topic 7 nuclear magnetic resonance

7/29/2019 Topic 7 Nuclear Magnetic Resonance

1/37


2/37

The Electromagnetic Spectrum

NMR, MRI

EPR/ESR


3/37

What is NMR?

NMR is an experiment in which the resonance

frequencies of nuclear magnetic systems areinvestigated.

NMR always employs some form of magnetic field

(usually a strong externally applied field B0)

NMR is a form of both absorption and emission

spectroscopy, in which resonant radiation is absorbed by

an ensemble of nuclei in a sample, a process causing

detectable emissions via a magnetically induced

electromotive force.


4/37

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 motion

Chemical dynamics and exchange

Diffusion rate 3D Distribution of NMR spins in a medium an image!

(Better known as MRI)

Plus many more things of interest to chemists


5/37

History of NMR

1920-1930: physics begins to grasp the

concepts of electron and nuclear spin

1936: C. J. Gorter (Netherlands) attempts tostudy 1H and 7Li NMR with a resonance

method, but fails because of relaxation

1945-6: E. M. Purcell (Harvard) and F. Bloch

(Stanford) observe 1H NMR in 1 kg of parafin at

30 MHz and in water at 8 MHz, respectively 1952: Nobel Prize in Physics to Purcell and

Bloch

1957: P. C. Lauterbur and Holm

independently record 13C spectra

1991: Nobel Prize in Chemistry to R. R. Ernst

(ETH) for FT and 2D NMR

2002: Nobel Prize in Chemistry to K. Wuthrich

2003: 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


6/37

Nuclear Magnetism

A nuclear electromagnet is

created by the nucleons (protonsand neutrons) inside the atomic

nucleus.

This little electromagnet has a

magnetic moment (J T-1)

The magnetic moment is

proportional to the current

flow through the nuclear

loop

The nucleus looks like a dipole to

a distant charge centre

N

SFromhttp://education.jlab.org


7/37

Basic NMR Theory

In a strong applied magneticfield (B

0), certain atomic nuclei

will align or oppose this field.

This alignment is caused bythe magnetic moments of thenuclei, which themselves arecaused by the internalstructure of the nucleus. Two

nuclear properties stand out: Spin (1/2 for1H, 13C, etc)

Gyromagnetic ratio

An excess of alignments isfound in the lower energy state

(determined by a Boltzmanndistribution).

At room temperature, thisexcess is very small, typicallyonly 1 part per trillion!


8/37

Nuclear Spin

In a classical sense the bulk nuclear

magnetization is observed toprecess at the Larmor frequency

(usually several hundred MHz):

The constant is the magnetogyricratio.

2

00

B=00 B =

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

B0


9/37

Elements Accessible by NMR

Figure from UCSB MRL website

White = only spin

Pink = spin 1 or greater (quadrupolar)

Yellow = spin or greater


10/37

Pulsed vs. Continuous-Wave NMR

NMR effects are most commonly detected by resonant radio-

frequency experiments

Continuous-wave NMR: frequency is swept over a range (e.g.

several kilohertz), absorption of RF by sample is monitored

Historically first method for NMR

Poor sensitivity

Still used in lock circuits

Pulsed NMR short pulses (at a specific frequency) are

applied to the sample, and the response is monitored. Much more flexible (pulse sequences followed from this)

Short pulses can excited a range of frequencies


11/37

NMR Theory: The Rotating Frame The magnetization precesses at the Larmor frequency, the RF field(s)

oscillate at or near this same frequency

The rotating frame rotates at this frequency, simplifies the picture for

analysis and understanding

Frame rotating at the Larmor frequency

hundreds of MHz Frame is now still

eye

z z

x

y


12/37

Spin Systems

The reason NMR is so applicable to structural problems is

that the governing interactions can be separated andtreated individually

Experimentally, this results in spectral simplification (in that

transitions are not hopelessly entangled) and also allows for

detailed manipulations (pulse sequences) to extract information

This involves separation of electronic Hamiltonian from

the 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 13C nucleus


13/37

NMR Theory: RF Pulses

z

x

y

Drawing depicts a 90o pulse

z

x

y

RF pulses are used to drive the bulk magnetization to the desired position

The action of an RF pulse is determined by its frequency, amplitude, length and

phase

For an on-resonant pulse, the right hand rule predicts its action

Drawing depicts a 180o pulse


14/37

NMR Theory: RF Pulses and Spin Echoes

An RF pulse:

Two pulses:

echo

(delays and extra

pulse)

Actually not solid,

contains RF

frequencies


15/37

Selection Rules

Single-quantum transitions (m =

+/- 1) are allowed by angularmomentum rules (which govern

spins in NMR).

