Damien Murphy Flashcards
What can be studied with EPR?
EPR is the acronym for Electron Paramagnetic Resonance Spectroscopy. It encompasses a large variety of techniques both in CW (continuous wave) and pulsed mode. The theory and fundamental physics of EPR is analogous to the better-known NMR technique. Paramagnetic states are used. We cannot study paramagnetic states with NMR
- Low power waves of a fixed frequency (9.5 GHz) contrinously irradiates a sample within a resonator while the applied magnetic field is swept.*
- EPR is a magnetic resonance technique used to study systems containing unpaired electrons. Such systems are paramagnetic and attracted my magnetic fields.*
- Organic free radicals in solution*
- Organic radicals in solids*
- Transition metal ions*
- Inorganic free radicals*
- Atomic and molecular gases*
- Biological samples*
- Photoexcited molecules*
- Point defects in solids*
What is spectroscopy?
Spectroscopy: how electromagnetic radiation (field) interacts with matter (dipole moments).
What was the Stern Gerlach experiment? Why was this important?
The Stern Gerlach experiment showed that silver (containing one unpaired electron – paramagnetic)when aimed between two magnets, electrons separated to two energy levels: either a higher energy level if the electrons didn’t align with the magnetic field, or a lower energy state if aligned. We can calculate the difference in energy between these fields. It was then assumed electrons have a 4th quantum number from this experiment: spin.
What is EPR Composed of? What are field interacting with? Where are dipole moments arising from? How is this different to NMR?
What regions of the electromagnetic spectrum?
- All spectroscopic techniques are concerned with the interaction of electromagnetic radiation with matter. Excitation between two states or energy levels is induced by absorption of radiation. The electromagnetic radiation is composed of oscillating electric and magnet*ic propagating through space with a constant speed.
- In plane polarized radiation, E1 and B1 fields are perpendicular and varu sinusoidally fomring a transverse wave with a specific wavelength. Radiation is composed of photons carrying energy and angular momentum interacting with matter.*
- only when the energy of a photon matches the energy separation between two states, resonance absorption occurs.*
Electromagnetic (EM) radiation is composed of oscillating electric (E1) and magnetic (B1)fields.
In EPR and NMR, the B1 field interacts with permanent dipole moments in the sample.
In EPR the permanent dipole moments come from the unpaired electrons.
EPR and NMR, electric (E1) and magnetic (B1) fields interact with spin (electron for EPR) or nucleus (for NMR).
EPR is microwave based, NMR is radio wave based.
What is magnetic moment? What is the equation for it?
How is this different for NMR and EPR? What is the meaning for this?
There is a large charge/mass ratio for EPR compared to NMR. Magnetic moment is at least 680 times larger for EPR compared to NMR. This means higher frequencies, shorter time scales (10 ps-1 ms), higher sensitivity and longer distance.
- EPR transitions are characterised by small energy gaps (long wavelengths) compared to other spectroscopic methods. The low-energy radiation mens it doesn’t damage the sample and is therefore non-invasive.*
- The populations of different energy levels are similar as energy gap is small. Sensitvity of both EPR and NMR is lmitred.*
- Bohr magneton (uB) is the unit expressing the magnetic moment of the electron, whereas the nucear magneton (uN) expresses magnetic dipoles of heavy particles like nucli.*
- The origin of mangetic moment comes from spin angular momentum of unpaired electron. Resonance occurs when the sample bearing upaired electrons absorbs sufficient energy to induce a spin transition from one energy to the next.*
What is EPR used for?
EPR is a very powerful method to study organic radicals in solution and solids, transition metal ions, inorganic free radicals, atomic and molecular gases and biological samples. Example spectra include:
- Molecular and supramolecular structure
- electronic structure
- dynamics
- concentration
Can therefore quantify free radical intermediates in chemical reactions, reactive oxygens species which are both important for biological and medicinal studies and can help determine antioxidant properties.
What is the EPR spectrum? What is happening to the sample and what is recorded on the graph (axes)?
What does greater intensity indicate?
Can we quanitfy both axes?
The sample is exposed to the magnetic field (B1) of the EM radiation of fixed frequency (9 GHz= microwave), and an external laboratory magnetic field (B) is swept.
The resulting spectrum is thus a plot of MW energy absorbed versus the applied magnetic field.
In CW experiments, the resonance absorption is polotted as a first derivative rather than absorption mode.
