isotopic variants of e.g N2O ? 36 S 35.967 080 88(25) 0.01(1) and Coplen et al. (2002) Isotopocules Toyoda et al. (2015): Mass Spectrom Rev DOI 10.1002/mas.21459

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3 Definition Isotopologue / Isotopomer Definition Isotopologue

Isotopologues: further examples How many isotopologues from water and 1 1 2 2 1 18 2 18 carbon dioxide are possible? H O, CO H2O, H HO, H2O, H2 O, H2 O … 2 2 Naturally occurring stable H- and O-isotopes:

1 2 16 17 18 Isotopomers: further examples H2O: H, H, O, O, O 12 13 13 12 With which masses ? CH3 CH2OH / CH3 CH2OH

Naturally occurring stable C- and O-isotopes:

12 13 16 17 18 CO2: C, C, O, O, O With which masses ?

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Definition Isotopologue Definition Clumped isotopic species How many isotopologues from water and Clumped isotopic species are very rare …

carbon dioxide are possible? H2O, CO2 Mass Isotope Abundance CO2

9 different H2O isotopologues There will be a 1 16 2 18 short introduction with mass from 18 ( H2 O) to mass 22 ( H2 O) in "clumped isotopes" on next Friday

12 different CO2 isotopologues starting from 12 16 13 18 Estimated by PhD thesis mass 44 ( C O2) to mass 49 ( C O2) Jesper Olson (2006), University of Aarhus, DK

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4 Definition Isotopomers Definition Isotopomers How many isotopomers are possible for How many isotopomers are possible for

water and methane? H2O, CH4 ? water and methane? H2O, CH4 ?

H2O: H2O: none No (chemical) differentiation possible between the two hydrogen atoms of the water molecule !

CH4: CH4: none ?

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Definition Isotopomers Definition Isotopomers

How many isotopomers are possible for CH ? Methylene -group 4 Ethanol H H 1H 2HC C1H O1H ? 2 2 Methyl 1 1 2 1 . Stable isotopes: 1H and 2H ? H C C OH H3C C H H O H -group Hydroxyl 1 1 2 H H H3C C H2 O H No Isotopomers -group Lewis structures of the constitutional isotopomers of EtOH . Including radioactive 3H ? A1H 2 H B 1 2 2 1 HS HR HS HR No Isotopomers ? 1 H C C O 1 H

H C OH H C OH . With four different substituents 1 H 1 H 3 3 • No mirror plane possible • R- and S-form possible Isotopomers Fischer projections of the stereo-isotopomers of EtOH No isotopomers for isotopic methane !!

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5 Part 1 Different properties of isotopes

For the detection of isotopes measurable differences in properties of isotopes (isotopologue molecules) are necessary.

• Nuclide-physical reactivity (radioactivity) • Nuclear magnetism (NMR) • Nuclear mass and volume  different spectra • Nuclear mass -> Density, Diffusion, different properties in gravity fields etc. Further-on we will concentrate on

Mass-dependent isotope effects

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Why is it interesting to measure “isotopes” ? Isotopologues - Different physical properties

. Isotopes of an element have the same number of protons and electrons and therefore same electronic structure

. The chemical behaviour of an atom is largely determined by its electronic structure, therefore different isotopes exhibit:

. Nearly identical chemical behaviour but …

. Can have different physical properties.

. Analogously, two molecules which differ only in the isotopic nature of their atoms (isotopocules) will have:

. Identical electronic structure, and therefore similar chemical properties. f . Can have different physical properties. gaer

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6 Isotopologues - Different physical properties Isotopologues - Different physical properties

. Differences in behaviour in a magnetic field between isotopic variants is the basis of isotope ratio mass spectrometry

. Most commonly used technique  Next Lecture !

1 2 m U r = B e

. I.e.: When all else is equal, the radius of deflection varies as the square root of the mass of the isotopologue.

