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**Electron Spin Resonance Spectroscopy**

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**ESR Spectroscopy Electron Spin Resonance Spectroscopy**

Also called EPR Spectroscopy Electron Paramagnetic Resonance Spectroscopy Non-destructive technique Applications Oxidation and reduction processes Reaction kinetics Examining the active sites of metalloproteins Electron spin resonance (ESR) spectroscopy, also referred to as electron paramagnetic resonance (EPR) spectroscopy, is a versatile, nondestructive analytical technique which can be used for a variety of applications including: oxidation and reduction processes, biradicals and triplet state molecules, reaction kinetics, as well as numerous additional applications in biology, medicine and physics.

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**What compounds can you analyze?**

Applicable for species with one or more unpaired electrons Free radicals Transition metal compounds Useful for unstable paramagnetic compounds generated in situ Electrochemical oxidation or reduction However, this technique can only be applied to samples having one or more unpaired electrons.

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Energy Transitions ESR measures the transition between the electron spin energy levels Transition induced by the appropriate frequency radiation Required frequency of radiation dependent upon strength of magnetic field Common field strength 0.34 and 1.24 T 9.5 and 35 GHz Microwave region As we know, spectroscopy is the measurement and interpretation of the energy difference between atomic or molecular states. The absorption of energy causes a transition of an electron from a lower energy state to a higher energy state. In EPR spectroscopy the radiation used is in the gigahertz range. Unlike most traditional spectroscopy techniques, in EPR spectroscopy the frequency of the radiation is held constant while the magnetic field is varied in order to obtain an absorption spectrum.

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**How does the spectrometer work?**

Shown is a block diagram for a typical EPR spectrometer. The radiation source usually used is called a klystron. Klystrons are vacuum tubes known to be stable high power microwave sources which have low-noise characteristics and thus give high sensitivity. A majority of EPR spectrometers operate at approximately 9.5 GHz, which corresponds to about 32 mm. The radiation may be incident on the sample continuously (i.e., continuous wave, abbreviated cw) or pulsed. The sample is placed in a resonant cavity which admits microwaves through an iris. The cavity is located in the middle of an electromagnet and helps to amplify the weak signals from the sample. Numerous types of solid-state diodes are sensitive to microwave energy and absorption lines then be detected when the separation of the energy levels is equal or very close to the frequency of the incident microwave photons. In practice, most of the external components, such as the source and detector, are contained within a microwave bridge control. Additionally, other components, such as an attenuator, field modulator, and amplifier, are also included to enhance the performance of the instrument.

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**What causes the energy levels?**

When an electron is placed within an applied magnetic field, Bo, the two possible spin states of the electron have different energies. This energy difference is a result of the Zeeman effect. The lower energy state occurs when the magnetic moment of the electron is aligned with the magnetic field and a higher energy state where m is aligned against the magnetic field. The two states are labeled by the projection of the electron spin, MS, on the direction of the magnetic field, where MS = -1/2 is the parallel state, and MS = +1/2 is the antiparallel state. Resulting energy levels of an electron in a magnetic field Ebsworth, E. A. V.; Rankin, David W. H.; Cradock, Stephen Structural Methods in Inorganic Chemistry; CRC Press: Boca Raton, 1987.

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Spectra Like most spectroscopic techniques, when the radiation is absorbed, a spectrum is produced similar to the one on the left. In EPR spectrometers a phase-sensitive detector is used. This results in the absorption signal being presented as the first derivative. So the absorption maximum corresponds to the point where the spectrum passes through zero. This is the point that is used to determine the center of the signal. When phase-sensitive detection is used, the signal is the first derivative of the absorption intensity

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**Describing the energy levels**

Based upon the spin of an electron and its associated magnetic moment For a molecule with one unpaired electron In the presence of a magnetic field, the two electron spin energy levels are: E = gmBB0MS g = proportionality factor mB = Bohr magneton MS = electron spin B0 = Magnetic field quantum number (+½ or -½) So for a molecule with one unpaired electron in a magnetic field, the energy states of the electron can be defined as: E = gmBBoMS = ±1/2gmBBo where g is the proportionality factor (or g-factor), mB is the Bohr magneton, Bo is the magnetic field, and MS is the electron spin quantum number. From this relationship, there are two important factors to note: the two spin states have the same energy when there is no applied magnetic field and the energy difference between the two spin states increases linearly with increasing magnetic field strength.

