Vij D.R. Handbook of Applied Solid State Spectroscopy

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values (1.79, 1.89, 2.024) reported for bovine cyt bc

with stigmatellin in

solution. Those yielded the cosine directions, which define the orientation of

the principal axes relative to the crystal axes and made it possible to establish

the orientation of the g-tensor axes relative to the molecular axes of the

cluster. The g-tensor axes have slightly different orientations relative to the

iron-sulfur cluster in the two halves of the dimer. The g-tensor principal axes

are skewed with respect to the Fe-Fe and S-S atom direction in the [2Fe-2S]

cluster. The g ~ 1.79 axes makes an average angle of 30

with respect to the

Fe-Fe direction and the g ~ 2.024 axis an average angle of 26

with respect to

the S-S direction.

Figure 3.11 Top—The g-factor of the Rieske ISP as a function of rotation about the crystal c-

axis. The solid lines are the fits to the individual monomers in the asymmetric unit.

Experimental data points monomer A (x) and two distinct sets ( and d) of symmetry-related

sites in monomer B. The directions corresponding to the a- and b-axes are indicated below the

rotation angles. Bottom —The structure of the [2Fe-2S] cluster shows the orientation of the g-

tensor axes of monomer B in chain R and monomer A in chain E relative to the molecular axes

of the cluster. The two histidine ligands to the cluster are shown to provide its orientation but

the two cysteine ligands on the other Fe are not. The figure has been redrawn for “crossed-eye”

stereoviewing. (From M.K. Bowman, E.A. Berry, A.G. Roberts, and D.M. Kramer, 2004

Biochemistry 43 430–6, with permission)

125

3.4 Applications of EPR Spectroscopy

3. Electron Paramagnetic Resonance Spectroscopy

These data were used to test a theoretical model of the g-tensor in the iron-

sulfur cluster. In addition, knowledge of the g-tensor orientation relative to the

molecular axes is important for interpretation of

magnetic resonance data in

the context of the crystal structure, because hyperfine and quadrupole

couplings with ligand nuclei are referred to the coordinate system of the g-

tensor.

The determination and analysis of the g-tensors of the transition metal ions

and inorganic radicals in single crystals is a significant part of EPR

spectroscopy, more fully expounded in several classical monographs and

textbooks [3, 4, 11, 12].

3.4.1.2 Analysis of Hyperfine Couplings

Hyperfine couplings of the central metal nuclei in transition metal complexes,

and of D, E atoms in radicals, have often been measured in single crystals.

From measurement of the orientation-dependence of hyperfine couplings

from the splittings of spectral components, the principal values of the

hyperfine tensors and their orientation relative to the crystal axes could be

found. The design of the experiment and the analysis of the data are similar to

those for the g-tensor given in previous section. Particular examples

describing the experimental determination of hyperfine tensors (and nuclear

quadrupole tensors for nuclei with I t 1), and their subsequent analysis in

characterization of the electronic structure, are described in detail elsewhere

[2–12].

3.4.1.3 Electron Spin-Echo Envelope Modulation (ESEEM)

Since the ESEEM frequencies come from nuclear transitions and depend on

the hyperfine and quadrupole interactions the study of the angular dependence

of the ESEEM frequencies yields the same information as that obtained from

analysis of the angular dependence of the splittings between the components

in the EPR spectra. These are the principal values of the hyperfine and nuclear

quadrupole tensors, and the orientation of their principal values. The

difference between the pulsed and CW approaches is in the values of the

interaction energies. In CW-EPR, the only couplings that can be studied are

those that exceed the linewidth, which in single-crystal studies have a value of

the order of several 0.1 mT. In contrast, ESEEM resolves the couplings that

are masked by EPR broadening in the CW experiment. The lower boundary of

the nuclear frequencies for measurement in ESEEM spectroscopy is limited

by the time of the relaxation decay, or the acquisition time of the echo

envelope, since the period of oscillation cannot exceed these times. This

boundary can be estimated with an accuracy of several tenths of a MHz. The

upper boundary of the measured ESEEM frequencies is limited by the

126

possibility of simultaneous excitation of the allowed and forbidden transi-

tions, separated by the splitting described by equations (3.30) (Figure 3.4). Its

value reaches ~ 30-50 MHz in modern pulsed EPR spectrometers.

