nuclear magnetic resonance (nmr) introduction : nuclear magnetic resonance (nmr) measures the...

Nuclear Magnetic Resonance (NMR) Introduction:

Nuclear Magnetic Resonance (NMR) measures the absorption of electromagnetic radiation in the radio-frequency region (~4-900 MHz)

- nuclei (instead of outer electrons) are involved in absorption process- sample needs to be placed in magnetic field to cause different

energy states

NMR was first experimentally observed by Bloch and Purcell in 1946 (received Nobel Prize in 1952) and quickly became commercially available and widely used.

Probe the Composition, Structure, Dynamics and Function of the Complete Range of Chemical Entities: from small organic molecules to large molecular weight polymers and proteins.

NMR is routinely and widely used as the preferred technique to rapidly elucidate the chemical structure of most organic compounds.

One of the One of the MOSTMOST Routinely used Analytical Techniques Routinely used Analytical Techniques

Typical Applications of NMR:1.) Structural (chemical) elucidation

‚ Natural product chemistry‚ Synthetic organic chemistry

- analytical tool of choice of synthetic chemists- used in conjunction with MS and IR

2.) Study of dynamic processes‚ reaction kinetics‚ study of equilibrium (chemical or structural)

3.) Structural (three-dimensional) studies‚ Proteins, Protein-ligand complexes‚ DNA, RNA, Protein/DNA complexes‚ Polysaccharides

4.) Metabolomics5.) Drug Design

‚ Structure Activity Relationships by NMR6.) Medicine -MRI

MRI images of the Human Brain

NMR Structure of MMP-13 complexed to a ligand

O

O

O

O

OH

OO

O

HO

NH

OH

OO

O

O

Taxol (natural product)

1937 Rabi predicts and observes nuclear magnetic resonance1946 Bloch, Purcell first nuclear magnetic resonance of bulk sample1953 Overhauser NOE (nuclear Overhauser effect)1966 Ernst, Anderson Fourier transform NMR1975 Jeener, Ernst 2D NMR1984 Nicholson NMR metabolomics1985 Wüthrich first solution structure of a small protein (BPTI)

from NOE derived distance restraints1987 3D NMR + 13C, 15N isotope labeling of recombinant proteins (resolution)1990 pulsed field gradients (artifact suppression)1996/7 residual dipolar couplings (RDC) from partial alignment in

liquid crystalline mediaTROSY (molecular weight > 100 kDa)

2000s Dynamic nuclear polarisation (DNP) to enhance NMR sensitivity

Nobel prizes1944 Physics Rabi (Columbia)1952 Physics Bloch (Stanford), Purcell (Harvard)1991 Chemistry Ernst (ETH)2002 Chemistry Wüthrich (ETH)2003 Medicine Lauterbur (University of Illinois in Urbana ), Mansfield (University of Nottingham)

NMR HistoryNMR History

NMR HistoryNMR History First NMR Spectra on Water

Bloch, F.; Hansen, W. W.; Packard, M. Bloch, F.; Hansen, W. W.; Packard, M. The nuclear induction experiment.The nuclear induction experiment. Physical Review (1946), 70 474-85. Physical Review (1946), 70 474-85.

11H NMR spectra of waterH NMR spectra of water

NMR HistoryNMR History First Observation of the Chemical Shift

11H NMR spectra ethanolH NMR spectra ethanol

Modern ethanol spectra Modern ethanol spectra

Arnold, J.T., S.S. Dharmatti, and M.E. Packard, J. Chem. Phys., 1951. Arnold, J.T., S.S. Dharmatti, and M.E. Packard, J. Chem. Phys., 1951. 1919: p. 507. : p. 507.

Bloch EquationsBloch Equations

Net Magnetization (M) placed in a magnetic Field (B) will precess:Net Magnetization (M) placed in a magnetic Field (B) will precess:

and relax (R)and relax (R)

and relax individual components: and relax individual components:

Course GoalsCourse Goals

• We will NOT Cover a Detailed Analysis of NMR Theory• We will NOT Derive the Bloch Equations

• We will NOT Discuss, in detail, a Quantum Mechanical Description of NMR

• We will NOT use Product Operator Formulism to Describe NMR Experiments

• If Interested, Dr. Harbison will Cover These Topics in a Separate Special Topics Course

• We Will Discuss Practical Aspects of Using an NMR• We Will Take a Conceptual Approach to Understanding NMR

• A Focus of the Course will be the Application of NMR to Solving the Structure of Organic Molecules

• We Will Discuss the Basic Operations of an NMR Spectrometer.

• We Will Discuss the Proper Approaches to the Set-up, Process and Analysis of NMR Experiments

• We Will Use NMR to Solve the Structure of Unknowns

• The Goal is to Not Treat an NMR Spectrometer as a Black Box, but to be a Competent Experimentalist


N-(2-Fluoroethyl)-1-((6-methoxy-5-methylpyrimidin-4-yl)methyl)-1H-pyrrolo[3,2-b]pyridine-3-carboxamide (9) MS (ES+) m/z: 344. 1H NMR (300 MHz, DMSO-d6): δ 2.24 (s, 3H), 3.67 (d, J = 5.46 Hz, 1H), 3.76 (d, J = 5.46 Hz, 1H), 3.93 (s, 3H), 4.50 (t, J = 4.99 Hz, 1H), 4.66 (t, J = 4.99 Hz, 1H), 5.69 (s, 2H), 7.26 (dd, J = 8.29, 4.71 Hz, 1H), 7.94 (d, J = 8.52 Hz, 1H), 8.28 (s, 1H), 8.41 (s, 1H), 8.49 (d, J = 4.57 Hz, 1H), 8.95 (s, J = 5.89, 5.89 Hz, 1H). HRMS (M + H) calcd for C17H18FN5O2, 344.1517; found, 344.15242.

To Be Able to Go From This:To Be Able to Go From This:

To This:To This:

And Understand How to Read and Interpret the NMR Spectral DataAnd Understand How to Read and Interpret the NMR Spectral Data


To Be Able to Go From This:To Be Able to Go From This:

To This:To This:

2-phenyl-1,3-dioxep-5-ene2-phenyl-1,3-dioxep-5-ene

1313C NMR spectraC NMR spectra

11H NMR spectraH NMR spectra

Each NMR Observable Nuclei Yields a Peak in the SpectraEach NMR Observable Nuclei Yields a Peak in the Spectra““fingerprint” of the structurefingerprint” of the structure

Information in a NMR SpectraInformation in a NMR Spectra

ObservableObservable NameName QuantitativeQuantitative InformationInformation

Peak position Chemical shifts () (ppm) = obs –ref/ref (Hz) chemical (electronic)

environment of nucleus

Peak Splitting Coupling Constant (J) Hz peak separation neighboring nuclei (intensity ratios) (torsion angles)

Peak Intensity Integral unitless (ratio) nuclear count (ratio) relative height of integral curve T1 dependent

Peak Shape Line width = 1/T2 molecular motion peak half-height chemical exchange

uncertainty principaluncertainty in

energy

A Basic Concept in ElectroMagnetic TheoryA Basic Concept in ElectroMagnetic Theory

Magnets Attract and Align


A Direct Application to NMR

A moving perpendicular external magnetic field will induce an electric current in a closed loop

An electric current in a closed loop will create a perpendicular magnetic field

For a single loop of wire, the magnetic field, B through the center of the loop is:

o – permeability of free space (4 x 10-7 T · m / A) R – radius of the wire loopI – current


RIB o2

Faraday’s Law of InductionFaraday’s Law of Induction• If the magnetic flux (B) through an area bounded by a closed conducting loop changes with time, a current and an emf are produced in the loop. This process is called induction.

• The induced emf is:

dt

d B


Simple AC generator

Lenz’s LawLenz’s Law• An induced current has a direction such that the magnetic field of the current opposes the change in the magnetic flux that produces the current.

• The induced emf has the same direction as the induced current


Direction of current follows motion of magnet

Quantum Description

Nuclear Spin (think electron spin)• Nucleus rotates about its axis (spin)• Nuclei with spin have angular momentum (p) or spin

1) total magnitude

1) quantized, spin quantum number I

2) 2I + 1 states: I, I-1, I-2, …, -II=1/2: -1/2, 1/2

3) identical energies in absence of external magnetic field

l

Theory of NMRTheory of NMR

)1( II

NMR Periodic TableNMR Periodic Table

NMR “active” Nuclear Spin (I) = ½: 1H, 13C, 15N, 19F, 31P biological and chemical relevanceOdd atomic mass

I = +½ & -½

NMR “inactive” Nuclear Spin (I) = 0:12C, 16OEven atomic mass & number

Quadrupole Nuclei Nuclear Spin (I) > ½:14N, 2H, 10B

Even atomic mass & odd numberI = +1, 0 & -1

Magnetic Moment (Magnetic Moment ())• spinning charged nucleus creates a magnetic field

Similar to magnetic field created by electric current flowing in a coil

Magnetic moment

““Right Hand Rule”Right Hand Rule”• determines the direction of the magnetic field around a current-carrying wire and vice-versa

