chem 430 nmr spectroscopy chapter 5

NMR Spectroscopy

CHEM 430Fall

2011

SPIN-LATTICE AND SPIN-SPIN RELAXATION

• Remember that spin– lattice, or longitudinal, relaxation returns the system to equilibrium along the z axis, with time constant T1 and rate constant R1 = (1/T1)

• T1 relaxation occurs because of the presence of natural magnetic fields in the sample that fluctuate at the Larmor frequency--excess spin energy can flow into the molecular surroundings or lattice,

• Causes of Relaxation. The major source of these magnetic fields is magnetic nuclei in motion or the process of dipole– dipole relaxation [ T1( DD)],

• It involves the interaction of the resonating nuclear magnetic dipole with the dipole of the nucleus in motion that causes the fluctuating field of the lattice.

NMR – Advanced 1-D Techniques 5-1

CHEM 430 – NMR Spectroscopy

2


• The resulting relaxation time depends on • The number of nearby nuclei - n• Nuclear properties of both resonating and moving nuclei, g• Distance between them, r-6

• Rate of motion of the moving nucleus tc

• Mathematically for 13C relaxed by protons:

• Mathematically for protons relaxed by protons:



3


• 13C relaxation is faster when • There are more attached protons• The internuclear distance C—H is less• When rotation in solution decreases

• Quaternary 13C has a long relaxation time because it lacks an attached proton and because the distance rCH to other protons is large.

• The ratio of the 13C relaxation time of CH to CH2 to CH3 is 6: 3: 2 (1: ½ : ), ⅓

• Because the rate of molecular tumbling in solution slows as molecular size increases, larger molecules relax more rapidly.

• Thus, cholesteryl chloride relaxes more rapidly than phenan-threne, which relaxes more rapidly than benzene.



4


• The previous equations are an approximation to a more complete equation and represents what is called the extreme narrowing limit for smaller molecules.

• Because the frequency of motion of the moving nuclear magnet must match the resonance frequency of the excited nuclear magnet, dipolar relaxation becomes ineffective for both rapidly moving small molecules and slowly moving large molecules.

• Many molecules of interest to biochemists fall into the latter category,

• Similarly rapid internal rotation of methyl groups in small molecules also can reduce the effectiveness of dipole– dipole relaxation.

• The optimal correlation times tc for dipolar relaxation lie in the range of 10-7 to 10-11 s (inverse of the resonance frequency).



5


• When dipolar relaxation is slow, other mechanisms of relaxation become important. Fluctuating magnetic fields also can arise from:1. Interruption of the motion of rapidly tumbling small molecules or

rapidly rotating groups within a molecule ( spin rotation relaxation), 2. Tumbling of molecules with anisotropic chemical shielding at high fields3. Scalar coupling constants that fluctuate through chemical exchange or

through quadrupolar interactions4. Tumbling of paramagnetic molecules (unpaired electrons have very large

magnetic dipoles)5. Tumbling of quadrupolar nuclei

• In the absence of quadrupolar nuclei or paramagnetic species, these alternative mechanisms often are unimportant.



6


Measurement of Relaxation Time. • The actual value of T1 must be known at least approximately in order to

decide how long to wait between pulses for the system to return to equilibrium (the delay time).

• In addition, T1( DD) offers both structural information, from dependence on rCH, and dynamic information, from dependence on tc.

• For these reasons, a convenient method has been developed for measuring T1: inversion recovery.

• Remember we have covered this before when we introduced T1 and T2



7

2


Measurement of Relaxation Time.

Intensity measured at a series of times t follows first order decay kinetics:



8

2


Measurement of Relaxation Time.



9

As ipso-C to chlorine has no directly attached proton relaxation for C- 1 is not complete even by 80 s!


Structural Ramifications. • Proton spin– lattice relaxation times depend on the distance between the

resonating nucleus and the nearest- neighbor protons.

• The closer the neighbors are, the faster is the relaxation - shorter T1.

• The two isomers (anomers) below may be distinguished by their proton relaxation times:



10

H1 is ax and close to the 3 and 5 ax protons, T1 of 2.0 s

H1 is eq with more distant neighbors: T1 of 4.1 s.


Anisotropic Motion. • When a molecule is rigid and rotates equally in any direction (isotropically),

all the carbon relaxation times (after adjustment for the number of attached protons) should be nearly the same.

• The non-spherical shape of a molecule, however, frequently leads to preferential rotation in solution around one or more axes (anisotropic rotation).

