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UNIT - 4 Nuclear Magnetic Resonance and Resonance Spectroscopy Nuclear Magnetic Resonance Spectroscopy (NMR)

NMR is a powerful analytical tool- Purcell and Pound-1946

RF waves induce transition between magnetic levels of the nuclei of the

Magnetic levels are created by keeping the nuclei in magnetic field

No mag field-spin states of the nuclei are degenerate-no NMR

Mag field applied – spin states are separated –RF –transition-NMR

Nuclear Magnetic Resonance Spectroscopy (NMR) NMR is the study of by the interaction of radiofrequency (RF) electromagnetic radiations with the nuclei

Nuclei (I ≥ 1/2=integral or half integral spin)of molecules placed in a strong magnetic field- exhibit NMR RF energy is small-not enough to rotate, vibrate or excite but enough to affect the nuclear spin

Nucleus absorbs RF radiation and change the direction of spin

Nucleus- positive charge- a spinning nucleus give rise to electric current and a mag. field associated with it

Nucleus- a tiny bar magnet with its axis coinciding with the axis of spin of the nucleus

A spinning nucleus when placed in a magnetic field(H) experiences a torque and tend to align along the field and processes along the field direction tells us that a nucleus of spin I will have 2I+1 possible orientations. [I,(I-1),.....-(I-1), -I]

I=1/2, mI = 1/2 , -1/2 I=3/2, mI =3/2, 1/2, -3/2, -1/2 For I=1/2, 2 orientations

Low energy orientation-nuclear mag mom is parallel to app field

High energy orientation- nuclear mag mom is antiparallel to app field

Protons flip from antiparallel to parallel direction by absorbing RF radiation

Freq of RF radiation=Freq of processional nucleus, leads to resonance takes place

Freq of nucleus is proportional to B(magnetic field strength) Rules for finding nuclear spin Subatomic (, and ) can be imagined as spinning on their axes.

In many atoms (such as 12C) these spins are paired against each other, such that the nucleus of the has no overall spin. However, in some atoms (such as 1H and 13C) the nucleus does possess an overall spin.

If the number of P and N are even, I=0 If the number of N + P is odd, I= half integral spin (i.e. 1/2, 3/2, 5/2) If the number of N and P odd, I= integral spin (i.e. 1, 2, 3)

F19 odd P odd N –ang mom P31 even P even N – ang mom=0 N14 n cancels n , p cancels P H1 H2

A nucleus with spin 1/2 will have 2 possible orientations.

In the absence of an external magnetic field, these orientations are of equal energy( doubly degenerate).

If a magnetic field is applied, then degeneracy is removed and the energy levels split. Each level is given a magnetic , mI. The absorption of radiation by a nucleus in a magnetic field Imagine a nucleus (of spin 1/2) in a magnetic field

This nucleus is in the lower energy level (i.e. its does not oppose the applied field).

The nucleus is spinning on its axis.

In the presence of a magnetic field, this axis of rotation will precess around the magnetic field; The of precession is termed the Larmor frequency, which is identical to the transition frequency.

The of the precessing nucleus is given by; E = - μ H cos θ where θ is the angle between the direction of the applied field and the axis of nuclear rotation.

If energy is absorbed by the nucleus, then the angle of precession θ will change.

For a nucleus of spin 1/2, absorption of radiation "flips" the magnetic moment so that it opposes the applied field (the higher energy state). Quantum description of NMR

The nucleus has a positive charge and spins, generates a small magnetic field.

Spin angular momentum G=Ћ [I(I+1)]1/2 = Ћ [I2(1+1/ I)] 1/2 ~I Ћ

Magnetic moment of nucleus μ =γ х G = γ I Ћ= = γ I (h/2π)

The nucleus possesses a magnetic moment is proportional to its spin I

g is gyromagnetic ratio and is a fundamental nuclear constant which has a different value for every nucleus. E= -μH ( for I=1/2 , mI=1/2,-1/2) where μ =γ х G

Energy of a particular energy level is given by E I = - γ I Ћ H

E m I = - γ m I Ћ B= - γ (h/2π ) m I H

E1=E m I=1/2 = -( γ/2) (h/2π ) H

E2=E m I=-1/2 = ( γ/2) (h/2π ) H

The difference in energy between the levels =E2-E1

ΔE= hν= γ (h/2π ) H

ν = (γ /2π ) H -- Larmor equation --Resonance condition for NMR H varied, precessional freq of nucleus increases=freq of app field Resosnance takes place – RF rad is absorbed Where H is the strength of the magnetic field at the nucleus.