Greater intensity = more radicals
We never study the y-axis because this is sample/instrument dependent so meaningless. Intensity is the y-axis and is the amount absorbed. We just don’t quantify this. X-axis is the applied magnetic field.
What is the resonator (cavity) in EPR?
The resonator matches the frequency. 9 GHz has a wavelength of 2 cm which is the size of the resonator. NMR measures absorption, however if we derivated this (dy/dx) then we would get a graph the same shape as EPR.
The sample is placed into an EPR cavity (or resonator) such that the B1 field of the EM radiation is maximum along the sample direction while E1 field is minimum.
Looking at the figure: B1 is like a figure of 8. This field perturbs as many magnetic moments as possible. The electronic field (E1) does nothing and doesn’t help sensitivity.
Magnetic and electronic fields form a mode/ standing wave inside the resonator, which is called the TE102mode. This is the mode in which NMR and EPR are made. We want to maximise B1 and minimise E1.
What are the key dinmensions for EPR spectroscopy?
Key dimension sand what these can tell us (shown in the middle):
- Position: g-factor
- Linewidth: tumbling speed, dynamic effects, unresoled superhyperfine, hyperfine interactions
- Separation: coupling - Hyperfine - dictated by nuclear spin I
- Intensity: nucleus interactions, anisotropy of paramagnetic system
As EPR needs paramgnetic species, this is an advantage as it reduces noise!
What is the spin hamiltonian for EPR?
Free radicals have unpaired electrons.
Electrons spin on their axis forming magnetic fields. This causes either attraction or repulsion with the magnetic field.
The spin Hamiltonian describes energy of the electron spin in real paramagnetic systems.
Various interactions contribute to the Hamiltonian. The magnitude of these interactions will dictate the perturbations in the EPR spectrum.
What are some of the interactions that contribute to the spin hamiltonian?
The yellow box contains the only types we need to be concerned with:
1. Electron Zeeman interaction: occurs when we have a lab magnetic field and introduce an electron and observe the interaction. This is electron spin/ static magnetic field. We are interested in ge.
2. Hyperfine interaction: when a proton and electron interact, we get an A value.
3. Nuclear Zeeman interaction: is the interaction of a proton and lab magnet (NMR!). We are interested in the gn value.
- Zero-field splitting (ZFS): strong electron spin-electron spin interactions
- Nulclear Quadrupole - nuclear spin interaing with electric field gradients in nucleus
Discuss the Electron Zeeman Interaction (angular momentum and electron magnetic moments)
unpaired electron can exist in either +1/2 state or -1/2 state (ms)
When placed in an external magnetic field, degeneracy is lifted as ms= -1/2 state is lower in energy as it is antiparallel
The separation between the two states is proportional to the magnitude of the applied magnetic field:
Because the separation of the two states is proportional to the applied magnetic field, as frequency increases (the energy), the separation increases. The certain amount of energy required to life degeneracy matches the frequency at which this occurs: E = hv = geubB.
If the gap is too big, then the excitation energy is not enough. We have a fixed frequency being applied therefore we must find the magnetic field at which the energy gap matches so absorption is detected.
How can we work out the frequency of the electronic transition? What does 1 telsa equal?
Discuss the origin of the resonant equation and g factor:
What are the two important considerations from the basic electron Zeeman interaction shown above?
- As B increases, v must also increase. The resolution (in g) will therefore increase at higher field:v=g*uB*B/h
- As B increases, sensitivity normally increases. At thermal equilibrium, the spin populations in the two Zeeman levels is given by the Maxwell Boltzmann equation:
If the gap increases, sensitivity increases. The population difference is tiny. J band has greater sensitivity than X band.
Exam question: Why do we change the frequency of EPR? What are the advantages/disadvantages of high and low temperature and different frequencies?
(High field EPR)
As B increases, v must also increase. The resolution (in g) will therefore increase at higher field:v=g*uB*B/h
Exam question: Two radicals have similar gvalues of 2.0023 and 2.0044. Calculate the resonant field positions of the radicals at L & J band, using the resonant equation:
As B increases, v must also increase. The resolution (in g) will therefore increase at higher field:v=g*uB*B/h
What is The nuclear Zeeman Interaction (the Nuclear spin & Hyperfine Interaction)
How can we now describe the energy of the electron?