Example: toluene rotates around the long axis so that less mass is in motion. On average, these carbons (and their attached protons) move less in solution than the ortho and meta carbons, because atoms on the axis of rotation remain stationary during rotation.



11


Segmental Motion. • When molecules are not rigid, the more rapidly moving pieces relax more

slowly because their tc is shorter.

• Example: In decane the methyl carbon relaxes most slowly, followed by the ethyl carbon, and so on, to the fifth carbon in the middle of the chain.

• The structure gives the values of nT1 (n = # of attached protons), So these values reflect the relative rates of motion of each carbon with the attached protons normalized out:

NMR – Advanced 1-D

Techniques5-1


12


Partially Relaxed Spectra. • The inversion recovery experiment used to measure T1 also may be exploited

to simplify spectra: In the inversion recovery example the spectrum for t = 40 s lacks the ipso carbon resonance

• Such partially relaxed spectra can be used not only to obtain partial spectra in this fashion but also to eliminate specific peaks.

• When D2O is used as the solvent, the residual HOD peak is undesirable. An inversion recovery experiment can reveal the value of for which the water peak is nulled.

• Solvent suppression: Apply the 180° pulse selectively only at the resonance position of water. Selection of t for nulling of this peak then produces a spectrum that lacks the water peak but otherwise is quite normal for the remaining resonances.


Techniques5-1


13


Partially Relaxed Spectra – Solvent Suppression


Techniques5-1


14

HOD

2mM Sucrose in H2O:D2O 9:1


Quadrupolar Relaxation. • The dominant mode of spin– lattice relaxation for nuclei with spins greater than

½ results from the quadrupolar nature of such nuclei.

• These nuclei are considered to have an ellipsoidal rather than a spherical shape. When I = 1, as for 14N or 2H, there are three stable orientations in the magnetic field: parallel, orthogonal, and antiparallel:

• When these ellipsoidal nuclei tumble in solution within an unsymmetrical electron cloud of the molecule, they produce a fluctuating electric field that can bring about relaxation.


Techniques5-1


15


Quadrupolar Relaxation. • The mechanism is different from dipole–dipole relaxation in two ways.

1. It does not require a second nucleus in motion; the quadrupolar nucleus creates its own fluctuating field by moving in the unsymmetrical electron cloud.

2. Because the mechanism is extremely effective when the quadrupole moment of the nucleus is large, T1 can become very short ( < milliseconds).

• By the uncertainty principle the product of DE and t must remain constant: (DE·t ~ h) when the relaxation time is very short, the linewidth becomes very ∴large.

• Nuclei with large quadrupole moments often exhibit very large linewidths— for example, about 20,000 Hz for the 35Cl resonance of CCl4.


Techniques5-1


16


Quadrupolar Relaxation. • The common nuclides 17O and 14N have smaller quadrupolar moments and

exhibit sharper resonances, typically tens of hertz.

• The linewidth also depends on the symmetry of the molecule, which controls how unsymmetrical the electron cloud is. Systems with p electrons are more unsymmetrical and give broader lines


Techniques5-1


17

REACTIONS ON THE NMR TIME SCALE

• NMR is an excellent tool for following the kinetics of an irreversible reaction traditionally through the disappearance or appearance of peaks over periods of minutes to hours.

• The spectrum is recorded repeatedly at specific intervals, and rate constants are calculated from changes in peak intensities.

• Thus, the procedure is a classical kinetic method, performed on the laboratory time scale.

• The molecular changes take place on a time scale much longer than the pulse or acquisition times of the NMR experiment.


Techniques5-2


18


• More importantly, NMR has the unique capability for study of the kinetics of reactions that occur at equilibrium and that affect line shapes:

• EA in the range from 4.5 to 25 kcal·mol-1

• Rates in the range from 100 to 104 s-1.

• This NMR time scale refers to the rough equivalence of the reaction rate in s-1 to the frequency spacing in Hz

• Remember the study of axial and equatorial protons in cyclohexane-d11 as a function of temperature:• When interchange of two such chemical

environments occurs faster than the frequency differences between the two sites, the result is a single peak

• When the interchange is slower than the frequency differences, the NMR result is two distinct peaks


Techniques5-2


19


Hindered Rotation. • Normally, rotation around single bonds has a barrier below 5 kcal·mol-1 -

faster than the NMR time scale.

• Rotation around the double bond of alkenes, on the other hand, has a barrier that is normally above 50 kcal·mol-1 and is slow on the NMR time scale.