If the nucleus has a relatively large gyromagnetic ratio, then ΔE is correspondingly large.

When the nucleus is in a magnetic field, the initial populations of the energy levels are determined by Boltzmann distribution.

The lower energy level will contain slightly more nuclei than the higher level.

It is possible to excite these nuclei into the higher level with electromagnetic radiation.

The frequency of radiation needed is determined by the difference in energy between the energy levels.

This instrument consists of nine major parts:

Sample holder • It is a glass tube which is 8.5 cm long and 0.3 cm in diameter. •Chemically inert, durable, transparent to RF radiation

Sample

Sample+Solvent(CCl4)+(CH3)4Si

Permanent magnet •It helps in providing a homogenous magnetic field at 60 – 100 MHZ •Electro magnets are also used •Strength and direction should not change from point to point •Strength –very high(20000gauss) •Super conducting magnets at liquid He temp-used nowadays •For Temp control- physical dimension of magnets –maintained Magnetic coils

• Magnetic coil generates magnetic field whenever current flows through it

•B =const, freq of RF varied (freq sweep system) •Freq of RF =const, freq of app field is varied (sweep field system)

•Freq of nucleus=freq of app field •Freq of precessional nucleus =freq of RF– makes nucleus resonate

Sweep generator

• Modifies the strength of the magnetic field which is already applied. •Suppies current to Helmholtz coil and field can be varied RF transmitter ❖ It produces a powerful but short pulse of the radio freq. Waves

❖Coil of the oscillator is wound sample holder

❖RF oscillator is perpendicular to the app mag field

❖So that RF field will not change

RF Receiver •It helps in detecting radio dispersed or absorbed and emitted by the sample

•Same coil may be used as transmitter and receiver by RF bridge

•Separate coils (crossed coils ) Dispersion and absorption signals are 180 degrees out of phase. RF detector – It helps in determining unabsorbed radio frequencies

Recorder – It records the NMR signals which are received by the RF detector. Weak signal is amplified and fed to the read out system

Readout system – A computer that records the data Chemical Shift

•Chemical Shift(δ) is the shift in the position of NMR resonance signal from reference material due to shielding and deshielding of nucleus by electrons

•Frequency at which nucleus comes into resonance=ν = (γ /2π ) H

• Frequency can be calculated if H is known.

•Knowing H from NMR is not very easy

•But difference in peaks( sample and reference) is observed

•Difference freq= Position of resonance freq of sample w.r.t. Resonance freq of the reference material= chemical shift

•According to the resonance condition, all protons should absorb energy at the same magnetic field

• However it is not the case even under low resolution

• The spectrum of acetaldehyde (CH3CH0) showed two lines with intensity 2 ratio 1:3 whereas ethanol (CH3CH OH) showed 3 lines in the ratio 1:2:3 ❖Moving electrons in a molecule constitute currentswithin the molecule

❖This produces a secondary magnetic field which acts in a direction opposite to the applied magnetic field

❖The nucleus finds itself in an effective field less than the actual field applied

❖The nucleus is screened by the surrounding electrons.

❖ σ is (dimensionless ) screening constant or shielding parameter.

❖It depends on the electron density around the . The situation for a shielded spin ½ nucleus

Bare and screened, spin ½ nucleus in a

magnetic field H0 ➢ The absolute magnitude of mag field of the sample is extremely small.

➢If Hr , Hs be the magnetic field at which resonance occurs for the reference and given sample; H0 is applied field

➢σr and σs are extremely small, a different unit is usually selected in terms of field or frequency for expressing the chemical shift.

