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Lectu re Date: February 11 th , 2008

Nuclear Magnetic Resonance 1

Nuclear Magnetic Resonance

Reading for NMR: Chapter 19 of Skoog, et al. Handout: What SSNMR can offer to organic chemists

Nuclear Magnetic Resonance (NMR) Nuclear spin transitions, in the 5-900 MHz range Magnetic resonance imaging (MRI)


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Things that can be learned from NMR data

Covalent chemical structure (2D structure) Which atoms/functional groups are present in a molecule How the atoms are connected (covalently bonded)

3D Structure Conformation Stereochemistry

Molecular motionChemical dynamics and exchangeDiffusion rate

3D Distribution of NMR spins in a medium an image! (Better known as MRI)Plus many more things of interest to chemists

History of NMR

1920-1930: physics begins to grasp theconcepts of electron and nuclear spin1936: C. J. Gorter (Netherlands) attempts tostudy 1H and 7Li NMR with a resonancemethod, but fails because of relaxation1945-6: E. M. Purcell (Harvard) and F. Bloch(Stanford) observe 1H NMR in 1 kg of parafin at30 MHz and in water at 8 MHz, respectively1952: Nobel Prize in Physics to Purcell andBloch1957: P. C. Lauterbur and Holm independently

record13

C spectra1991: Nobel Prize in Chemistry to R. R. Ernst(ETH) for FT and 2D NMR2002: Nobel Prize in Chemistry to K. Wuthrich2003: Nobel Prize in Medicine to P. C.Lauterbur and P. Mansfield for MRI

P. C. Lauterbur F. Bloch

E. M. Purcell R. R. Ernst

Photographs from www.nobelprize.org


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Nuclear Magnetism

A nuclear electromagnet iscreated by the nucleons(protons and neutrons) insidethe atomic nucleus.

This little electromagnet has amagnetic moment (J T -1) The magnetic moment is

proportional to the current flowthrough the nuclear loop

The nucleus looks like a dipoleto a distant charge center

N

SFromhttp://education.jlab.org

Basic NMR Theory

In a strong applied magnetic field(B0), certain atomic nuclei willalign or oppose this field.

This alignment is caused by themagnetic moments of the nuclei,which themselves are caused bythe internal structure of thenucleus. Two nuclear propertiesstand out:

Spin (1/2 for 1H, 13 C, etc) Gyromagnetic ratio

An excess of alignments is foundin the lower energy state(determined by a Boltzmanndistribution).

At room temperature, this excessis very small , typically only 1 partper trillion!


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Nuclear Spin

In a classical sense the bulk nuclearmagnetization is observed toprecess at the Larmor frequency(usually several hundred MHz):

The constant is the magnetogyricratio.

2 0

0

B00 B

angular (rad/s) linear (Hz, cycles/s)

B0

Elements Accessible by NMR

Figure from UCSB MRL website

White = only spin Pink = spin 1 or greater (quadrupolar)

Yellow = spin or greater


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Pulsed vs. Continuous-Wave NMR

NMR effects are most commonly detected by resonantradio-frequency experiments

Continuous-wave NMR: frequency is swept over a range(e.g. several kilohertz), absorption of RF by sample ismonitored Historically first method for NMR Poor sensitivi ty Still used in lock circuits

Pulsed NMR short pulses (at a specific frequency) areapplied to the sample, and the response is monitored. Much more flexible (pulse sequences followed from this) Short pulses can excited a range of frequencies

NMR Theory: The Rotating Frame

The magnetization precesses at the Larmor frequency, the RF field(s)oscillate at or near this same frequencyThe rotating frame rotates at this f requency, simplifies the picture foranalysis and understanding

Frame rotating at the Larmor frequencyhundreds of MHz

Frame is now still

eye

z z

x

y


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Spin Systems

The reason NMR is so applicable to structural problems isthat the governing interactions can be separated andtreated individually Experimentally, this results in spectral simplification (in that

transitions are not hopelessly entangled) and also allows fordetailed manipulations (pulse sequences) to extract information

