Chem 781 Part 9

Relaxation and Dynamics, and advanced methods

• NOE is a relaxation phenomenon• Measure of dipolar interaction between two

spins• NOEs can not be observed between two

equivalent nuclei.• Direct measurement of relaxation time allows

for measurement of dipolar coupling between equivalent spins

Measurement of longitudinal relaxation time T1

180 90x

T Acquisition

180 90x

T Acquisition

z

y

1 8 0 x

z

y

T

z

y

9 0

z

y

x

z

y

9 0

Inversion recoveryThe experiment is repeated with values of T between 0 and 5 T1

Relaxation of longitudinal magnetization

By definition, longitudinal relaxation is the recovery of z magnetization towards equilibrium. For two spins IA and IB coupled by dipolar coupling it is

dIzA/dt = (2 W1

A + W0 +W2) (I0A – Iz

A) + (W2-W0) (I0B – Iz

B)

If IA ≠ IB (for example 13C-1H) and we decouple IB (1H), then longitudinal relaxation depends only on the first term and Iz

B = constant = 0 throughout the experiment. As already mentioned in part one of the lecture we get an mono exponential recovery of z-magnetization:

The above equation assumes Mz(0) = 0 (90° pulse or saturation). The second term in 9.1 only influences the equilibrium value M0 by accounting for the NOE.

9.1

T1 recovery curve

Mz(T) = Mz0 [1-2 exp(-T/T1)]

Obtain T1 by fitting recovery curve to exponential equation with Mz(0) = - Mz0 :

Longitudinal Relaxation by dipolar coupling

Using the relations for W1, W0 and W2 used for NOE, one obtains for non-equivalent spins from 9.1:

1/T1A =  (2W1

A + W0AB + W2) = 1/10D2

AB[J(ωA-ωB) + 3J(ωA) + 6J(ωA+ωB)]

(heteronuclear)

For equivalent spins (IA = IB) one obtains from 9.1 with IzB = Iz

A

1/T1A = (2W1

A+2W2AB) = 3/10 D2

AB [J(ωA) + 4J(2ωA)] (homonuclear)

The expressions depend both on the dipolar coupling and the motion of the molecule:

• DAB = (γAγB ℏ2)/rAB3

contains the distance information

• Contains the motion of the moleculeJ c

c

( )

1 2 2

Longitudinal relaxation (T1) and distance

• To measure distance using T1 we need to know motion

• One could try to measure motion (τc) independently, but that is typically not easily possible

• Relaxation will be most efficient when .

• This point can be often obtained by changing the temperature and finding the minimum T1 (the correlation time will depend on temperature)

• T1(min) only depends on the distance and the field:

τC = 2 / 5 /ω0 τC = 2 / 5 /ω0

1/T1min = 615/910 2 / 5 γA

4 4/(ω0 r6AB)1/T1

min = 615/910 2 / 5 γA4 4/(ω0 r6

AB)

Example: Dihydride vs. dihydrogen complex

T1(min) of 0.23 s is only compatible with dihydride structure. However, the value can not be used to calculate the exact bond distance, since the equation assumed an isolated pair of protons. There are other protons around, and other relaxation mechanisms possible.

Schematic Spin-Lattice vs. Spin-Spin relaxation

s

s

Relaxation of x,y magnetization (transverse relaxation)

• Dephasing of x,y magnetization is caused by both random transitions between levels (longitudinal relaxation) AND incomplete averaging of orientation dependent shifts (dephasing by chemical exchange)

• That results in an additional J(0) term

• 1/T2A = 1/10D2

AB [4 J(0) + J(ωA-ωB) + 3J(ωA) + 6J(ωA+ωB)]

Spin-Lattice (Same as T1)Spin-spin

Fast tumbling averages dipolar coupling to zero

Measurement of T2

Spin echo experiment

Take a series of experiments and vary the number of 180⁰ pulses with refocusing delay (n). The intensity of the resulting spectrum will decay with T2 : Mx,y = exp(-2nτ/T2)

We need to separate the effects of inhomogeneity (reversible) from relaxation of x,y magnetization (irreversible):

90 180

τ τ n Acquisition τ : a few ms

90 180

τ τ n Acquisition τ : a few ms

T1 and T2 vs. correlation time

• For short correlation times (small molecules), T1 = T2

• For long correlation times,(large molecules), T2 is getting shorter and shorter=> Lines are getting broader as molecule gets larger

Relaxation Mechanisms

Relaxation can occur through many mechanisms:• While cross relaxation (and thus NOE) is solely determined by dipolar

coupling, other mechanisms can contribute additive to the overall longitudinal relaxation rate

• 1/T1total = 1/T1

dipol + 1/T1CSA + 1/T1

Quad + 1/T1SR + 1/T1

paramagnetic ...

