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Simulation of EPR spectra and Bioinorganic applications of

multi-frequency EPR

Alejandro Solano-Peralta

[email protected]

Unidad de Servicios de Apoyo a la Investigación e Industria (USAII)Facultad de Química, UNAM,

LR

PE

Mathematical simulation of EPR spectra

System with S = 1/2

Simulating EPR spectra comprises a set of computational methods that allow the extraction of parameters of magnetic spin Hamiltonian from one or set of EPR spectra.

Various levels of spin physics theory and the proper use of least squares algorithms are used to adjust the theoretical spectra to those obtained experimentally.

Simulation of EPR spectrum


Why is it necessary to make calculations?

To complement, support and / or confirm an experiment

To calculate unmeasurable

To understand

To predict


IIQSJSSSDISaSBg

IQISJSSDSIASSgBH

21e

21eS

Spin Hamiltonian:

SgBH eZeeman

IASHHS

Electronic Zeeman :

Hyperfine coupling:

IQIHQ

Cuadrupolar Interaction :

21exanisSS SJSSDSHHH

Spin – spin Interaction :


Theoretical background

Relaxation time (linewidth)

2

22

1

3

2

1

1

2

2

22

2

0 0

Gs

pp

rGs

Lz

pp

r

Lz

r

B

;BB

expBF

B

;BB

BF

ddsin,,BBF,PN

BS

See; A. Lund & W. Liu, 2013



See; D. M. Murphy, 2009.



EPR spectra of single crystal vs powder or solution

EPR spectra of single crystal vs powder or solución

Figure 1.11 (a) Single crystal type (selected orientations of θ = 0 ° , 55 ° and 90 °) and (b) first derivative powder type EPR lineshapes for a randomly oriented S = 1/2, I = 1/2 spin system with uniaxialsymmetry. The angular dependence curve ( θ vs field) for mI = ± 1/2 is shown in (c).

D. M. Murphy 2009.


Alcohol Deshidrogenase (ADH) en maíz

A. S. P.

ADH + NO

300 350 400 450 500 550 600

0.0

0.5

1.0

1.5

2.0

0 1000 2000 3000 4000 5000 6000 7000

-2.0

-1.5

-1.0

-0.5

0.0

k2 = 3.35 X 10

-4 s

-1

k1 = 2.08 X 10

-4 s

-1

ln (A

OO - A

t)

Time (s)

Ab

sorb

an

ce

Wavelength (nm)

3100 3200 3300 3400 3500

Linewidth

x-direction = 30 G

y-direction = 7 G

z-direction = 25 G

Inte

nsity

[ ]

Field [G]

G

ONA

y = 25 MHz

ONA

x = 31 MHz

ONA

x = 60 MHz

ONA

x = 30 MHz

Simulated

FR + [2F-2S] + Fe(heme)-NO

gx = 2.0795

gy = 2.0090

gz = 1.9740

FR + [2Fe-2S]

+

Heme-Fe(II)-NO

N ON O(heme) FeII + (heme) FeII..

Cyt c4

E4= +210 mV

Cyt c1-3

E1 = -64 mV

E2 = -8 mV

E3 = +185 mV

N O. N O(heme) FeII + (heme) FeIII

+5 +3 +2 +1 0 -2 -3

Acidic solution

Basic solution

NO3-

+0.01NO2

--0.46

NO+0.79

N2O+0.94

N2

-1.16N2H4

+0.01N2H4

HNO3

+0.94HNO2

+1.00NO

+1.59N2O

+1.77N2

-0.23N2H5

+1.28NH4

+

Sosa-Torres, personal comunication

Detection of Nitric Oxide by (MGD)2Fe(II)--NO adduct (spin traps)

MGD; N-methyl-D-glucaminedithiocarbamate

Chemical structure of water soluble

dithiocarbamate-iron complexes and their NO

radical adducts. a, MGD. b, N-

(dithiocarboxy)sarcosine.c, 2-hydroxyethyl

dithiocarbamate. d, proline dithiocarbamate.

Koichiro Tsuchiya et al. J. Biol. Chem.