Single-quantum states are

directly detected in NMRexperiments

However, it is possible to excite

double-quantum states (or zero-

quantum, triple-quantum, etc),

let them evolve with time, then

convert them back to SQ states

for observation

Energy levels for two coupled spins

showing SQ (single quantum)

transitions ingreenand forbidden

ZQ (zero quantum) and DQ (double

quantum) transitions inred

SQX

X


16/37

NMR Theory: T1 Relaxation

T1relaxation: longitudinal

relaxation (re-establishment

of Boltzmann equilibrium)

by spins interacting with the

lattice

In practice, T1 controls how

quickly FT experiments can

be repeated for signal

averaging

Measurements of T1can

provide useful data on

molecular motions

x

z

y


17/37

NMR Theory: T2 Relaxation

T2relaxation transverse

relaxation (dephasing of

coherence) by spins

interacting with each other

Controls how long

magnetization can be kept

in the x-y plane

Controls the linewidth(FWHH) of the NMR

signals:

x

z

y

*

2

2/1

1

T

=


18/37

NMR Theory: The Chemical Shift

The electrons around a nucleus

shield are circulated by the big

magnetic field, inducing smallerfields.

Anisotropy:

Units ppm:

Shift-structure correlations thebasis of NMR as an analytical

tool.

Shift-structure correlations are

available for1H, 13C, 15N, 29Si, 31P

and many other nuclei

TPPO

PbSO4

x

y

z

( )

ref

refxppm

=610)(

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


19/37

Typical 1H NMR Chemical Shielding


20/37

Typical 13C NMR Chemical Shielding


21/37

Other Nuclei: 17O NMR

Note 17O NMR requires labeling or concentrated solutions, and suffers

from large solution-state linewidths (caused by quadrupolar relaxation)


22/37


Contributions from electronegativity and ring current

effects:

Correlation of1H Chemical Shift and Group

Electronegativity 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 5.0

Relative Chemical Shift ()

GroupElectronegativ

it


23/37


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


24/37

NMR J-Coupling

The J-coupling is an effect inwhich nuclear magnetic dipolescouple to each other via the

surrounding electrons. The effect is tiny but detectable!

Typical J-values

2-4JHH

can range from 15 to +15 Hz

and depends on the number ofbonds, bond angles, and torsion

angles

1JCH

can range from 120 to 280 Hz,

but typically is ~150 Hz in mostorganics

2-4

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

HH

The narrow ranges that certain 1H and13C J-coupling values fall into make

spectral editing and heteronuclear

correlation experiments possible!!!


25/37

J-Coupling: Effects on NMR Spectra

Two basic types of coupling

Homonuclear (e.g. 1H-1H)

Heteronuclear (e.g. 1H-19F) Weak coupling

Large difference in frequency

>> J #Lines = 2 nI+ 1

All heteronuclear coupling is

weak

More complex splitting patterns

can be visualized using

Pascals triangle

Strong coupling

Small difference in frequency

~ J Complex patterns


26/37

J-Coupling: Effects on NMR Spectra Example:

monofluorobenzene

Homonuclear couplingbetween 1H:

ortho-coupling

meta-coupling

para-coupling

Heteronuclear coupling

between 1H and 19F:

As above (ortho, meta,

andpara).

Observed from the 19F,

appears as a doublet of

triplets of triplets (ttd)

Fluorine can be decoupled

from the 1H spectrum (not

shown)

para

orthometa


27/37

Structural and Conformational Analysis

J-coupling is widely used (in conjunction with 2D NMR)

to assemble 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/biochemical

systems in solution

In this case, the J-coupling is measured e.g. to the nearest 0.1

Hz and analyzed more closely


28/37

J-Coupling: Angle Effects

Karplus relationships the

effects of bond and torsion

angles on J-coupling Bond angles, dihedral

(torsion) angles, 4 and 5-

bond anglesIn[1]:= J_ :4.22Cos 2 0.5Cos 4.5

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

0.5 1 1.5 2 2.5 3

6

7

8

9

Out[3]= Graphics Dihedral angle (radians)

Couplingconstant(Hz)


29/37

Dipolar Coupling

The magnetic dipolar interaction between

the moments of two spin-1/2 nuclei

One spin senses the others orientation

directly through space

The dipolar coupling is simply related to the

internuclear distance between the spins:

The truncated (secular) dipolar Hamiltonians (relevant to NMR) have the

form:

( ) ( )[ ]++

+= SISISIDH zzrHomonuclea

D 412 cos31

( ) [ ]zzearHeteronuclD SIDH cos31 2=

38 rD SI

20

=


30/37

The Nuclear Overhauser Effect

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

experiment.

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

Overhauser predicted that saturation of the conduction

electron spin resonance in a metal, the nuclear spinswould be polarized 1000 times more than normal!!!


31/37

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 rapid

molecular tumbling.

However, the dipolarinteraction can stillplay a role via in

solution-state NMR

via dipolar cross-

relaxation

mechanisms, better

known as the

nuclear Overhauser

effect(NOE).


32/37

NMR Spectrometer Design

The basic idea:

NMR Magnets


33/37

NMR Magnets

Superconducting magnets:


34/37

Resonance

The natural frequency of a inductive-capacitive circuit:

LCr

1=

The NMR system requires a resonant circuit to detect

nuclear spin transitions this circuit is part of the probe

R t Ci it i P b


35/37

Resonant Circuits in Probes

Figure from Bruker Instruments


36/37

NMR Probe Design

The NMR probe

designed to efficientlyproduce an

inductance (~W) and

detect the result (

topic 7 nuclear magnetic resonance

Documents