• CSA: Chemical shift anisotropy Quad: Quadrupol coupling SR: Spin rotation

• For protons and C-H, N-H usually dipolar coupling is dominant, but for non protonated carbons or quadrupolar nuclei other relaxation mechanisms become important. In paramagnetic molecules, the electron-nucleus interaction is often dominant.

Relaxation by chemical shift anisotropy:

• Chemical shielding can depend on the orientation of the molecule with respect to the field. While in solution only an average isotropic shift is observed, the nucleus actually experiences an fluctuating local field.

• For axial symmetry the magnitude of the field fluctuation is given by the difference between the orientations with maximum and minimum shielding (σ∥ and σ⊥):

ΔB0CSA = 1/3 γ B0 (σ- σ )

1 2

1 5 11

202 2

02 2T

BC SA

c

c

( )||

Importance of CSA

• CSA is an important relaxation mechanism for tertiary C=O and C≡ groups as there are no protons nearby and the anisotropy of the shielding is particulary large.

• CSA is also important for heavy I = ½ nuclei (103Rh, 183W, ...) As they also exhibit large chemical shift ranges.

• Note the dependence on B02 for 1/T1

CSA. At higher fields this relaxation mechanism becomes more important. That is good news for metal NMR as repetition times are reduced, but may cause less than maximum NOE’s for C-H groups at very high field.

• Measurement of T1 at different fields allows to separate T1CSA from T1

DD and other relaxation

Relaxation from Quadrupol interaction

• This mechanism occurs only for I > ½ as those nuclei are not spherical but shaped like an ellipsoid

• In a non symmetric environment different orientations of the nucleus relative to the environment will have different energies

(interaction with electric field gradient).

• As this energy can be quite large (several MHz) it

is the dominant relaxation mechanism for all

I > ½ nuclei and results in often extremely

short relaxation times for these nuclei.

Consequences of quadrupolar relaxation

• I > ½ nuclei usually have very broad lines except when in very symmetric environments (octahedral or tetrahedral) and/or for nuclei with very small quadrupolar coupling constant (2D, 11B, 7Li)

• A very small repetition delay d1 (0.1s) and acquisition time (td = 4k) can be used in many cases

• almost never is NOE observed for any of those nuclei (7Li NMR is one exception)

• For neighboring nuclei the fast relaxation acts like decoupling (if 1/T1 > J) and couplings are often not observed: that is why we don’t see 14N-H coupling (14N > 99%). Only very large couplings or couplings to low QC nuclei is observed, or in case of a very symmetrical molecule like NH4

+. In some cases, neighboring coupling partners will appear broadened: one other reason why N-H protons might appear broadened

Other relaxation mechanisms

• Interaction with unpaired electrons (spin) will be discussed with NMR of paramagnetic compounds. Note that O2 is paramagnetic and best NOE results of small molecules require degassing of sample.

• Spin Rotation: currents induced by rotation of molecule, only important for very small molecules and in gas phase, sometimes methyl groups

Problem of measuring ultra large molecules

T2 relaxation time becomes shorter asMolecule becomes bigger

Increasing line width not only causes more overlap, but also at some point makes magnetization transfer impossible

Typically, different relaxation mechanisms are additive.

However, as the motions leading to different relaxation mechanisms are the same, the effects can sometimes cancel or subtract

Motions modulating the different mechanisms are not independent

1/T1total = 1/T1

dipol + 1/T1CSA + 1/T1

Quad + 1/T1SR + 1/T1

paramagnetic ...

• The different relaxation rates will only add up if the motions are independent for the different mechanisms

• Since often different interactions are modulated by the same motion, the different relaxation mechanisms are often not independent

• Cumulative effects of different relaxation mechanisms are not straightforward

Example: Dipolar- and CSA relaxation of N-15

Consequences of correlated relaxation

• Nitrogen N-Ha line will relax faster than the N-Hb line

• For large molecules, T2 for the N-Ha line will be shorter and the line will be broader, and the N-Hb line will be sharper

• At high enough magnetic field magnitude of CSA will equal dipolar coupling, and the two interactions will cancel for N-Hb line

n0N

Hb

Hb

• For a peptide N-H nitrogen, CSA and dipolar relaxation cancel for one doublet line, and add for the other

• In a regular N-15 decoupled HSQC the

broader line would still dominate the

linewidth of the spectrum

• Instead it is better to take an experiment

that observes only the sharp line and

discards the other.