ESEEM spectroscopy has been used for investigation of radiation-induced

organic free radicals in single crystals of organic acids, and in ions of transi-

tion metals, introduced as paramagnetic impurities into single crystals of

inorganic compounds [25, 32, 33].

3.4.2 Orientation-Disordered Samples

3.4.2.1 CW-EPR Lineshape

In orientationally disordered solids, powders, glasses, or polymers, the

paramagnetic species are randomly oriented with respect to magnetic field.

The EPR spectrum of such samples is a superposition of the resonances from

isotropically distributed molecular orientations with corresponding statistical

weight. The formation of the powder EPR-lineshape can be easily

demonstrated in the case of the axial g-tensor anisotropy.

For the spin Hamiltonian written in the g-tensor principal axes system the

resonance g-factor is equal to

1/2 1/2

22 2 2 2 2 2 2

sin cos ( ) cosgg g g gg

AAA

ªºª º

TT T

¬¼¬ ¼



(3.41)

where T is an angle between the symmetry axis (along g

) and the magnetic

field direction. This expression leads to the conclusion that the resonance field

B in the spectrum varies with the angle T:



1/2

2222

cos

ggg

ªº

 T

¬¼



(3.42)

between the limiting values B

and B

defined as:

= g

(3.43)

with B = B

for T = 0 and B = B

for T = S/2.

Taking account of the fact that the fraction of the symmetry axes occurring

between angles T and T + dT, which is equal to

sin (cos )

ddTT T

, is pro-

portional to the probability P(B)dB of the resonance contribution between B

and B + dB, one finds that





1/2

22 22

()~ .PB g g



BB



(3.44)

This function has the limiting value when B = B

and becomes infinite at

B=B

, reflecting the contributions to the intensity of numerous orientations

from the plane normal to the symmetry axis at this field. Thus, this analysis

predicts the powder pattern for the axial g-tensor shown in Figure 3.12. In real

127

3.4 Applications of EPR Spectroscopy

3. Electron Paramagnetic Resonance Spectroscopy

samples P(B) needs to be convoluted with a suitable individual lineshape

function that smoothes the step-type resonance features at B

and B

Examples of real lineshape in first derivative modes are shown (see Figures

3.13 and 3.14).

Figure 3.12 Distribution of intensity in powder EPR spectra for axial (top) and orthorhombic

then the lineshape will have additional features resulting from the hyperfine

structure. For the coincident principal axes of the axial g-tensor and hyperfine

A tensor there are two types of features, corresponding to the parallel and

perpendicular orientations of magnetic field relative to the symmetry axis,

located at:

()







(3.45)

A schematic presentation of such a structure is shown in Figure 3.13. This

type of spectrum is typical for Cu(II) and VO(II) ions, where hyperfine

structure results from nuclei with the spin I = 3/2 and 7/2, respectively.

In the case of an orthorhombic g-tensor, with principal values g

> g

the powder EPR pattern is located between the fields B

and B

and it has a

maximum at the field B

(Figure 3.12) where again

= g

. (3.46)

(bottom) systems.

128

If an electron spin with an axial g-tensor interacts with the nuclear spin I,

Figure 3.13 EPR spectrum (a) of [VO(H

]

; trace (b) is the matrix diagonalization

simulation. The additional traces show the eight individual M

= –7/2,..., +7/2 powder patterns.

