In the case of a free electron inspace, the e- is the only sourceof magnetism in the sample:
When unpaired electron couples to
1) Empty orbital (e.g., d1), g < ge
2) Occupied orbital (e.g., d9), g > ge
Generally 1.3 < g < 9
In the case of an e- in a molecule, SOC (spin-orbit coupling constant ) adds or subtracts orbital angular momentum to that of free electronand we lump that into “gobs” or “g”:
• For transition metals, large deviations from ge possible
• g can be measure to high accuracy (±0.0001)
• g is the “chemical shift” equivalent of EPR
• g depends on structure of radical, excitation energies, strengths of spin-orbit couplings
Note for later: g is anisotropic and not a scalar but a tensor.
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Energy of the Zeeman transition (and hence the “g-value”) is determined at a fixed microwave frequency with H0 being scanned. The “g-value”is a unique property of the molecule as a whole and independent of any electron – nuclear spin interactions.
What is the origin of g‐values different from 2.0?
Deviations from g = 2.0 due primarily to Spin‐Orbit Coupling. SOC constant, ζ, is metal‐ion dependent: can be small (150 cm‐1; Ti3+) or large (830 cm‐1; Cu2+).
An electron acquires orbital motion so to favorably experience the magnetic field of a nucleus, hence lowering its overall energy.
Specifically, an electron in an orbital (e.g., xy), can, via SOC, gain orbital angularmomentum via mixing with other orbital trajectories defined by rotationaloperators. Hence, an electron in xy can gain xz character via rotation about X, where such a rotation has a barrier, Δx.
For an electron that rotates into an empty orbital, the "current" created by the rotating electron leads to a magnetic field that opposes the applied magnetic fieldB0. This requires a larger applied field to achieve resonance, and hence a loweringof g.
For an electron that rotates into an occupied orbital, the sense of the current created by the rotating electron leads to a magnetic field that aligns with the applied magnetic field B0. This requires a smaller applied field to achieve resonance, and hence a raising of g.
What is the origin of g‐values different from 2.0?
For an electron that rotates into an empty orbital, the "current" created by the rotating electron leads to a magnetic field that opposes the applied magnetic field B0. This requires a larger applied field to achieve resonance, and hence alowering of g.
So, one must be careful to avoid “power saturation”: i.e., driving the populations into exactly equal fractions by driving transitions faster than spin relaxationand therefore losing all net change in magnetization.
To enhance S/N and locate broad signals, EPR spectrometers use modulation detection 1st Derivative spectra: Signal Ampl / mag field
Instrumentally, the mag field is modulated using coils aligned with mag field (Helmholtz coils) to oscillate H0 a bit (0.01 to 20 G) at ~100 kHz. Detection is then phase locked to that frequency.
Kramer’s Doublets: Effective half-integer spin states (S = 5/2, 3/2, 1/2, etc.) that are split under an applied magnetic field to the ±Ms microstates (Zeeman Splitting).
Example: A 4T1 state is split under axial zero-field splitting into three sets of Kramer’s doublets (S = 5/2, 3/2, and 1/2), which are separated by Zeeman splitting to the ±3/2 and ±1/2 microstates.
s3 There are many Cytochrome P450 enzymes, and they catalyse oxidation of various organic substrates (e.g. medicines) in living organisms. At the centre of these enzymes is a haem centre (iron porphyrin), bonded to the protein through an Fe-S bond to a cysteine side-chain. In the resting state of the enzyme, the iron centre is in the +III oxidation state. Successive one-electron reduction, binding of dioxygen, one-electron reduction, addition of two protons, and loss of water, leads to formal transfer of an oxygen atom to the iron atom. The resulting key intermediate, referred to as "Compound I", formallyhas an iron atom in the +V oxidation state (in fact, part of this charge is delocalised on the porphyrin ring and the oxygen atom, so that the iron is better described as being in the +IV or even +III oxidation state).stuart, 2/22/2006
Blumberg and Peisach’s plot of a large family of low spin hemes showing howdata cluster into five domains. The first four (C, B, H, O) have similar rhombicdistorHons but increasing axial fieldstrength. These assigned with histidine (axial 5th site) but 6th ligand is methionineC, neutral histidine H, anionic histidine B, and oxide O. The fifth family (P) are the P450 heme enzymes, with cysteine andwater as the axial ligands.
The Blumberg analysis tends to work best when V/Δ is quite large. These are knownas “Truth Tables”.
Relative populations are given by Boltzmann at thermal equilibrium (I<<S, hence populations of 1 & 2, 3 & 4 assumed identical)
Irradiate 1-3 transition (saturate at high power): that will give same populations in 1 & 3.
Irradiate system with RF (NMR) and sweep frequency while continually saturating EPR transition; observe the intensity of its absorption
When RF frequency matches |I-a/2|, transition 3-4 will be induced, restoring some population difference between levels 1&3
More EPR absorption now possible: that is ENDOR signal
Equally, when RF frequency matches |I + a/2| (1-4 transition), this time a pumping from 1-4 occurs (as 4 has the higher population) and a population difference between 1&3 is again achieved and EPR transition enhance – the second ENDOR signal
In practice, need to consider spin lattice relaxation processes
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