Lecture #2

Pulsed NMR experiments

Introducing the Chemical Shift

Problems, Problems, Problems……

RF Pulses and NMR Experiments

• Until the mid 1970’s all NMR spectrometers worked by shining a RF freq on sample and slowly scanning the magnetic field

• One passage took ca. 12min• Lots of those minutes were expended on

scanning through regions with only empty baseline

RF Pulses and NMR

• Recall the thinking on Fourier Analysis• Measure all frequencies at once (better use of time)

deconvolute later• How to do this? Hold magnet constant and irrad with a

short pulse that contains all the relevant RF frequencies• All the magnetic moments oscillating at characteristic RF

freq should come into resonance (absorb energy)• In returning to equilibrium, they should release energy,

oscillating at their proper frequencies• Oscillating magnets should induce an AC voltage in a

nearby coil• Thank you Professor R. Ernst

Let’s look at this as a picture…Z

X

Y

M

x

y

z

Recall that this is vector resultant from individuals all oscillating around Z at Larmor frequency

RF pulse with whole range of frequencies

Absorbs energy

Destroys Boltzmann excess

M Still has precessional torque around z (field) axis

The RF Pulse Generates Phase Coherence

X

Y

Z

X

y

x-Pulse tips the ensemble of M down to the y axis of the x-y plane.

Another effect is to start them precessing about z at the same time point, therefore with the same phase. This is called coherence

Free Precession of M about z…

x

y

z

x

y

z

x

y

z

x

y

z

x

y

z

x

y

z

time

But, M shows a Damped Oscillation….

x

y

z

x

y

z

x

y

z

x

y

z

x

y

z

x

y

z

time

Because M is spiraling back to the Boltzmann equilibrium

x

y

z

x

y

z

x

y

z

x

y

z

x

y

z

x

y

z

time

And we are left to see the oscillation of the projection that remains in x,y plane

Pictoral of how this becomes the NMR experiment

H0

If we apply a second field at the same frequency, but from a different direction, the same kind of torque is experienced by I. This amounts to perturbing the population equilibrium

And now a miracle occurs..This “perturbation” acts like any other momentum vector in the H0 field and begins to precess about z (what frequency?)

The secret is creation of a phase-coherence that starts off the individual vectors comprising Iy having the same phase

This induced precession can be detected by contriving to have a sensing coil at right angle to H0. Coil produces voltage at same periodicity.

H0Induction!!!

Our Friend, the Chemical Shift

The Chemical Shift

• The Chemical shift makes NMR useful in Chemistry (they

named it after us)

• Arises from the electrons surrounding our nuclei, responding to

a magnetic field.

• Induced circulation of electrons, Lenz’s law; this circulation

generates a small magnetic field opposed to H0

• The small negative field diminishes the H0 experienced by a

nucleus. This differentiates sites, based on chemical nature

• Effect grows directly proportional to H0

Some History

W.G. Proctor, F.C Yu; Physical Review, 77, 717 (1950)

W.C. Dickinson; Physical Review, 77, 736 (1950)

An early example, revealing the sorting out by chemical environment, and response proportional to number of hydrogen atoms

Theory Underlying the Chemical Shift

• Bulk Susceptibility is corrected for by internal shift reference

• Shielding by electron cloud is experienced at the nucleus

• Induced circulation of electrons such that a “current flow” is set up, generating a magnetic field counter to H0 (Lenz’s Law)

• Implies that if we know about the electron cloud distribution, we could Predict chemical shifts

• Predicts direct proportionality of the chemical shift (when expressed in Hz) to the applied field. The ppm scale normalizes out this effect. This means that a 3ppm shift on a 100 MHz instrument is 300 Hz from TMS. The same 3ppm signal on a 500 MHz instrument is 1500 Hz from TMS.

A Picture of this…

A Vector Picture Chemical shift is the ultimate precessional frequency of the vector component of M in the plane perpendicular to H0

Precesses at a frequency

This is in units of (radians)/sec

At some time, has distinct angle and as a vector in x,y can be resolved into x, y components.