In a real system, the electron will not only interact with the applied magnetic field, but also with the magnetic moments from surrounding spin active nuclei. In this case, the energy of the electron is perturbed further. The resulting energy (E) is given by:
For g and a (=hyperfine) parameters are the most valuable pieces of information available from EPR spectra. In real systems, the radical is not isolated. Electrons interact with a big magnetic field, electrons sense magnetic field and nuclei. Nucelli also interact with the field.
The interaction of the nuclear spin with B results in a nuclear Zeeman splitting and resulting interaction between electrons and nucelar magnetic moments is described by the hyperfine interactions. These interactions give rise to additional terms in equation. This creates a small but signigicant perturbation to the electron spin energies.
Discuss the hyperdfine parameters for nuclear Zeeman Interaction:
- What occurs for simple proton couplings vs. if the unpaired electron responsible for the proton coupling is present in a pi-orbital?
Hyperfine: arises from interaction between electron and nuclear magnetic dipole moments with each toher. Create perturbation of nuclear zeeman energy levels towars higher or lower energy.
Hyperfine interaction (isotropic) - small probability electron can enter nuclear volume. Hyperfine field originating from nuclear magnetic fipole is constant in all directions. This is isotropic interaction and is a measure of interaction between electron and nuclear magnetic dipole moments as a result of finite probability that the unpaired electron will be located at the nucleus.
What are the EPR and NMR Selection rules?
The EPR selection rules are ;
Change in spin = +/- 1, Change in Ml = 0
. The NMR selection rules: ;
Change in spin = 0, change in MI = +/- 1
Electrons can change spin but not nuclei in the same process.
Sketch the energy level diagram for electron zeeman splitting showing the NMR, EPR transitions, Eelectron zeeman transitions, nuclear zeeman transitiona and hyperfine:
- Energy it of the two states realted to orientation of magnetic dipole moment in external magnetic field
- Nuclei that possess a non-zero nuclear spin quantum number will also have associated magnetic moment uI
- Nucleasr spin angular momentum is formed by coupling angular momentum of nucleons. Isotop my have different nuclear spin quantum numbers. In the absence of magnetic field they have the same energy. Magnetic fields remove degeneracy
- Energy of nuclear zeeman levels is known : E=gnunBMi
- gn can be positive (14N) or negative (15N), magnetic dipole moments of nuclei will align with or against the applied field.
What does the number of lines tell us about EPR of radicals in solution? Why do we get so many lines?
Number of lines = 2nI+1, multiplicative increase for n inequivalent nuclei
- Consider an unpaired electron that experiences a hyperfine interaction with a nucleus of spin 1. As seen in chapter 2, this system has 2n+1 energy levels for each ms. EPR spectrum of a radical that experinces a hyperfine interaction with a nucleus of I shows 2I+1 lines.*
- For commonly used microwave frequencies (X band), the energy fo the hyperfine interaction for organic radicals is much smaller than the energy of the electron zeeman interaction. This is known as the high field approximation.*
- The EPR transitions are therefore characterised by small energy gaps, and probabilities of these are similar. Hyperfine lines in EPR spectra have equal intensity.*
- ml levels are evely spaced, Distances beteween 2I+1 lines in EPR spectrum are equivalent.*
What does the intensity tell us about EPR of radicals in solution?
Intensity is given by the coefficient of binomial expansion (1 + x)i
What does the position of the lines tell us for EPR spectroscopy?
Position of lines is given by B=Bo - Sum of (aimi)
What are we expected to deduce from EPR?
- We want to know the g values
- We also want to find out the hyperfine value ‘a’. If we see hyperfine coupling, all of a values will be equal. For the graph below, we have three identical a value. The radical is on the carbon.
- In all exam examples, presume frequency =9.5 GHz = 9.5x109Hz; X BAND
- WHATEVER YOU MEASURE ON ONE SIDE, DO IT FOR THE OTHER TO MAKE SURE
- The first difference is the smallest hyperfine coupling constant!
- All g values will be between 1.95-2.22 and they are dimensionless
Exam question: How can we measure the hyperfine coupling of the following EPR spectra?
Discuss how different EPR spectra come about?
Exam question:
- Find the hyperfine interaction
- The spin pattern
- B
- g
aHa and aHband Pca, Pcb
Discuss the difference between the two liquid phase EPR spectra:
What are the general rules for interpreting liquid phase EPR spectra?
How does solid state NMR come about? Is this better data?
