NMR Methods in Inorganic Chemistry

Gyromagnetic ratio is the ratio of the nuclear magnetic dipole to the angular momentum

γ=μz

I z

The value can be positive or negative.

Nuclear Spin – I

Nuclear spin is a property of the nucleus. I may be zero, an integer or a multiple of ½. The nuclear spin depends on the nucleus.

Even mass number Even atomic number Zero spinOdd mass number Multiple of ½ spin

Even mass number Odd atomic number Integer nuclear spin

Chemical Shift δ

When a magnetic field is applied to a sample, its nuclei can either align with or against the field.

The charged nucleus in NMR will express precessional motion around an external magnetic field at a specific frequency known as the Larmor frequency. The Larmor frequency is related to the strength of the magnetic field, B0.

Larmor frequency=γ B02π

γ = Gyromagnetic ratio

B0 = Magnetic field strength

Nuclei experience different effective magnetic fields due to other nuclei and electrons in the molecule. Therefore it is useful to define the chemical shift relative to a standard. The calculated shift will be identical regardless of what spectrometer was used as it is calculated independent of spectrometer frequency.

δ=(ν¿¿obs−νref )

νref x106 ¿

I = Angular Momentum

I =Nuclear Spin

Spin ½ nuclei can have their coupling intensities determined

using Pascal’s triangle.

νobs = resonant/Larmor frequency observed for particular nucleus

νref = resonant frequency observed for a reference nucleus

Coupling Constant – J

Direct/through space coupling (dipolar) can be observed in solid state NMR. In solution, it averages out to zero and is therefore not usually observed. It is the less common type of the two.

Indirect coupling, also known as Scalar or J-couplings, are mediated through chemical bonds connecting two spins. It is an indirect interaction between two nuclear spins. J-couplings provide information on the connectivity of molecules. The spin state of neighbouring nuclei results in different possible electronic environment.

Multiplicity observed for J-coupling:

Number of spectral lines=2∋+1

Wheren is the numberof magnetically equivalent adjacent nuclei able ¿couple ¿the observednucleus∧I is the spin of thenucleiunder observation

Valid for quadrupolar nuclei (Any nuclei that has a spin of greater than ½) and ½ spin nuclei ONLY.

1) Generally, the fewer bonds involved in the coupling, the larger the coupling constant (J) will be.

2) The large γ, the larger the J-coupling will be

Relative Sensitivity

relative sensitivity=¿

The relative sensitivity of an element, X, gives one indication of how easy it might be to observe NMR spectra of this molecule relative to 1H.

Relaxation

Process which allows nuclear spins to lose energy and drop from the excited state to the ground state non-radiatively (i.e. without emitting an NMR signal).

A nucleus can non-radiatively transfer energy via two ways: either to the surroundings (spin-lattice relaxation) or to other nuclear spins (spin-spin relaxation).

13C I = ½, 1H I = ½. The second term in the equation is equal to 1. (6.7283/26.5720)3=1.59x10-2. Remember the γ can be calculated by dividing the nuclear dipole μz by the angular momentum Iz. The sensitivity

relative to 1H at natural abundance can be found by:Sensitivity value x natural abundance

Spin-spin relaxation

Energy is exchanged between nuclear spins but the overall energy of the molecule does not change.

Spin-lattice relaxation

Energy of the excited state is lost to the surroundings.

Relaxation times vary for different nuclei A suitable interval is therefore required to allow for complete relaxation 13C spectra are NOT integrated due to long relaxation times

Instrumentation

Continuous wave (CW) and Fourier Transform (FT) spectrometers are the two most widely used types for NMR instrumentation. CW is a slower technique and large quantities of sample are required.

FT technique uses an intense pulse containing a wide range of frequencies that ensures all environments are excited. It is the relaxation of these excited environments back down to their ground state environments that gives the observable signals (Free induction decay). The process is repeated multiple times with the multiple FIDs summated, to give a better signal to noise ratio.

FT requires 1mg or less of sample, as compared to 30mg required by CW.