The receiver works by counting how many times this electric vector whizzes past in a unit of time

X

Y

H0(Z)t

X

Y

H0(Z)

After a pulse…

t

Free Precession, Rotating Frames and the Chemical Shift

•Our vector picture can help

Rotates at H0 MHz

Stands Still!

What if we could contrive to measure

once every H0 seconds? Strobe effect

Is The Rotating Frame

Now, more than one chemical shift wil move with just a difference from H0

Don’t have to distinguish 25000002 from 25000005 Hz, but 2 cf. 5

Imagine a “blinking eyeball”, (strobe effect) blinks at Larmor frequency……

What would our “blinking eyeball” receiver in the X,Y plane see, watching

this Vector over time?

Time

Vol

tage

The strobe effect cancels out the Larmor (MHz) frequency, leaving behind the chemical shift frequency

Seems to “die away…

Because the nuclear spin is also spiraling back to the Boltzmann equilibrium, leaving less “signal” in the x,y plane. (The red vector is “seen” by the x,y plane detector)

“Practical” Theory

• The real triumph of the shift theory is in its relationship to electronegativity and hybridization and easy prediction of trends based on qualitative notions from structural theory.

• Withdrawing electron density diminishes the screening ability of the electron cloud and the nucleus goes to higher field.

• Feeding in electron density sends nucleus to lower field.• “Moving” electrons have some real consequences on

nearby chemical shifts.

Defining Shift Scales

Some Useful Shift Ranges

0246810

Acids, H-bonded OH aromatic

alkenyl

CH2 allylic, acetylenic, to carbonyl

CHX CHR-Omethylene methyl

CH=O

OH, br, variable, SH sh. ca 1.5

CHR-N

ppm from TMS

1H

04080120160200

C=O aldehyde, ketone C=O,

acid

C=O, amide

CH aromatic, alkene

heteroaromatic

CR(-O)-O

C-subs aromatic, alkene

Alkyl N-subs

O-subs

13C

O-subs aromatic, alkene

15N Chemical Shift Ranges

Taken from G. Levy in Concepts in Magnetic Resonance, 6, p 338 (1994) Shifts vs. NH3(liq) Subtract 380.4 to scale to nitromethane=0.0

See also G.C. Levy and R.L. Lichter, “15N Nuclear Magnetic Resonance Spectroscopy”, J. Wiley and Sons (1979); also a massive collection of tabulated data in NMR: Principles and Applications 18, in the Chemistry Library at Temple

Chemical Shifts Sense and Report on Structure

• 13C Shift is sensitive to branching, e.g.branched hydrocarbons

Kth Carbon =

€

Bs + DM2

4

∑ ASM +γ S NK 3 + Δs NK 4

NKP = number of carbons P bonds away

DM = number of carbons bonded to Kth carbon,

with M attached carbons

S = number of carbons bonded to Kth carbon

• Sterics, electronegativity, strain, hybridization all contribute to the observed value for chemical shift

Electronegativity and substituent Shift Effects

• More Reliable in 13C

• Best used as general predictive for trends. Evaluate for consistency

• Here probably separation into resonance, inductive would help

• Changes in hybridization

• Other contributor is steric compression effect (branching?), shielding effect

Electronegativity Effects on 13C

Shifts

No Surprises Here

Chemical Shifts; Predicting and Additivity Rules

• Sometimes prediction works

• Better for carbon than for proton

• Multiple substitution can lead to push-pull deviations due to resonance, etc.

• Protons have larger relative effects on them from anisotropic neighboring fields mostly because the range of the shift domain is so small.

• Best efforts are in interpolation schemes based on mapping of assigned shifts in chemical-bond space

• The good news is that relevant model compounds are really effective in predictive value

Anisotropic Shielding Near Electrons

H

Circulating Electron Cloud responding to H0

Increases the total .field felt at H by ca

1.5 ppm

Deshielding Region

Shielding Region

Applied H Field0

Induced Current Induced Magnetic Field

Pronounced effect for aromatic, in line with e circulation

Other Anisotropic Shielding Cones Nitriles, acetylenes

isonitriles

Carbonyl, alkene +

+

++

+

++

+

++

++

In planedeshielded

Above, below planeshielded

OC

Polarized effect

Small pos

• Effects are ca. 2 ppm at most.