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Molecular vibrations of a diatomic molecule Potential energy and internuclear distance

Molecule vibration = periodic motion of atoms in a molecule Analogy to a spring

Repulsion --> tension / relaxation Diatomic molecule as a simple example Both atoms are moving

Harmonic oscillator potential curve Diatomic molecules have one normal mode of vibration: X H

Stretching (and compressing) of the chemical bond r e X H n E X-2H

E Act

between the atoms (here O2) l Dissociation limit

Molecular motion: i

t 1

n Translation, rotation not influencing chemical EAct X- H

e t Attraction bonds to the same extent as vibration. o

O2 Non-harmonic oscillator potential curve

1 1 0(X- H) ZPE X- H Model Should be the other  2 ZPE X-2H 0(X- H) ZPE = energy at way. The heavier HCl one should vibrate 1 2 rX- H rX- H 0 K Vibrations of a methylene group (-CH2-) 3 atoms Correct scenario? less frequent?

https://en.wikipedia.org/wiki/Molecular_vibration#Vibrations_of_a_methylene_g Internuclear Distance https://en.wikipedia.org/wiki/Molecular_vi bration roup_(%E2%80%93CH2%E2%80%93)_in_a_molecule_for_illustration

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7 Different zero point and activation energy Isotopes and reaction rates

Summary: KIE: Transition State Reaction rate

Product • Bonds with heavier atoms have a lower vibration frequency than lighter ones. • Thus: More energy is needed to break the bonds of heavier isotopologues. ZPED(GS) Ground State • Thus: Heavier atoms/molecules react more J Bigeleisen (1965): Science AJ Bennet (2012): Curr Opin Struct 147:463-471 Biol 16:472-478 slowly than the lighter ones, because the bond strength is higher. • Increasing mass lowers vibration • Reaction coordinate describes • This results in lower turnover rates, causing frequency progress through the reaction isotope fractionations, e.g. during CO2 fixation • The heavier isotope has lower ZPE • Difference in ZPE between in C3-plants through RuBisCO • More energy needed for bond cleavage reactant and transition state or product describes isotope effect • Higher EAct and lower reaction rate k DZPEGS < DZPETS  normal KIE

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Definition Isotope effects Definition Isotope effects

Why is it interesting to measure “isotopes”? Kinetic isotope effect (KIE): Ratio of rate constants for the reaction involving light (Mass-dependent) isotope effects and heavy isotopologues

KIE = Lk/Hk

Equilibrium isotope effect (EIE): Ratio of the equilibrium constants for the reaction involving light and heavy isotopologues

EIE = LK/HK

https://goldbook.iupac.org/

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8 Kinetic isotope effect Kinetic isotope effect

. A kinetic isotope effect occurs when the rate of an • What will happen in case of 100 % or irreversible chemical reaction is sensitive to the atomic quantitative reaction ? mass: 12 13 13 13 ( k/ k)C-1 = 1.0093 0.9 % faster C of CO2 = C of C1 carbon atom of pyruvate

12 13 ( k/ k)C-2 = 1.0213 2.1 % faster • In case of a turnover of < 100 %? (12k/13k) = 1.0031 0.3 % faster 13 < 13 C-3 C of CO2 C of C1 carbon atom of pyruvate

Melzer & Schmidt (1987)

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Kinetic isotope effect Thermodynamic or equilibrium isotope effect

. Kinetic isotope fractionation occurs in … . When a system is in chemical or physical equilibrium . Unidirectional chemical/biological reactions an equilibrium isotope effect will cause the heavy . Unidirectional physical processes (evaporation, diffusion isotope to concentrate in the chemical compound in etc.) which the element is bound most strongly. . Open systems  products can "escape"

. A normal kinetic isotope effect favours the light isotope . Bonds break faster for the light isotope . The equilibrium isotope effect depends on rate constants. . However inverse kinetic 18 isotope effects occur: 4 % more O in CO . Electron effect 2 16 18 . Stabilised intermediates .  O concentrate in H2O and O in CO2. H-O-H O=C=O

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9 Equilibrium isotope effect Exercise: Isotopic equilibria in mineral water

Equilibrium (exchange) isotope fractionation occurs in … Consider a closed bottle of mineral water … . Which compounds are occurring ? . Chemical equilibria H2O and CO2, (residual air) . Phase changes in closed systems . Kinetic or equilibrium isotope fractionation ? . Isotope exchange reactions and biological reactions that are . Chemical bonding of molecules ? not rate limiting can approach chemical (& isotopic) equilibrium H-O-H O=C=O . Would depend on how exchange reaction equation is "written". . Which compound is more enriched in 18O ? Normally listed relative to «reference molecules» like e.g. H2O for 2H and 18O. Two cases: Within or between molecules ?