➢Chemical shift δ is usually expressed in parts per million (ppm) ➢The numerator is usually expressed in hertz, and the denominator in megahertz, δ is expressed in ppm.

➢The reference is selected in such a way that it gives the resonance at a very high field; δ is +ve in most of the cases.

A different chemical shift τ which is the one commonly used by chemists, is some times employed.

The reference sample generally used is tetramethyl silane (CH3)4 Si, ( TMS).

It is chemically inert; Low boiling point; Si-low electronegativity; contains 12 protons of the same type; high shielding; δ =0;Very little reference sample is required; it gives a very intense sharp peak

The τ value for TMS is 10.

Positive shielding ❖Moving electronsin a molecule constitute currents within the molecule

❖This produces a secondary magnetic field which acts in a direction opposite to the applied magnetic field

❖The nucleus finds itself in an effective field less than the actual field applied

❖More field is needed to bring it to resonance

❖The nucleus is shielded by the surrounding electrons.

Upfield: Secondary field produced by the circulating electron opposes the applied field and the effective field reduces(+ve shielding); resonsance position moves upfield Negative shielding ❖Moving electronsin a molecule constitute currents within the molecule

❖This produces a secondary magnetic field which acts in a direction of the applied magnetic field

❖The nucleus finds itself in an effective field greater than the actual field applied

❖Less field is needed to bring it to resonance

❖The nucleus is deshielded by the surrounding electrons.

Downfield: Secondary field produced by the circulating electron increases the applied field and the effective field increases(-ve shielding); resonsance position moves downfield

✓Electronegative atoms like halogens, N 2 , O 2 deshield the protons and absorption occurs downfield

✓The extend of deshieldingproportional to ✓(i)electronegativity (halogen,hydrogen, nitrogen) ✓(ii) its nearness to proton ✓Graeter the deshieldingprotons larger the δ value

✓CH3 CH2Cl ✓CH2 protons have greater deshielding than CH3 protons

✓CH3F greater downfield than CH3 Cl ✓F is more electronegative than Ci

✓Ethanol CH3 CH2OH ✓ showed 3lines in the ratio 1:2:3

✓Acetaldehyde CH3 CHO= 2 lines in the ratio 1:3 ✓ 3 protons are equivalent ✓CHO –more electronegative; ✓Needs less field for resonance than CH3 Line Width The resolution or separation of absorption lines depends on how close the lines are and the width absorption line ( freq over which absorption takes place)

1. Homogeneous Field

constant over all parts of the sample

If not constant the freq of the absorbed radiation will vary in different parts of the sample

This variation results in a wide absorption line

Wide absorption line leads to overlapping of neighbouring peaks

Fortunately we can control field 2.Relaxation time

•The length of time the excited nucleus stays in the

• :ΔE х Δt= constant •When Δt =small, ΔE=large

•E = hν; h = constant, any variation in in E will result in variation in ν

• If E varies by E+ ΔE then ν varies as ν+ Δν •E+ ΔE = h(ν+ Δν) •Δt is small then ΔE =large; Δν= large •Frequency over which absorption takes place widens- leads to wide absorption line

•The length of time the excited nucleus stays in the excited state (=Δt) is controlled by the rate at which the nucleus loses its energy of excitation

•The process of losing energy is called RELAXATION •Two modes of relaxation • Longitudinal or spin -lattice relaxation • Transverse or spin -spin relaxation a) SPIN -LATTICE RELAXATION TIME

• The excited nucleus loses its energy to the surrounding molecules

• System warms up; as the energy is changed to heat

• No appears

• No other nucleus get excited

• As large no of nuclei lose energy in this fashion

• Temp of the sample goes up

• The process is quite fast in liquids b) SPIN -SPIN RELAXATION TIME

• The excited nucleus transfers its energy to an unexcited nucleus of a similar nearby molecule

• Nearby nucleus gets excited and the previously excited nucleus become unexcited

• No net change of energy in the system

• But the length of time the nucleus spends in excited state is shortened • In liquids spin-spin relaxation time is long and narrow absorption line