• Most Significant when a nucleus is fixed in geometry with respect to the neighboring field.

Best description is in

L.M. Jackman, S. Sternhell, Applications of Nuclear Magnetic Resonance Spectroscopy in Organic Chemistry, Pergamon Press, (1969) ch.2

Examples of Anisotropic Shielding

OH

O

H

1.27 1.67

H H

-.7 (to higher field)

Shielding by cyclopropyl ring

Use for both assigning signals, and interpreting the structure

Powerful Application in Study of Aromaticity

H

H

0.2 ppm

8.9 ppm

The shift anisotropy cone from the aromatic ring current requires a deshielding region outside and a shielding on the inside. An excellent review of the use of this probe is found in W. LeNoble, Highlights of Organic Chemistry, Marcel Dekker , (1974) ch. 9

L.M Jackman, F Sondheimer, A.A Bothner-By, Y. Gaoni, R. Wolovsky, Y. Amiel, D.A. Ben-Efraim, J Amer. Chem Soc. 84, 4307 (1962)

18-AnnuleneAlso for porphyrins, etc

9.2 ppm

-3 ppm

Deshielding from the C-OH bond

• Here is a dramatic example

H HOH

H

3.88 0.55

Isotropic vs. Anisotropic Chemical Shifts

• Anisotropic has shifts differ according to the angle of the molecule compared to H0

• Solids

• Preserves all the information about the interaction

• Isotropic has motions fast enough to average the chemical shift, and remove the dependency on the angle

• Liquids• Simple enough to understand

because some information is lostPowder Patterns and Chemical

Shift Anisotropy

Pattern on Right is onlyfor axial shift tensors

Typically these patternsare 10’s of ppm wide

σA ( )is the normal liquid or“isotropic” shift

To be effective at wiping out these patterns the spinning must occur at a rate comparable to thelinewidth.

3-8 This amounts to spinning at KHz for NMR field strengths commonly. .used Spin rate must be stable

Imagine frozen cyclopentadiene. Its grid has angle w.r.t. magnetic field

Different interaction of electrons with H0--Different chemical shifts! H0

In Liquids motions Averages out the Chemical Shift

The same average shift for the same chemical-electronic environment

Here the CH2s are all the same, as are all the CH next to the methylene, etc.

How do we know what “same” means?

H0

Magnetic field

How many signals do we Expect in an NMR Spectrum?

• The Chemical shift implies that we see (potentially) a different signal for every different chemical environment.

• Chemical environment here is the electronic structure (electrons, hybridization, charge, polarizability etc.) These are all things able to be predicted to some extent by theory.

• What do we mean by “different”?

When are NMR signals from a nucleus Equivalent?

• Isochronous (same frequency)• Only if the atoms are exchanged by any* symmetry operation

for the molecule. Example C2, C6

• Could be made equivalent in rapid chemical process, e.g rotation, exchange

• True always in achiral solvents• *Atoms only exchanged by mirror plane symmetry are

enantiotopic. Non-equivalent in chiral solvents• For molecules as units, similarly, enantiomers are only

distingushed with different shifts in chiral solvents. Diastereomers, like other isomers have different shifts regardless of solvent.

Are two signals equivalent, or not?

Some definitions and examples…

Homotopic

Enantiotopic

Diastereotipic

Relationship Example: 2CH3 Appearance

CH3CH3

CH3CH3

OH

CH3CH3

H

In any solvent

In chiral solvent

In any solvent

In normal solvent

A test for enantiotopic protons or 13C

Draw two structures, successively replacing A, then B.

If the two structures are enantiomers, then the signals will be enantiotopic. The carbon they are attached to is termed “prochiral”.

Basis for a lot of structure work

• Number of symmetry different positions can differ for isomeric possibilities--rule structures out

• Symmetry, Symmetry, Symmetry…..but….