• => Transverse Relaxation Optimized Spectroscopy (TROSY)

Small molecule example of TROSY:

5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 ppm

P- 31 NMR, no proton decouplingNa HPO in Ethylene Glycol / MeOD2 3

223 K

233 K

273 K

H -PO -

OO -

Use viscous solvent and low temperature to achieve short T2

2D TROSY selects

6 .46 .66 .87 .07 .27 .47 .6 p p m

Na HPO P- 31 T=298K 2 3

p p m

6 .26 .46 .66 .87 .07 .27 .47 .6 p p m6 .0

5 .5

5 .0

4 .5

4 .0

3 .5

3 .0

2 .5

2 .0

1 .5

1 .0

0 .51 31H { P} H SQ Cno decoupling in f1 and f2

1 31H { P} TR O SY

Large Molecule application of TROSY

Rubin group, UC Santa Cruz http://qb3.berkeley.edu/qb3/nmr/5.cfm

2D 1H-15N TROSY spectrum of a 35 kDa tumor suppressor protein at 900 MHz.

2D 1H-15N HSQC spectrum of the same 35 kDa tumor suppressor protein

NMR and dynamics

Relaxation and molecular dynamics

• If the magnitude of the interaction (i.e. distance) is known, the relaxation times can be used to probe for molecular motion

• Example 13C-H bonds: Due to its low natural abundance, and the r-6 dependence on the distance, relaxation of the 13C nucleus of a C-H group usually solely depends on dipolar relaxation to the directly attached hydrogen.

• As there are many data on C-H bond lengths, 13C relaxation measurements can be used to probe for molecular motion

• For small molecules the relaxation time is proportional to the correlation time::

1 1

61

2 2 2

6

2 2 2

6T r r DC H

C HC

C H

C H diff

Example aliphatic chains

• The above equation is valid for a rigid spherical molecule. In real molecules, fast internal rotation about single bonds will contribute to the diffusion coefficient, resulting in different correlation times for rigid and flexible parts of the molecule.

• Relaxation measurements thus can reveal internal rotations in the MHz range.

CH3

CH3

3.31.4 0.8 0.58 0.45

2.0 0.96 0.72 0.53

1.0

Anisotropic and internal rotation• Often the overall tumbling of the molecule is anisotropic, i.e. tumbling about

different axes takes place at different rates.

• Bistolane and the shown cobalt cluster complex are cigar shaped and the relaxation of the phenyl carbons depends on three diffusion coefficients: tumbling perpendicular to the main axis (D ), tumbling parallel to the main axis (D⊥ ∥) and internal rotation RPh. Quantitative analysis of such data can become very tedious:

where A = (3 cos2Θ-1)/4, B = 3 sin2Θ cos2Θ and C = (3 sin4Θ)/4 with Θ the angle between the C-H bond and the rotational axis.

For Cpara the C-H bond is part of the rotation axis for both internal rotation and D∥. Dipolar coupling for this for this group is thus only modulated by D⊥ which is considerably smaller and thus relaxation times for these carbons are much shorter.

Backbone dynamics of proteins

• Relaxation data reveal increased flexibility in the linker region.

• Also, the difference in correlation time of the two domains can be related to the slightly different sizes of the domains.

Calmodulin:

148 residuesMW: 16000gmol-1

2+binds 4 Ca

two globulardomains joined by a linker

1.0

1.5

2.0

2.5

R1

Residue number

5

10

15

R2

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

sec. structure

0.20.40.60.8

S2

6789

c/n

s

/s-1

/s -1

Dynamics from Lineshape• Relaxation is sensitive for dynamics in the scale of MHz

• Dynamics has an effect on the the line shape of a signal when interchange between two groups of different chemical shift becomes of the same order of magnitude as the chemical shift separation measured in Hz

• Typically 1 s-1 – 10-3 s-1

• Much faster interchange gives one average signal

• Much slower exchange gives two separate signals

Example N,N-dimethylformamide

• In the intermediate temperature range the two peaks will broaden with rising temperature, merge into one and then gradually sharpen to give one sharp signal.