• There are numerous examples of intermediate bond orders, whose rotation occurs within the NMR time scale. Hindered rotation about the bond in amides such as N,N-dimethylformamide provides a classic example of site exchange:• RT - exchange is slow and two CH3 resonances are observed,

• > 100° C, exchange is fast and a single resonance is observed. • Measured barrier is about 22 5 kcal·mol-1 .


Techniques5-2


20


Hindered Rotation. • Hindered rotation occurs on the NMR time scale for numerous other

systems with partial double bonds, including carbamates, thioamides, enamines, nitrosamines, alkyl nitrites, diazoketones, aminoboranes, and aromatic aldehydes.

• Formal double bonds can exhibit free rotation when alternative resonance structures suggest partial single bonding.

• Calicene has a barrier to rotation about the central bond of 20 kcal·mol-1:


Techniques5-2


21


Hindered Rotation. • Steric congestion can raise the barrier about a single bond enough to bring

it into the NMR range.

• Rotation about the single bond in the biphenyl shown is raised to a measurable 13 kcal·mol-1 by the presence of the ortho- substituents, which also provide diastereotopic methylene protons as the dynamic probe:


Techniques5-2


22


Hindered Rotation. • Hindered rotation about an s–bond can sometimes be observed when at

least one of the carbons is quaternary.

• Example: At – 150 °C the tert-butyl group in tert-butylcyclopentane gives two resonances in the ratio of 2: 1, since two of the methyl groups are different from the third C :


Techniques5-2


23


Hindered Rotation. • Hindered rotation has frequently been observed in halogenated alkanes.

• The barrier probably arises from a combination of steric and electrostatic interactions. 2,2,3,3-Tetrachlorobutane at - 40° C exhibits a 2: 1 doublet below from anti and gauche rotamers that are rotating slowly on the NMR time scale.:

• When both atoms about a s-bond possess lone electron pairs, the barrier often (due to electrostatic interactions or repulsions) is often observable; for example the S—S bond in dibenzyl disulfide 7 kcal·mol-1 .


Techniques5-2


24


Ring Reversal. • Axial-equatorial interconversion through ring reversal has been studied in

a wide variety of systems in addition to cyclohexane:

• 8-membered rings such as cyclooctane have been examined extensively; The d15-derivative exhibits dynamic behavior below - 100° C, with an EA of 7.7 kcal·mol-1.

• Cyclooctatetraene undergoes a boat–boat ring reversal. side chain methyl groups provide the diastereotopic probe to estimate the barrier of 14.7 kcal·mol-1.


Techniques5-2


25


Atomic Inversion. • Trisubstituted atoms with a lone pair, such as amines, may undergo the

process of pyramidal atomic inversion on the NMR time scale.

• The resonances of the two methyls in the aziridine become equivalent at elevated temperatures through rapid N-inversion.

• The high barrier of 18 kcal·mol-1 is due to angle strain in the three- membered ring, which is higher in the transition state

• The effect is observed to a lesser extent in azetidines (9 kcal·mol-1) and in strained bicyclic systems (10 kcal·mol-1).


Techniques5-2


26


Atomic Inversion. • The inversion barrier may be raised when nitrogen is attached to highly

electronegative elements.

• This substitution increases the s character of the ground- state lone pair. Since the transition- state lone pair must remain p- hybridized, the barrier is higher, as in N- chloropyrrolidine:

• When neither ring strain nor electronegative substituents are present, barriers are lower, as in N- methylazacycloheptane 7 kcal·mol-1


Techniques5-2


27


Atomic Inversion. • Inversion barriers for elements in lower rows of the periodic table

generally are above the NMR range: chiral phosphines and sulfoxides are isolable.

• Barriers must be brought into the observable NMR range by substitution with electropositive elements, as in diphosphine CH3(C6H5)P—P(C6H5)CH3, with a barrier of 26 kcal·mol- 1

• The barrier in phosphole is lowered because the transition state is aromatic. Compare its barrier of 16 kcal·mol- 1 to 36 kcal·mol- 1 in a saturated analogue:


Techniques5-2


28


Valence Tautomerizations and Bond Shifts. • The barriers to many valence tautomerizations fall into the NMR range.

• A classic example is the Cope rearrangement of 3,4- homotropilidine, at low temperatures, the spectrum has the features expected for the five functionally distinct types of protons (disregarding diastereotopic differ-ences).