At room temperature for NMR? compounds are tumbling so we get average spectra. We can freeze these down and get solid state. This quenches tumbling and we now have a solid system. This gives more complicated but much more informative spectra.
What is the g factor in terms of theory and analysis of EPR spectra in the solid state?
What does g aniosotropy mean in terms of EPR spectra in the solid state?
The shape of the EPR spectrum in solid state depends on relative orientation of B with respect to the orientation of paramagnetic species. The local symmetry around the site is crucial.
The basics of EPR resonance equation must consider sample orientation
This is a schematic illustration of the three independent axes systems relevant to the EPR analysis, including the magnetic field axes (X’,Y’,Z’), principal g axes (X,Y,Z). In solid state systems we usually only consider the orientation of the external applied magnetic field B with respect to the principal orthogonal gtensor axes (x,y,z), using right handed cartesian coordinates with polar angles theta and thi.
Energy depends on closeness of dipole moments of electrons and the dipole
Energy is also affected by orientation!
When hv=guBBwe are assuming g is isotopicin liquid phase. However isotopic independencies are averages!
If energy changes, then g changes
Always see field rotating, we visualise it this way, but actually it is the other way around
How does g depend on sample orientation for EPR in the solid state?
Discuss the single crystal case for solid state EPR spectra:
Discuss how poweder spectra differ for solid state EPR spectra:
Most commonly, EPR are recorded in frozen solutionsor as polycrystalline powders. We need to study under operating conditions (i.e. in vitroconditions for enzymes etc)
In this case, the powder spectrum is dominated by all contributions from the g anisotropy
Again, for S= ½ , I=0, in uniaxial site, the variation in g depends only on theta and B
Remember that the values of gIIand g^set the range of Bover which absorption occurs
When gII> g^no absorption occurs at fields lower than:
Discuss how different shapes of complexes can be identified using powder EPR spectra:
Discuss these examples of powder sepctra:
What is hyperfine A anisotropy?
How can the energy be calculated? (Edip)
The hyperfine interaction occurs when the unpaired electron interacts with the magnetic moment of a nearby nucleus of spin I > ½. The isotropic a value is now replaced with an isotropic A value. A also has orientational dependency.
In liquid phase = a, but in solid phase = A
The A value has two contributions: the isotropic Fermi contact term (a) and the anisotropic dipolar term (T).
The energy of this anisotropic dipole-dipole interaction (Edip) term can be approximated to
For the hyperfine A anisotropy, what is the magnitude of Edip depending on?
Discuss for the hyperfine A coupling whty the spin effect can go through bonds and also through dipole-dipole interactions?
For a pure through-space dipole-dipole interaction, the Pake pattern is observed (figure c below). If a paramagnetic metal centre interacts weakly with a hydrogen we see this pattern. We don’t observe this is the metal is associated with C or H. The metal ‘sees’ the proton through bond and space and this is where the isotropic contribution is from
Discuss the combination of g/A anisotropy:
Discuss the hyperfine vs. superhyperfine
Discuss types of powder spectra and their appearances. Iso, axial and rhombic. How does axial differ?
How can we identify g-values from powder spectra?
Make sure you can discuss the following:
Discuss the following:
Discuss the theory and anaylsis of ENDOR spectra in the liquid state:
Electron spins can interact with remote ligand nuclear spins via the hyperfine interaction
Dipolar interactions between one electron and one nucleus (or two interacting nuclei), depends on the relative position of the spins with respect to each other, so the EPR or NMR spectra can yield information on nuclear co-ordinates.
For a paramagnetic complex, NMR cannot be easily used, because the presence of the unpaired electron will broaden the NMR lines considerably.
Hence EPR & ENDOR are required to extract the couplings to the local and remote nuclei in order to obtain structural information about the system under study
In EPR the hyperfine couplings may be directly observable in the spectrum; BUT in many cases, the interactions are so weak(i.e., the electron-nuclei distance is long), they are buried under the EPR line
In this case, Electron Nuclear DOuble Resonance (ENDOR) is used to detect these weak coupling
In ENDOR, the NMR quanta are detected in the microwave, rather than the RF range (known as a quantum transformation) resulting in a sensitivity enhancement of several orders of magnitude over conventional NMR spectroscopy
Therefore, ENDOR can be regarded as NMR spectroscopy on an EPR spectrometer
What are the 2 main advantages of ENDOR?