Gyromagnetic ratio (Gyromagnetic ratio ())

• related to the relative sensitive of the NMR signal

• magnetic moment () is created along axis of the nuclear spin

where: p – angular momentum – gyromagnetic ratio (different

value for each type of nucleus)

• magnetic moment is quantized (m)

m = I, I-1, I-2, …, -I

for common nuclei of interest:

m = +½ & -½

IIh

2p

Gyromagnetic ratio (Gyromagnetic ratio ())

• magnetic moment is quantized (m)

m = I, I-1, I-2, …, -I

for common nuclei of interest:

m = +½ & -½

Isotope Net Spin / MHz T-1 Abundance / %

1H 1/2 42.58 99.98

2H 1 6.54 0.015

3H 1/2 45.41 0.0

31P 1/2 17.25 100.0

23Na 3/2 11.27 100.0

14N 1 3.08 99.63

15N 1/2 4.31 0.37

13C 1/2 10.71 1.108

19F 1/2 40.08 100.0

Bo

= h / 4

Magnetic alignmentMagnetic alignment

In the absence of external field,each nuclei is energetically degenerate

Add a strong external field (Bo) and the nuclear magnetic moment: aligns with (low energy)

against (high-energy)

Spins Orientation in a Magnetic Field (Energy Levels)Spins Orientation in a Magnetic Field (Energy Levels)

• Magnetic moment are no longer equivalent

• Magnetic moments are oriented in 2I + 1 directions in magnetic field

Vector length is:Vector length is:

Angle (Angle () given by:) given by:

Energy given by:Energy given by:

)1( II

)1(cos

II

m

oBI

mE

where,where,BBoo – magnetic Field – magnetic Field

– – magnetic momentmagnetic momenthh – Planck’s constant – Planck’s constant

For I = 1/2


• The energy levels are more complicated for I >1/2


• Magnetic moments are oriented in one of two directions in magnetic field (for I =1/2)

• Difference in energy between the two states is given by:

E = h Bo / 2

where:Bo – external magnetic fieldh – Planck’s constant – gyromagnetic ratio

Frequency of absorption: = Bo / 2


• Transition from the low energy to high energy spin state occurs through an absorption of a photon of radio-frequency (RF) energy

RF

NMR Signal (sensitivity)NMR Signal (sensitivity)

• The applied magnetic field causes an energy difference between the aligned () and unaligned () nuclei

• NMR signal results from the transition of spins from the to state

• Strength of the signal depends on the population difference between the and spin states

• The population (N) difference can be determined from the Boltzmann distribution and the energy separation between the and spin states:

N / N = e E / kT

Bo = 0

Bo > 0 E = h

Low energy gap

NMR Signal (sensitivity)NMR Signal (sensitivity)

Since:

E = hE = hand

= Bo / 2then:

The E for 1H at 400 MHz (Bo = 9.39 T) is 6 x 10-5 Kcal / mol

Very Small !Very Small !~60 excess spins ~60 excess spins per million in lower per million in lower statestate

N/N = e(hBo/2kT)N / N = e E / kT

NMR SensitivityNMR Sensitivity

EhBo /2

NMR signal (s) depends on:

1) Number of Nuclei (N) (limited to field homogeneity and filling factor)

2) Gyromagnetic ratio (in practice 3)

3) Inversely to temperature (T)

4) External magnetic field (Bo2/3, in practice, homogeneity)

5) B12 exciting field strength (RF pulse)

N / N = e E / kT

Increase energy gap -> Increase population difference -> Increase NMR signalIncrease energy gap -> Increase population difference -> Increase NMR signal

E ≡ Bo≡

s 44BBoo22NBNB11g(g()/T)/T

- Intrinsic property of nucleus can not be changed.

C)3 for 13C is 64xN)3

for 15N is 1000x

1H is ~ 64x as sensitive as 13C and 1000x as sensitive as 15N !

Consider that the natural abundance of 13C is 1.1% and 15N is 0.37%relative sensitivity increases to ~6,400x and ~2.7x105x !!


• Relative sensitivity of 1H, 13C, 15N and other nuclei NMR spectra depend on Gyromagnetic ratio (Gyromagnetic ratio ()) Natural abundance of the isotope Natural abundance of the isotope

1H NMR spectra of caffeine8 scans ~12 secs

13C NMR spectra of caffeine8 scans ~12 secs

13C NMR spectra of caffeine10,000 scans ~4.2 hours


Increase in Magnet Strength is a Major Means to Increase Sensitivity


But at a significant cost!