• At higher temperatures, the rearrangement becomes fast on the NMR time scale, and only three types of resonances are observed (barrier of 14 kcal·mol- 1 for the 1,3,5,7- tetramethyl derivative).


Techniques5-2


29


Valence Tautomerizations and Bond Shifts. • When a third bridge is added, as in barbaralone steric requirements of the

rearrangement are improved, and the barrier is lowered to 9.6 kcal·mol- 1 .

• When the third bridge is an ethylenic group, the molecule is bullvalene where all three bridges are identical, and a sequence of Cope rearrangements renders all protons (or carbons) equivalent.

• Indeed, the complex spectrum at room temperature becomes a singlet above 180 oC.

• Molecules that undergo rapid valence tautomerizations often are said to be fluxional.


Techniques5-2


30


Valence Tautomerizations and Bond Shifts. • Rearrangements of carbocations also may be studied by NMR methods.

• The norbornyl cation may undergo 3,2-and 6,2-hydride shifts, as well as Wagner–Meerwein rearrangements.

• The sum of these processes renders all protons equivalent, so that the complex spectrum below -80 oC becomes a singlet at room temperature.

• The slowed process appears to be the 3,2- hydride shift, whose barrier was measured to be 11 kcal·mol- 1


Techniques5-2


31


Valence Tautomerizations and Bond Shifts. • Fluxional organometallic species have also been observed with NMR

• Tetra-methylalleneiron tetracarbonyl exhibits three distinct methyl resonances in the ratio 1: 1: 2 at - 60° as depicted:

• Above room temperature, however, the spectrum becomes a singlet as the Fe(CO)4 unit circulates about the allenic structure by moving orthogonally from one alkenic unit to the other.


Techniques5-2


32


Valence Tautomerizations and Bond Shifts. • In cyclooctatetreneiron tricarbonyl, the spectrum below –150 °C indicates

four protons on carbons bound to iron and four on carbons not bound to iron, consistent with the structure shown.

• Above –100 °C all the protons converge to a singlet as the iron atom moves around the ring as shown.

• A bond shift occurs with each 45° movement of the iron atom. Eight such operations result in complete averaging of the ring protons or carbons.


Techniques5-2


33


Quantification. • For the simple case of two equally populated sites that

do not exhibit coupling (ex: cyclohexane) the rate constant (kc) at the point of maximum peak broadening (the coalescence temperature Tc, d11 approximately - 60° C) is

kc = pDn/ √2

• Dn is the distance in Hz between the two peaks at slow exchange.

• The free energy of activation then may be calculated as DGc

‡ = 2.3RTc [10.32 + log(Tc / kc )]

• This result is extremely accurate and easy to obtain, but the equation is limited in its application.


Techniques5-2


34


Quantification. • For the two- site exchange between coupled nuclei the rate constant at Tc

kc = (p Dn2 + 6J2)½ / √2

• To include unequal populations, more complex coupling patterns, and more than two exchange sites, it is necessary to use computer programs such as DNMR3, which can simulate the entire line shape at several temperatures.

• Such a procedure generates Arrhenius plots from which enthalpic and entropic activation parameters may be obtained.

• The procedure is more elegant and more comprehensive, but it is more susceptible to systematic errors involving inherent linewidths and peak spacings than is the coalescence temperature method.


Techniques5-2


35


Quantification. • The proportionality between kc and Dn means that the rate constant is

dependent on the field strength

• Thus, a change in field from 300 to 600 MHz alters the rate constant at Tc. The practical result is that changes.

• Since the slow exchange peaks are farther apart at 600 MHz, a higher temperature is required to achieve coalescence than at 300 MHz.

• At a given field strength, two nuclides such as and have different values of for Dn analogous functionalities and achieve coalescence at different temperatures.

• Since Dn is usually larger for than 1H than for 13C the coalescence temper-ature often is much higher for 13C.


Techniques5-2


36

MULTIPLE RESONANCE

• Special effects may be routinely and elegantly created by using sources of radiofrequency energy in addition to the observation frequency , n1 = gB1

• The technique is called multiple irradiation or multiple resonance and requires the presence of a second transmitter coil in the sample probe to provide the new irradiating frequency n2 = gB2

• When the second frequency is applied, the experiment, which is widely available on modern spectrometers, is termed double resonance or double irradiation.

• We already have seen several examples of double irradiation experiments, including the removal of proton couplings from 13C, the elimination of solvent peaks by peak suppression, the sharpening of NH resonances by irradiation of 14N.