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**Proportionality Factor**

Measured from the center of the signal For a free electron For organic radicals Typically close to free- electron value For transition metal compounds Large variations due to spin-orbit coupling and zero-field splitting As mentioned earlier, an EPR spectrum is obtained by holding the frequency of radiation constant and varying the magnetic field. Absorption occurs when the magnetic field “tunes” the two spin states so that their energy difference is equal to the radiation. This is known as the field for resonance. As spectra can be obtained at a variety of frequencies, the field for resonance does not provide unique identification of compounds. The proportionality factor, however, can yield more useful information. For a free electron, the proportionality factor is For organic radicals, the value is typically quite close to that of a free electron with values ranging from For transition metal compounds, large variations can occur due to spin-orbit coupling and zero-field splitting and results in values ranging from

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**Proportionality Factor**

MoO(SCN)52- 1.935 VO(acac)2 1.968 e- 2.0023 CH3 2.0026 C14H10 (anthracene) cation 2.0028 C14H10 (anthracene) anion 2.0029 Cu(acac)2 2.13 acac = acetylacetonate Atherton, N. M. Principles of Electron Spin Resonance; Ellis Horwood: Chichester,

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**Hyperfine Interactions**

EPR signal is ‘split’ by neighboring nuclei Called hyperfine interactions Can be used to provide information Number and identity of nuclei Distance from unpaired electron Interactions with neighboring nuclei E = gmBB0MS + aMsmI a = hyperfine coupling constant mI = nuclear spin quantum number Measured as the distance between the centers of two signals In addition to the applied magnetic field, unpaired electrons are also sensitive to their local environments. Frequently the nuclei of the atoms in a molecule or complex have a magnetic moment, which produces a local magnetic field at the electron. The resulting interaction between the electron and the nuclei is called the hyperfine interaction. Hyperfine interactions can be used to provide a great deal of information about the sample including providing information about the number and identity of nuclei in a complex as well as their distance from the unpaired electron. This interaction expands the previous equation to: E = gmBBoMS + aMSmI where a is the hyperfine coupling constant and mI is the nuclear spin quantum number for the neighboring nucleus. It is important to note that if a signal is split due to hyperfine interactions, the center of the signal (which is used to determine the proportionality factor) is the center of the splitting pattern. So for a doublet, the center would be half way between the two signals and for a triplet, the center would be the center of the middle line.

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**Which nuclei will interact?**

Selection rules same as for NMR Every isotope of every element has a ground state nuclear spin quantum number, I has value of n/2, n is an integer Isotopes with even atomic number and even mass number have I = 0, and have no EPR spectra 12C, 28Si, 56Fe, … Isotopes with odd atomic number and even mass number have n even 2H, 10B, 14N, … Isotopes with odd mass number have n odd 1H, 13C, 19F, 55Mn, … The rules for determining which nuclei will interact are the same as for NMR. For every isotope of every element, there is a ground state nuclear spin quantum number, I, which has a value of n/2, where n is an integer. For isotopes which the atomic and mass numbers are both even, I=0, and these isotopes have no EPR (or NMR) spectra. For isotopes with odd atomic numbers but even mass numbers, the value of n is even leading to values of I which are integers, for example the spin of 14N is 1. Finally for isotopes with odd mass numbers, n is odd, leading to fractional values of I, for example the spin of 1H is ½ and the spin of 51V is 7/2.

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**Hyperfine Interactions**

So a single nucleus with a spin ½ will split each energy level into two, as shown above, and then two transitions (or absorptions) can be observed. The energy difference between the two absorptions is equal to the hyperfine coupling constant. Interaction with a single nucleus of spin ½ Ebsworth, E. A. V.; Rankin, David W. H.; Cradock, Stephen Structural Methods in Inorganic Chemistry; CRC Press: Boca Raton, 1987.

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**Hyperfine Interactions**

Coupling patterns same as in NMR More common to see coupling to nuclei with spins greater than ½ The number of lines: 2NI + 1 N = number of equivalent nuclei I = spin Only determines the number of lines--not the intensities The coupling patterns that are observed in EPR spectra are determined by the same rules that apply to NMR spectra. However, in EPR spectra it is more common to see coupling to nuclei with spins greater than ½. The number of lines which result from the coupling can be determined by the formula: 2NI + 1 where N is the number of equivalent nuclei and I is the spin. It is important to note that this formula only determines the number of lines in the spectrum, not their relative intensities.

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**Hyperfine Interactions**

Relative intensities determined by the number of interacting nuclei If only one nucleus interacting All lines have equal intensity If multiple nuclei interacting Distributions derived based upon spin For spin ½ (most common), intensities follow binomial distribution The relative intensities of the lines is determined by the number of interacting nuclei. Coupling to a single nucleus gives lines each of equal intensity.