System: H2O <--> CO2 . The Keq can be > 1 (toward forming more product) or < 1 (toward forming more educt) and H2O(l) <--> H2O(g) ?? What happens when K = 1 ?? sparkling eq 18 CO2 is more enriched in O . The heavy isotopes concentrate in the most strongly bonded 16 Less energy needed to bring H2 O into the gas species 18 18 phase than H2 O H2O(l) is more enriched in O

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Kinetic vs. thermodynamic isotope fractionation Exercise: Isotopic equilibria in mineral water

1) 2) 12 k1 [ B] A B K12 = k eq 12 2 [ A] Reaction at equilibrium Equilibrium constant 3) 4) Isotope fractionation D k12 /k13 12 13 1 1 Deq = D(AB) – D(BA) Keq/Keq = 12 13 k2 /k2 Equil. Kinetic

Equilibrium isotope effect KIE on forward & back reaction

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10 Exercise: Isotopic equilibria in mineral water Exercise: Isotopic equilibria in mineral water Bottle of mineral water: Opening the bottle will lead to? Closed system  open system Equilibrium will be disturbed

In case [CO2]in > [CO2]out, CO2 will diffuse out. The diffusive CO2 is enriched or depleted in 18O and/or in 13C? Kinetic isotope fractionation dominates Build-up of a new equilibrium depends on a.o. availability of liquid water and carbon dioxide.

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Equilibrium perturbation by isotope substitution Equilibrium perturbation by isotope substitution

Chemical equilibrium vs. isotopic equilibrium Chemical equilibrium vs. isotopic equilibrium

+ + Malate-2-d + NADP <=> pyruvate + CO2 + NADPH Malate-2-d + NADP <=> pyruvate + CO2 + NADPH Malate artificially enriched in 2H ME catalysed by malic enzyme Malate artificially enriched in 2H ME catalysed by malic enzyme Equilibrium perturbed Question: Result: What happens after putting There is need for chemical all educts & products and and isotopic equilibrium: the enzyme together at The NADPH level first drops, Equilibrium equilibrium concentrations? the equilibrium is perturbed. Re-established (chemical equilibrium) After a while chemical and isotopic equilibrium is re- established. Equilibrium perturbation of NADPH level when malate-2-d and unlabeled NADPH are used with Isotope equilibration is really malic enzyme (Schimerlik et al., 1975) occurring ("chemical principle")

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11 Isotope fractionation d formula Delta Notation: “old” formula

R(Sample) - R(Standard) d [‰] = . 1000 R(Standard)

The d-notation was introduced by McKinney et al. (1950).

‘Unit’: [‰]Standard (‘per mill’) = per thousand deviation from a standard isotope ratio For example:

13 15 18 2 34 37 d CVPDB, d NAIR-N2, d OVSMOW, d HVSMOW, d SVCDT, d ClVSMOC

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Definition isotope fractionation factor a Definition a and e

Isotope fractionation factor a

Isotope enrichment factor e

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12 Definition isotope fractionation factor a Definition isotope fractionation factor a

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Definition isotope fractionation factor a Measures of isotope fractionation

"Big-Delta"

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13 Big Delta D Big Delta D

Irreversible reaction in an open system:

compounds R and P (e.g. CO2 and derived (plant) carbon): Why is it interesting to use D ?

R  P 13 Case: C fractionation during CO2 fixation by RubisCO

DR-P = dP – dR ≈ 1000 ln(aP/R) ≈ eP/R 1) Plants growing under different CO2 source and same environmental conditions aP/R = RP/RR = (dP + 1)/(dR + 1)

2) Plants growing under same CO source but different dP = aP/R * dR + eP/R often simplifies to dP = dR + eP/R 2 environmental conditions

In case of multi-isotope analysis  13D, 2D …

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Big Delta D Isotope fractionation in multi-step reactions

Different !!! After Schmidt et al. (2015) IEHS 51, 155-199

• Isotope effects (IE) are not always expressed as isotope fractionation (IF) • Metabolic branching is needed for measurable IF • The overall IF will depend only on the rate-limiting reaction step. See e.g. C towards E show no isotope fractionation, because they all proceed ap- proximately to completion.