These traces are shown in absorption mode rather than as a derivative as in the CW-EPR

spectrum for simplicity. Experimental conditions are as follows: v

= 9.68 GHz; MW power =

~25 mW; modulation amplitude = 8.0 G; time constant = 20.48 ms; conversion time =

40.96 ms; temperature = 49 K. (Taken from C.V. Grant, W. Cope, J.A. Ball, G. Maresch,

B.J. Gaffney, W. Fink, R.D. Britt, 1999 J. Phys. Chem. B 103: 10627–31, with permission)

In conclusion, the powder EPR spectra of paramagnetic species with

anisotropic g-tensor is particularly useful for determination of the principal

values of the g-tensor, although, in contrast to the single crystal, they cannot

provide direct information about the orientation of the g-tensor principal axes

in the molecular coordinate system. The features corresponding to the g-

tensor components are easily recognizable in first-derivative spectra, where

they approximate in shape to the derivative of individual components of the

absorption line of the composite powder pattern (Figure 3.14).

129

3.4 Applications of EPR Spectroscopy

3. Electron Paramagnetic Resonance Spectroscopy

Figure 3.14 First derivative EPR spectrum of the cyt bc

complex showing the [2Fe-2S] cluster

3.4.2.2 Structural Applications of the CW-EPR in Solid State: High-field EPR

EPR spectroscopy attracts the attention of researchers because it is a direct

and sensitive technique for the detection and the characterization of the

paramagnetic species. Usually, it requires only a small volume of material,

with a concentration of the paramagnetic species from the micro- to

millimolar range, depending on the width of the EPR spectrum. In any type of

EPR experiment, information about the electronic and spatial structure of the

paramagnetic species follows directly from the interactions of the electron

magnetic moment with the applied magnetic field, and with the magnetic

moments of surrounding nuclei, i.e., from the g-tensor and hyperfine tensors.

The principal values of the g-tensor of a particular species vary within a

narrow interval, and can be used for identification of that species. As an

example, Table 3.3 shows principal values of the g-tensor for the iron-sulfur

clusters participating in the electron transport in many proteins. It is clear that

the difference in the principal values makes it possible to distinguish the type

of cluster and its electronic state.

Table 3.3 Principal values of the g-tensor for biological iron-sulfur clusters in proteins.

Cluster g

[2Fe-2S]

(SR)

1.87–1.88 1.95–1.96 2.04–2.05 1.96

[2Fe-2S](SR)

(His)

1.73–1.83 1.89–1.92 2.01–2.04 1.91

[3Fe-4S]

(SR)

~2.01 ~2.01

[4Fe-4S]

(SR)

1.87–1.88 1.92 2.06 1.93

[4Fe-4S]

(SR)

2.04 2.04 2.11–2.14 2.07

[Fe-O-Fe] 1.56–1.66 1.72–1.77 1.92–1.96

Data are taken from [34–36].

2.1 2.0 1.9 1.8 1.7

g factor

130

of the ISP, with an orthorhombic g-tensor.

Often, and this is especially true for radicals, the anisotropy of the g-tensor

is low, and the features corresponding to its principal values are not resolved

in X-band spectra. Their resolution can be achieved with an increase of the

microwave frequency (or field). This approach is illustrated in Figure 3.15,

which shows several CW-EPR spectra of the cation radical of canthaxantin on

a silica-alumina surface obtained at microwave frequencies between 95 and

670 GHz.

Figure 3.15 HF-EPR spectra of radical cation of the carotenoid canthaxanthin, adsorbed on

silica-alumina: solid lines, experimental spectra recorded at 5 K: dotted lines, simulated spectra

using g-tensor values g

= 2.0032 and g

= g

= 2.0023 and line width of 1.36 mT. (Structure

of canthaxanthin is shown on the right side above). (From T.A. Konovalova, J. Krzystek,

P.J. Bratt, J. van Tol, L.-C. Brunel, L.D. Kispert, 1999 J. Phys. Chem. B, 103: 5782–6, with

permission)

One can see that the spectrum of this radical is a single isotropic line even

at 95 GHz (W-band), which is ten times higher in frequency than traditional a

X-band. Anisotropic splitting in the spectrum was only apparent at

frequencies ~300 GHz. Complete separation of the g

and g

««

peaks was

achieved only at frequencies higher than ~ 600 GHz. This measurement has

provided the g-tensor for this radical with g

= 2.0023 and g

««

= 2.0032 [37].

