NMR Spectroscopy

Randolf

What does NMR spectroscopy probe?

It probes the absorption and emission of energy between nuclear spin energy levels when they are excited

Where does nuclear spin arise from?

Unpaired protons or neutrons in the nucleus

What does I represent?

Spin quantum number (angular momentum quantum number)

When number of protons and neutrons are both even…

Spin (I) is zero, these nuclei aren’t NMR active

If protons = odd and neutrons = even, or the other way round…. What is an example of a nuclei like this?

Spin is a 1/2 integral 1/2, 3/2…e.g.

13C p = 6 n = 7

19F p = 9, n = 10

Odd number of protons and neutrons?

Spin integral 1,2,3…

What is the problem with paramagnetic nuclei?

The magnetic moment of an unpaired electron is 1000 greater than that of nuclei, leading to additional magnetic fields leading to **large chemical shifts**, and an effective relaxation, leading to **broadened NMR signals**

When I = 1/2

We get good interpretable results, sharp lines

When I > 1/2

We can get broad signals, which are problematic. They can still be used though, and we’d need to look at the quadrupole moment of the nucleus

Energy levels in NMR arise from interactions of the nuclear spins with 3 things, what are they?

The spectrometer magnetic field B0

The magnetic fields created by the electrons in the system (shielding dampens external field)

The magnetic fields created by other nuclear spins in the system- which result in coupling

The gyromagnetic ratio tells us

How large the splitting is in NMR, bigger is better

A negative gyromagnetic ratio results in negative…

NOE enhancement, which is worth considering when decoupling NMR spectra.

The smaller the quadrupole moment in I>1/2 nuclei, the…

Easier it is to observe splitting and transitions

What are some commonly used I > 1/2 nuclei?

2H, 7Li, 10B, 11B, 14N, 51V

A spinning nucleus possesses…, governed by the equation

Nuclear spin angular momentum P,

I is the angular momentum quantum number

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The spinning of a charged nucleus generates a vector, the…, governed by the equation…

Nuclear magnetic moment μ

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Again, how is the sensitivity of the detection of a nuclide dependent on gamma the gyromagnetic ratio?

Large gamma, = easy to observe , or sensitive

Small gamma = hard to observe, insensitive

Equation lining magnetic moment with gyromagnetic ratio?

What is m_I? What does it represent?

The magnetic quantum number, it represents the component of the nuclear spin I along the z axis I_z

What are the possible values of m_I

I, I-1, … -I. To total 2I + 1 values of m_I associated with nuclear spin I

If a nucleus of angular momentum P and magnetic moment m is placed in a magnetic field strength of B_0 oriented along the z axis, the nuclear angular momentum orients so that

Different orientations of the nuclear magnetic moment will have different …. and therefore different … depending on…

Different orientations of the nuclear magnetic moment will have different

magnetic moments and therefore different energies depending on their

orientation with respect to the direction of the applied field, B0

Why are only certain orientations of μ allowed to interact with the applied field B?

Each orientation corresponds to a different m_I value, this ie because of quantisation of I

Equation for energy of a magnetic dipole in a field?

Selection rule for NMR transitions between spin states?

Change m_I = p/m 1

There are … possible transitions for a spin I nucleus, with energy…, meaning that…

2I

The same energy = -gamma hbar B0

Only one resonant frequency for the nucleus is expected, irrespective of the value of I for the nuclide

Equation for frequency of energy transition

What is the Larmor frequency V_L

The resonant frequency, or the frequency the nucleus precesses around the Z axis of the field, 54 degrees

In NMR spectroscopy, interactions with other magnetic fields from…. leads to alterations of the … and often much more than … being observed.

However, in NMR spectroscopy interactions with other magnetic fields from

the spin of other nuclides and electrons leads to alterations of the nuclide’s

resonant frequency and often to much more than a mere single resonance

being observed – Chemical Shift and Coupling!

Since frequency v depends on spectrometer field strength, how do we standardise this for nuclei?

We use chemical shift

Typical order of magnitude for a resonant frequency?

100 MHz

Do nuclear isotopes have different gyromagnetic ratios? If so, how are they related?

An isotope will have its own distinct gyromagnetic ratio, defined by

Why don’t we see 1H or 195Pt nuclei signals in a 31P NMR spectrum?

Transitions are induced between different energy levels by irradiating with a superimposed field B1 of the correct quantum energy, so we tune to the nuclide of choice!