2000;275:1551

Detection of Nitric Oxide by (MGD)2Fe(II)--NO adduct (spin traps)

Medina-Andrés , et. al (2015), PLoS ONE 10(3): e0119400. doi:10.1371/journal.pone.0119400

“…The EPR spectrum of (MGD)2Fe(II)NO adduct at 297 K isolated from the control protonema extracts revealed a well-resolved three-line spectrum with an isotropic g value = 2.040 and an hyperfine coupling, aN, value of 13 G typical of the EPR signal of (MGD)2Fe(II)NO compounds in aqueous solution”

MGD; N-methyl-D-glucaminedithiocarbamate

Fig 4. Nitric oxide detection by EPR in P. patens protonemagrowing in high nitrate

References;

D. M. Murphy, EPR (Electron Paramagnetic Resonance) Spectroscopy of Polycrystalline Oxide Systems in Metal Oxide Catalysis, edited by S. D. Jackson and J. S. J. Hargreaves, WILEY-VCH, 2009, Ch. 1

A. Lund & W. Liu, Continuous Wave EPR of radicals in solids in EPR of Free Radicals in Solids I: Trends in Methods and Applications, edited by A. Lund, M. Shiotani, Springer, Ch. 1, 2013.

S. Stoll , Computational Modeling and Least-Squares Fitting of EPR Spectra in Multifrequency Electron Paramagnetic Resonance: Data and Techniques, edit by S. K. Misra, Wiley-VCH , 2014, ch. 3, p. 69.


Some software for EPR spectra simulation

Software Characteristics Site web

XSophe A computer simulation software “suite” of Bruker© for simulation de CW-EPR

www.bruker.com/es/products/mr/epr/epr-software/ simulation-suites/ overview.html

SimFonia Program of Bruker © for fast and efficient simulations on a PC

WinSim Dedicated to solution spectra of spin traps

http://www.niehs.nih.gov/research/resources/software/tox-pharm/tools/index.cfm

SimEPR Program that accepts arbitrary Hamiltonian matrices as input (ms)

Glerup, J. and Weihe, H. (1991), Acta Chem. Scand., 45, 444–448.

PEST WinSIM Program to calculate the simulation of multiple species of isotropic EPR spectrum.

www.niehs.nih.gov/research/resources/software/tox-pharm/tools/index.cfm

Easyspin Software package for simulation and analysis of wide range of EPR spectra. It is based on Matlab ©

S. Stoll (2003), EPR newsletter, 3 (1-2) , 24; http://www.easyspin.org/

http://www.niehs.nih.gov/research/resources/software/tox-pharm/tools/index.cfm

http://www.easyspin.org/

Some software for EPR spectra simulation

Software Characteristics Site web

Orca The program is a modern electronic structure program. It is for quantum chemistry with specific emphasis on spectroscopic properties . EPR-parameters: ZFS, g-tensors, hyperfine couplings, quadrupoletensors from Hartree-Fock, DFT and MR-CI. relativistic corrections at theZORA level.

https://orcaforum.cec.mpg.de/

Gaussian It provides state of the art capabilities for electronic structure modeling. Calculate the hyperfine coupling constants anisotropic.

http://www.gaussian.com/

https://orcaforum.cec.mpg.de/

3480 3500 3520 3540 3560

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

Inte

nsity [ ]

Field [G]

RL3_RT2

Freq. 9.861338 GHz

N

O

Tempo(2,2,6,6-tetramethyl-

1-piperidinyloxyl)

Rad. nitróxido


3480 3500 3520 3540 3560

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

Inte

nsity [ ]

Field [G]

RL3_RT2

Freq. 9.861338 GHz

g =

2.0051

15.2 G

Tempo(2,2,6,6-tetramethyl-

1-piperidinyloxyl)

Rad. nitróxido

2.1 G

N

O


Experimental Data

EPR spectrum in solution

Freq; 9.861338 GHz

g = 2.0051

a = 15.2 G

B p-p = 2.1 G

Type of Line; ¿Lorentzian o Gaussian?