• The temperature where the signal is at its broadest is called the coalescence point

• The rate at the coalescence point is given by

From: “Measuring Rates by NMR”, Hans Reich, http://www.chem.wisc.edu/areas/reich/nmr/08-tech-03-dnmr.htm

N

CH3

CH3O

H

kcoal = π/ 2 (νA-νB) = π/ 2 B0 ΔδABkcoal = π/ 2 (νA-νB) = π/ 2 B0 ΔδAB

Approximations to measure rates

• Finding the exact coalescence temperature is not always trivial or practical• At temperatures below the coalescence point (slow exchange limit) the line width can be

used to approximately determine kAB.

kAB = π Δνex (Slow exchange limit)

The exchange broadening Δνex is obtained from the line width by

subtracting the natural line width Δνex = Δνobs - Δν0

• at temperatures above the coalescence point:

kAB = π(νA-νB)2/(2Δνex) (Fast exchange limit)

Note the need to determine or at least estimate the chemical shift difference

Line shape analysis

• exchange can involve more than two species • Intermolecular exchange can involve species of different populations (equilibrium

constant KC)

• => the broadening pattern can become very complex and the above approximations will not be applicable.

• Full simulation of line shape possible with a computer to determine rate constants (line shape analysis) becomes necessary

• This allows the rate constant to be determined for multiple temperatures

(Ph P) Cu3 2

X1

2

H

N

N

CH3

CH3H

S3

41

5

(Ph P) Cu3 2

X1

2

H

N

N

CH3

CH3

H

S3

41

5

(Ph P) Cu3 2

X

k

k

k

kk

k

k

kk

k

A

A

B

B

C

C

Ir

Ir

Co

C oCo

C o

Cp

C pCp

C p

H

H

Cp

C p

CH

C H

*

*

3

3

Ir

Ir

Co

C oCo

C o

Cp

C pCp

C p

H

H

Cp

C p

CH

C H

*

*

3

3

Ir

Ir

Co

C oCo

C o

Cp

C pCp

C p

H

H

Cp

C pCH

C H *

*

3

3

Ir

Ir

Co

C oCo

C o

Cp

C pCp

C pH

H

Cp

C pCH

C H *

*

3

3

Ir

Ir

Co

C oCo

C o

Cp

C pCp

C p

H

H

Cp

C pCH

C H*

*

3

3

Ir

Ir

Co

C oCo

C o

Cp

C pCp

C pH

H

Cp

C pCH

C H*

*

3

3k

kCC'

C C '

BC

B CBC

B C

AB

A BAB

A B

AA'

A A '

T = 181 K

T = 210 K

T = 230 K

T = 250 K

T = 280 K

k = 750 sAB

-1

k = 3x10 sBC

5 -1

k = 34 sAB

-1

k = 1.8x10 sBC

4 -1

k = 3.0 sAB

-1

k = 1500 sBC

-1

k = 0.23 sAB

-1

k = 400 sBC

-1

k = 5x10 sAB

-1-3

k = 6.0 sBC

-1

Ir

Co Co

Cp

CpCp

H

*

CH3

Experimental simulated

Exchange and magnetization transfer

Chemical exchange which is slow on the chemical shift time scale can have a similar effect on NOE spectra as relaxation via W0 . In order to be effective two conditions have to be fulfilled:

• one has to observe two separate signals, which means kAB << ΔδAB

• the rate of exchange needs to be larger or at least not much slower than longitudinal relaxation rate

• The condition for magnetization transfer via exchange is

(νA-νB) > kAB > 1/T1

• Exchange too slow to give broadening still can still be probed by NMR using magnetization transfer. Usually that is the case for rate constants of the order 10 -2 s-1 - 10 s-1

1D Magnetization transfer

-25.4 ppm

14.9 ppm

Numerical best parameter fit

2D NOESY techniques:

Fitting NOE cross peak intensities

Rate constants and activation barriers

• Measuring the temperature dependence of rate constants yields activation barrier

• Eyring equation: kAB : rate constant of exchange

k : Boltzmann constant

• Typically a logarithmic plot is obtained:

• The accuracy in particular of ΔS≠

depends strongly on the temperature

range sampled.

kkT

heA B

G

R T

ln

in t

k h

kT

G

R

H

R T

S

RA B

slo p e ercep t

1

Sensitivity of NMR ExperimentsSignal/Noise N∙ ∙ ∼ Polarization ∙ μobserved ∙ induction ∙ T2

*/T1 ∙QProbe ∙ Efficiency

γB0/kT γ ∼ =

N: number of spinsS concentrationS isotope abundanceS tube diameterS length of coil

T22**: determines line width

Efficiency: how much of thetotal magnetitization can betransferred, loss due to T2

ns: number of accumulations

Q: Quality factor of probe - coil geometry - fill factor (Microprobe) - Cryogenic Probe