Thus, in this system, the best way to determine the g-tensor was to make

measurements at a sufficiently high field for B

Another typical example is that of EPR of radicals in powders where the

spectrum is dominated by hyperfine structure. Application of the high-field

EPR provides new levels of information, allowing very precise conclusions

about electronic structure of the radical. One can illustrate this by experiments

with the stable tyrosyl radical (Y

122

) (Figure 3.16) in Escherichia coli

131

3.4 Applications of EPR Spectroscopy

3. Electron Paramagnetic Resonance Spectroscopy

ribonucleoside diphosphate reductase (RDRP) [38]. The X-band EPR

spectrum ( ~ 9 GHz) of shows the doublet splitting resulted from the proton

hyperfine interaction. In contrast the D-band spectrum (~139.5 GHz) clearly

resolves g-tensor anisotropy. The principal values of the g-tensor (2.00912,

2.00457, 2.00225) are readily obtained from the canonical features of the

rhombic powder pattern. In addition, a doublet structure is evident at each

canonical position from the E-methylene proton, with a large isotropic

interaction ( ~ 2 mT) and small hyperfine anisotropy described by the tensor

(2.07, 1.98, 1.88 mT). Some additional splittings are seen at the low- and

high-field edges of the spectrum, assigned to the 3,5-ring protons with the

couplings ~ 0.45–0.90 mT along different axes of the g-tensor.

Figure 3.16 EPR spectra of the tyrosyl radical (Y

122

) present in RDPR. (a) High frequency

(139.5 GHz) spectrum of 5 PL of a 200 PM solution of the B2 subunit. (b) Simulation. The

inset is a 9-GHz EPR spectrum of ~ 0.3 mL of the same sample. (From G.J. Gerfen,

Soc. 115: 6420–1, with permission)

Multifrequency EPR, i.e., experiments at different microwave frequencies, is

often employed to interpret and to perform a quantitative analysis of powder

spectra with complex lineshapes resulting from g-tensor anisotropy and

hyperfine structure. The analysis of such spectra is often not trivial because it

depends not only on the principal values of the tensors, but also on their

relative orientations.

Many paramagnetic metal ions have magnetic nuclei, which produce

additional hyperfine structure in the powder EPR spectra. Usually, splittings

between these lines are larger than 2–3 mT. The hyperfine structure depends

on nuclear spin, and has an easily recognizable typical lineform for many

ions. Figure 3.13 shows examples of EPR spectra with hyperfine structure for

VO(II). Table 3.4 shows general EPR characteristics for selected important

transition metals.

B.F. Bellew, S. Un, J.M. Bollinger Jr. J. Stubbe, R.G. Griffin, D.J. Singel, 1993 J. Am. Chem.

132

Table 3.4 CW-ESR characteristics for selected transition metals.

Mn(II S = 5/2, 6 line of hyperfine structure from

Mn (I = 5/2, natural

abundance 100%).

Cu(II)

S = 1/2, axial g-tensor, g

~ 2.2, g

~ 2.0,

hyperfine structure from two nuclear isotopes

Cu (I = 3/2)

and

Cu (I = 3/2) with natural abundance 69.2% and 30.8%,

respectively.

Fe(III) S = 5/2, large g-tensor, anisotropy, g ~ 2–9.

S = 1/2 (low spin state), rhombic g-tensor: 2.4, 2.2, 1.8,

stable nuclear magnetic isotope

Fe (I = 1/2, 2.3% ).

VO(II)

S = 1/2, axial g-tensor, g

~ 1.94, g

~ 1.98,

hyperfine structure from nuclear isotope

V (I = 7/2, 99.756%).

