Overview of Multi-Frequency EPR

Most EPR (Electron Paramagnetic Resonance) experiments are performed at X-band (9-10 GHz). Many factors contribute to the choice of this frequency. One factor is the availability of components: with the development of RADAR and the end of World War II, there was a glut of surplus X-band mil- itary microwave equipment available to the early EPR pioneers. In addition to historic factors, convenience plays an important role. The mag- netic field requirements for X-band are usually satisfied easily by electro- magnets. The 3 cm wavelength ensures convenient sample sizes and sample handling. A third consideration is sensitivity. As the Boltzmann factor and sample size increase, they increase the spectrometer’s sensitivity. Alas, the two factors are not independent. The Boltzmann factor increases with increasing frequency, but the improvement in sensitivity is tempered by the decrease in sample size with increasing frequency. If you have sufficient sample, albeit at a low con- centration, X-band often offers the best sensitivity. These factors lead to the almost universal acceptance that EPR is performed at X-band. Given all the advantages of X-band EPR, why would researchers wish to perform experiments at lower or higher frequencies? Performing EPR spectroscopy at multiple frequencies sheds additional light on the properties of the sample. If we were to see everything only in black and white, we would miss all the extra information that color vision affords us. In an analogous fashion, if we were to measure our samples at X-band only (black and white), we would miss the complete picture that other microwave frequencies (color vision) could offer us. The appearance of EPR spectra depends strongly on the interplay of magnetic field dependent and magnetic field independent interactions. By operating at several frequencies, we are able to resolve the contributions from the two types of interactions and thereby obtain unambiguous answers to the ques- tions posed by our sample. In this overview we shall consider the advantages of going higher or lower in frequencies compared to X-band. We shall explore the benefits from the com- plementary information offered by high and low frequencies. Finally, the methodology and technical aspects of multi-frequency EPR spectroscopy will be introduced.

Overview of Multi-Frequency EPR Some Preliminary Definitions

Some Preliminary Definitions 1

This overview will make use of certain terms that may not be common knowledge for many people using EPR spectroscopy. Here we shall define some of those terms. Multi-frequency EPR embodies the use of high and low microwave frequen- cies in studying paramagnetic samples. High frequency is defined as micro- wave frequencies above X-band (~10 GHz). Low frequency is defined as microwave frequencies below X-band. Frequencies are often identified by the waveguide size known as frequency bands. Table 1 lists the most commonly used bands. In EPR, the definitions sometimes differ from the electrical engi- neering definitions. Column 3 shows the frequencies used by Bruker Biospin Corporation for some of the frequency bands.

Common Microwave Frequency Microwave Frequency for EPR Band Frequencies (GHz) (GHz)

L 1-2 ~1 S 2-4 ~4 C 4-8 X 8.2-12.4 9.2-9.9

Ku 12.4-18 K 18-26.5 ~24 Q 26.5-40 ~34 V 40-75 W 75-110 ~94 D 110-170 Table 1 Frequencies for commonly used microwave bands.

Frequencies lower than 1 GHz are often designated as VHF (the seemingly incongruous term Very High Frequency). Frequencies above 18 GHz are often labeled as millimeter waves because the wavelength is approaching 1 cm or less. The microwave frequencies commonly used in EPR were not chosen arbi- trarily. With the exception of K-band, the common EPR frequencies corre- spond to minima in the atmospheric absorption of microwaves. (See Figure 1.) This has the advantage that systems do not have to be purged to displace oxygen or water vapor in the waveguide and resonator. In addition, there are more components available at these frequencies because these are the frequencies that would be used for RADAR and communications pur- poses.

2 Why Use Multiple Frequencies?

Average Atmospheric Absorption of Millimeter Waves 100

40 20

10 D-band HO HO 2 ) 2

m 4

K O / 2

B 2 d W-band

(

n 1

o

i

t

a Q-Band u O

n 0.4 2

e

t

t

A 0.2

0.1 X-Band

0.04 HO2 0.02

10 15 20 25 30 40 50 60 70 80 90100 150 200 250 300 400 Frequency (Ghz)

Figure 1 Atmospheric absorption of microwaves at different frequen- cies.