Atom spin Nat. Ab. (%)

14N 1 99.6

15N 1/2 0.37

16O 0 99.8

17O 5/2 0.04

12C 0 98.9

13C 1/2 1.1

1H 1/2 99.9

N

O

Simulate EPR spectrum with SimFonia (Bruker)


SimFonia (Bruker)

Final Results


Freq; 9.861338 GHz

giso = 2.0052

a (14N) = 15.35 G

Line L / G = 0.2

Lw = 2.5 G

Fit of data = ¿multivariate analysis, c2?

3470 3480 3490 3500 3510 3520 3530 3540 3550 3560

Inte

nsity [ ]

Field [G]

Experimental

Simulated

N

O


Another Example;

Perinaphthyl rad.

(PNT)

3450 3460 3470 3480 3490 3500 3510

-3000

-2000

-1000

0

1000

2000

3000

Inte

nsity [ ]

Field

PNT

Freq. 9.7998 GHz

McConnell & Dearman(1958), J. Chem. Phys., 28, 51.

giso


Perinaphthyl rad.

(PNT)

3458 3460 3462 3464 3466 3468 3470 3472

-2000

-1000

0

1000

2000

Inte

nsity [ ]

Field [G]

PNT

Freq. 9.7998 GHz

a1 = 1.815 G

a2 = 6.264 G

1 3 3 1 6 18 18 6 11 33…


The intensity of each line follows Pascal's triangle, for I=1/2 nuclei.

3460 3470 3480 3490 3500 3510

Field

PNT(exp)

Sim

Freq. 9.7998 GHzSimFonia (Bruker)

Final Results


Freq; 9.861338 GHz

g = 2.01208

a1 (1H) = 1.815 G

a2 (2 1H) = 6.295 G

Line (L / G) = 1.0

Lw = 0.07 G

Best - fit of data;

¿c2?


Final Results


Freq; 9.861338 GHz

g = 2.01208

a1 (1H) = 1.815 G

a2 (2 1H) = 6.295 G

Q = -22.5 G

1= 0.081 (Exp)

2= 0.280 (Exp)

McConnell (1958), J. Chem. Phys., 28, 51g = 2.01208a1 (1H) = 2.2 Ga2 (2 1H) = 7.3 G

aj = Q j

Q = -22.5 G1= -0.176 (Exp; 0.098) 2 = +0.321 (Exp; 0.325)


3460 3470 3480 3490 3500 3510

Field

PNT(exp) Freq. 9.7998 GHzFinal Results

Rad. Perinaftenil (PNT)

EPR spectrum (solution)

Freq; 9.861338 GHz

g = 2.01208

a1 (1H) = 1.815 G

a2 (2 1H) = 6.295 G

giso

Simulation of EPR spectrumTree diagram

Alejandro Solano-Peralta

[email protected]

Unidad de Servicios de Apoyo a la Investigación e Industria (USAII)Facultad de Química, UNAM,

LR

PE

Bioinorganic applications of multi-frequency EPR

Over 95% of all the EPR spectroscopy is performed in X-band (9 GHz). Most systems EPR continuous wave (CW-EPR) operates at X-band (9.8 GHz). Therefore, the first step in CW-EPR is another multi-frequency operating frequency.

Microwave frequency bands and magnetic fields used

* All these frequencies are permissible depending on our selection of magnets.

A lot of information to facilitate the interpretation of the spectra and often changes his appearance, especially in the range of powders or frozen solutions (glass).

EPR Multi-frequency

L S X K Q W D HF

v (GHz) 0.8-1.2 3.4-3.8 9-10 24 34 94 120 263

g = 2 (T) 0.035 0.13 0.34 0.85 1.22 3.35 4 8

Why other frequencies are used?

Many factors contribute to the choice of experiments are performed at X-band (9-10 GHz).

• One factor is the availability of components,

• The magnetic field requirements for X-band are usually satisfied easily by electromagnets (1.8 T),

• The 3 cm wavelength ensures convenient sample sizes and sample handling,

• The sensitivity . As the Boltzmann factor and sample size increase, they increase the spectrometer’s sensitivity.