NMR signals strength depends on

The population between the ground and excited states

The two processes occur at the same energy

therefore the intensity of the observed NMR signal depends on the

difference between the numbers of absorption and emission

processes occurring – net movement

What does net movement between spin states depend on?

The population difference given by Boltzmann statistics, since the probabilities of emission and absorption are equal.

N_upper/ N _lower = ….

Usually a very small population difference!

The observed signal is proportional to

N-a - N_b

If the populations in each state are exactly equal, what happens

Saturation, no signal is observed

Nuclides with low gyromagnetic ratios tend to give…

Sensitivity of a nucleus is proportional to? For a fixed B

Weaker signals

Relative receptivity is given relative to… What equation form do we use?

1H or 13C

How else can we increase the sensitivity of an NMR experiment? (3 ways)

Use a stronger magnet in the spectrometer, by increasing B_0 the Boltzmann distribution becomes more favourable

We can also lower sample temperature, which increases population difference to give a stronger, but broadened signal

Use more concentrated samples

Describe the FT NMR experiment, why do we do it?

We use pulsed NMR to irradiate all spectral frequencies at once, then detect all the resonances at the same time.

When the states relax they emit radiation, which comes out as a FID signal, converted to a real spectrum by Fourier Transform techniques.

It is very time efficient and allows “rapid multiple passes” so a good signal to noise ratio can be established.

Chemical shift is defined with respect to…

The nuclei in a reference compound, whose chemical shift is usually given the arbitrary value of zero.

The convention for +ve and -ve chemical shifts, relating to shielding, direction, field frequency?

\+ve shift, higher than standard frequency, indicating deshielded environment, and is low-field. (left)

Coupling to n chemically equivalent nuclei gives rise to….

Different spin states result in

Different energies/frequencies/shifts

In a coupling tree, we should start with

The higher coupling constants

How many peaks does this compound have

2 P31 resonances, since 2 different chemical environments

What coupling pattern should arise from this compound?

2 doublets with equal intensity

What is a first order splitting pattern?

Like the one above, where

When do second order effects occur, and what do I expect to see?

When the difference in shifts delta P- delta P is similar to the coupling constant 2J_pp

We expect to see roofing distortions, in an A=B system. If it becomes A2, we only see a singlet and no coupling

What 3 big factors affect the magnitude of the coupling constant J?

%S character, higher like SP is better than SP3. Nuclear spin interacting with electrons needs electrons close to the nucleus, s electrons have a non-zero probability of being at the nucleus.

Stereochemistry, trans couplings are stronger, since we need good alignment of bonds

Number of bonds between nuclei, 1J is 10x higher than 2J, which is similar to 3J

What is broad band decoupling, and why do we use it?

31P NMR spectra of some phosphines get complicated multiplets due to H-P coupling

We simplify them by broad band decoupling the proton frequency, by irradiating the 1H frequency as well as 31P, so there is no coupling to protons

Given the molecule PF5, why do we observe 1 signal at RT?

The exchange of fluorine NMR states is too fast for the NMR timescale (fluxionality)

If we wanted to see it, then we could cool the sample down.

What are isopotomers?

Compounds with isotopes of nuclei resulting in slightly different chemical shifts

What dilute I = 1/2 nuclei could we expect to display satellites?

What does quadrupole moment arise from?

Electric field gradient at nucleus from uneven charge distribution

What do quadrupoles do to lines?

The electric field gradient interacts with the magnetic field, leading to rapid relaxation of nucleus

Peak width increases with 1/T2

Nuclei with I > 1/2 possess a quadrupole moment Q

• an electric field gradient that interacts the nuclear magnetic moment

• results in fast relaxation of the nuclei, which scrambles energies of the spin

states

• meaning that NMR spectra are broad (expressed as width at half height Dv1/2)

• coupling is often not resolved

• line widths proportional to Q^2

Do we want large or small quadrupole moments?

Small

What is the name of the process where we see broad lines due to rapid relaxation rates?

Heisenberg broadening

When can we still use quadrupolar nuclei for NMR?

When we have a highly symmetrical environment like octahedral or tetrahedral

These give line widths as if I = 1/2

Less symmetric increases relaxation rate, defining the energy levels poorly for broad signals.

Why are couplings washed out in quadrupolar nuclei?