Why Use Multiple Frequencies? 2

In the introduction, the importance of magnetic field dependent and magnetic field independent interactions was briefly mentioned. Here, we shall expand on this idea. Often, a spin-hamiltonian of the form:

      H = eS g B0 + S D S + S A I [1] } } magnetic magnetic field field dependent independent

describes the EPR spectrum well. The symbols have the following meanings:
• e = Bohr magneton • S and I = electronic and nuclear spin operators • g = electronic g matrix

• B0 = the externally applied magnetic field • D = the ZFS (Zero Field Splitting) matrix • A = the nuclear hyperfine matrix Because they are often weaker than electronic Zeeman and hyperfine interac- tions, we shall not consider the nuclear Zeeman and quadrupolar interactions. The first term in the spin-hamiltonian is the electronic Zeeman interaction and owing to the B0 variable, this is the magnetic field dependent term of the expression. The second two terms, the ZFS and nuclear hyperfine interac- tions, are the magnetic field independent terms. The ZFS term only contrib- utes for spin systems where S>1/2.

Overview of Multi-Frequency EPR 3 The Effects of g-Values

Each of the spin-hamiltonian parameters offers us specific information about our sample. The g-value can help identify a paramagnetic species as well as tell us about the electronic state and symmetry of the paramagnetic site. The ZFS terms inform us about the spin and valence state as well as symmetry of paramagnetic centers. The nuclear hyperfine interactions supply us with iden- tity, number, and distances of surrounding nuclei. Therefore, each of the spin-hamiltonian parameters gives important and different information. Ideally, we would like to obtain an EPR spectrum in which the spin-hamilto- nian parameters are evident from visual inspection of the spectrum’s features. Alas, several factors such as linewidths and anisotropy may mask the features we wish to interpret. In addition, second-order* effects can make interpreta- tion difficult. Higher magnetic fields make the electronic Zeeman term more dominant, thereby suppressing second-order effects and making the spectra more first-order. Simulations with least-squares analysis may yield the desired spin-hamiltonian parameters in such cases, however, the parameters obtained may not be unique values or an unambiguous interpretation of the spectrum. One solution to this problem is to perform EPR experiments at different fre- quencies. By using different frequencies, we establish different magnetic fields for resonance from our sample and thereby we emphasize or accentuate the effects of the magnetic field dependent or independent terms of our spin- hamiltonian on our EPR spectrum. By going to very low and very high fre- quencies, we can achieve limiting cases where magnetic field independent or dependent effects dominate, offering us the opportunity to unambiguously measure the parameters we need. Even if we cannot measure our sample in these limiting conditions, having data at several frequencies often supplies the needed constraints to successfully and unambiguously obtain the spin-hamiltonian parameters from simulation and simultaneous least-squares minimization of the multi-frequency EPR data.

The Effects of g-Values 3

Our NMR colleagues have been exploiting increasingly higher fields and fre- quencies in order to attain increasingly better resolution. The higher frequen- cies accentuates the chemical shift to the point where the shift is greater than the linewidth. The corresponding spin-hamiltonian parameter for EPR is the isotropic g-value. In the absence of other interactions, the field for resonance is given by:

h B = ------[2] 0  g e

* First order means that the electronic Zeeman interaction is much greater than the other interactions and they contribute simple corrections to the energy levels. Second order means that the electronic Zeeman interaction is only slightly greater than the other interactions and they contribute large and more complicated corrections to the energy levels.

4 The Effects of g-Values

where h is Planck’s constant, is the microwave frequency, g is the isotropic
g-value, and e is the Bohr magneton. If we were to have two paramagnetic species in our sample with a small g-value difference of g, the difference in fields for resonance, B, is approximately proportional to the microwave fre- quency:

h g B = ------. [3]   egg+ g

If B can be made greater than the linewidth by increasing the microwave frequency, we can unambiguously identify the two species in our sample. Figure 2 shows such an example. The sample consists of a mixture of two nitroxides (proxyl and TEMPOL) with slightly different g-values. At X-band, the broad small shoulder on the low field line hints that there may be two spe- cies. By repeating the experiment at higher frequency (W-band), the signals from the two species are sufficiently split that we can unambiguously say there are two species. In addition, the resolution is sufficient that we can even measure the relative concentrations of the two species.

X-Band

W-Band

Figure 2 Using a higher microwave frequency to resolve nitroxides (proxyl and TEMPOL) with slightly different g-values.