Part Two: NMR Spectroscopy

i) 1 H NMR Spectroscopy

A hydrogen atom bound to a metal centre is shielded and its chemical shift is found at high field. The metal is slightly positive and the hydrogen is slightly negative (i.e. hydridic)o (CO)5Mn-H (-7.5ppm), (CO)4Co-H (-10.7ppm), trans-(Pet3)2Pt(Cl)-H (-16.8ppm)

A hydrogen atom bridging between two metal centres is further shielded and therefore has an even higher field chemical shift.

However, if d orbitals of a metal are empty or completely filled, less shielding is observed.

GENERALLY, the more negative the charge on the complex, the more shielding there is.

Dihydrogen complexes

The NMR signals are shifted upfield and the broad signals are due to slow relaxation times. Anything under 150ms (usually in the range of 2-100ms) indicates the formation of a dihydrogen complex.

Hydrides are much slower with relaxation times greater than 350ms.

The closer the metal is to hydrogen in a 1H NMR, the more effect it has on the chemical shift (only small however, 1-4ppm).

13 C NMR Spectroscopy

TMS is used as a reference. Strong electropositive elements (such as metals) will give shifts upfield beyond zero.

Upon coordination, there is an upfield shift due to increased shielding.

Metal carbonyls have long relaxation times and are therefore difficult to observe.

The size of the coupling constant is related to the s character of the bond as well as other things. The larger the nuclei, the larger the coupling constant.

31 P NMR Spectroscopy

31P is a spin half and is 100% abundant; it is therefore very useful for NMR Spectroscopy.

The reference used is H3PO4 (phosphoric acid). It is used externally due to it being reactive.

31P has a wider chemical shift range and as mentioned above, is spin half, meaning the intensities of its peaks can be calculated using Pascal’s triangle, as long as relaxation times are short.

19 F NMR Spectroscopy

13F is spin-half and 100% abundant. The reference is often CFCl3 but it is a CFC. CF3CO2H is therefore also used. Intensity is calculated using Pascal’s triangle and the splitting is governed by the 2nI+1 rule.

Quadrupolar Nuclei Coupling To Spin Half Nuclei

In theory, Quadrupolar nuclei can couple to spin half nuclei. This can be seen when the Quadrupolar nucleus is measured, rarely by measuring the I=½ nucleus.

Why Coupling May Not Be Observed

Lack of magnetic nucleus s(1H-12C) Coupling constant is too small (Usually anything greater than 3J not observed, unless in aromatic

system) Magnetic equivalence (Methyl protons, H3) Natural abundance is too low (e.g. 1H-15N) Outer lines of multiplet is of too low intensity

Fast chemical exchange (Think of NH protons from dinosar ligand in labs) Short lifetime of spin states

Part Three: Factors affecting chemical shift

It has already been mentioned that the larger the nucleus, the larger the chemical shift range. For any given nucleus, the possible variables include:

The oxidation state The coordination number The bonding type (ionic/covalent, σ/π) The substituents (their steric size and electronic factors)

Variation of Chemical Shift With Oxidation State

The lower the oxidation state, generally the higher field the shift is due to increased shielding. Paramagnetic compounds are usually NOT measured using NMR as they give rise to broad peaks due to the lone pairs interfering with the nucleus’ response to the magnetic field strength.

Variation of Chemical Shift With Coordination Number

Higher coordination numbers tend to give higher field shifts.

Pt (PEt3)4: -5262ppm

Pt (PEt3)3: -4562ppm

This is not always the case, however.

Pt (PCy3)3: -4567ppm

Pt (PCy3)2: -6555ppm

Group 14 NMR Nuclei

Every element in the group has at least one spin active nucleus and all except Germanium have spin half nuclei. Group 14 can be used to demonstrate a range of aspects of inorganic NMR spectroscopy.

Nucleus Spin13C ½29Si ½73Ge115Sn ½117Sn ½119Sn ½207Pb ½

13 C NMR Spectroscopy

Copied from section above

TMS is used as a reference. Strong electropositive elements (such as metals) will give shifts upfield beyond zero.

Upon coordination, there is an upfield shift due to increased shielding.