• Solids- transverse relaxation time is short - wide absorption line

• Solvation process (dissolving small amt of solvent) increases transverse relaxation time of solids - line width- decreased

3. MAGIC ANGLE

Orientation of the nuclei to the magnetic field=54.7˚ Narrow Relaxation Process

•Magnetic moment of the nucleus precesses in ext. mag. field and comp of magnetic field along field direction is unaltered

•For magnetization to occur dipoles must orient along field direction- flip from antiparallel to parallel

•For orientation of dipoles exchange of energy with surrounding is important

2 MECHANISMS

•Spin-spin relaxation •Spin – lattice relaxation Spin-Spin Relaxation

•Paramagnets- permanent dipoles

•spin finds itself in fluctuating internal field Hi due to surrounding dipoles

•When Hi>Ho , Magnitude of mag field unaltered – direction changes

•Dipoles precess and net magnetization results- interaction between spin and field

•No exchange of energy between spin and lattice

•At high freq & small field

-10 •Temp independent ; τ2=10 s Spin-lattice Relaxation

When Hi

Magnitude of mag. field varies – direction constant

Magnetization increases dipoles change from antiparallel to parllel orientation

Exchange of energy between spin and lattice

Temp dependent

At strong field and low frequency

-4 τ1=10 s

If H1 is strong and degree of saturation is not negligible; then Mz

ESR also known as Electron paramagnetic resonance (EPR) spectroscopy - to the study of samples with one or more unpaired electrons - - region

Paramagnetic substances NO, NO2,O2 – absorb – transition between levels of electron with unpaired spin- magnetic energy levels splitting occurs by applying magnetic field

ESR exhibited by (i) Atoms having odd no of electrons (ii) having perfectly filled inner shell (iii) transition metal ions, rare earth elements (iv) Free radicals having unpaired electrons created by breaking by irradiating sample with UV or gamma rays (life time > =10-6 s) (v) Unstable paramagnetic substances produced as intermediates by irradiation of stable molecule with a beam of nuclear particles (α,β,γ) or with UV, gamma rays Theory of ESR

Energy levels are produced by interaction of magnetic moment of an unpaired electron In a molecule with applied field

Transition between energy levels by absorbing radiations of microwave frequency

For electron,

S=1/2, spin angular momentum quantum number ms= +1/2, -1/2

No magnetic field – 2 energy levels –degenerate magnetic field is applied – degeneracy is removed- non

Lower energy level ms= -1/2 Spin mag. mom aligned parallel to applied field

Higher energy level , spin mag. mom. aligned antiparallel to applied field, ms= +1/2

E= -μeH= - (gβS)H {μe= gβS}

E = - (gβmS)H μe= mag. mom. of spinning electron

H- mag. mom of spinning electron

γ - freq of absorbed radiation

g - Lande’s splitting factor- not a constant

g = tensor quantity

E = - (gβmS)H

For mS=1/2 ; E1= - (1/2gβ)H

For mS=-1/2 ;E2= (1/2gβ)H

ΔE= gβH hγ= gβH ---resonance condition for ESR Lande’s splitting factor

(i)For free electron, g=2.0023; Slightly modified for electron and molecule

(ii)Free radicals and ionic g=2.0023±0.003; in free radicals, electrons behave like free electrons

(iii) In some crystals, g varies from 0.2 to 0.8 Unpaired electrons localised in a particular orbit; orbital ang mom couples with spin ang mom give rise to a low value of g

(iv)Value of g depend on orientation of the molecule having unpaired electron with mag field

(v) In and solutions the molecules have free and the value of g is averaged over all orientations (vi) In crystals electrons are not free ; the value of g is the same in all directions

(vii)For paramagnetic ions or radical situated in a of low symmetry g depends on orientation;

There are 3 axes in a crystal; gx , gy , gz along x, y, z directions

In tetragonal site ; gx=gy=g┴ is obtained when mag field is ┴ z axis

The value of gz is obtained when mag. field is parallel to z axis gz=g║

2 2 2 2 2 g =g║ cos ϴ + g┴ sin ϴ

DiPhenyl 2 Picryl Hydrazyl ---Reference material --DPPH g = gs (1-ΔH/H) Instrumentation-ESR Spectrometer

Successful observation of the ESR spectrum requires suitable values for the frequency and the magnetic field B

For continuous absorption one can either vary the frequency across resonance keeping the magnetic field B constant

The magnetic field is varied keeping the frequency constant.