Because the field difference, B, increase with microwave frequency, the g-anisotropy (g-values varying with the orientation of B0 at the paramagnetic site) and g-strain (a distribution of g-values arising from variations among the paramagnetic sites) in a solid sample may lead to a broadening or spreading out of the EPR spectrum with increasing frequency. At first thought, this broadening may seem counterproductive because we are losing resolution. Whereas the g-strain broadening masks spectral features, the g-anisotropy offers us the opportunity to measure the principal values of the g matrix. Inhomogeneous broadening can often mask the turning points for the g matrix. One option is to prepare a single crystal sample and perform rota- tional studies to extract information regarding the electron Zeeman interac- tion. This option is often not possible or easy from a sample preparation or

Overview of Multi-Frequency EPR 5 The Effects of g-Values

measurement time standpoint. By performing experiments at higher frequen- cies, we can emphasize and accentuate the field dependent term, the electron Zeeman term, so that it dominates over the inhomogeneous linewidth. An example of how this effect is exploited is shown in Figure 3. PSAO (Pea Seedling Amine Oxidase) has a rhombic symmetry Cu+2 active site. It was conjectured that upon binding of the inhibitor PHZ (Phenylhydrazine), the active site becomes more symmetric. X-band echo-detected spectra show only slight differences in the native and inhibited forms. W-band spectra show a very different picture. The native form is plainly rhombic; the inhib- ited form is more symmetric and approaches axial symmetry.

X-Band W-Band

PSAO

PSAO + PHZ

100 mT 800 mT

Figure 3 W-band emphasizes the g-anisotropy effects sufficiently that even without quantitative g-values, one can immediately see the change in symmetry upon binding the inhibitor phenylhydrazine to pea seedling amine oxidase. Sample courtesy of Prof. J. L. McCracken. Note: the sharp high field lines are due to Mn+2 in the buffer.

6 The Effects of Nuclear Hyperfine Couplings

The Effects of Nuclear Hyperfine Couplings 4

Sometimes we may be interested in the nuclear hyperfine couplings. For example, we may be interested in the number and identity of the nuclei in a radical or metal site. Unfortunately, the g-anisotropy or g-strain can mask the splittings that would give us this information. In order to minimize this effect and enhance the effect of the nuclear hyperfine coupling, we need to perform the experiments at frequencies lower than X-band. A nice example where a lower microwave frequency can yield more informa- tion than X-band is shown in Figure 4. In the X-band spectrum, the nitrogen hyperfine splittings are masked by the g-anisotropy. At S-band, the effects are decreased and a 1:4:6:4:1 triplet is resolved indicating four coordinating nitrogens.

X-Band S-Band

Figure 4 Type 2 Cu+2 in pMMO (particulate Methane MonoOxygenase) from Methylomicro- bium album BG8 grown with 15N and 63Cu+2 at 77 K. Spectra courtesy of Professor W. E. Antholine.

Overview of Multi-Frequency EPR 7 The Effects of Nuclear Hyperfine Couplings

Sometimes, very unusual features can be observed in low frequency spectra. If the hyperfine interactions approach the size of the Zeeman interaction, higher order shifts are visible if there are multiple equivalent nuclei and the linewidths are narrow. Below is the spectrum of PNT (perinaphthenyl) at both X and L-band. The lines are split at L-band due to the large hyperfine cou- pling constant of the six equivalent nuclei.

L-band

X-band

L-band

X-band

Figure 5 Higher order splittings in the L-band EPR spectrum of a liq- uid solution of PNT in oil. Spectra were acquired at room temperature.

8 The Effects of Zero Field Splittings

The Effects of Zero Field Splittings 5

Large ZFS (Zero Field Splittings) that are greater than h may make observa- tion of EPR impossible sometimes. The magnetic field to bring the sample into resonance may be prohibitively high for microwave frequencies less than the ZFS. Microwave frequencies higher than the ZFS can bring the field for resonance down to achievable values.

E High Frequency Low Frequency

High Frequency

B0

Figure 6 Fields for resonance: h > ZFS or h < ZFS.

If spectra are observed, for samples with h < ZFS, the spectra can be diffi- cult to interpret because of second order splittings. Performing experiments at higher frequency often results in simplified spectra. The relative values of the ZFS and hyperfine interactions exert a strong influence on the spectral shape.

W-band X-band

4D

+2 Figure 7 Simplification of the spectrum of Mn in NH4Cl by going to higher frequencies.

Overview of Multi-Frequency EPR 9 The Effects of Zero Field Splittings

So far, we have seen that higher frequencies usually lead to broader lines owing to g-anisotropy and g-strain. One case where lines become narrower with increasing frequency is a high spin system with no g-anisotropy. Zero field splittings can often lead to very broad lines at low frequency owing to anisotropy. Second order perturbation theory treatment of the spin hamilto- nian predicts the anisotropy of the EPR spectrum decreases with increasing frequency. Performing experiments at higher frequencies can yield substan- tial resolution enhancement for high spin systems.