These factors lead to the almost universal acceptance that EPR is performed at X-band.

But, why would researchers wish to perform experiments at lower or higher frequencies?

EPR Multi-frequency

The appearance of EPR spectra depends strongly on the interplay of magnetic field dependent and magnetic field independent terms.

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 questions posed by our sample.

EPR Multi-frequency

IIQSJSSSDISaIBgSBgH 21NNeS

EPR Multi-frequency

hn = g mBB0

Banda Frecuencia

(GHz)

L 1 – 2

S 2 – 4

X 8.2 – 12.4

P 12.5 18

K 18 – 26

Q 26.5 – 40

W 75 -110

D 110 - 170

G 180

Conventional

High Frequency (HF-EPR)

Very High Frequency (VHF-EPR)

IIQSJSSSDISaSBgH 21eS

EPR Multi-frequencyThe microwave frequencies commonly used in EPR were not chosen arbitrarily. With the exception of K-band, the common EPR frequencies correspond to minima in the atmospheric absorption of microwaves. 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 purposes.

R. Weber, Overview of Multi-Frequency EPR, Bruker Bio-spin.

Running more than one frequency helps to interpret the spectral characteristics. Interplay of dependent and independent terms to the field in the spin Hamiltonian used

The spin Hamiltonian can be divided into a dependent part of field (ie, terms Zeeman) and a separate part of the field (ie, hyperfine terms, zero field, quadrupole, etc.).

EPR Multi-frequency

IIQSJSSSDISaSBg

IQISJSSDSIASSgBH

21e

21eS

MHz) 006( 9029990

MHz) 004( 0.999934

MHz) 003( 9999720n

n

BE

HRMN

lower

upper

0

1

.

.

Multi-frequency EPR is the tool to unravel the dependent terms independent of magnetic field.

Multifrequency EPR spectra enables much more efficient simulation. In addition, motion effects can be studied over a broad time interval.

Tk

E

lower

upperBe

n

n

EPR Multi-frequency

(98.5GHz) 9840100

GHz) 534( 0.994370

GHz) 859( 9983890n

n

BghE

RPE

lower

upper

0Be

.

.

..

n

T = 20 °C (293 K)kB = 1.3806488x10-23 J KB = 9.72401x10-24 J / T(1H) = 2.6752x108 rad /T s

EPR Multi-frequencyIdeally, we would like to obtain an EPR spectrum in which the spin-

hamiltonian parameters are evident from visual inspection of the spectrum’s features.

However, several factors may mask the features we wish to interpret such as;

• Linewidths and anisotropy.

• Second-order* effects can make interpretation 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.

EPR Multi-frequencyThis can add a lot of information to facilitate the interpretation of the spectra and

often changes its appearance, especially in the spectrum of powder samples.

H = ßB.g´.S - ßnB.gn.I + S.A.I + S.D.S + I.P.I + higher-order terms.

• If the magnetic field is enough high …– The nuclear and electronic spins are quantified by the external field and

– A first-order spectrum is observed,

– A better resolved anisotropy g.

But

– Information on nuclear quadrupole term, I.P.I, and the zero field term , S.D.S, is lost.

• In downfield; – The terms of electronic or nuclear Zeeman may be comparable to the terms of zero field. This

results in a mixture of state and observation of forbidden transitions.

So, for the analysis of specific terms in the Hamiltonian you can select and record spectra at various frequencies.

EPR Multi-frequency

The effects of g-valuesIf 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 frequency:


EPR Multi-frequency

g-anisotropy vs g-strainBecause 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.

One option is to prepare a single crystal sample and perform rotational studies to extract information regarding the electron Zeeman interaction.


EPR Multi-frequency

g-anisotropy vs g-strain


PSAO (Pea Seedling Amine Oxidase) and inhibitor PHZ (Phenylhydrazine), 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 inhibited form is more symmetric and approaches axial symmetry.