This involves separation of electronic Hamiltonian fromthe nuclear spin Hamiltonians

NMR is thus simplified in that its data can be linked back

to spin systems. Examples of spin systems: Several 1H nuclei (i.e. hydrogen) within 2 or 3 covalent bonds of

each other A 1H nucleus attached to a 13 C nucleus

NMR Theory: RF Pulses

z

xy

Drawing depicts a 90 o pulse

z

x

y

RF pulses are used to driv e the bulk magnetization to the desired positionThe action of an RF pulse is determined by its frequency, amplitude,length and phaseFor an on-resonant pulse, the right hand rule predicts i ts action

Drawing depicts a 180 o pulse


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NMR Theory: T 1 Relaxation

T1 relaxation: longitudinal

relaxation (re-establishmentof Boltzmann equilibrium)by spins interacting with thelattice

In practice, T 1 controls howquickly FT experiments canbe repeated for signalaveraging

Measurements of T 1 canprovide useful data onmolecular motions

x

z

y

NMR Theory: T 2 Relaxation

T2 relaxation transverserelaxation (dephasing ofcoherence) by spinsinteracting with each other

Controls how longmagnetization can be keptin the x-y plane

Controls the linewidth(FWHH) of the NMRsignals:

x

z

y

*2

2/1 1T


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NMR Theory: The Chemical ShiftThe electrons around a nucleus

shield are circulated by the bigmagnetic field, inducing smallerfields.

Anisotropy:

Units ppm:

Shift-structure correlations the

basis of NMR as an analyticaltool.Shift-structure correlations areavailable for 1H, 13 C, 15 N, 29 Si,31 P and many other nuclei

TPPO

PbSO 4

x

y

z

ref

ref x ppm

610)(

Above: the chemical shift in solids is not a single peak!

Typical 1H NMR Chemical Shielding


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Typical 13 C NMR Chemical Shielding

Other Nuclei: 17 O NMR

Note 17 O NMR requires labeling or concentrated solutions,and suffers from large solution-state linewidths (caused byquadrupolar relaxation)


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NMR Theory: The Chemical Shift

Contributions from electronegativity and ring current

effects:

Dailey et. al., J. Am. Chem. Soc., 77, 3977 (1955 ).

Correlation o f 1H Chemical Shift and GroupElectronegativity for CH3X Compounds

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0.0 1.0 2.0 3.0 4.0 5.0Relative Chemical Shift ( )

G r o u p

E l e c

t r o n e g a

t i v

i t y

NMR Theory: The Chemical Shift

Contributions from ring current effects

Above center of ring (z-axis): shielding

In plane of ring ( axis): deshielding

Figure from http://www.chemlab.chem.usyd.edu.au/thirdyear/organic/field/nmr/ans02.htm


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NMR J-CouplingThe J-coupling is an effect in whichnuclear magnetic dipoles couple to

each other via the surroundingelectrons.The effect is tiny but detectable!Typical J-values

2-4J HH can range from 15 to +15 Hzand depends on the number ofbonds, bond angles, and torsionangles

1J CH can range from 120 to 280 Hz,but typically is ~150 Hz in mostorganics

2-4J CH ranges from 15 to +15 Hzand depends on effects similar tothe 2-4J HH

The narrow ranges that certain 1H and 13 CJ-coupling values fall into make spectralediting and heteronuclear correlationexperiments possible!!!

J-Coupling: Effects on NMR Spectra

Two basic types of coupling Homonuclear (e.g. 1H-1H) Heteronuclear (e.g. 1H-19 F)

Weak coupling Large difference in frequency

>> J#Lines = 2 n I + 1

All heteronuclear coupling isweakMore complex splitting patternscan be visualized usingPascals triangle (see text)

Strong coupling Small difference in frequency

~ JComplex patterns

Figure simulated in Bruker Topspin 2.0 DAISY moduleInspired by S. W. Homans, A Di ctionary of Concepts in NMR, Oxford 198 9, p297.