Ni(III) S = 1/2, axial or rhombic g-tensor, 2.02–2.30,

stable nuclear magnetic isotope

Ni (I = 3/2, 1.13%).

Co(III) S = 1/2, isotropic g ~ 2.0,

nuclear magnetic isotope

Co (I = 7/2, 100%).

Mo(V) S = 1/2, rhombic g-tensor, 1.99, 2.00, 2.09,

6 lines of hyperfine structure from

95,97

Mo (I = 5/2, 15.9% and

9.6%).

Summarizing this brief consideration of CW-EPR applications in powder

solids, one can conclude that this technique provides initial identification of

paramagnetic species based on the g-tensor anisotropy and possible hyperfine

structure. However, CW-EPR spectra usually do not give any indication about

the interaction with the magnetic nuclei in the ligands of the paramagnetic

species and more distant environment. Interactions of the electron spin with

these nuclei are weak (they produced splitting usually less than 0.3–0.5 mT or

10–15 MHz) and are not resolved in powder EPR spectra. Study of such

interactions requires application of other experimental approaches, in

particular pulsed EPR spectroscopy, based on observation of the electron spin

echoes.

3.4.2.3 Powder-ESEEM

The ESEEM experiments in solids can usually be divided into two different

cases, depending on the EPR lineshape. In one case, the EPR line has a width

comparable to the excitation width of the microwave pulses, which is usually

in the range < 1.0–1.5 mT. This case can be considered as a complete

excitation of the powder EPR spectrum because the ESEEM pattern obtained

contains contribution from all possible orientations of paramagnetic species

relative to the applied magnetic field. An important peculiarity of this case

arises from the fact that there is no externally defined molecular coordinate

133

3.4 Applications of EPR Spectroscopy

)

3. Electron Paramagnetic Resonance Spectroscopy

system, and analysis of the data is usually performed using the coordinate

system of hyperfine or quadrupole tensor principal directions. ESEEM

measurement on powder systems provides information about the principal

values of the tensors. However, they do not give any direct information about

the orientation of these tensors.

As shown in Section 3.2.7.5, the two pulse sequence is expected to

produce four ESEEM frequencies from an I = 1/2 nucleus. A powder

spectrum may have a completely different number of resolved features,

because nuclear frequencies have different dependences on the orientation of

magnetic field. The spectral form is determined by the relative values

of nuclear Zeeman frequency, the isotropic constant a, and the components of

anisotropic hyperfine tensor T.

The peculiarities of ESEEM in powder solids one can demonstrate in a

simple case—the interaction of an electron spin with a remote nucleus when

they are coupled via weak anisotropic coupling. This can be considered in the

approximation of point dipoles [23, 25]. In this case the hyperfine tensor is

purely anisotropic, with the diagonal components (–T, –T, and 2T), where

eeII

T

(3.47)

and r is the distance between electron and nucleus.

If T is the angle between the vectors of external magnetic field B

and

symmetry axis z of the axial tensor, then the terms A and B in the expression

(3.25) for the nuclear frequencies of I = 1/2 are

(3cos 1)

3sincos.

T

(3.48)

Assuming that A and B << Q

and considering small terms only in the first

order, one can rewrite the nuclear frequencies as:

() I

Q|Qr

(3.49)

and obtain the expression (3.35) for the two-pulse ESEEM in a form

( ) 1 1 cos2 cos2 cos 2 (2 ) cos2 ( )

22 2

ªº

§·

¨¸

«»

©¹

¬¼

W   SQW S  S QW S W

(3.50)

In a disordered sample, E(W) should be averaged over all orientations of the

magnetic field:

() ()sin

EEd

W W TT

(3.51)

After averaging, (3.50) becomes

( ) 1 2 4cos 2 ( ) cos2 (2 ) (2 )

EFF

ªº

W   SQW W SQW W

¬¼

(3.52)

where F(TW) is the normalized function decaying with the increase of TW.

134