The latter method is usually preferred since it is easier to vary the magnetic field keeping the stability at very high levels.

Some of the basic requirements of a ESR spectrometer are :

(i) An electromagnet capable of supplying a homogeneous magnetic field which can be varied linearly on either side of the magnetic field- 50-5500G

(ii) SOURCE:

Klystron-Source of microwave radiation in the region of 9.5 GHz Freq proportional to applied voltage

Isolator-A ferrite material passes microwave in one direction

Wavemeter- to find the freq of microwave produced by Klystron

Attenuator- has an absorption material like neutral filter in expts adjust the level of microwave power irradiated on sample (iii) Suitable sample cavity (Heart of ESR spectrometer) Rotating cavities-anisotropic effects in single crystal Dual cavitites- simultaneous observation of sample and resonance material (iv)Circulator(MagicT)-Arrangements for transmitting the radiation energy in to the sample cavity Arm1- microwave enters Arm2 -terminating load absorbs power reflected from detector arms Arm3- to resonant cavity and sample Arm4 – detector Bridge balance – affected when sample absorbs radiation (v) Detection system to measure the variation in microwave power

Crystal detector- microwave rectifier- converts microwave power to DC o/p

(vii) Audio amplifier and Phase sensitive detector-rejection of noise component and narrow band amplification

(vi) Suitable oscilloscope or recorder. The usual source of radiation is a klystron oscillator which produces monochromatic radiation of the required frequency.

The radiation from the source is transmitted to the sample cavity through a microwave impedance bridge.

The rectangular microwave cavity which contains the sample is kept in between the pole pieces of the electromagnet.

A dummy load is kept in the third arm and a semi–conductor crystal in the fourth arm of the microwave bridge.

The radiations that arrive in the 4th arm are detected by the crystal.

It is then amplified and fed to a suitable recorder phase sensitive detectors are usually to detect ESR signals and represented as absorption or first derivative curves. The magnetic field is swept over a small range across the resonance condition by varying the current in a pair of sweep coils mounted on the cavity walls Working

When the bridge is in a balanced positive microwave power flows only in the two arms – the one cavity and the others to the dummy load

There will be no power in the fourth arm.

Power will be in the fourth arm when the bridge is not balance.

Thus, if balance exists, initially no signal appears at the detector and when the sample absorbs, the balancing of the bridge is lost and power appears in the fourth arm The width of ESR lines are fairly large and hence the spectrum is usually recorded in the first derivative mode which enable one to fix up the frequency position and estimation of intensity more precisely

Another advantage of derivative mode is that it gives a well defined line width

Even if there are overlapping signals, it is still possible to do a good estimate of H ESR Hyperfine splitting

It is caused by the interaction between spinning electron and adjacent spinning nucleus.

A single electron interacts with one nucleus the no. of splitting =2I+1 (I – spin q. no. of nucleus)

If a single electron interacts with n number of nuclei , the signal is split into 2nI+1

Eg. 1.; 1proton (spin I=1/2 ) and 1 electron ( spin S=1/2)

In the absence of magnetic field, the spin states of electron is doubly degenerate.