1. More detailed hyperfine coupling
Large resolution enhancementfor organic radicals (i.e. each group of equivalent nuclei contributes only two lines to the ENDOR spectrum)
2. Centred on vn (very useful!)
- The couplings are centred on the nuclear Lamour frequency of the interacting nucleus. Since vn is field dependent, as the field is varied then vn measured experimentally will also vary.*
(eg. , For 1H, vn= 14.90218 MHz at 0.35 T, but vn= 500MHz at 11.74. T ! common in NMR)
3. Structural informationabout the sample can be obtained (Orientation Selective ENDOR (topic 4))
In EPR we have a large hyperfine coupling, however for ENDOR this is very very small. The yellow highlighted box is the nuclear Lamour frequency. This is the frequency of procession in the magnetic field. Frequency is dependent on the nucleus. EDOR pairs of lines are centred on this frequency. This allows us to determine what nucleus is present. Before in EPR we would compare splitting intensities (i.e. 1:2:1 vs. 1:1:1 to study elements) but this is simpler.
What are the basic principles of ENDOR?
In EPR we observe frequency (MW) is used to excite the EPR transition
In a double resonance experiment, a second (RF) irradiating field is used
In ENDOR the MW field is used to excite electrons, whilst the RF field excited the nuclei
In ENDOR, one monitors the effects on an EPR transition of a simultaneously driven NMR transition and essentially detects the NMR absorption with much greater inherent sensitivity
How can resolution be enhanced of ENDOR?
In the above case (S = ½ , I = ½ ), two lines were observed in the EPR spectrum and two in ENDOR spectrum.
In EPR coupling are given in magnetic field units, in ENDOR couplings are given in frequency units.
However, when there are numerous I = ½ nuclei, then the simplicity of ENDOR becomes evident
Discuss EPR vs. ENDOR Spectra: Mutiplicative vs. Additive
Expressed another way, each set of equivalent nuclei contributes only two lines to the ENDOR spectrum
Addition of non-equivalent nuclei has a multiplicative increaseon the number of EPR lines, but only an additive increaseon the number of ENDOR lines
Hence the spatial density in ENDOR is far less compared to EPR (i.e. easier to interpret)
Comment on the origin of the ENDOR Spectrum:
In ENDOR, the NMR transitions are indirectly observed vis the intensity changes in the MW absorption of a simultaneously irradiated EPR transition. Remember Zeeman splitting is the difference between G.S and E.S (pop<0.01%).
Consider the population difference between the energy levels for (S = ½ , I = ½ )- need to know boltzmann equation Nupper/Nlower= exp(-guBB/KT) = 1 - (gubB/KT)
The difference between the nuclear spin levels (c,b and d,a) can be neglected (v small)
If eis defined as guBB/KT, the initial population difference between upper and lower levels is: *See image*
There needs to be a population difference for EPR. After tuning with MW (amplifier with correct frequency), electrons now in excited state and cannot relax. We are individually observing NMR on an EPR spectrometer.
Thermal populations in levels a and bremain constant provided EPR transition a –> b is included with sufficiently low microwave power (scheme 1)
At higher microwave power, the induced absorption rate competes with electronic spin relaxation rate; saturation of levels a and boccurs. A much smaller EPR signal is observed (scheme 2)
If RF power is applied between b and c, the EPR line becomes desaturated (i.e. restoration of population difference between a and b) viainduced absorption
This equalizes population levels of band c(Figure 3)
The application of RF partially desaturates the EPR signal, thereby increasing EPR response
This increase in EPR signal constitutes an ENDOR response, and the first ENDOR line is observed corresponding to NMR1 frequency
If the RF power is subsequently applied between levels a and d,the EPR signal is also desaturated, but induced emission, and a second ENDOR signal appears, corresponding to NMR 2 frequency
The partial desaturation of the EPR signal by the RF field can be regarded as a decrease in the effective spin lattice relaxation time. This decrease is characteristic of the most general type of ENDOR mechanism
What is the steady state ENDOR effect?
In the ENDOR experiment, the NMR resonances are not observed directly, but rather indirectlyvia their influence on the EPR line (the quantum transformation)
Relaxation effects are not considered in the above scheme
In the presence of a saturating MW and RF field, all three energy levels a, b and cwould become equally populated after a short time and ENDOR would disappear
The steady state ENDOR effect provides a relaxation pathway so that a continuous ENDOR signal is detected
Consider the relaxation pathways available in the two spin systems (S= ½ and I= ½) as shown:
Solid lines (red, blue)= radiation induced transitions; dashed lines = radiationless electron-spin lattice (We), nuclear spin lattice (Wn) and cross relaxation processes (Wx1and Wx2)
Wx1= I+-> –> I - + > (flip flop transition)
Wx2= I++> –> I - -> (flop floptransition)
This is the same drawing as above just pulled apart!