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J-Coupling: Effects on NMR Spectra

Example:

monofluorobenzeneHomonuclear couplingbetween 1H:

ortho -coupling meta -coupling para -coupling

Heteronuclear couplingbetween 1H and 19 F:

As above ( ortho , meta ,and para ).

Observed from the 19 F,appears as a doublet of

triplets of triplets (ttd)Fluorine can be decoupledfrom the 1H spectrum (notshown)

para

orthometa

Structural and Conformational Analysis

J-coupling is widely used (in conjunction with 2D NMR) toassemble portions of a molecule In this case, the J-coupling is simply detected in a certain range

and its magnitude is not examined closely

J-coupling is also used to study conformation andstereochemistry of organic/organometallic/biochemicalsystems in solution In this case, the J-coupling is measured e.g. to the nearest 0.1 Hz

and analyzed more closely

W. A. Thomas, Prog. NMR Spectros., 30 (1997) 183-207.


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J-Coupling: Angle Effects

Karplus relationships the

effects of bond and torsionangles on J-couplingBond angles, dihedral(torsion) angles, 4 and 5-bond angles

In[1]:= J q _ : = 4.22Cos q + - 0.5Cos q + 4.5

In[3]:= Plot J q , q, 0, p

0.5 1 1. 5 2 2. 5 3

6

7

8

9

Out[3]= Graphi cs Dihedral angle (radians)

C o u p l

i n g c o n s t a n

t ( H z )

Dipolar Coupling

The magnetic dipolar interactionbetween the moments of two spin-1/2nuclei

One spin senses the others orientation directlythrough space

The dipolar coupling is simply related tothe internuclear distance between thespins:

The truncated (secular) dipolar Hamiltonians (relevant toNMR) have the form:

S I S I S I D H z zr Homonuclea D 412 cos31 z zear Heteron ucl D S I D H cos31 2

38 r D S I 20


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Dipolar Coupling

The permeability constant (in kg m sec - 2 A- 2) and Planck's constant (in Joule sec):

m0 = 4 p 10 - 7 ; = 6.62608 10 - 34 2 p ;

The gyromagnetic ratios for 13C and 15N, in units of radians Tesla - 1 sec- 1 :

gI = 6.728 10 7 ;gS = - 2.712 10 7;

R r_ : =gI gS

r 3

2 p

m04 p

N R 1.32 10 - 10

- 1331. 53

The dipolar coupling is therefore 1.332 kHz.

Example whats the dipolar coupling between a 13 C and a 15 Nnucleus 1.32 angstroms apart?

The Nuclear Overhauser Effect

The idea: detect the cross-relaxation caused byinstantaneous dipolar coupling in an NMR or EPRexperiment.

This was conceived by A. W. Overhauser, while agraduate student at UC Berkeley in 1953

Overhauser predicted that saturation of the conductionelectron spin resonance in a metal, the nuclear spinswould be polarized 1000 times more than normal!!!


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The Nuclear Overhauser Effect

Dipolar coupling is a direct magnetic interaction

between the moments of two spin-1/2 nuclei.The coherent effects of dipolar coupling areaveraged away in solution-state NMR by rapidmolecular tumbling.

However, the dipolarinteraction can stillplay a role via insolution-state NMRvia dipolar cross-relaxationmechanisms, better

known as thenuclear Overhausereffect (NOE).

NMR Spectrometer Design

The basic idea:


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NMR Magnets

Superconducting magnets:

Resonance

The natural frequency of a inductive-capacitive circuit:

LC r

1

The NMR system requires a resonant circuit to detectnuclear spin transitions this circuit is part of the probe


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Resonant Circuits in Probes

Figure from Bruker Instruments

NMR Probe Design

The NMR probe designed to efficientlyproduce aninductance (~W) anddetect the result (

nuclear magnetic resonance 1

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