Techniques5-3


37

MULTIPLE RESONANCE

Spin Decoupling. • One of the oldest and most generally applicable double-resonance

experiments is the irradiation of one proton resonance (HX) and observation of the effects on the AX coupling (JAX) present in another proton resonance (HA).

• The traditional and intuitive explanation for the resulting spectral simplification, known as spin decoupling, is that the irradiation shuttles the X protons between the spin states so rapidly that the A protons no longer have a distinguishable independent existence.

• As a result, the A resonance collapses to a singlet. This explanation, however, is inadequate in that it fails to account for phenomena at weak decoupling fields (spin tickling) and even some phenomena at very strong decoupling fields.


Techniques5-3


38

MULTIPLE RESONANCE

Spin Decoupling. • The actual experiment involves getting the coupled nuclei to precess about

orthogonal axes.

• The magnitude of the coupling interaction between two spins is expressed by the scalar, or dot, product between their magnetic moments and is proportional to the expression:

Jm1 · m2 = Jm1m2cosf

• The quantity f is the angle between the vectors (the axes of precession of the nuclei).

• So long as both sets of nuclei precess around the same (z) axis, f is zero, cos 0o is 1, and full coupling is observed.


Techniques5-3


39

MULTIPLE RESONANCE

Spin Decoupling. • The geometrical relationship between the spins may be altered by

subjecting one of them to a B2 field.

• Imagine observing 13C nuclei as they precess around the z axis at the frequency B2.

• When the attached protons are subjected to a strong B2 field along the x axis, they will precess around that axis.

• The angle f between the 1H and 13C nuclear vectors is 90° as they respectively precess around the z and x axes.

• As a result, their spin– spin interaction goes to zero because the dot product is zero . The nuclei are then said to be decoupled.


Techniques5-3


40

MULTIPLE RESONANCE

Spin Decoupling. • Spin decoupling has been useful

in identifying coupled pairs of nuclei.

• Consider ethyl trans-crotonate, the alkenic protons split each other, and both are split by the allylic methyl group to form an ABX3 spin system.

• Irradiation at the methyl resonance frequency produces the upper spectrum in the inset for the alkenic protons, which have become a simple AB quartet.


Techniques5-3


41

MULTIPLE RESONANCE

Spin Decoupling. • A more complex example is illustrated using the bicyclic sugar mannosan

triacetate, which has a nearly first-order spectrum with numerous coupling partners.

• Irradiation of H5 @ d 4.62 produces simplification of the resonances of its vicinal partners H4, H6/1 H6/2 as well as its long- range zigzag partner H3:


Techniques5-3


42

MULTIPLE RESONANCE

Difference Decoupling. • In complex molecules, the difference between coupled and decoupled

spectra can be used as a probe for nuclear relationships

• Features that are not affected by decoupling are subtracted out and do not appear.

• The procedure provides coupling relationships when spectral overlap is a serious problem.

• This and other simple spin-decoupling experiments have been entirely superseded by two- dimensional experiments in recent years


Techniques5-3


43

MULTIPLE RESONANCE

Difference Decoupling. • Consider the 1H spectrum of 1- dehydrotestosterone:


Techniques5-3


44

b) irradiation of the 6 resonance shows little change as the result of double irradiation. But if the original spectrum (a) is subtracted from (b), the remaining resonances must be from the effect of the 7 protons (c).

MULTIPLE RESONANCE

Classes of Multiple Resonance Experiments. • Homonuclear double-resonance experiments: both the irradiated and the

observed nuclei are identical – represented by the notation 1H{1H}. (irradiated nucleus is denoted by braces)

• Heteronuclear double-resonance experiements: the observed and irradiated nuclei are different – denoted by the notation 13C{1H} (as in proton-decoupled 13C spectra) or 13C{1H}{31P} for a triple-resonance experiment.

• Double-resonance experiments also may be classified according to the intensity or bandwidth of the irradiating frequency.

• If irradiation is intended to cover only a portion of the resonance frequencies, the technique is known as selective irradiation or selective de-coupling.


Techniques5-3


45

MULTIPLE RESONANCE

Classes of Multiple Resonance Experiments. • Non-irradiated resonances can exhibit a small movement in frequency, called

the Bloch–Siegert shift, which is related to the intensity of the B2 field and the distance between the observed and irradiated frequencies.