X-Band

W-Band

Figure 8 An example of resolution enhancement of spectra for high spin systems at higher fre- quencies owing to suppression of second-order effects. The sample is Mn+2 EDTA in H2O at room temperature.

10 Relaxation Times

Relaxation Times 6

Many mechanisms can contribute to relaxation times. Commonly, tempera- ture studies of relaxation rates are performed to distinguish between different mechanisms, but such studies do not always yield an unambiguous answer. Some mechanisms for T1 (spin lattice relaxation) are frequency independent such as the Raman or local-mode process and some are frequency dependent such as the direct or thermally activated process. By studying both the fre- quency and temperature dependence, sufficient constraints are placed on the results to identify dominant relaxation mechanisms. For example, T1 for TEMPOL in 4-OH-2,2,6,6 tetramethyl-piperidinol at temperatures higher than 160 K exhibits contributions from a Raman process and either local mode or thermally activated process. Because T1 is frequency dependent, we can conclude that a thermally activated process is contributing to T1. If the paramagnetic species is rapidly tumbling, anisotropies can be averaged out, resulting in narrow lines and consequently long T2. As the anisotropy increases, the anisotropies are not completely averaged out, resulting in broader lines and consequently shorter T2. This effect is the familiar mI line- width dependence. Dramatic changes in linewidths can appear at higher microwave frequencies because the high magnetic fields accentuates the effects of the g-anisotropy. Higher frequency spectra are often more sensitive to fast molecular motions than lower frequency spectra.

x8 W-band

X-band

Figure 9 Microwave frequency effects on linewidths of VO(acac)2 in toluene at room temperature.

Overview of Multi-Frequency EPR 11 The Role of Sample Properties & Sensitivity

The Role of Sample Properties & Sensitivity 7

Quite often, we do not have a choice about the size, concentration, or dielec- tric properties of our samples. These properties play an important role in the choice of microwave frequency. If we have a large sample, we need a large resonator. As the microwave fre- quency increases, the size of the resonator usually decreases. In order for the sample to fit inside the resonator, we need to use lower frequencies. Applica- tions where you may encounter large samples would be in-vivo spectroscopy and imaging. Samples exhibiting high dielectric losses such as aqueous sam- ples can be difficult to measure at higher frequencies because of absorption and penetration problems. These type of samples also benefit from lower microwave frequencies.

Figure 10 Large samples, in-vivo spectroscopy, and imaging are best performed at low microwave frequencies. The images of an infected sycamore sapling were acquired at L-band. The mouse is in a Bruker ER 6502 resonator.

Sometimes we can only obtain a very small sample, such as samples that are difficult to isolate, synthesize, or crystallize. Even worse, the samples can be small by nature such as a single cell. In these cases, high frequencies can yield superior sensitivity.

Figure 11 W-band EPR spectrum of a 3 mm long single human hair.

12 Technology and Methodology

Technology and Methodology 8

Each of the different microwave frequency bands requires different technol- ogy and techniques in order to successfully perform EPR experiments. The microwave frequency greatly effects the choice of resonator, transmission line, sample tube, and magnet.

Magnets 8.1 The magnetic field required to bring a g=2, S=1/2 sample into resonance rises linearly with the microwave frequency at a rate of approximately 28 MHz/mT. Figure 12 displays this behavior graphically.

4

1

)

T

(

d

l

e

i F 0.1

0.01 1 10 100 Frequency (GHz)

Figure 12 The microwave spectrum and field values for g=2.

Table 2 shows the field values for the frequency bands offered by Bruker Bio- spin Corp. with the magnetic field values for a g = 2 sample.

Frequency Microwave Frequency Magnetic Field for Band (GHz) g=2 (mT)

L 1 35.68248 S 4 142.72993 X 9.8 349.68834 K 24 856.3796 Q 34 1213.20443 W 94 3354.15343 Table 2 Field for resonance for commonly used microwave frequency bands.

Overview of Multi-Frequency EPR 13 Technology and Methodology

Given enough electricity, cooling water, and floor strength, an iron electro- magnet can supply magnetic fields up to 2T.

Figure 13 An iron electromagnet.

For fields higher than 2 T, a superconducting magnet is required. Their high inductance make them difficult to sweep quickly. Therefore, these magnets are often fitted with some room temperature resistive coils as well, so that one can quickly and conveniently sweep the magnet about its persistent field.