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**Relative Intensities for I = ½**

1 1 : 1 2 1 : 2 : 1 3 1 : 3 : 3 : 1 4 1 : 4 : 6 : 4 : 1 5 1 : 5 : 10 : 10 : 5 : 1 6 1 : 6 : 15 : 20 : 15 : 6 : 1 Relative intensities of splitting patterns observed due to hyperfine coupling with a nucleus with I = ½. The splitting patterns are named similar to those in NMR: 2 lines = doublet 3 lines = triplet 4 lines = quartet 5 lines = quintet 6 lines = sextet 7 lines = septet

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**Relative Intensities for I = ½**

Computer simulations of EPR spectra for interactions with N equivalent nuclei of spin 1/2.

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**Relative Intensities for I = 1**

1 1 : 1 : 1 2 1 : 2 : 3 : 2 : 1 3 1 : 3 : 6 : 7 : 6 : 3 : 1 4 1 : 4 : 10 : 16 : 19 : 16 : 10 : 4 : 1 5 1 : 5 : 15 : 20 : 45 : 51 : 45 : 20 : 15 : 5 : 1 6 1 : 6 : 21 : 40 : 80 : 116 : 141 : 116 : 80 : 40 : 21 : 6 : 1 Relative intensities of splitting patterns observed due to hyperfine coupling with a nucleus with I = 1.

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**Relative Intensities for I = 1**

Computer simulations of EPR spectra for interactions with N equivalent nuclei of spin 1.

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**Hyperfine Interactions**

Example: VO(acac)2 Interaction with vanadium nucleus For vanadium, I = 7/2 So, 2NI + 1 = 2(1)(7/2) + 1 = 8 You would expect to see 8 lines of equal intensity

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**Hyperfine Interactions**

EPR spectrum of vanadyl acetylacetonate

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**Hyperfine Interactions**

Example: Radical anion of benzene [C6H6]- Electron is delocalized over all six carbon atoms Exhibits coupling to six equivalent hydrogen atoms So, 2NI + 1 = 2(6)(1/2) + 1 = 7 So spectrum should be seven lines with relative intensities 1:6:15:20:15:6:1 An example is shown by the EPR spectrum of the radical anion of benzene, [C6H6•]-, in which the electron is delocalized over all six carbon atoms and therefore exhibits coupling to six equivalent hydrogen atoms. As a result, the EPR spectrum shows seven lines with relative intensities of 1:6:15:20:15:6:1.

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**Hyperfine Interactions**

EPR spectrum of benzene radical anion

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**Hyperfine Interactions**

Coupling to several sets of nuclei First couple to the nearest set of nuclei Largest a value Split each of those lines by the coupling to the next closest nuclei Next largest a value Continue 2-3 bonds away from location of unpaired electron If an electron couples to several sets of nuclei, then the overall pattern is determined by first applying the coupling to the nearest nuclei, then splitting each of those lines by the coupling to the next nearest nuclei, and so on.

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**Hyperfine Interactions**

Example: Pyrazine anion Electron delocalized over ring Exhibits coupling to two equivalent N (I = 1) 2NI + 1 = 2(2)(1) + 1 = 5 Then couples to four equivalent H (I = ½) 2NI + 1 = 2(4)(1/2) + 1 = 5 So spectrum should be a quintet with intensities 1:2:3:2:1 and each of those lines should be split into quintets with intensities 1:4:6:4:1 An example of this can be seen in the radical anion of pyrazine. Where coupling to two equivalent 14N (I = 1) nuclei gives a quintet with the relative intensities of 1:2:3:2:1 which are further split into quintets with relative intensities of 1:4:6:4:1 by coupling to four equivalent hydrogens.

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**Hyperfine Interactions**

EPR spectrum of pyrazine radical anion

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**Conclusions Analysis of paramagnetic compounds Compliment to NMR**

Examination of proportionality factors Indicate location of unpaired electron On transition metal or adjacent ligand Examination of hyperfine interactions Provides information on number and type of nuclei coupled to the electrons Indicates the extent to which the unpaired electrons are delocalized As NMR spectroscopy does not usually provide useful spectra for paramagnetic compounds, analysis of their EPR spectra can provide additional insight. Analysis of the coupling patterns can provide information about the number and type of nuclei coupled to the electrons. The magnitude of a can indicate the extent to which the unpaired electrons are delocalized and g values can show whether unpaired electrons are based on transition metal atoms or on the adjacent ligands.

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