• Closer examination of the mannosan triacetate experiment reveals several such shifts, found by comparing the relative positions of the resonances in the upper and lower spectra:


Techniques5-3


46

MULTIPLE RESONANCE

Classes of Multiple Resonance Experiments. • When all frequencies of a specific nuclide are irradiated, the experiment is

termed nonselective irradiation or broadband decoupling.

• The invention of this technique was instrumental in the development of 13C NMR spectroscopy as a routine tool. To cover all the 1H frequencies, B2 was modulated with white noise (previously), so the technique often was called noise decoupling.


Techniques5-3


47

MULTIPLE RESONANCE

Classes of Multiple Resonance Experiments. • There are two significant problems with this method.

1. Application of rf energy at the decoupling frequency generates heat - As B0 fields increased from 60 to 900 MHz, higher decoupling intensities were required generating heat that was unacceptable for biological samples and for many delicate organic or inorganic samples.

2. Second, with higher field strengths, it became increasingly more difficult for B2 to cover the entire range of 1H frequencies, which had been about 600 Hz at 60 MHz, but became 5000 Hz at 500 MHz.

• To overcome these problems of heteronuclear decoupling, modern methods replaced continuous irradiation with a series of pulses that eliminate the effects of coupling.


Techniques5-3


48

MULTIPLE RESONANCE

Classes of Multiple Resonance Experiments. • In this experiment a 90° B1 pulse applied to the observed 13C nuclei along the

x direction moves magnetization from carbon coupled to either spin-up or spin- down protons into the xy plane along the y axis:


Techniques5-3


49

MULTIPLE RESONANCE

Classes of Multiple Resonance Experiments. • The reference frequency is considered to coincide with the y axis and be

midway between the frequencies of the carbons associated with the spin-up Ha and spin-down Hb protons.


Techniques5-3


50

MULTIPLE RESONANCE

Classes of Multiple Resonance Experiments. • The two carbon vectors then diverge in the xy plane after the 90° pulse, one

becoming faster and the other slower than the carrier frequency


Techniques5-3


51

MULTIPLE RESONANCE

Classes of Multiple Resonance Experiments. • Then a 180° proton pulse (B2 of the decoupling experiment) switches the

locations of the vectors. The slower-moving vector that was dropping behind is replaced by the faster- moving vector and vice-versa, so that both carbon vectors start to move back toward the y axis:


Techniques5-3


52

MULTIPLE RESONANCE

Classes of Multiple Resonance Experiments. • After an equal second period , the two vectors coincide on the y axis, only

one frequency or peak occurs, and coupling to the protons disappears The process is repeated during acquisition at a rate (in hertz) that is faster than the coupling constant, so that the effects of coupling are removed.


Techniques5-3


53

MULTIPLE RESONANCE

Classes of Multiple Resonance Experiments. • In this way, decoupling can be achieved with short pulses during acquisition

rather than with a continuous, high-intensity field during the entire experiment.

• In practice, the method is limited because the 180° pulse must be very accurate and because the B2 field is inhomogeneous.

• Refinements of this experiment have been achieved by replacing the 180° pulse with several pulses (composite pulses) and by cycling their order ( phase cycling) to cancel out the inaccuracies

• One of these methods is WALTZ-16, which achieves full decoupling across a much wider range than the original continuous method and with a fraction of the power – used by our Bruker 400


Techniques5-3


54

THE NUCLEAR OVERHAUSER EFFECT

Introduction.• Dipole–dipole relaxation occurs when two nuclei are located close together

and are moving at an appropriate relative rate

• Irradiation of one of these nuclei with a B2 field alters the Boltzmann population distribution of the other nucleus and therefore perturbs the intensity of its resonance.

• No J coupling need be present between the nuclei. The original phenomenon was discovered by Overhauser, but between nuclei and unpaired electrons.

• The Overhauser effect when both spins are of nuclei was observed first by Anet and Bourne and is of more interest to the chemist. It has great structural utility, because the dipole–dipole mechanism for relaxation depends on the distance between the two spins


Techniques5-4


55


Origin.• Consider a molecule that contains a

13C atom and a nearby (though not necessarily spin-coupled) 1H atom.

• The combinations of spin states for this two-spin system are shown:

• Energy is the vertical axis.