Figure 14 A Bruker Hybrid3 superconducting magnet fitted with room temperature resistive sweep coils.

14 Technology and Methodology

Wavelength & Sample Size 8.2 The wavelength decreases with increasing frequency in the following man- ner:

c  = --- [4]

where  is the wavelength in mm, is the microwave frequency in Hz, and c is the speed of light, 2.998x1011 mm/s. Table 3 shows the wavelengths for the frequency bands offered by Bruker Biospin Corp.

Frequency Microwave Frequency Wavelength (mm) Band (GHz)

L 1 300 S 475 X 9.8 30 K 24 12.5 Q 34 10 W 94 3 Table 3 Wavelengths for commonly used microwave frequency bands.

Because the size of the resonator is influenced by the wavelength (See Section 7.), longer wavelengths allow you to use larger samples.

Frequency Microwave Frequency Sample Tube O.D. Band (GHz) (mm)

L 130 X 9.8 4 Q 34 2 W 94 0.9 Table 4 Sample tube sizes for commonly used microwave frequency bands.

Overview of Multi-Frequency EPR 15 Technology and Methodology

W-band Q-band

X-band

L-band

Figure 15 Sample tubes for some commonly used microwave fre- quency bands.

Wavelength & Transmission Lines 8.3 Microwave energy is transmitted or transported in the bridge and between the bridge and resonator via transmission lines. The microwave frequency influ- ences the choice of transmission line. As can be seen in Table 5, the size of waveguide increases with wavelength. At low frequency, the waveguides become prohibitively large: an L-band bridge constructed of waveguide would be almost the size of a room.

Frequency Microwave Frequency Waveguide Band (GHz) Dimensions (Inches)

L 1 6.50 x 3.25 S 4 3.40 x 1.70 X 9.8 0.900 x 0.400 K 24 0.420 x 0.170 Q 34 0.280 x 0.140 (actually Ka) W 94 0.100 x 0.050 Table 5 Waveguide dimensions for commonly used microwave frequency bands.

There are other technologies available such as semi-rigid coaxial cable that work well up to X-band. Above X-band, the propagation losses become too high. The big advantage of semi-rigid coax is its compact size and conve- nience. It is extensively used from L to X-band. For W-band and higher frequencies, fundamental mode waveguides start to become prohibitively lossy to transmit microwaves over long distances. One solution is to used over-sized (over-moded) waveguide. At even higher fre-

16 Technology and Methodology

quencies (> 140 GHz) quasi-optical techniques such as corrugated guides, mirrors, and lenses offer low-loss microwave propagation.

Q-Band

X-Band

Semi-rigid

Figure 16 Different transmission lines.

Wavelength & Resonators 8.4 Resonators are used to enhance the sensitivity of the spectrometer. A resona- tor helps increase sensitivity by “focusing” or “concentrating” the microwave power at the sample and storing the microwave energy. Cavities are the most common type of resonator. They consist of a short sec- tion (an integral number of half wavelengths) of rectangular or circular waveguide in which a standing wave is produced. As with waveguides, cavi- ties get progressively larger as the frequency decreases. At X-band and higher frequencies, the cavities are conveniently sized. At lower frequencies, they become prohibitively large.

Figure 17 A Bruker ER 4119HS cavity resonator (left) and a Bruker TeraFlex W-band cavity (right).

Overview of Multi-Frequency EPR 17 Technology and Methodology

In order to reduce the size of the resonator, different structures and approaches are necessary. Size reduction is not only important at low fre- quencies, but is also necessary for X-band pulse spectroscopy, in which small resonators efficiently convert microwave power to the large required B1 (microwave magnetic field) at the sample. One approach is to use a dielectric resonator in which the wavelength is considerably shorter than the free space wavelength, thus shrinking the size of the resonator. Another approach is to use a different type of structure such as a split-ring or loop-gap resonator.

Q = 100 - 5000 Q = 100 - 1000

B1 B1

Dielectric Resonator Split Ring Resonator

Figure 18 The Bruker ER 4118 FlexLine series. Dielectric and split ring resonators.

Sometimes, a homogeneous B1 is required over a large volume, such as in imaging experiments. To accomplish this homogeneity requires borrowing some technology from our NMR colleagues. Bird cage resonators can be built even at 1GHz.

Figure 19 A Bruker E540 GCR L-band birdcage resonator.

18