Takes the route: c –> b –> a –> d (bypass route)
Wn1is very slow. C –> B is stuck and takes a very long time (for electrons). We could also pump the pathway to force electrons. This doesn’t happen without help. B –> a is quick and favoured. Wn2is very slow. Apply RF of a –> d
In ENDOR, the EPR transition (vEPR1) is irradiated with MW power high enough to assure spin lattice radiation rate Wel does not compete with the induced transition
The most effective route for electron relaxation is from c –> d (We1)
However, a –>b –>c –>d is available and called the bypass route
This route is not effective in normal EPR experiments. Wn1 and wn2 are much less than We1 causing a buildup of spins in levels b and d.
The bottleneck caused by Wn1 is partially removed by pumping transition c –> b with saturating RF field (of frequency vNMR1); this effectively short circuits Wn1
This improves the efficiency of the bypass route, increases the effective spin lattice relaxation rate, and so leads to desaturation of the EPR transition and a corresponding increase of the EPR signal intensity
It is exactly this effect that is detected in ENDOR experiments. This is known as the steady state ENDOR effect
How do we analyse ENDOR Liquid Phase spectra for I = 1/2 systems (only)
Exam question: what would you expect to observe if the 1H ENDOR spectrum was recorded at the field position of 3465G:
How is the ENDOR Spectrum plotted?
Discuss orientation selective ENDOR:
- All of advanced hyperfine measurements described are typically recorded at low temperatures and produce anisotropic EPR spectra. Elements of the hyperfine A tensor and its relative oridentation with respect to the g tensor can be determined from variations in the magnitude of the hyperfine coupling at different magnetic field settings thorugh orientation selective hyperfine measurements.*
- Polycrytalisne EPR spectrum can be considered as a superposition of resonances from randomly orientated molecules so that the applied field B is swept and adopts all possible orientations with respect to chosen molecular frame. In orientation selective measurements (ENDOR) a series of hyperfine measurements are performed at fixed magnetic field positions across the full width of EPR spectrum. Hyperfine response at each field position arises from the subset of molecules having orientations that contribute to the EPR intensity at that field.*
The most important consideration is the solid state ENDOR – the orientation dependency of g and Atensors (we need to know how g varies with theta)
The profile and shape of the ENDOR spectrum depends on which field position was selectedin the EPR spectrum to record the ENDOR spectrum
This requires knowledge about how to unravel and interpret polycrystalline EPR spectra and thereby knowing which positions in the EPR powder pattern will yield single-crystal ENDOR spectra as opposed to powder ENDOR spectra
This can be achieved by orientation selection or angular selective ENDOR
The concept of angular selective or orientation selective ENDOR provides a means of recording spectra at selected turning points in the EPR spectrum (to select a single value of theta).
The first step involves the determination of the g tensor orientations contributing to the EPR resonance positions at the selected magnetic fields B. ENDOR spectra are then recorded at fixed magnetic fields, so that the response from a polycrystalline sample arises only from the subset of molecules having orientations that contribute to the EPR intensity at that particular B field.
How can we extract distances through dipolar coupling (T)?
Hyperfine interaction has 2 contributions aand T(Lecture 2/3, topic 2)
In solid state ENDOR we are ultimately trying to extract the hyperfine tensor (A)of an interacting nucleus, since analysis of this tensor gives information on distances
The hyperfine tensor (A)is composed of an isotropic part (aiso)and an anisotropic part (T): (Shown on the front slide)
The isotropic, or scalar part, provides information of the spin densityat a particular nucleus in the complex. This is also known as the Fermi contact interaction (don’t need to know).
Comment on the ‘road map’ for axial g tensor, with no metal hyperfine interaction:
Axial gtensor, with no metalhyperfine interaction (i.e. with a 1H interaction only)
Why are ENDOR spectra different in solid state?
How can we explain the sign of the hyperfine tensor for solid state ENDOR?