Techniques5-4


56

N1

N3

N2

N4

C H

C H

C H

C H


Origin.• Red arrows indicate the resonance

n of the 13C nuclei (resulting in the 13C signal on the spectrum)

• Blue arrows indicate the resonance nH of the 1H nuclei (resulting in the 1H signal on the spectrum)

• Remember that the resonance nH is four times that of nC


Techniques5-4


57

N1

N3

N2

N4

C H

C H

C H

C H

nH

nH

nC

nC


Origin.• By the Boltzman distribution we

know that at equilibrium the population of carbon and proton is slightly larger in the lower energy state (+½)

• We denote the excess population as DC for carbon and DH for proton, so:


Techniques5-4


58

N1

N3

N2

N4

C H

C H

C H

C H

nH

nH

nC

nC

State Population

N4 - DH - DC

N3 - DH + DC

N2 +DH - DC

N1 +DH + DC


Origin.• For the carbon signals the energy

difference between the N1 to N2 and N3 to N4 states is 2DC as shown in the table below.

• We simply subtract one population from the other to get the difference between states:


Techniques5-4


59

N1

N3

N2

N4

C H

C H

C H

C H

nH

nH

nC

nC

State Population Difference

N4 - DH - DC } 2DCN3 - DH + DC

N2 +DH - DC } 2DCN1 +DH + DC


Origin.• The 13C signal we observe results

from N1 N2 and N3 N4 transitions where the population difference is 2DC in both cases.



60

N1

N3

N2

N4

C H

C H

C H

C H

nH

nH

nC

nC


N4 - DH - DC } 2DCN3 - DH + DC

N2 +DH - DC } 2DCN1 +DH + DC


Origin.• Now let’s saturate the 1H states by

double resonance decoupling.

• DH now becomes zero disturbing the Boltzmann controlled equillibrium

• DH goes to zero



61

N1

N3

N2

N4

C H

C H

C H

C H

nH

nH

nC

nC


N4 - DC } 2DCN3 + DC

N2 - DC } 2DCN1 + DC


Origin.• The populations of the N1 and N4

states are now polarized.

• In an attempt to restore equilibrium a number of N4 carbon nuclei relax to the N1 state by Dr



62

N1

N3

N2

N4

C H

C H

C H

C H

nH

nH

nC

nC


N4 - DC } 2DC + DrN3 + DC



Origin.• This leakage caused by saturation

and polarization of the N4 state by Dr will increase the population of N1 and therefore increase the signal detected

• This is the Nuclear Overhauser Effect!



63

N1

N3

N2

N4

C H

C H

C H

C H

nH

nH

nC

nC





Quantification.• The NOE is an example of polarization transfer – polarization of one set of

nuclear spin states results in the polarization of another

• For small molecules the maximum effect h is limited by the following equation:

• The increase is always less than maximum as other non-polar relaxation processes compete and the observed nucleus can also relax through other non-irradiated nuclei

• For homonuclear NOE girr = gobs so the maximum effect is a ½ or 50% enhancement of signal



64


Quantification.• For the heteronuclear 13Cobs/1Hirr system the g for 1H to 13C is ~ 4:1

• NOE enhancement is the principle reason why 13CH3- and –13CH2- signals are enhanced in 1H-decoupled spectra relative to quaternary carbons

• The maximum enhancement for 13Cobs/1Hirr system is ~200%

• In general:1. NOE experiments work best when girr ⩾ gobs

2. The signal enhancement is usually positive, however some nuclei (15N) have negative g – you will see a negative peak!



65


Difference NOE.



66


Difference NOE.



67

SPECTRAL EDITING

Spin-Echo Experiment

• How can you know what T2 is?

• We cannot measure it directly like T1

• Pulse sequence is used called spin-echo sequence



68

180y (or x)90y

tD tD

SPECTRAL EDITING

Spin-Echo Experiment• What it does:



69

z

x

y

x

y

x

y

x

y

x

y

tD

180y (or x)

tD

dephasing

refocusing

SPECTRAL EDITING

Spin-Echo Experiment• What it does:



70

z

x

y

x

y

x

y

x

y

x

y

tD

180y (or x)

tD

dephasing

refocusing

SPECTRAL EDITING

Spin-Echo Experiment• If we acquire the FID right after the spin-echo sequence, the

intensity of the signal after FT will only be affected by T2 relaxation and not by dephasing due to B0 imperfections.

• Upon repetition for different tD values, we plot the intensity versus 2 * tD and get a graph similar to the one we got for inversion recovery, but in this case the decay rate will be equal to T2.