Poorly defined energy levels

How does coupling in 2D or 6Li differ from a triplet from 1H (I= 1/2)

I = 1, so 3 peaks BUT all at same intensity since the 3 possible spin states M= 1,0,-1 all have equal probability

1:1:1 triplet

Predict the 13C NMR of C6D6

Does Pascal’s triangle hold for I > 1/2 nuclei

No

How do work out the coupling pattern for n nuclei of I = 1?

Signal increase by factor … for N scans

Noise increases by factor…

Signal by N

Noise by sqrt(N)

For N scans, signal to noise ratio increases by

sqrt (N)

If we have 1/N concentration, how many more scans do we need to get the same quality spectrum, at same width

N^2 scans

In this example, how many more scans do we need to do for 1 to have the same S/N as the other?

Why is there no net magnetisation for molecules in solution?

The molecules are randomly tumbling, in the absence of an applied field, all the nuclear magnetic moments will be randomly oriented

Heisenberg uncertainty principle in FT NMR

By limiting irradiation time, we have less uncertainty in time and energy, so length of pulse is uncertainty over time.

Shorter pulse on range of frequencies

Shorter pulse = larger range of frequenciess

Nuclear spin transitions cause

A displacement of M from the z’ axis towards the y’ axis by an angle theta, the pulse/tip angle

What determines the pulse angle through which M is tipped?

The strength/time length of the excitation pulse B1

After the pulse has been applied, M…

precesses about the z’ axis until it returns to the pre-pulse state, relaxing back

The observable NMR signal is

the projection of this precession onto the x’-y’ plane. Since the receiver coil is oriented along the y’ axis, the intensity of the signal depends on the amount of magnetisation in the y’ direction, My

Maximum signal intensity if observed at, and zero intensity expected at

Mzximum at theta = 90 degrees

Zero at 0 degrees

What happens to energy and magnetisation during relaxation?

The magnetisation begins to revert back to its eqm state, the excited nuclear spins lose energy and drop to the GS

Timescale of relaxation

seconds to hours

Generally, relaxation occurs by…

transfer of magnetisation to other dipoles

What is dipole-dipole relaxation?

Dipole-Dipole relaxation occurs when the sample contains other nearby magnetic dipoles that can interact with the nuclear magnetic moment e.g. nuclei or electrons

Effectiveness of relaxation depends on and is proportional to, so for two nuclei, the higher … will give faster relaxation.

What determines how fast a nuclear magnetisation relaxes to equilibrium magnetisation?

The number and distance to neighbouring dipoles

In the absence of more effective relaxation mechanisms, relaxation time will depend on…

number of nearby H atoms (due to high g ratio) and is dominated by directly bonded H CH3 > CH2> CH >>> C

Long relaxation times occur with (4)

Low viscosities, high temperatures and small molecular masses and concentration.

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Are long relaxation times desirable?

Yes

Dipole dipole interactions occur by 2 clear mechanisms, what are they?

Spin-spin relaxtation T2

Spin-lattice relaxation T1

The shorter the relaxation times, the … the signals

The shorter the relaxation times, the

broader the signals

T1 vs T2 in isotropic media

T1 = T2

Equation for T2

When can we expect effective relaxation and broad lines? (5)

Viscous media

Large molecular mass (proteins)

Low temperature (more viscous)

Quadrupole moments with lower than cubic symmetry

Nuclei interact with paramagnetic centres (paramagnetic shift reagents)

In Spin-Spin relaxation T2, a nucleus of 1 atoms…

A nucleus of one atom imparts or exchanges its energy (magnetisation) to

another surrounding nuclei resulting in no overall change in spin

populations

Spin- spin relaxation corresponds to the magnetisation...

Fading away in the x’-y’ plane

Longer values of T2 give

Narrow line widths

W1/2 = 1/ pi T2

Describe Spin-Lattice relaxation T1

Decay of magnetisation by the tipped nucleus returns to its normal state by exchanging magnetisation energy with surroundings- the lattice. It corresponds to the growing back of magnetisation along the z’ direction

What is T1 important for>

It determines how frequently we can pulse the nucleus since it is the slower process when compared to T2, in the extreme case they’re the same

Describe the the process to measure T1

Inversion recovery, we probe signal inetnsity after time tau. We plot intensity against tau, and use the model to find T1

At zero intensity, tau =

ln2 (T1)

What 2 things does quadrupolar relaxation depend on (when I>1/2)

Nuclear quadrupole and electric field gradient of nucleus