Lecture Date: February 11th, 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)

The Electromagnetic Spectrum

NMR, MRI

EPR/ESR

What is NMR?

NMR is an experiment in which the resonance frequencies of nuclear magnetic systems are investigated.

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.

A. Abragam, The Principles of Nuclear Magnetism, 1961, Oxford: Clarendon Press.

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…

History of NMR

1920-1930: physics begins to grasp the concepts of electron and nuclear spin

1936: C. J. Gorter (Netherlands) attempts to study 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

Nuclear Magnetism

A nuclear electromagnet is created by the nucleons (protons and 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 center

N

SFrom http://education.jlab.org

Basic NMR Theory In a strong applied magnetic field

(B0), certain atomic nuclei will align or oppose this field.

This alignment is caused by the magnetic moments of the nuclei, which themselves are caused by the internal structure of the nucleus. Two nuclear properties stand out:

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

An excess of alignments is found in the lower energy state (determined by a Boltzmann distribution).

At room temperature, this excess is very small, typically only 1 part per trillion!

Nuclear Spin

In a classical sense the bulk nuclear magnetization is observed to “precess” at the Larmor frequency (usually several hundred MHz):

The constant is the magnetogyric ratio.

2

00

B00 B

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

B0

Elements Accessible by NMR

Figure from UCSB MRL website

White = only spin ½Pink = spin 1 or greater (quadrupolar)

Yellow = spin ½ or greater

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

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

Spin Systems

The reason NMR is so applicable to structural problems is that the governing interactions can be separated and treated 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

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

NMR Theory: RF Pulses and Spin Echoes

An RF pulse:

Two pulses:

echo(delays and extra

pulse)

Actually not “solid”, contains RF frequencies

Selection Rules

Single-quantum transitions (m = +/- 1) are allowed by angular momentum rules (which govern spins in NMR).

Single-quantum states are directly detected in NMR experiments

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 in green and forbidden ZQ (zero quantum) and DQ (double

quantum) transitions in red

SQX

X

NMR Theory: T1 Relaxation

T1 relaxation: 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 T1 can provide useful data on molecular motions

x

z

y

NMR Theory: T2 Relaxation

T2 relaxation 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

NMR Theory: The Chemical Shift

The electrons around a nucleus shield are circulated by the big magnetic field, inducing smaller fields.

Anisotropy:

Units – ppm:

Shift-structure correlations – the basis of NMR as an analytical tool.

Shift-structure correlations are available for 1H, 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!

Typical 1H NMR Chemical Shielding

Typical 13C NMR Chemical Shielding

Other Nuclei: 17O NMR

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

NMR Theory: The Chemical Shift

Contributions from electronegativity and ring current effects:

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

Correlation of 1H 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 5.0Relative Chemical Shift ()

Gro

up

Ele

ctr

on

eg

ati

vit

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

NMR J-Coupling The J-coupling is an effect in which

nuclear magnetic dipoles couple 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 of bonds, bond angles, and torsion angles

– 1JCH can range from 120 to 280 Hz, but typically is ~150 Hz in most organics

– 2-4JCH ranges from –15 to +15 Hz and depends on effects similar to the 2-

4JHH

The narrow ranges that certain 1H and 13C J-coupling values fall into make spectral editing and heteronuclear correlation experiments possible!!!

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 n I + 1 All heteronuclear coupling is

“weak” More complex splitting patterns

can be visualized using Pascal’s triangle (see text)

Strong coupling

– Small difference in frequency ~ J Complex patterns

Figure simulated in Bruker Topspin 2.0 DAISY moduleInspired by S. W. Homans, A Dictionary of Concepts in NMR, Oxford 1989, p297.

J-Coupling: Effects on NMR Spectra

Example: monofluorobenzene

Homonuclear coupling between 1H:

– ortho-coupling

– meta-coupling

– para-coupling

Heteronuclear coupling between 1H and 19F:

– As above (ortho, meta, and para).

– 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

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 and stereochemistry 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

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

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 angles

In[1]:= J_: 4.22Cos2 0.5Cos 4.5

In[3]:= PlotJ,, 0,

0.5 1 1.5 2 2.5 3

6

7

8

9

Out[3]= Graphics Dihedral angle (radians)

Cou

plin

g co

nsta

nt (

Hz)

Dipolar Coupling

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

– One spin senses the other’s 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

zzearHeteronucl

D SIDH cos31 2

38 rD SI

20

Dipolar Coupling

The permeability constant (in kg m sec2 A2) and Planck's constant (in Joule sec):

0 4 107;

6.62608 10342 ;The gyromagnetic ratios for 13C and 15N, in units of radians Tesla1 sec1 :

I 6.728 107;

S 2.712 107;

Rr_:ISr3

2 0

4

NR1.32 10101331.53

The dipolar coupling is therefore 1.332 kHz.

Example – what’s the dipolar coupling between a 13C and a 15N nucleus 1.32 angstroms apart?

The Nuclear Overhauser Effect

The idea: detect the “cross-relaxation” caused by instantaneous dipolar coupling in an NMR or EPR experiment.

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

Overhauser predicted that saturation of the conduction electron spin resonance in a metal, the nuclear spins would be polarized 1000 times more than normal!!!

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 are averaged away in solution-state NMR by rapid molecular tumbling.

However, the dipolar interaction can still play a role via in solution-state NMR via dipolar cross-relaxation mechanisms, better known as the nuclear Overhauser effect (NOE).

NMR Spectrometer Design

The basic idea:

NMR Magnets

Superconducting magnets:

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

Resonant Circuits in Probes

Figure from Bruker Instruments

NMR Probe Design

The NMR probe – designed to efficiently produce an inductance (~W) and detect the result (< mW)

NMR Electronics NMR transmitter and receiver designs

Further Reading

A. E. Derome, “Modern NMR Techniques for Chemistry Research”, Pergamon 1987.

P. W. Atkins and R. S. Friedman, “Molecular Quantum Mechanics, 3rd Ed.”, Oxford 1997.

A. Abragam, “Principles of Nuclear Magnetism”, Oxford, 1961.

R. R. Ernst, G. Bodenhausen, and A. Wokaun, “Principles of Nuclear Magnetic Resonance in One and Two Dimensions”, Oxford, 1987.

C. P. Slichter, “Principles of Nuclear Magnetic Resonance”, Springer-Verlag, 1996.