Diastereotopic Signals

O

O

CH3CH3

OH

CH3

H

H

These methyl groups are not chemical shift equivalent--No matter how fast they rotate, they never see the same environment

Symmetry and

Equivalence

A Symmetry Example

HOH

H

HH

OH

H

H

H

H

OHH

H

HOH

HH

H

H

H c

c

R,S pair

Ha,b are diastereotopic and never have same chemical shift

Hc are equivalent except in chiral solvent

Ring flipping only able to distinguish at low temperature (use highest symmetry)

d

eC2

OHOH

H

HH

HH

H

H

H

a

bMeso

d

e

Ref: E. Eliel and S. Wilen, Stereochemistry of Organic Compounds, J. Wiley & Sons (1994) ch. 6R. Silverstein, G.C. Bassler, T. Morrill, Spectrometeric Identification of Organic Compounds, Wiley, (3rd Ed is 1974) ch. 4

Use What We Learned about Symmetry and Chemical Shifts

How many 13Carbon signals would we predict for these compounds?

Motion has an EffectTwo protons or carbons that are technically not exchanged by a symmetry operation can be nevertheless equivalent, if they are exchanged by a chemical process on a time scale faster than the NMR time scale.

Example, ring flipping of conformers; rotation of methyl groups.

H

H

H

H

H

H

H

HH

H O

ax

eq

ax, eq. H not symmetry equivalent but you could only see the difference at low temperature

O

Ha

Hb

At room temperature, motions make it seem “flat” with Ha, Hb at same shift.

What is meant by “The NMR Time Scale”?

•Imagine two signals that are chemically changing their identities.

•They have chemical shifts, 1, 2

•These shifts are also separated by a given number of Hz; (=1-2)

•Remember, that Hz has units of 1/sec.

•The chemical shift difference in Hz can be compared to a “chemical lifetime” or its reciprocal the reaction rate constant k. k has units of 1/sec.

•If the reaction rate k is faster than , we can only observe a signal at the average of the two chemical shifts. Intensity will be the sum.

•We can address this experimentally by making k smaller (lower the temperature) or making bigger (use a higher field NMR magnet)

•Practically, the relevant time scale for exchange here is 10s of msec.

Pictorally,

A B

An irony, samples appear “colder” w.r.t. kinetics on higher field NMR systems

Problems…

A Mini-ParadigmTabulate

Observation or Fact Inference about StructureStep 1.

Do we have enough Data? What questions do we need to address?

Molecular Weight (mass Spec)?

Inventory proton,carbon counts into shift categories, number of unique signals

Assess purity, can we “ignore” some signals?

From above, can we write down Molecular Formula?

UV chromophore?

Step 2. Tabulate Obvious features

Check the IR spectrum, and 13C NMR for Functional groups (C=O, CN, OH etc.

Mass Spectrum--Any Fragments or losses that are structurally useful? (loss of water, CO2, CH2=CH2; tropylium, acylium present?

Evaluate chromophore, from UV if available

Are there obvious 1H NMR signals by inspection? (methyls, methoxys, aromatics,

Evaluate exchangeable H from mass spec, or 1H NMR (D2O exchange)

Step 3. Start putting the pieces together

From the list of inferences in our table write out fragments that must be present.

Some must be at ends, some must be internal

Compare to molecular weight and deduce formula

Can we infer the presence of heteroatoms?

Compute DBE

Specify Fragments from 1H NMR spin patterns

Recognize that some of the parts and fragments overlap or are redundant. Tabulate this

Write down trial structures. Cross check against data.

Formulate questions. (how can I exclude ….?; how could I distinguish A from B, etc. Symmetry comes in.

Step 4. Confirmatory

Exact Mass

Comparison with known structure

Literature, data bases

“Fingerprint” available?

Inductive and Deductive Reasoning

The steps discussed frame a sort of inductive reasoning

Your knowledge of Chemistry, e.g. valence, what bonds to what, molecules you know, provide for inductive reasoning.

These two converge when you can write down a reasonable structure that agrees with all the data.