Metal carbonyls have long relaxation times and are therefore difficult to observe.

The size of the coupling constant is related to the s character of the bond as well as other things. The larger the nuclei, the larger the coupling constant.

sp3 (25% s) Predict 125 Hz sp2 (33% s) Predict 167 Hz sp (50% s) Predict 250 HzH-CH3 125.0 Hz H2C=CH2 156.2 H-C≡C-H 249H-CH2CH3 124.9 H2C=C=CH2 168.2 H-C≡C-Ph 248H-CH(CH3)2 119.4 Bn-H 159 H-C≡C-F 275H-C(CH3)3 114.2 H-C≡N 269H-CH2NH2 133.0 H-C≡N+-H 320

Electronegative substituents cause increases in the 1JCH. Electropositive substituents a decrease.

29 Si NMR Spectroscopy

29Si has a negative gyromagnetic ratio (γ) and a long relaxation time.

The shift range is approximately 150ppm to -130ppm.

TMS is used as the reference.

Peaks in 29Si cannot be integrated due to long relaxation times.

An increase in coordination results in an increase in shielding, resulting in a decrease in chemical shift, as seen with 13C NMR.

Si-H coupling is the most common coupling observed. The more electropositive the substituent, the smaller the coupling constant. The more electronegative the substituent, the larger the coupling constant (think about the substituent pulling away from the Si centre, thus making the bonds longer, therefore making the J value larger).

An increase in s character results in an increase in J.

SiF62 108 Hz (sp3)

SiF5- 140 Hz (sp3d)

SiF4 170 Hz (sp3d2)

Satellites

29Si has a spin ½ and is 4.7% abundant. The 19F NMR spectrum for SiF4 is has a strong central peak for molecules containing the NMR inactive silicon. A doublet can be observed on either side of the central peak due to the 29Si containing molecules are the 29Si satellites.

In TMS, a strong central peak is observed due to the 28Si. Two ‘shoulder satellites’ are observed on either side, the 4.7% abundant 29Si.

29 Si Coupling in H 3Si-SiH3

28Si is 95.3% abundant, I=0

29Si is 4.7% abundant, I=½

The chance of finding the possible couplings below:

H3 28Si- 28SiH3 = 0.953 x 0.953 = 90.82%

H3 28Si- 29SiH3 OR H3

29Si- 28SiH3 = 2 x (0.953 x 0.047) = 8.96%

H3 29Si- 29SiH3 = 0.047 x 0.047 = 0.22%

73 Ge NMR Spectroscopy

A quadrupolar nucleus, I=

Will be discussed later.

115 Sn, 117 Sn, 119 Sn NMR Spectroscopy

119Sn is the most sensitive of all three spin half nuclei. 115Sn is 0.35% abundant, 117Sn 7.61% and 119Sn is 8.58% abundant.

The coupling constant for 119Sn is larger than for 115Sn due it being a larger nuclei and its gyromagnetic ratio being larger (γ119Sn/ γ117Sn=1.0465).

There may be couplings present in a molecule that are not observed in a normal spectrum. The abundance of 115Sn is very low and it has a small gyromagnetic ratio and J value.

Tin coupling constants can also be used to illustrate the increase in size of coupling constants with increasingly electronegative substituents.

SnH4: 1J119Sn-H: 1930 Hz

SnClH3: 1J119Sn-H: 2448 Hz

Analysis

Sn(NEt3)4 has an oxidation state of 4, a coordination number of 4 and a δ of -122ppm.

Sn[N(SiMe3)2]2 has an oxidation state of 2, coordination number of 2 and δ of 767 ppm.

It is expected a lower oxidation state would result in higher field shifts. However, the higher coordination number ‘won’ and has caused the higher field chemical shift.

207 Pb NMR Spectroscopy

Lead has a wide shift range of ~16000ppm. The higher the coordination number, the higher the field shift.

Nucleus 1J M-H/ Hz13C 12529Si 84119Sn 1774207Pb 2295

The larger the size of the nuclei, the larger the coupling constant.