71

timeinte

nsi

ty

I(t) = I * ( 1 - 2 * e - t / T2 )

SPECTRAL EDITING

The Attached Proton Test• Very similar to the Spin-Echo Sequence, except we will use JCHn to adjust the

time between pulses:

• For the methine resonance – note how after the 90o pulse the C vector splits into a doublet (one vector +, the other -). Another 180o pulse in the y-coordinate has them refocus on the – y-axis.



72

SPECTRAL EDITING

The Attached Proton Test• If the same experiment were carried out for a CH2 system:

• For the CH2 resonance, the middle peak will remain on the y-axis (middle of triplet), here we wait 1/2J for a second period and repulse the sample to bring the – vector we saw before with –CH- back to the + y-axis.



73

SPECTRAL EDITING

The Attached Proton Test• Similar to the methine system,

the pulse sequence will give a negative peak for CH3 and a positive peak will result from quaternary carbons with no splitting by H.

• Proton irradiation (selective pulses like WALTZ-16) carefully decouples the spectrum.

• At right is the APT for cholesteryl acetate (C, CH2 positive, CH and CH3 negative)



74

SPECTRAL EDITING

The Attached Proton Test• Similar to the methine system,

the pulse sequence will give a negative peak for CH3 and a positive peak will result from quaternary carbons with no splitting by H.

• Proton irradiation (selective pulses like WALTZ-16) carefully decouples the spectrum.

• At right is the APT for cholesteryl acetate (C, CH2 positive, CH and CH3 negative)



75

SPECTRAL EDITING

DEPT – Distortionless Enhancement by Polarization Transfer• A sequence that takes advantage of the surplus 1H population to see 13C

signals and it can edit the signals in order to obtain response from CH, CH2 and CH3 according to the settings of the sequence:



76

90x

180x90x

tD

fy

1H:

13C:

tD

180x

{1H}tD

SPECTRAL EDITING

DEPT – Distortionless Enhancement by Polarization Transfer• As we just pointed out, the relaxation times for 13C are strongly a factor

of T2 processes – where spin is transferred and the resulting signal shifts out of phase with what is being detected

• If different pulse widths are applied in a 13C determination, the resulting phase shift (and signal intensity) will be different depending on how many 1H atoms the 13C can transfer its spin to

• In a typical DEPT experiment, a 45, 90 and 135 pulse are applied successively to the sample and the results compared to the original carbon spectrum

• Unfortunately, it relies on the creation and manipulation of multiple quantum magnetization (the 13C p/2 pulse) which we cannot see or represent with vectors.



77

SPECTRAL EDITING

DEPT – Distortionless Enhancement by Polarization Transfer• If we plot the responses for different carbons versus the tip angle f of

the 1H pulse, we get:



78

CH2

CH3

CH90 13545

SPECTRAL EDITING

DEPT – Distortionless Enhancement by Polarization Transfer• In summary:



79

• At 45o we observe all positive 13C resonances except 4o

• At 90o we observe no 13C resonances for CH2, CH3 or 4o

• At 135o we observe positive resonances for CH and CH3, negative resonances for CH2 and none for 4o

SPECTRAL EDITING

DEPT – Distortionless Enhancement by Polarization Transfer• Most useful to run is the DEPT-135 and if needed a DEPT-90:



80

DEPT Pulse Sequence

methyl methylene methine quaternary

DEPT-45 Positive peak Positive peak Positive peak Not observed

DEPT-90 No obs. peak No obs. peak Positive peak Not observed

DEPT-135 Positive peak Negative Peak Positive Peak Not observed

SPECTRAL EDITING

DEPT – Distortionless Enhancement by Polarization Transfer• Most useful to run is the DEPT-135 and if needed a DEPT-90:



81

DEPT Pulse Sequence

methyl methylene methine quaternary

DEPT-45 Positive peak Positive peak Positive peak Not observed

DEPT-90 No obs. peak No obs. peak Positive peak Not observed

DEPT-135 Positive peak Negative Peak Positive Peak Not observed

SPECTRAL EDITING

DEPT – Distortionless Enhancement by Polarization Transfer• Example:



82

160 150 140 130 120 110 100 90 80 70 60 50 40 30 20f1 ppm

160 150 140 130 120 110 100 90 80 70 60 50 40 30 20f1 ppm

O

SPECTRAL EDITING

DEPT – Distortionless Enhancement by Polarization Transfer• Example:



83

ODEPT 135

DEPT 90

DEPT 45

chem 430 nmr spectroscopy chapter 5

Documents

partially

nmr time scale

nuclear overhauser

dc dc

state lone

dept distortionless

unsymmetrical

dipole dipole