• Question: CO2-Assimilation shows IF  where is the branching point ??

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14 d formula Isotope abundance Delta Notation: The abundance ratio of an isotope will be given as the mean natural isotope abundance in atom fraction (former atom-%). R(Sample) - R(Standard) d = Isotope effects on phase transitions (equilibrium IE) and on biochemical reactions (kinetic IE) will R(Standard) lead to temporal and spatial variations from the The d-notation was introduced by McKinney et al. (1950). mean natural isotope abundance. ‘Unit’: [‰] (‘per mill’) = per thousand deviation Standard Thermodynamic IE: Ratio of corresponding from a standard isotope ratio equilibrium constants of isotopologues. For example:

13 15 18 2 34 37 Kinetic IE: Ratio of corresponding rate constants d CVPDB, d NAIR-N2, d OVSMOW, d HVSMOW, d SVCDT, d ClVSMOC of isotopologues. Equilibrium IE = Thermodynamic IE

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Isotope abundance d formula Atom fraction x (former atom-%). Delta Notation: “old” formula According to the 8th SI brochure (BIPM, 2006) the term 'atom-%' now is deprecated. R - R (Sample) (Standard) . 13 d [‰] = 1000 n( C)S R atom fraction x(13C) = (Standard) S 12 13 n(13C) = amount of 13C in substance S n( C)S + n( C)S S The d-notation was introduced by McKinney et al. (1950). ‘Unit’: [‰] (‘per mill’) = per thousand deviation Calculation of atom fraction x numbers from d-values Standard from a standard isotope ratio 1 x(13C) = For example: S 1 1 + d13C , d15N , d18O , d2H , d34S , d37Cl 13 VPDB AIR-N2 VSMOW VSMOW VCDT VSMOC ( d CS/VPDB + 1) * RVPDB

13 12 RVPDB = C/ C ratio of VPDB standard. See also Coplen (2011)

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15 d-Notation II d-Notation III

R(Sample) - R(Standard) Definition d d = This isotope d is a dimensionless quantity; R(Standard) following that d is according to the SI rules a "quantity of dimension one" with the unit Meanwhile: The extraneous factor 1000 in the symbol "1". That might be also the reason for „old“ d-formula does not fit to SI (Système not allowing anymore the factor 1000. International d’Unités) rules. The above listed formula should be used instead. The corresponding d-values can be either listed in "Milli-1" for per mill or "micro-1" for per meg really sounds odd the familiar [‰]Standard-scale or be given e.g. as 103 d18O.

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d-Notation IV Calculating with d-values

Brand and Coplen (2012): 1.250 Range of natural 1.200 "A proposal to replace the single-magnitude variation for 13C is: 1.150 ‰-'unit' with an expression fitting the SI 0.98 to 1.15 % 1.100 system" (Rosman & Taylor 1.050 (1998) mUr (milli Urey) instead of ‰ (per mill) 1.000

C Atom fraction [%] [%] fraction Atom C 0.950 13 0.900 In recognition of Harold C. Urey (1934 nobel -120 -70 -20 30 80 13 prize in chemistry for his discovery of the 2H d C [‰]V-PDB isotope 'Deuterium'). mUr Calculating with d-values: Minimum d-value of -1000 ‰ means

WA Brand & TB Coplen (2012): Isotopes in Environmental and Health Studies no heavier isotope available. Maximum d-value is ∞. 48, 393-409

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16 Isotope jargon Ranges of kinetic isotope effects

Depleted in 13C 1.250 Enriched in 13C ("lighter") 1.200 ("heavier") 1.150 d13C is more 1.100 d13C is more negative than 1.050 positive than that of the 1.000 that of the standard 0.950 standard

C Atom fraction [%] [%] fraction Atom C 0.900 13 -120 -20 80 13 d C [‰]V-PDB

For carbon isotope ratio measurements the standard is VPDB (Vienna PeeDee Belemnite) with an accepted 13C/12C of 11180.2 x 10-6. The standard itself is not (no longer) existing, but reference materials can be bought from IAEA Calculated range given above more or less realistic

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