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Nuclear Magnetic Resonance (NMR) Spectroscopy

Dr. Vincent J. Storhaug

NMR Spectroscopy

NMR spectroscopy is a form of absorption

spectrometry.

Most absorption techniques (e.g.

Ultraviolet-Visible and Infrared) involve the

electrons in the case of NMR, it is the nucleus

of the atom which determines the response. An

applied (magnetic) field is necessary to

develop the energy states (produce a separation

of the energy states) necessary for the

absorption to occur.

Development of Energy States of Nuclei in an

Applied Magnetic Field

Spin Â½ Nucleus Bar Magnet

Development of Energy States of Nuclei in an

Applied Magnetic Field

Spin Â½ Nucleus Bar Magnet

Populations of the Energy States of Hydrogen

Nuclei (Spin Â½ Nuclei) in a Magnetic Field

Ea

Without an applied magnetic field, there is no

division of energy states to discuss.

Development of Energy States of Nuclei in an

Applied Magnetic Field

The nuclei have a property of spin,

characterized by

p angular momentum quantized in units of

h/(2p) I spin quantum number will be in integer

or half-integer values

This angular momentum is directly related to the

magnetic dipole moment, Âµ, by

? magnetogyric ratio, dependent on the type of

nucleus

Development of Energy States of Nuclei in an

Applied Magnetic Field

There will be 2I1 discrete energy states, as

indicated by

???

I

I-1

I-2

-I

This value is called the magnetic quantum state,

mI.

The simplest situation, therefore is a system of

two energy states, i.e. I Â½.

The value of I for 1H, 13C, 19F, and 31P is Â½, so

we have

Â½

-Â½

Magnetic Properties of the Four Most Commonly

Observed Nuclei

Magnetogyric Ratio (radian T-1 s-1)

Relative Sensitivity

Absorption Frequency (MHz)

Nucleus

1H 13C 19F 31P

2.6752 x 108 6.7283 x 107 2.5181 x 108 1.0841

x 108

1.00 0.016 0.83 0.066

400 100.6 376.5 162.1

All of these nuclei have spin I

Â½! http//www.chem.tamu.edu/services/NMR/periodi

c/index.shtml

Development of Energy States of Nuclei in an

Applied Magnetic Field

Potential energy, E, and the energy difference

between two given states

0

Transition of Nucleus from One Energy State to

Another

Planck relationship, between ?E and an applied

radio frequency, ?0 is

Relationship Between Resonance Frequency and the

Applied Field Strength

Boltzmann Distribution of Nuclei Among the Energy

Levels

Nj the number or nuclei occupying the higher

energy state N0 the number or nuclei occupying

the lower (ground) energy state

Since (for NMR active nuclei) when you apply a

magnetic field, Bo , a nonzero difference between

the energy states develops, ?E, then we know that

Nj will always be smaller than N0.

Boltzmann Distribution of Nuclei Among the Energy

Levels

Experimentally, we can do only two things in

order to increase the difference in populations

of the ground and excited states 1. We can

increase the strength of the applied field,

B0. 2. We can decrease the absolute temperature,

T.

Example Calculation of the Distribution of Nuclei

Among the Energy Levels

1H NMR, calculate the ratio Nj/N0, for an NMR

system where the magnet has a field of 4.69 T,

and the temperature is 20 ÂºC.

i.e. The populations differ by less than 0.004!

Basics of Fourier Transform NMR Relying on

Nuclear Precession

NMR Relying on Radio Frequenciesand Nuclear

Precession

Continuous Wave (CW) NMR

B0

B0

?0

?

Absorption

ÂµZ

Âµ

ÂµZ

Âµ

?

?

Emission

?

?0

m1/2

m-1/2

Circularly Polarized Radiation

ÂµZ magnetic field vector (magnetic vector from

the rotating frame of reference) Âµ spin axis of

the nucleus ? angle between the magnetic field

vector and the spin axis of the particle

Continuous Wave (CW) NMR

Continuous Wave (CW) NMR

- Low magnetic field strength needed (advantage

AND disadvantage) - Low sensitivity, and limited to a single sweep

of the spectral window - (If you have a small amount of material, you

are simply out of luck) - Low resolution (1 Hz linewidth FWHM - is

considered great resolution for CW) - Limited mostly to 1H NMR ONLY. 13C NMR not

possible due to decreased sensitivity - (and single sweep)
- No computer is necessary, direct plotting of

spectrum, but also no way to digitally - save spectrum.