T11: determines repetitiontime

Polarization: Excess ofexcited spins in lower level γB0/kTμobserved depends on nature ofobserved isotope

induction: actual voltage induced in coil

• Higher magnetic field (20 T currently max.) $$$$• Reduce noise of electronics: cool detection circuit and preamplifier with cold

heluim gas (cryo probe) or nitrorogen gas (cryo probe Prodigy) $$• Concentrate sample and scale down dimension of probe ( micro probe)

Improving sensitivity: manipulate Boltzmann distribution

In some cases, coupling to higher energy levels (rotational, optical, electron spin) can be used to obtain highly improved population differences

• Dynamic Nuclear Polarization (DNP)• Chemically induced nuclear polarization (CIDNP)• Para hydrogen induced Nuclear Polarization

All methods are currently commercialized for more general use

Dihydrogen Gas is a mixture of two Spin Isomers

Singlet-Triplet conversion forbidden, and each isomer is stable in pure hydrogen gas

At room temperature: 75% orthohydrogen (expected from Boltzmann distribution)

At 77 K (Liq. N2): 50 % parahydrogen NOT expected by a simple splitting20 K > 99% parahydrogen of levels by J = 240 Hz

Singlet Para-hydrogen Triplet Ortho-hydrogen

-ab ba

S (singlet) I =0, m =0tot s

T (triplet) I =1tot

ms

aa

+1

+ab ba

0

bb

-1

J

Origin of the high energy differenceΨDihydrogen = ψtrans • ψvibr • ψrot • ψspin

The whole nuclear wave function needs to be considered

General Pauli Principle: The total wave function of spin ½ particles is always anti symmetric with respect

to exchange of two particles Ψ(1,2) = - Ψ(2,1)

• Translation only depends on center of gravity} Always Symmetrical

• Vibration only depends on absolute distance

• Rotation levels can be symmetrical for even quantum numbers 0,2,4,… (s,d,…) or anti symmetrical for odd quantum numbers 1,3,5,… (p,f, …)

• Singlet spin function is anti symmetric, triplet spin function is symmetric

• symmetric rotational function can only combine with anti symmetric spin function and vice versa

Population difference of spin states determined by Rotational states

S (singlet) I =0, ms=0tot

T (triplet) I =1tot

ms

+1

0

-1

J

S (singlet) I =0, ms=0tot

T (triplet) I =1tot

ms

+1

0

-1

J

S (singlet) I =0, ms=0tot

T (triplet) I =1tot

ms

+1

0

-1

J

Rotational StatesJ

0 (sym)

1(anti sym)

2 (sym)

Erot

Only combination of symmetrical rotational state and anti-symmetrical spin function OR anti symmetrical rotational state with symmetric spin function are allowed

• Population difference will be given by rotational energy, several orders of magnitude larger than magnetic interaction

• In absence of a catalyst, there will be no inter-conversion of triplet to singlet state

• Also, no transitions are allowed between S and T

Analogy to Hund’s rule:Two electrons in two degeneratre orbitals ϕ1 and ϕ2:

Two possible wave functions , one symmetric and one anti symmetric:

ΨS(1,2) = ϕ1(1) ϕ 2(2) + ϕ1(2) ϕ2(1) symmetric

ΨA(1,2) = ϕ1(1) ϕ 2(2) - ϕ1(2) ϕ2(1) anti-symmetric

• Energies of ΨA and ΨS will be different, with ΨA lower in energy due to electron repulsion

• As total wave function needs to be anti-symmetric, ΨA will only go with symmetric spin function, and Ψ S only with anti symmetric spin function

• Also note that if ϕ1= ϕ2 (two electrons in the same orbital), ΨA will be zero and only Ψ S will exist.

ΨS(1,2)

ΨA(1,2)

∆E determined by difference in electron wave function (coulomb e-- e- repulsion)

How does that help with NMR ?