~$800,000 ~$2,00,000 ~$4,500,000


An Increase in concentration is a very common approach to increase sensitivity

30 mg

1.2 mg

http://web.uvic.ca/~pmarrs/chem363/nmr%20files/363%20nmr%20signal%20to%20noise.pdf

http://web.uvic.ca/~pmarrs/chem363/nmr%20files/363%20nmr%20signal%20to%20noise.pdf


But, this can lead to concentration dependent changes in the NMR spectra (chemical shift & line-shape) resulting from compound property changes

Beilstein J. Org. Chem. 2010, 6, No. 3.

Dimerization as concentration increases from 0.4 to 50 mM

Beilstein J. Org. Chem. 2010, 6, 960–965.

H-bond and multimer formation as concentration increases from 1 to 30 mM


An Increase in the number of scans (NS) or signal-averaging is the most common approach to increase sensitivity (signal-to-noise (S/N)

S/N ≈ NS1/2


But, it takes significantly longer to acquire the spectrum as the number of scans increase:

Experimental Time = Number of Scans x Acquisition Time

8 scans ~12 secs

10,000 scans ~4.2 hours

Dalton Trans.,2014, 43, 3601-3611


Lowering the temperature is usually not an effective means of increasing sensitivity because of chemical shift changes and peak broadening

Significant peak broadening

Significant chemical shift changes

Classical Description

Theory of NMRTheory of NMR

• Spinning particle precesses around an applied magnetic field

A Spinning Gyroscopein a Gravity Field

)1(cos

II

m


• Angular velocity of this motion is given by:

o = Bo

where the frequency of precession or LarmorLarmor frequency is:

= Bo/2

Same as quantum mechanical description

Classical Description• Net Magnetization

Nuclei either align with or against external magnetic field along the z-axis. Since more nuclei align with field, net magnetization (Mo, MZ) exists parallel

to external magnetic field. Net Magnetization along +Z, since higher population aligned with Bo.

Magnetization in X,Y plane (MX,MY) averages to zero.

Mo

z

x

yy

x

z

Bo Bo

Net Magnetization in a Magnetic Field

Mo

y

x

z

x

y

z

Bo Bo

Bo > 0 E = h

Bo

Classic View:- Nuclei either align with or against external magnetic field along the z-axis.

- Since more nuclei align with field, net magnetization (Mo) exists parallel to external magnetic field

Quantum Description:- Nuclei either populate low energy (, aligned with field) or high energy (, aligned against field)

- Net population in energy level.

- Absorption of radio- frequency promotes nuclear spins from .

An NMR ExperimentAn NMR Experiment

Mo

y

x

z

x

y

z

Bo Bo

We have a net magnetization precessing about Bo at a frequency of o with a net population difference between aligned and unaligned spins.

Now What?

Perturbed the spin population or perform spin gymnasticsBasic principal of NMR experiments

The Basic 1D NMR Experiment

Experimental details will effect the NMR spectra and the corresponding interpretation

B1 off…

(or off-resonance)

Mo

z

x

B1

z

x

Mxy

y y1

1

Right-hand rule

resonant condition: frequency (1) of B1 matches Larmor frequency (o)energy is absorbed and population of and states are perturbed.


And/Or:And/Or: Mo now precesses about B1 (similar to Bo) for as long as the B1 field is applied.

Again, keep in mind that individual spins flipped up or down(a single quanta), but Mo can have a continuous variation.

RF pulse

B1 field perpendicular to B0

Mxy

Mz

Classical Description• Observe NMR Signal

Need to perturb system from equilibrium. B1 field (radio frequency pulse) with Bo/2frequency

Net magnetization (Mo) now precesses about Bo and B1

MX and MY are non-zero

Mx and MY rotate at Larmor frequency

System absorbs energy with transitions between aligned and unaligned states

Precession about B1stops when B1 is turned off

Classical Description• Rotating Frame

To simplify the vector description, the X,Y axis rotates about the Z axis at the Larmor frequency (X’,Y’)

B1 is stationary in the rotating frame

Mxy

Mz

+

Classical Description• NMR Pulse

Applying the B1 field for a specified duration (Pulse length or width)

Net Magnetization precesses about B1 a defined angle (90o, 180o, etc)

B1 off…

(or off-resonance)

Mo

z

x

B1

z

x

Mxy

y y1

1

1 = B1

90o pulse

Classic View:- Apply a radio-frequency (RF) pulse a long the y-axis

- RF pulse viewed as a second field (B1), that the net magnetization (Mo) will precess about with an angular velocity of 1

-- precession stops when B1 turned off

Quantum Description:- enough RF energy has been absorbed, such that the population in / are now equal

- No net magnetization along the z-axis

B1 off…

(or off-resonance)

Mo

z

x

B1

z

x

Mxy

y y1

1

1 = B1

90o pulse

Bo > 0

E = h

Please Note: A whole variety of pulse widths are possible, not quantized dealing with bulk magnetization

Absorption of RF Energy or NMR RF PulseAbsorption of RF Energy or NMR RF Pulse

Absorption of RF Energy or NMR RF PulseAbsorption of RF Energy or NMR RF Pulse

10o

20o

35o

60o

90oA whole variety of pulse widths are possible, not quantized dealing with bulk magnetization

Signal intensity decreases significantly when not at optimal 90o pulse length


What Happens Next?

The B1 field is turned off and Mxy continues to precess about Bo at frequency o. z

x

Mxy

Receiver coil (x)

y

NMR signal

o

FID – Free Induction Decay

y y y

Mxy is precessing about z-axis in the x-y plane Time (s)

= Bo/2RF pulse along Y

Detect signal along X

X

y


• Observe NMR Signal Remember: a moving magnetic field perpendicular to a coil will induce a

current in the coil. The induced current monitors the nuclear precession in the X,Y plane

NMR Signal Detection - FIDNMR Signal Detection - FIDThe FID reflects the change in the magnitude of Mxy as the signal is changing relative to the receiver along the y-axis

Again, the signal is precessing about Bo at its Larmor Frequency (o).

RF pulse along Y

Detect signal along X

NMR Signal Detection - FIDNMR Signal Detection - FID

The appearance of the FID depends on how the frequency of the signal differs from the Larmor Frequency

Time Domain

Frequency Domain

Larmor Frequency

NMR Signal Detection - Fourier TransformNMR Signal Detection - Fourier Transform

So, the NMR signal is collected in the Time - domain

But, we prefer the frequency domain.

Fourier Transform is a mathematical procedure that transforms time domain data into frequency domain

NMR Signal Detection - Fourier TransformNMR Signal Detection - Fourier Transform

After the NMR Signal is Generated and the B1 Field is Removed, the Net Magnetization Will Relax Back to Equilibrium Aligned Along the Z-axis

T2 relaxation

Two types of relaxation processes, one in the x,y plane and one along the z-axis

Peak shape also affected by magnetic field homogeneity or shimming

NMR Relaxation

a) No spontaneous reemission of photons to relax down to ground state Probability too low cube of the frequency

b) NMR signal relaxes back to ground state through two distinct processes

NMR Relaxation

c) Spin-Lattice or Longitudinal Relaxation (T1)

i. transfer of energy to the lattice or solvent material

ii. coupling of nuclei magnetic field with magnetic fields created

by the ensemble of vibrational and rotational motion of the

lattice or solvent.

iii. results in a minimal temperature increase in sample

Mz = M0(1-exp(-t/T1))

Recycle Delay: General practice is to wait 5xT1 for the system to have fully relaxed.

NMR Relaxation

c) Spin-Lattice or Longitudinal Relaxation (T1)

i. Commonly measure T1 with an inversion recovery pulse sequence

5xT1 fully relaxed

NMR Relaxation

d) spin-spin or transverse relaxation (T2)i. exchange of energy between excited

nucleus and low energy state nucleus

ii. randomization of spins or magnetic moment in x,y-plane

Mx = My = M0 exp(-t/T2)

NMR Relaxation

d) spin-spin or transverse relaxation (T2)

iii. related to NMR peak line-width

(derived from Heisenberg uncertainty principal)

Please Note: Line shape is also affected by the magnetic fields homogeneity

NMR Relaxation

d) spin-spin or transverse relaxation (T2)

iii. Usually measured with a Carr-Purcell-Meiboom-Gill (CPMG) Pulse sequence

NMR Relaxation

d) Another way to look at T1 and T2

i. T2 is the time it takes a stove to heat a house and T1 is the time it takes for the heat to be lost to the surrounding environment

ii. If the house is insulated, T1 will be larger than T2

NMR Relaxationd) One more way to look at T1 and T2

i. Relaxation of 13C occurs through two distinct interactions

ii. Magnetic fields produced by the 1H magnetic dipoles are felt by the 13C spin

• These magnetic fields are modulated by random Brownian motions (rotational, translational)

iii. Relaxation between 13C and 1H in same molecule - intramolecular relaxation (T2)

iv. Relaxation between 13C and 1H from solvent- intermolecular relaxation (T1)

nuclear magnetic resonance (nmr) introduction : nuclear magnetic resonance (nmr) measures the...

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