Basics of Fourier Transform NMR Relying on

Nuclear Precession

where ?0 is the angular velocity of the

precession, in radians/second

Experimentally, we need to convert this angular

velocity to its corresponding frequency in the

electromagnetic spectrum

where ?0 is now in millions of rotations per

second units, or commonly, Megahertz (MHz). ?0

is referred to as the Larmor Frequency.

The Fourier Transform Pulsed NMR Technique

M0

B0

B0

Laboratory (Static) Frame of Reference

Rotating Frame of Reference

Where the Quantum Explanation Ends, and the

Classical One Takes Over

Basics of Fourier Transform NMR Relying on

Nuclear Precession

z

Rotating Frame of Reference

M0

y

x

B0

The Fourier Transform Pulsed NMR Technique

time

Delay

Pulse

Delay

Acquisition

time

The Fourier Transform Pulsed NMR

Technique(Rotating Frame of Reference)

time

90Âº

M0

RF

M0

B1

B0

B0

The Fourier Transform Pulsed NMR

Technique(Rotating Frame of Reference)

a

RF

M0

Mz

My

B1

B1

B0

B0

a angle of rotation in radians ? magnetogyric

ratio (radians T-1 s-1) B1 induced magnetic field

(T) t pulse width (s)

The Fourier Transform Pulsed NMR

Technique(Rotating Frame of Reference)

time

M0

B0

The Fourier Transform Pulsed NMR

Technique(Rotating Frame of Reference)

0

time

M0

M0

M0

M0

Basics of Fourier Transform NMR Measuring the

Precession Frequency

Relaxation Process in NMR

Spin-Lattice Relaxation, T1 The absorbed energy

is lost through vibrational and rotational motion

to the magnetic components of the lattice of

the sample. Problem The temperature of the

sample can rise over time. Spin-Lattice

relaxation processes cause an exponential decay

of the excited state population. The more viscous

a sample is, or the more restricted the motion of

a molecule is, the larger the T1. Spin-Lattice

relaxation is the slower of the relaxation

processes. Spin-Spin Relaxation, T2 Several

processes are lumped under this term, but one

of the predominant techniques is spin diffusion,

a process requiring neighboring nuclei to have

the same precession rates, but different magnetic

quantum numbers. Another cause is a disruption in

the homogeneity of the magnetic field through the

sample caused by the sample itself. (e.g.

formation of dimers, trimers, etc. that change

the relaxation rates of nuclei.) Spin-Lattice

relaxation is the faster of the relaxation

processes. Thus, T2 is the primary influence on

line broadening in the spectrum.

Spin-Spin Relaxation, T2

Mxy

time

z

y

x

time

Longitudinal Spin-Lattice Relaxation, T1

Mxy

time

My

Mz

Longitudinal Spin-Lattice Relaxation, T1

The time constant, T1,describes how MZ returns to

its equilibrium value. The equation governing

this behavior as a function of the time t after

its displacement is T1 is therefore

defined as the time required to change the Z

component of magnetization by a factor of e. If

the net magnetization is placed along the -Z

axis (i.e. pw 180Âº), it will gradually return

to its equilibrium position along the Z axis

at a rate governed by T1. The equation governing

this behavior as a function of the time t after

its displacement is

Relaxation of Mxy During Fourier Transform NMR

Responses Due to T1 AND T2

Basics of Fourier Transform NMR The Free

Induction Decay

Signal to Noise Improvement

With digital summations of FIDs (or rather,

transients),

where n is the total number of scans acquired.

Signal to Noise Improvement Practical

Considerations

- Running a 13C NMR spectrum.
- Not limited so much in the amount of sample, but

by the solubility of the compound in the

available solvent (deuterated CDCl3) - Ran the sample for 4 hours, and it looks like

In order to increase the S/N by a factor of 2,

this would need to run for 16 hours. In order to

increase the S/N by a factor of 4, this would

need to run for 64 hours (almost 3 days).

CW vs FT NMR

Continuous Wave

Fourier Transform

- Samples are run neat
- Less expensive, no deuterated
- solvents are necessary
- Larger quantities of sample are
- needed (gram)
- Limited primarily to 1H NMR (dedicated)
- Slow acquisition, have to sweep the
- frequencies
- Signal to Noise limited in what can be
- seen in a single sweep

- Samples are run diluted
- More expensive, MOST of the sample
- actually being a deuterated solvent
- Very small quantities (ltlt mg) are
- possible
- Interchangeable probes, multiple nuclei.
- All frequencies are measured in a rapid scan
- (milliseconds)
- Theoretically, the Signal to Noise is limited
- only by the time available to acquire the
- spectrum