When a magnetic field is applied the degeneracy is removed- split into 2 levels with ms= - 1/2 ; spin parallel to the field ms= +1/2; spin opposite to the field

Spectrum for a free electron

Single peak corresponding to the transition between these two levels When interaction between the electron and the nucleus is considered

Each energy state is split into 2 levels mI= - 1/2 ; mI= +1/2;

Nuclear Spin Ang. Momentum =mI For two energy states, 4 energy levels are obtained ESR spectrum of hydrogen has 2 peaks – 2 allowed transitions of 4 levels ;

E(ms , mI)= gβH ms + A mIms A- hyperfine coupling constant

Selection Rule :

ΔmI =0, Δms = ±1

E(1/2,1/2) = ½ ( gβH ) +1/4 (A) E(1/2,-1/2) = ½ ( gβH ) -1/4 (A) E(-1/2,-1/2) = -½ ( gβH ) +1/4 (A) E(-1/2,1/2) = -½ ( gβH ) -1/4 (A)

According to selection rule 2 transitions are possible; with the frequencies of the two lines are:

E(1/2,-1/2) - E(-1/2,-1/2) = [½ ( gβH ) -1/4 (A)] –[-½ ( gβH ) +1/4 (A) ] hυ 1= gβH -1/2 (A)

E(1/2,1/2) - E(-1/2,1/2) = [½ ( gβH ) +1/4 (A)] –[-½ ( gβH ) -1/4 (A) ] hυ 2= gβH+1/2 (A) 2 2. Deuterium – Isotope of hydrogen H 1 [ 1 – proton, 1-electron, 1- ] ; n=2; I=1/2;

Interaction between 1 electron and Nucleus (2 nucleons)

I= 1/2 +1/2 =1; 3 orientations possible (2I+1)=3, mI=1,0,-1

S=1/2; 2 orientations possible(2S+1)=2; mS= +1/2, -1/2 For mS= +1/2, mI=1,0,-1 For mS= -1/2, mI=1,0,-1

Selection Rule :

ΔmI =0, Δms = ±1

3 allowed transitions ; 3 lines of equal intensity in ESR spectrum E(mS , mI)= gβH ms + A mIms

E(1/2,1) = ½ ( gβH ) +1/2 (A) ---(1) E(1/2,0) = ½ ( gβH ) ---(2) E(1/2,-1) = ½ ( gβH ) -1/2 (A) ---(3)

E(-1/2,-1) = -½ ( gβH ) +1/2 (A) ---(4) E(-1/2,0) = -½ ( gβH ) ---(5) E(-1/2,1) = -½ ( gβH ) -1/2 (A) ---(6) E(1/2,-1) = ½ ( gβH ) -1/2 (A) ---(3) E(-1/2,-1) = -½ ( gβH ) +1/2 (A) ---(4) (3) –(4) hυ1= gβH-A

E(1/2,0) = ½ ( gβH ) ---(2) E(-1/2,0) = -½ ( gβH ) ---(5) (2)-(5) hυ2= gβH

E(1/2,1) = ½ ( gβH ) +1/2 (A) ---(1) E(-1/2,1) = -½ ( gβH ) -1/2 (A) ---(6) (1)-(6) hυ3= gβH+A For Methyl Radical - CH3 For C (6 protons and 6 neutrons) so nuclear spin =I=0 ; For electron spin =S=1/2

Interaction between unpaired electron of carbon and 3 hydrogen nuclei

For electron; S=1/2 ; ms= - 1/2 , 1/2

3 hydrogen nuclei; I= 3x(1/2)=3/2;

4 orientations possible (2I+1) =

2(3/2 )+1=4; mI= -3/2, -1/2, 1/2, 3/2

E(mS , mI)= gβH ms + A mIms

Selection Rule :

ΔmI =0, Δms = ±1 E(1/2, 3/2) = ½ ( gβH ) +3/4 (A) E(1/2, 1/2) = ½ ( gβH ) +1/4 (A) E(1/2, -1/2) = ½ ( gβH ) -1/4 (A) E(1/2, -3/2) = ½ ( gβH ) -3/4 (A)

E(-1/2, -3/2) = -½ ( gβH ) +3/4 (A) E(-1/2, -1/2) = -½ ( gβH ) +1/4 (A) E(-1/2, 1/2) = -½ ( gβH ) -1/4 (A) E(-1/2, 3/2) = -½ ( gβH ) -3/4 (A)

4 lines with intensities in the ratio 1:3:3:1