To be useful for NMR, two conditions need to be met:

• conversion ortho – para needs to be fast to enrich para-H2 in reasonable time

• After enrichment, symmetry needs to be broken fast enough to observe transitions between former T to S states while maintaining polarization

Presence of metal catalysts to speed up para to ortho equilibrium

HH H M

H

H

Metalcatalyst

• Ortho and Para hydrogen usually do not interconvert

• Temporary breaking of H-H bond will allow equilibrium to be achieved

• Any metal that weakly binds hydrogen will do

• Frozen solutions of hydrogenation catalysts stored under hydrogen gas at liquid nitrogen temperature will do, for example inside NMR tube

Hydrogenation reaction breaks symmetry of dihydrogen molecule

B = 0J > 0

B > 0J > 0 A B =

re a c tio n o utsid e m a g ne t,slo w b re a k o f sym m e try

re a c tio n insid e m a g ne tfa st b re a k o f sym m e try

Kirill V. Kovtunov a, Vladimir V. Zhivonitko a, Lioubov Kiwi-Minsker b and Igor V. Koptyug *a

Chem. Commun., 2010, 46, 5764-5766

Paramagnetic Molecules

• Molecules with unpaired electrons have net electron spin• Electron paramagnetic resonance same principle as NMR

• Negative γ from negative charge results in -1/2 (anti parallel) state lower in energy

• Similar parameters: g- value and hyperfine

coupling (electron-nucleus scalar coupling)

B0

E

m = -s

1/2

ms = +1/2

EPR spectra typically displayed in dispersion mode

H2C(OCH3) radical

NMR and EPR complimentary

• EPR is possible if electron relaxation is slow enough.

• NMR is typically not possible in those molecules

• If electron relaxation is fast, EPR becomes difficult, but NMR spectra are observable

• Typically in bi-radicals or metal complexes

Example transition metal complexes

CpCo

CoCp

CoCpC

O

C

O

Lines typically broad and extremely shifted

Shift can be positive or negative

Cp2Co 19 electrons δ(H) = - 50.5 ppm

46 electrons δ(H) = - 30 ppm

Origin of extreme chemical shift

• Shift in paramagnetic complexes arises from scalar coupling to electron (contact shift)

• Coupling is extremely large (MHz), so the two lines will not be equally populated

• Slow electron relaxation will effectively wipe out signal (but EPR is possible)

• Fast electron relaxation will give average signal that is shifted towards the higher populated line

• Depending on sign of coupling constant shift is positive or negative

hyperfine coupling: several MHza

slow electron relaxation(10 s): signal too broad -7

to be observed

neglecting electron relaxation:----assuming equal population of electron and states

excess population in lower electron spin state

fast electron relaxation(10 -10 s):-9 -10

----assuming equal population of electron and states

excess population in lower electron spin state

Application: Shift Reagent

Metallo- Protein and Metal DNA complexes

Multinuclear NMR

100 200 300 400 500

1

10

100 1H

13C

3H

3He

15N

19F

29S

i

31P

57F

e

77S

e

89Y

103R

h10

7Ag

109A

g

111C

d11

3Cd

115S

n

117S

n11

9Sn

123T

e

125T

e

129X

e

169T

m

171Y

b

183W

187O

s

195P

t

199H

g

203T

l20

5Tl

207P

b

% A

bund

ance

frequency (11 T) / MHz

0.01 0.1 1 10 100

0

20

40

60

80

100 1H

13C

3H3He

15N

19F

29S

i

31P

57F

e 77S

e

89Y

103R

h

107A

g

109A

g

111C

d11

3Cd

115S

n 117S

n11

9Sn

123T

e 125T

e

129X

e

169T

m

171Y

b

183W

187O

s

195P

t

199H

g

203T

l20

5Tl

207P

b

I = 1/2

% a

bund

ance

rel. sensitivity

0 50 100 150 200

1

10

100

D6L

i

7Li

9Be

10B

11B14

N

17O

23N

a

25M

g

27A

l

33S

35C

l

37C

l

39K

43C

a

45S

c

47T

i

51V

53C

r

55M

n59

Co

63C

u

67Z

n

71G

a

75A

s

83K

r

87R

b

93N

b

95M

o105P

d

115I

n

121S

n127I

133C

s13

9La

141P

r

181T

a

187R

e

193I

r197

Au

209B

i

235U

1H

I > 1/2 nuclei

% a

bund

ance

frequency (11T)/ MHz

0.01 0.1 1 10 100

0

20

40

60

80

100

D6L

i

7Li

9Be

10B

11B

14N

17O

23N

a

25M

g

27A

l

33S

35C

l

37C

l

39K

43C

a

45S

c

47T

i

51V

53C

r

55M

n

59C

o

63C

u

67Z

n

71G

a

75A

s

83K

r

87R

b

93N

b

95M

o105P

d

115I

n

121S

n

127I

133C

s13

9La

141P

r

181T

a

187R

e

193I

r19

7Au

209B

i

235U

I > 1/2 nuclei

% a

bund

ance

relative sensitivity