Part Four: Satellite Spectra and Effects of Low Abundance Spin Half Nuclei

Where several natural occurring isotopes exist in low concentration, satellite peaks may be observed around the main peaks.

In the 1H spectrum of CHCl3, one large peak will be observed at 7.23ppm for the single hydrogen present in the 98.9% of molecules containing the 12C. 1.1% will contain a 13C nucleus instead, which is spin half. The spin half nucleus will split the peak observed for the single hydrogen into a doublet.

A large peak will be observed in the middle, surrounded by two small satellite peaks corresponding to the 13C-1H doublet. The satellite peaks each only have an intensity of 0.55% so they are rarely seen, except on very intense signals.

Isotope Shift

An isotope shift is a displacement in chemical peaks due to the presence of other isotopes in the sample. In the case above, the satellite peaks are not exactly the same distance away from the central peak. This is because the hydrogen in 12C will be in a different environment compared to the hydrogen in 13C.

Other examples of satellite peaks are commonly encountered in 29S NMR on the 1H TMS peak (already seen).

More than one set of satellites can exist at once: in MeSn4 for example where there is one set from 117Sn and one from 119Sn. They both have an overall intensity of 8% each, which is split between their satellite peaks to 4%. In theory, there should be a set of satellites from the 115Sn but it has such a low intensity it is rarely seen.

Satellite peaks of higher natural abundance can also be observed: 195Pt for example. 195 Pt is 34% abundant and in the 31P NMR spectrum of Pt(PPh3)4, satellites are caused by a 1J 195Pt-31P coupling, with each satellite peak having an intensity of approximately 17%.

Qua

drup

olar

Quadrupolar Nuclei

The non-zero, non-spin-half nuclei do not have a spherical charge distribution unlike spin half nuclei.

A non-zero electric quadrupole moment arise for nuclei that are classically described as prolate (stretched) or oblate (squashed) spheroids. The nuclear charge distribution has axial symmetry and the axis of symmetry coincides with the direction of the nuclear angular momentum. The quadrupole moment is given the symbol Q. This is the strength of interaction will neighbouring electric field gradients.

Reference Standards

The standard used is usually as small and symmetrical as possible in order to yield narrow peaks. Group 1 and 2 atoms often have M+ and M2+ aqueous ions, whilst those in group 17 have X- ions used.

The number of peaks observed for quadrupolar nuclei (nuclei with a spin greater than ½) also obeys the 2nI+1 rule as each nucleus has 2I+1 allowed spin states.

Large multiplets are frequently observed for quadrupolar nuclei, such as GeF4. 73Ge has a spin of 9/2 and is 7.7% abundant so the GeF4 results in a singlet of intensity 92.3% superimposed on top of ten peaks resulting from the ten possible spin states of the 73Ge each with an intensity of 0.77%.

Factors Affecting the Observation of Quadrupolar Nuclei

Those that affect the electric field gradient at the nucleus are the most important factors to take into consideration. Quadrupolar nuclei are asymmetric; therefore averaging effects are very important. The main factors in the observation of quadrupolar nuclei are:

Spherical

The spin states of all ½ spin and quadrupolar nuclei can be determined using the following equation:2I+1

e.g. Spin 1 nuclei have three states, -1,0,1Spin 7/2 nuclei have eight states, -7/2, -5/2, -3/2, -1/2, ½, 3/2, 5/2, 7/2

Rate of motion: Rapid tumbling is good as it averages the effects from unsymmetrical structures

Size and shape of molecule: Smaller molecules will tumble better Viscosity of solvent: The more viscous the solvent the less rapid the tumbling

Broad lines are often observed in NMR due to the asymmetrical nature of quadrupolar nuclei. When drawing a spectrum, you will need to know the following about the nuclei:

Abundance Spin Gyromagnetic Ratio If Quadrupolar, you’ll want to know its linewidth factor.

The larger the value of the linewidth factor, the broader the lines.

l=Q2 . (2 I+3 )qzz

2 . τc[I 2 (2 I−1 )]

Where Q is the quadrupolar moment, qzz2 is the electric field gradient across the nucleus and τc is the

time it takes for the molecule to realign during tumbling. The larger I (nuclear spin) is, the narrower the lines tend to be.

Symmetrical molecules have lower field gradients across their nuclei and thus generally have narrower lines, leading to better observation. Octahedral, cubic and tetrahedral geometries are all symmetrical and therefore important in quadrupolar NMR Spectroscopy.

[NR4]+, [SO4]2- and [Co(CN)6]3- all have narrow peaks.

As the molecule become larger, more asymmetric and the time correlation increases, the linewidth also increases.

Linewidth is important when choosing which isotope should be used in NMR. 6Li has I=1 and is 7.4% abundant, whilst 7Li is 92.6% abundant with I=3/2. 7Li also has a relatively large linewidth compared to 6Li. Therefore, 7Li is used to identify if Li is present in the sample and 6Li is subsequently used to make detailed studies of the sample including coupling, as the lines are much narrower and hence easier to observe.

Relaxation time is the final factor being considered for quadrupolar NMR spectroscopy. It determines whether or not coupling will be observed.

EXAMPLE:

In 1H NMR spectroscopy, a hydrogen bound to a 14N nucleus is generally seen as a broad hump at room temperature.

BUT 14N HAS I=1. 2NI+1=3, THEREFORE A 1:1:1 TRIPLET?

The relaxation time is so fast however, that the individual lines of the triplet are observed as a broad peak.

It is because of fast relaxation times that we rarely see splitting or coupling of chlorine (35Cl and 37Cl) or bromine (79Br and 81Br), indeed any coupling between adjacent carbons or protons are not observed either. But it is usually seen with 2H and 11B.

Couplings to quadrupolar nuclei are generally larger for larger nuclei, resulting in peaks being further apart and therefore easier to see. It is difficult to predict whether coupling will be seen in a situation so in the exam, sufficient information will be given.

Coupling diagrams

Remember the 2nI+1 rule can be used when coupling to something with exactly the same coupling constant. For a 13C {H} spectrum of the CD3 group, the single carbon peak is coupled to the three identical deuterium atoms. Using the 2nI+1 rule, the single peak is primarily split into a triplet ((2x1x1) +1=3). Each of the triplet peaks are split into a triplet again and then a triplet again. The overlapping results in intensities that cannot be predicted by Pascal’s triangle.

The intensity is carried down to ultimately give a 1:3:6:7:6:3:1 ratio. The number of peaks can be predicted by the 2nI+1 rule.

= (2x3x1) +1=7 peaks, septet

The intensities are carried down (note numbers by lines).

NMR Standards

Definition of isotopomer: Same number of isotopes but in different arrangement. It is a contraction of the word isotopic isomer.

The 2nI+1 rule can be used to calculate:

The number of peaks The number of peaks of

each atom coupled to the atom in question

The standard used should be:

Inert Soluble

Volatile/easily removable Cheap

If the standard is reactive, it can be used externally, such as is the procedure with 31P NMR

Spectroscopy, where H3PO4 or phosphoric acid is used.

It is important to note which standard is used as a small difference in chemical shifts may occur

from using different standards. Assignment of peaks can be challenging when the standard used

differs from the one used in literature.

Summary

(i) γ= μI

Where μ is the magnetic dipole and I is the angular momentum.

(ii) Larmor frequency=γ B02π

(iii) δ=vobs−vref

vref x106

(iv) relative sensitivity=[ γ x

γH ]3

x(I x+1)/ I x

2

(I H+1)/ IH2

(v) Linewidth=Q. (2 I+3 ) . qzz

2 . τ c[ I 2 (2 I+1 )]

Dynamic Effects in NMR Spectroscopy (DNMR)

Chemical exchange and intra-/inter-molecular site exchange are just three examples of a number of dynamic processes that can be observed by NMR Spectroscopy.

If the rate of exchange is fast, an average is observed. If slow, separate resonances are obtained. Anything in between is observed as a broad peak.

Coupled nuclei that undergo chemical exchange lose their coupling. An example is ethanol:

We would expect the proton in the OH group to couple to the protons in the neighbouring CH2 group and therefore appear as a triplet. We would then expect the CH2 group to appear as a doublet of quartets. This only occurs in PURE samples.

When acid or water is present in the sample, the OH proton exchanges rapidly and the coupling is lost:

At lower temperatures, molecules do not rotate as quickly. In some cases, axial environments are different to equatorial environments, resulting in two chemical shifts. If the temperature increases however, the signals become broad. At the coalescence temperature, the signals collapse into each other and you get a flat ‘top’ to the signal. At the coalescence temperature and above, the chemical exchange is faster than the NMR so it is not picked up.

High temperature has an effect on chemical shift. NMR is slightly dependent on temperature and does affect the chemical shift.

Problems/Issues:

At low temperatures, it is important the solvent does not freeze and the sample remains in solution.

At higher temperatures, the solvent must have a high boiling point

Solid State NMR SpectroscopyAll spectra so far have been in homogeneous solutions. NMR spectroscopy of solids (powders, crystals, polymers, coal, wood etc.) has a few problems that are not encountered with solutions:

Dipolar couplings (strong through-space coupling of magnetic dipoles) are not averaged to zero by molecular tumbling. Long range coupling also occurs as nuclei remain static. This

results in BROAD NMR signals Chemical shifts are dependent on the orientation of the molecule with respect to the applied

magnetic field. This is not averaged in solid NMR Spectroscopy as it is with homogeneous samples, where molecular tumbling averages the signals.

Relaxation times may be long as the molecules remain static. The time taken to get a good signal: noise ratio may take a long time.

Quadrupolar nuclei will interact with the magnetic field strongly. Their NMR signals tend to be wider, the same problem quadrupolar nuclei face in solution NMR

BUT: The concentration of sample is much higher is solid state NMR Spectroscopy than in solution.

The factors above all result in broadening of the NMR peaks in solid state spectroscopy. It can be overcome by several methods:

1) Rapid spinning of sample2) The ‘Magic Angle’3) Cross polarisation

1) Rapid spinning of sample:

Spinning at a speed of 5-20 kHz (compare with just 30Hz for a solution sample) is spinning the sample at a similar magnitude to which coupling occurs. Spinning side bands are observed: the faster you spin the sample, the less intense the side bands are.

However, very fast spinning can cause problems with your solid sample.

2) The ‘Magic Angle’

There is a line broadening term with an angle θ in its equation. θ is the angle between the sample and the applied field. If this angle θ is set to 54.7°, the line broadening term becomes zero and line broadening is greatly reduced.

The combination of rapid spinning and the ‘magic angle’ results in reduction of line broadening of signals.

3) Cross polarisation

To reduce long spin-lattice (through space) relaxation times, cross polarisation may be used. Cross polarisation is combined with the ‘magic angle’, or MAS (Magic Angle Spinning), polarisation from abundant nuclei such as 1H, 19F and 31P can be transferred to rare or dilute nuclei like 29Si or 13C in order to enhance the signal: noise ratio. It is also a method used to reduce waiting time between successive experiments.

Cross polarisation is one of the most important techniques in solid state NMR. It enhances signal from dilute spins.

CP-MAS: stands for Cross Polarisation - Magic Angle Spinning.

Paramagnetic Shift Reagents for NMR Spectroscopy

Protons in diamagnetic compounds tend to have a small chemical shift range of ~15ppm. For complicated molecules with many contiguous CH2 and CH groups, the chemical shifts

tend to be very close together and coupling leads to broad groups of overlapping multiplets. Using high field spectrometers may be one way to overcome this problem Selective decoupling experiments may be another method to overcome the problem Another is coordinating a suitable functional group with a paramagnetic lanthanide ion A suitable functional group may be C-OH or C=O The paramagnetic lanthanide ion induces significant shifts in proton environments near the

paramagnetic centre This results in a simplification of complicated spectra

In the spectra below, many multiplets are overlapping.

The most efficient shift reagents are ions of the lanthanide group such as Europium (III) and Praseodymium (III).