With axial g tensors, discuss ENDOR with the metal hyperfine interaction:
Discuss this example:
In the above examples no metal hyperfine was considered (i.e. 1=0 for a metal)
When I does not= 0 for the metal, the analysis becomes more complex, e.g. 55Mn (I=5/2) in axial symmetry.
Look at these examples:
Discuss these metal hyperfine solid state ENDOR Examples:
Discuss these examples of metal hyperfine solid state ENDOR:
Exam question:
Let’s consider an axialEPR system with one spin 1nucleus (gII> g^)
Ifwe had a spin 1 system, and I = 1, we could get 2*n*I+1 = 3 hyperfine lines
In the liquid state we can look at the interactions taking place:
What would this look like?
Exam question: What would happen if we froze the solution to give solid phase?
- What would the single crystal and powder look like?
Exam question: Why do we draw an angular dependency curve for this spectra?
Exam question:
Exam question:
Exam question:
Exam question:
Exam question:
Book question:
Book Question:
Book Question:
Book Question:
Book Question:
Book question
- 02615
- 2439 T
g = hv/ubB
Book question:
2.00804
g = hv/uBB
Book question
- 89 mT
- 2013 T
g = hv/uBB
Exam question:
Book Question:
What are splitting diagrams for EPR?
EPR can be more complex in the presence of several nuclei posessing nuclear spin I not equal to 0.
We study how spignals are split into several lines due to a hyperfine interaction. When making a splitting diagram start with the interaction with the greatest hyperfine interaction.
In theory, it doesn’t matter which way around this is done as the same spectra should be obtained.
Sometimes the lines overlap and this adds to greater signal intensity of certain values. This is why we sometimes observe fewer than expected lines.
When we have several equivalent nuclei we consider it in the same way
- n equivalent nuclei with spin I will split EPR signals into 2n+1 lines.*
- However for protons, (I=1/2( the number of lines and intensity is given by binomial expansion coefficients.*
- I = 1; 1, 1:1:1 triplet, 1:2:3:2:1 quintet; 1:3:6:7:6:3:1 septet*
What are hyperfine coupling constants?
- Correspond to energy differences between EPR transitions and as such, they should be quoted in energy uints
- Conventionally they are quoted in MHz or cm-1
- In the high-field approximation, hyperfine constants correspond to the distance between resonances in EPR spectra and can be measured directly from EPR spectra and measured drom the spectrum and quoted in field units
- Remember the point for the peak is where the peak crosses the x axis, and this is sometimes between the min and max.
- We can work out energues by hv=gybB
- Normally we spot no interaction for nuclei >2 bonds away
Step-by-step of analysing isotropic EPR spectra:
- if radical structure known, identify all spin active nuclei, count nuber of equivalent spin-active nuclei in each environment and use 2n+1 rule, pascal’s triangle to determine multiplicity and relative intensity of hyperfine lines for each environment
- If overall specturm not summetrical, probably contains signals from several radicals that need assessing separatley
- Measure separation beween first two lines at the low field in the spectrum this distance correspons to the smallest hyperfine coupling (a)
- Check if more lines located at the same distance (hyperfine coupling) upfield from the second. They will likely belong to the same multiplet
- Check intensities. If the multilpet is not symmetrical probably overlaps with another.
- Measure distance from outermost line to first line which does not form multiplet A, this is the hyperfine coupling constant of multiplet B
- Hyperfine pattern of A will be superimposed on B too
- Measure hyperfine coupling towards B higher field untill all multiplets identified
- repeat 6-9 as many times as needed
What is spin polarizaton?
How can we dermine the distribution of spin density?
Exam question:
Draw a splitting diagram for the cyclohexyl radical and assign the hyperfine pattern to alpha and beta protons:
Exam question:
Sketch EPR of CH3CH2CD* paying attnetion to number of hyperfine lines, relative intensity, separation..
Exam question:
EPR spectrum of glycolic acid (HOOC-CH*-OH) shows 4 lines with coupling constants of 17 and 2.5G. Unpaired electrons mostly localised on carbon with some electron density on C and O atoms. Suggest geometry of glycolic acid radical: Deduce with H has larger hyperfine constant (17G) and estimate spin density:
Exam question: Predict the number of lines and their intensity in the EPR spectrum of C7H7 radical. Estimate hyperfine value and sketch appearance EPR:
Discuss continuous wave ENDOR:
Discuss resolution enhancement for ENDOR:
Discuss determination of the anisotropic hyperfine tensor for ENDOR:
