nuclear magnetic resonance · pdf fileprinciples of nuclear magnetic resonance...

Nuclear Magnetic Resonance

PRINCIPLES OF NMR SPECTROSCOPY

Contents

•Principles of nuclear magnetic resonance

•The nmr spectrometer

•Basic principles in nmr application

•NMR tools used to obtain information

•Nuclear spin state

•Electric quadrupole and nuclear magnetic moment

•Nuclear magnetic resonance

•Energy consideration of the precessing nucleus

•NMR experimentation and data acquisition

•Operation the NMR machine

•Sample preparation

•Deuterated NMR solvents

1 11/13/2014 Organic Spectroscopy

NMR Spectroscopy

Objectives

• To explain the principles of nmr as regard to nuclear spin

• To Describe the spinning of nucleus as it interacts with applied magnetic field and radiofrequency.

• To elaborate on how a 1H-nmr spectrum is generated

• To explain nuclear spin magnetization and relaxation in the course of data acquisition

• To distinguish absorption (= residual peaks) of various solvents used in 1H-nmr spectroscopy


Principles of nuclear magnetic resonance

• Spectroscopic technique which uses the longer wavelengths (radio frequency) absorption to give information about

– number, connectivity of each type of nuclei (e.g hydrogen/carbon) and

– the nature of its chemical environment.

• This low energy radiation affects only molecular vibration and nuclear spins.


Principles of NMR…

• The energy transition in NMR:

– for electron spin, the change in energy (∆E ) corresponds to energy in microwave region

– for nuclear spin, the ∆E corresponds to the energy of radio waves.


The NMR spectrometer • The NMR machine is

designed as a strong, big gas-cylinder like with two gas compartments, and shim tube running from top through the centre of the cylinder to the bottom

• The lower part of a shim tube which is surrounded with main coil for supplying electric field and magnetic field.


The NMR spectrometer..

• The helium dewar is surrounded by a liquid nitrogen dewar to reduce loss of the helium which is very expensive.

• The radio frequency are sent in and out through the probehead to the processor


The NMR spectrometer.. • Since the NMR machine is all

about powerful magnetic field, the line of forces projects several feet into the room which are concentrated at the top and bottom.

• Thus, working with iron objects like watches can be grabbed iron objects and accelerate.

• Also people with medically inserted magnetic sensitive materials are advice not to work close to the NMR facility.

An NMR spectrometer showing;

(a) Opening to probe,

(b) Vacuum-jacketed cryostat

(c) Solenoid coil of superconducting

alloy, suspended in liquid Helium

(d) Lines of force project several feet into

the room. 8 11/13/2014 Organic Spectroscopy

Basic components of an NMR spectrometer

• Powerful magnet

• radio frequency generator

• radio frequency receiver,

• Sweep coils and

• Sample tube


Schematic representation of an NMR spectrometer


Sample NMR tubes

• These are special-purpose glass tubes that are manufactured to certain specifications of high-quality glass that holds the sample.

– For evenly spinning

– avoid breaking

– allowing proper absorption of RF by the sample.


Basic principles in NMR applications

• Experiments on NMR involve absorption of radiofrequencies on electromagnetic spectrum, of which the signals are recorded as the function of frequencies.

• The plot of applied radiofrequency against absorption frequencies (usually in ppm) on a chemical shift scale is called an NMR spectrum.


Basic principles in NMR applications

• A signal in an NMR spectrum is referred to as resonance.

• 1H and 13CNMR spectroscopic experiment gives the number, type and connectivity of hydrogen and carbon atoms in a molecule, respectively.

• However, the only sensitive isotopes that are being detected are protons and carbon-13s


QN. Account for types and number of protons and carbon-13 of ethanol and pent-4-en-2-one, respectively

NB:

• The NMR spectra gives information about the nature of the chemical environment of each magnetically active nucleus in the molecule.

H3C

H2C

O

H

types of H atoms = 3

Number of H atoms= 6

types of C atoms= 5

Number of C atoms = 5

H3C C

O

CH2CH CH2


NMR tools used to obtain information

• There are three primary NMR tools used to obtain information

(1) Chemical shift which are concerned with local nuclear environment,

(2) Coupling constant (J) concerned with torsion angles and

(3) Nuclear overhauser Effect (NOE) concerned with internuclear distance


Two variables that characterize NMR

(1) an applied magnetic field,(βo) and

(2) the frequency of the radiation used for resonance (in MHz)‏ (To be discussed later)

• Therefore, the NMR spectroscopy is explained under the consideration of three phenomena, the property of the nucleus:

– Nuclear spin state

– Nuclear magnetic moment

– Nuclear magnetic resonance


Nuclear spin states

• NMR spectroscopy technique is only sensitive to any atomic nucleus which possesses either odd mass number or odd atomic number or both and thus has a quantized spin angular momentum and a magnetic moment ().

• Proton and carbon-13 have the spin quantum number l = ½ and has two allowed spin states, +½ and –½.


Nuclear spin states

Spin quantum number

• Recall that l is a physical constant for each nucleus, and there are 2 l + 1 allowed spin states which range with integral differences from + l to - l

– that is - l (-l + 1), …, (l –1), l.

• For the proton, allowed spin state = 2 l + 1 then, 2(½) + 1 = 2 allowed spin states


Electric quadrupole moment

• Electric Quadrupole Moment (eQ) is a parameter which describes the effective shape of the ellipsoid (non-spherical) of nuclear charge distribution.

• Usually, particular nuclei may have spherical charge distribution or non-spherical

(i.e ellipsoid: either prolate or oblate) charge


Illustration of spherical charge and no-spherical nuclear charge distribution

Spherical charge distribution Prolate charge distribution


eQ moment …

• A non-zero quadrupole moment indicates that the charge distribution is not spherically symmetric.

• That is, all nucleus with l = 0 or l = ½ have approximately spherical charge distribution within their nuclei hence small electric quadrupole moment.

• Whereas those with l > ½ have non-spherical (ellipsoidal) charge distribution within their nucleus hence large electric quadrupole moment (eQ).


eQ moment …

• Thus, all nuclei with non-zero spin (l >0) have magnetic moment, μ.

• Therefore, conventionally the value of eQ is taken to be positive if the ellipsoid is prolate and negative if it is oblate

1H 12C 16O 19F 2H < 14N << 35Cl, 37Cl << 79Br,81Br 127I

eQ negligible Increasing eQ (absolute value)


Nuclear magnetic moment

• The intrinsic magnitude of the generated dipole is expressed in nuclear magnetic moment, μ.

• The magnetic moment is generated by the charge and spin of a charged particle.

• The nuclear magnetic moment varies from isotope to isotope of an element and it can align with an externally applied magnetic field of strength Bo in only 2 l +1 ways, either re-enforcing or opposing Bo.

• So, nuclear magnetic moment can only be zero if the numbers of protons and of neutrons are both even.


Nuclear magnetic moment ..

• A characteristic of the collection of protons and neutrons (which are fermions) is that a nucleus of odd mass number, A will have a half-integer spin and a nucleus of even A will have integer spin.

• If the number of neutrons and the number of protons are both even, then the nucleus has NO spin. e. g

• If the number of neutrons + protons is odd, then the nucleus has a half-integer spin of , for , and , respectively.

• If the number of neutrons and the number of protons their sum is odd, then the nucleus has an integer spin (i.e. = 1

•


Spin state of some isotopic elements with respect to atomic number and atomic masses

Nuclear spin

(l )

Half integer

l = 1/2, 3/2, 5/2,

Have

Odd

Atomic mass

Odd or Even Atomic number

Integer

l = 1

Have

Even

Atomic mass

Odd

Atomic number

For zero

I = 0

Have

Even

Atomic mass

Even

Atomic number

l = : 1H, 13C, 19F

l = : 11B

l = : 17O

l =1: 2H, 14N l = 0: 12C, 16O


NMR phenomenon

• Applied magnetic field, circulation of electrons and induced field

• Local diamagnetic current & Diamagnetic anisotropy

• Precessing nucleus


Applied magnetic field, circulation of electrons and induced field

• Many moving charge (like proton nucleus) generates a magnetic field of its own and a weak secondary field (Bsec) due to movement of electron around it that opposes applied field and therefore shields the proton nucleus.

• Hydrogen nucleus may have +½ (α-spin state) or –½ spin (β-spin state) with magnetic moment, μ.

e-

Bo

e-

Bi

Bo


Precessing nucleus

• To understand this phenomenon, we need to consider hydrogen nuclei as a tiny bar magnet having North pole (N) and South pole (S) when placed in magnetic field.

• Thus, like-poles do repel each other and opposite poles attract each other.

• In this look, like-poles repel each other, thus in the spin states it’s the - spin state which is raised at higher energy.


Illustration of proton like a small magnetic bar placed in a magnetic field.


Precessing nucleus ...

• When the frequency of the oscillating electric field component of the incoming radiation just matches the frequency of the electric field generated by the precessing nucleus the two fields can couple, and energy can be transformed from the incoming radiation to the nucleus thus causing spin change.

• This situation is called Resonance. Spinning proton has electron which also do spin and both generate magnetic field. Therefore, the effective field (Beff) is the difference between Bo and Bsec 34 11/13/2014 Organic Spectroscopy

Spin flip

• Alignment of proton spin states when an external magnetic field, Bo is applied.

Aplied magnetic

field, Bo

spin + ½

aligned to Bo

spin - ½

oppose Bo


Energy consideration of a precessing nucleus


Energy consideration ...

E

spin state

spin state

Rel. energy

0

Bx

Increasing strength of

applied magnetic field, Bo

E



• From the illustration of the precessing nucleus with an angular velocity is given by the below expression;

o = o

Where ois the precessional frequency also called

Larmor frequency and

is the magnetogyric ratio (a nuclear constant which is the ratio between magnetic moment and angular momentum).

• So the magnetogyric ratio relates the magnetic moment and the spin number l for any specific nucleus

38

E

spin state

spin state

Rel. energy

0

Bx



E

11/13/2014 Organic Spectroscopy


o = o

= 2ν

ν = (/ 2 )o

• E = hν

E = (μ/l) o ??

• μ l

μ = (h/2). l

But

• ν = (μ /h. l)o

so,

ν = ((h/2). l /h. l)o

ν = (/ 2 )o

39

Search for various plausible derivations

E

spin state

spin state

Rel. energy

0

Bx



E



• The difference in energy, E between the two states is dependent on strength of the applied field, Bo.

• The charge distribution which is slightly excess in state (a lower energy level) is explain by Boltzmann charge distribution.

40

E

spin state

spin state

Rel. energy

0

Bx



E


Energy consideration ... Note:

• When the rate of precession equals the frequency of the rf radiation applied, the absorption of rf radiation take place and the nucleus spins either with +1/2 or -1/2

• Firstly, sample is placed in the magnetic field then irradiated with radiofrequency radiation.

• When the frequency the frequency of radiation satisfies the equation of angular velocity then magnetic component of the radiant energy becomes absorbed.

• Also RF may be kept constant and vary Bo absorption vs frequency of can be applied

• The term resonance is due to excitation to the nucleus to the high energy then decayed to the ground state

41

E

spin state

spin state

Rel. energy

0

Bx



E


Energy consideration…

Note:

• This equation (∆E = (hγ/2π)βo ) have to be modified due to secondary magnetic field by the nucleus i.e ν = βo (1- d)/2π; d is shielding factor

42

E

spin state

spin state

Rel. energy

0

Bx



E


Chemical shift

•Chemical shift is the frequency of signal on an NMR spectrum where the peak occurs

•Atoms in different chemicals environment will resonate at different frequency and will appear at different chemical shift

•The chemical shift scale is calibrated such that the frequency point is tetramethylsaline (TMS)


Why TMS?

• Since silicon is less electronegative than

carbon, TMS protons are highly shielded and

its signal defined as zero.

• Organic protons absorb downfield (to the left)

of the TMS signal

• It’s is inert to most organic samples (in old technique)

Si

CH3

H3C CH3

CH3


Chemical shift scale • Chemical shift scale can be expressed in two ways

– frequency in Hz

– Frequency in ppm (expressed as d)

• Chemical shift in Hz is dependent upon magnetic strength, Bo

• Whereas chemical shift in ppm (d) is independent of magnetic strength, Bo

• There are different of NMR machines of different strength, say 60, 90, 100, ….900 MHz)


Chemical shift scale…

• Protons with high electron density are said to be shielded (signal appear upfield)

• Whereas those with low electron density are said to be deshielded (signal appear downfield)


Illustration of 1H NMR spectrum of methanol

47

5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.00

1

2

3

4

5

6

7

less shielded

lower field (downfield)more shielded

high field (upfield)

Increasing magnetic field strength (Bo)

O C CH3

H

H

H


Atoms in different chemicals environment

will resonate at different frequency and will

appear at different chemical shift

Chemical shift expressed in Hz

• Chemical shift can be expressed in terms of Hz by setting the

TMS peak at 0 Hz.

• When chemical shifts are given in Hz the applied magnetic

frequency must be specified

i.e 60, 90,... MHz because the chemical shift in Hz is

directly proportional to Bo and therefore to the applied

radiofrequency


Chemical shift in Hz...

• The value of chemical shift, n in Hz is; n (in Hz)= ns – nr

• The number of Hz shift from TMS for a given proton (or nuclei) will depend on the strength of Bo

• In 100 MHz the shift in Hz from TMS is 5/3 larger than at 60 MHz. Thus, the resonance proton in an applied field of;

• 14,100 G magnetic strength is at approximately 60 MHz

• where 100 MHz is at field strength of 23,500 G.

• The SI unit Telsa (T) is the unit of measurement for magnetic strength, B, replacing the term Gauss (G).

i.e 1T = 104 G


Chemical shift in Hz...

• Therefore the ratio of the resonance frequency is the same as the ratio of the two field strength.

50

100 MHz

60 MHz

23,500 G

14,100 G

5

3= =


Dependence of chemical shift in Hz on magnetic strength

51

Reich, Chem 345,Univ. Wisconsin, Madison 11/13/2014 Organic Spectroscopy

Chemical shift expressed in d (ppm)

• Usually chemical shifts are expressed in d unit,

• It is independent of the field strength

(instrument used) due availability of

instruments with varying frequency (60, 90,

300, ... MHz).


Chemical shift in d…

• d is a proportionality and thus dimensionless.

• Therefore, chemical shifts in Hz are converted into d unit as shown below:

• For 60 MHz instrument has an oscillation frequency

6 106 Hz.

• The factor 106 is included in the equation to avoid fractional values, since d is expressed in ppm.

53

Observed shift from TMS in Hz Spectrometer frequency in Hz

x 106Chemical shift, dor ppm) =


Chemical shift in d ...

Independence of Chemical shift in d on Bo

• a peak at 60 Hz (n 60) from TMS at an applied frequency of 60 MHz would be at d1.00 or 1.00 ppm.

• the same peak of the same proton at 100 MHz would be at 100 Hz but would still be at d1.00 or 1.00 ppm.

54

d (or ppm)60

60

106= = 1.00 d (or ppm)

100

100

106= = 1.00


Problem 1

• What would be the chemical shift in d of a peak that occur 655.2 Hz downfield of TMS on a spectrum recorded using a 90 MHz spectrometer?

• Solution: d (or ppm) = [655.2 Hz/90x106

Hz]×106 = 7.28 ppm

55

Observed shift from TMS in Hz Spectrometer frequency in Hz

x 106Chemical shift, dor ppm) =


Problem 2

• A specific proton in an organic compound has a chemical shift of 3.4 ppm in a 60 MHz NMR spectrum. What will be the chemical shift in ppm if the spectrum is recorded using a 90 MHz instrument?


Solution • The chemical shift in d unit express the

amount by which a proton resonance is shifted from TMS in ppm of the spectrometer basic operating frequency.

• Hence the value of d for a given proton will always be the same irrespective of whether the measurement was made at 60 MHz or at 90 MHz.

• So the peak of that proton will be observed at 3.4 ppm.


Problem 3 (1) What does the term dispersion mean in NMR

spectroscopy?

(2)Two signals occur at 2.1 and 2.3 ppm in the proton spectrum in a spectrometer operating at 200 MHz for 1H.

(i) What is the frequency difference between the resonances in Hz?

(ii) What is their frequency difference (in Hz) in a spectrometer operating at 600 MHz for 1H observation?


Solution

(1) Dispersion is a term used to express the

notion of how well resonances in an NMR

spectrum are separated from one another (in

Hz)

• it is a qualitative term expressing the ease

with which signals can be distinguished.

11/13/2014 Organic Spectroscopy 59

Solution...(2)

i) Frequency difference between the resonances in Hz at 200 MHz

Chemical shift = {Frequency of signal - Frequency of reference (Hz)} divide by spectrometer frequency (in Hz)

At 200 MHz :

1ppm = 200 Hz,

0.1ppm = 20Hz

Difference in Hz = 0.2 ppm = 40Hz


Solution...

• (ii) Frequency difference between the resonances in Hz at 600 MHz.

At 600 MHz:

• 1 ppm = 600Hz,

• 0.2 ppm = 120 Hz


1. How many type of H’s? :This indicated by how many groups

of signals are there in a spectrum

2. What type of H’s?: Indicated by the chemical shift of each

group. e.g shielded or deshielded, CH, CH2, CH3 with respect

to chemical environment and multiplicity

3. How many H’s of each type are there?: Indicated by

integration (relative area of signal for each group)

4. What is the connectivity?: Look at the coupling patterns.

This tells you what is next to each group

Steps to consider in interpreting 1HNMR

spectrum


1H NMR for Benzyl acetate and Phenylacetone

Similarity • Both phenyl acetone and

benzyl acetate have δ = 7.3 ppm.

• Methyl groups attached directly to a carbonyl have resonance at δ = 2.1 ppm.

• Aromatic protons characteris-tically have resonance near 7-8 ppm

• Acetyl groups (methyl group of this type) resonance

~2 ppm. 11/13/2014 Organic Spectroscopy 63

01234567PPM

CO

OCH2

CH3H

H

H H

H (a)

(b)

(c)

(a)

012345678PPM

CH2

CH3

O

HH

H

H H

1H NMR for Benzyl acetate and Phenylacetone

Difference • Resonance of the benzyl (-

CH2-) protons comes at higher value of δ = 5.1 ppm in benzyl acetate than phenyl acetone δ = 3.6 ppm. Reason?

Been attached to an electronegative element (oxygen atom) these electrons are more deshielding than those in phenyl acetone 11/13/2014 Organic Spectroscopy 64

01234567PPM

CO

OCH2

CH3H

H

H H

H (a)

(b)

(c)

(a)

012345678PPM

CH2

CH3

O

HH

H

H H

• The higher the electron density the higher the

shielding hence the slow the resonance.

• The higher the shielding the more the external

energy is required.

Note:


• The intensity of an 1H-NMR signal is proportional to

the number of proton of each type in the molecule.

• The integral measures the area of the peak and gives

the relative ratio of the number of H’s for each peak.

• An FT-NMR instrument (to be discussed later)

digitally integrates each signal area and provides

ratios of number of hydrogen for each signal.

Working out integration on Proton NMR


1. For a known molecular formula

• Proton per unit is determined by taking total number of proton divide by total units.

Two ways to determine the # of H atoms under each signal from the measured heights.


# of Hs in signal =total heights of all integrals

total # of Hsheight of integral

x

2. For unknown molecular formula Integrate by determine the ratio between the signals and round off to a nearest whole number or multiply by a factor to produce a whole number

Example – Known Molecular formula (C11H16)

• signal 1 (8.8 units), signal 2 (2.9 units), signal 3 (3.8 units).

• Proton per unit is determined by taking total number of proton in a molecule divide by total units of all signals

• Number of protons per signal can be determined by multiplying the number of protons per unit by number of units per signal.

• #of H’s in signal 1 = 1.03 H per unit × 8.8 units ≃ 9.0 H.

• In the same way signal 2 = 3 H and signal 3 ≃ 4H


Example – Unknown molecular formula

• Assuming the previous case the molecular formula in not known then we need to use integral to determine the ratio between the signals and round off to a nearest whole number or multiply by a factor to produce a whole number

• i.e ratio of units in each signal to a nearest whole number ; 8.8:2.9:3.8 = 9.0:3.0:4.0 for signal 1, 2 and 3, respectively.


signal 1 (8.8 units), signal 2 (2.9 units), signal 3 (3.8 units).

Example (Multiplicity will be discussed later)



Given formula C5H10O

Solution

Signal units (units ÷ total units)× Total Hs # of Hs

(1) 2 (2 /10) x 10 = 2H

(2) 3 (3 /10) x 10 = 3H

(3) 2 (2 /10) x 10 = 2H

(4) 3 (3 /10) x 10 = 3H

Total 10 10 H

Calculating DBE = [(2C+2+N)-(H + h)]/2 =1; May be 1 double bond or a ring.

H3C

H2C

CH2

O

CH3(2)

(1)(4)

(3)

Possible structure pentan-2-one

Problem 4

• The line of integration of the two signals in the 1H-NMR spectrum of a ketone of molecular formula C7H14O raises 62 and 10 chart divisions, respectively. Calculate the number of Hydrogen atoms giving rise to each signal and propose a structural formula for this ketone.


Problem-5 Following compound I and II are constitutional isomers of

molecular formula C6H12O2. • Predict the number of signals in the 1H-NMR spectrum of

each isomer

• Predict the ratio of areas of the signals in each spectrum

• Show how you can distinguish these isomers in the basis of chemical shifts

• Draw and label the proposed 1H-NMR for each.

• Predict IR absorption frequencies of major FG’s and describe their spectrum


O

OO

O

I II

1. Stronger magnetic fields Bo cause the instrument to operate at higher frequency (v)

2. NMR field strength vs 1H operating frequency

1.41T => 60 MHz; 2.36T => 100MHz; 7.06T => 300 MHz

3. The d unit has been criticized because d values increased in the downfield direction. These are really negative numbers. Other scales are expressed in t values; t = 10.00 - d.

4. d unit is treated as positive number. Shifts at higher fields than TMS are rare, that is, if d = -1.00.

Then, t = 10.00- (-1.00) = 11.00.

3. Each ppm unit represents either a 1 ppm change in Bo (magnetic field strength, Tesla) or a 1 ppm change in the processional frequency in (MHz)

Summary 1H NMR chemical shift


6. The shift observed for a given proton in Hz also

depends on the frequency of the instrument used.

The Higher frequencies the larger shifts in Hz

i.e 60, 100 and 300 MHz( Operating frequency) is 60,

100 and 300 Hz (equivalent to 1 ppm), respectively.

n MHz x 10-6 = n Hz



• Larmor frequency is dependent upon MF strength, and the use of Hz position of the peaks are also dependent upon MF strength



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