The shifts induced result from contact and dipolar (pseudo-interactions) interactions between the paramagnetic ion and the organic molecule

Using a shift reagent that will interact with a multitude of functional groups at one time, induce a significant shift but cause minimal line broadening lead to the best results

Using transition metals as shift reagents result in broad lines: UNACCEPTABLE Eu(facam)3 is a chiral shift reagent used for enantiomers. When enantiomers complex with

the substrate, diastereomers are formed which results in differing chemical shifts The shift reagent is used in small quantities, so as not to obscure the compound being

studied. The magnitude of the induced chemical shift is down to the angle between the paramagnetic

atom and the observed nucleus. The quantitative relationship is given by the McConnell equation

Electron Paramagnetic Resonance SpectroscopyNowhere NEAR as important as NMR Spectroscopy!

EPR, also known as ESR (Electron Spin Resonance) spectroscopy, is a technique analogous to NMR, but where electron spins are excited instead of nuclear spins. The technique can be applied to chemical species (atoms, ions or molecules) with unpaired electron spins (i.e. with electron spins S>0, where NMR uses I>0).

Transition metal and lanthanide ions containing unpaired d- or f-electrons are examples of species that may be studied using EPR. Some stable organic compounds such as DPPH and TEMPO contain an unpaired electron. Organic ion radicals, biradicals and triplet-state organic molecules are other species examples.

The EPR is placed in a strong, static magnetic field and irradiated by an orthogonal high-frequency in GHz (microwave range). NMR uses MHz (radio frequency range).

Energy is absorbed when the radiation matches the energy difference between the two electron states (In NMR, it is the energy difference between the two nuclei states), if the transition satisfies the selection rules.

Electrons have a magnetic moment and spin quantum number of ½, with magnetic components ms=±1/2. In the presence of an external magnetic field with strength B0, an electron’s magnetic moment aligns itself either parallel (ms=-1/2) or antiparallel (ms=+1/2) to the field.

The separation between the states is:

ΔΕ=ge μB B0

Where ge is the ‘g-factor’ for a free electron. The equation above implies the energy difference is directly proportional to the magnetic field strength, B0.

The magnetic field strength in EPR is given in gauss (G), where 1G=10-4T. NMR uses Tesla (T).

μb is the Bohr magnetron and is equal to 9.2740 x10-24JT-1.

ge is equal to 2.0023193 for a free electron

An unpaired electron moves in between the two energy levels by either absorbing or emitting electromagnetic radiation of energy ε=hν such that the resonance condition ε=ΔΕ, is obeyed.

Using ΔΕ=ge μB B0 and ε=hν, the following equation can be justified:

hν=ge μB B0

By increasing the external magnetic field B0, the gap between the energy levels ms=+1/2 and ms=-1/2 increases until it matches the energy of microwaves. Then unpaired electrons can move between their two spin states.

Spectral parameters in EPR

Electrons are rarely ‘free’; they are associated with one or more atoms.

An unpaired electron in a real system gains or loses angular momentum, leading to a change in its g-factor, from ge to a new value. This is most significant for chemical systems with transitional metal ions and is analogous to the chemical shift in NMR

spectra. If an unpaired electron is nearby an atom with nuclear spin I>0, the electron is

affected by the magnetic moment. This causes hyperfine coupling, analogous to J-coupling in NMR, splitting the EPR signal into doublets, triplets, etc.

Unpaired electrons interact with their environment, thus influencing the shape of the EPR signal.

The g-factor and hyperfine coupling may not be the same for all orientations wrt B0.

The g-factor

As the g-factor varies with the environment of the unpaired electron, its value can be used to predict the environment of the paramagnetic centre.

Organic molecules have g values (1.99-2.01), close to that of the free electron.

Transition metal compounds vary more widely (1.4-3.0).

Hyperfine Coupling

If an electron interacts with a neighbouring nuclear magnetic dipole, the two energy levels (parallel and antiparallel to the field) are split by a value a. The hyperfine coupling constant is split into 2nI+1 energy levels where I is the nuclear spin and n is the number of nuclei with spin I.