EPR Multi-frequency

The effects of Nuclear Hyperfine CouplingsSometimes we may be interested in the nuclear hyperfine couplings. Forexample, we may be interested in the number and identity of the nuclei in aradical or metal site. Unfortunately, the g-anisotropy or g-strain can mask thesplittings that would give us this information. In order to minimize this effectand enhance the effect of the nuclear hyperfine coupling, we need to performthe experiments at frequencies lower than X-band.


EPR Multi-frequency

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 thelinewidths 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 coupling constant of the six equivalent nuclei.


EPR Multi-frequency

The Effects of Zero Field SplittingsLarge ZFS (Zero Field Splittings) that are greater than hn may make observation of EPR impossible sometimes. The magnetic field to bring the sample into resonance may be prohibitively high for microwave frequencies less than the ZFS.


EPR Multi-frequency

The Effects of Zero Field SplittingsIf spectra are observed, for samples with hn < ZFS, the spectra can be difficult 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.


EPR Multi-frequency

The Effects of Zero Field Splittingshigher 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 hamiltonian predicts the anisotropy of the EPR spectrum decreases with increasing frequency. Performing experiments at higher frequencies can yield substantial resolution enhancement for high spin systems.


EPR Multi-frequency

Relaxation Times Many mechanisms can contribute to relaxation times. Commonly, temperature 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 frequency and temperature dependence, sufficient constraints are placed on the results to identify dominant relaxation mechanisms.

Higher frequency spectra are often more sensitive to fast molecular motions than lower frequency spectra.


EPR Multi-frequency

Relaxation Times


EPR Multi-frequencyLas frecuencias que pueden ser utilizados rutinariamente varían de 1 a 100 GHz

(campos que van desde 0.03 a 3 T).

• La baja frecuencia EPR es la elección perfecta para muestras grandes y, en particular, estudios in-vivo.

• A altas frecuencias en EPR: Incremento de la sensibilidad. Decremento de la perdida

dieléctrica. Incremento de la resolución

de g. Escala de tiempo del

experimento corto. Acceso a diferencias de

energía más grandes. Cambio de importancia

relativa de las interacciones dependientes e independientes del campo.

EPR Multi-frequency¿Qué es alta frecuencia?

hν > 35 GHz (banda Q), es decir, todo a partir de banda W (95 GHz)

¿por qué hasta ahorita?

Magnetos superconductoresson necesarios.

Son comercialmente disponibles desde hace pocos años

S. K. Misra(Editor), Multifrequency Electron Paramagnetic Resonance: Theory and Applications, 2011 Wiley-VCH Verlag. DOI: 10.1002/9783527633531

K. Möbius and A. Savitsky (Editors),High-field EPR Spectroscopy on Proteins and Their Model Systems ...

S. K. Misra(Editor), Handbook of Multifrequency Electron Paramagnetic Resonance: Data and Techniques, 2011 Wiley-VCH Verlag. ISBN; 978-3-527-41222-8

I. D. Sahu, R. M. McCarrick, and G. A. Lorigan, Use of Electron Paramagnetic Resonance To Solve Biochemical Problems, Biochemistry, 2013, 52, 5967

Some references

Multi-frequency EPR spectra of a organic radical

D. M. Murphy, in Metal Oxide Catalysis. Edited by S. D. Jackson and J. S. J. Hargreaves,Wiley - VCH, 2009, Ch. 1

Simulated multi - frequency EPR spectra of a Cu(II) ion (g|| = 2.18, g ⊥ = 2.05, A|| = 140 G, A⊥ = 15 G)

Multi-frequency EPR spectra of a Cu(II) ion

Multifrequency EPR spectra of a copper(II) complex in which three nitrogen nucleiare equatorially coordinated to thecopper(II) ion. gx = 2.0884, gy = 2.0512, gz

= 2.2780 ; A(63Cu) : Ax = 16.95, Ay = 15.43, Az = 153.40; A(14N) : Ax = 14.54, Ay = 7.07, Az = 8.99 ; A(14N): Ax = 13.22, Ay = 15.2, Az= 9.50 x 10-4 cm-1

http://www.springerimages.com/Images/RSS/1-10.1007_978-90-481-2888-4_6-6


A. Ivancich, P. Dorlet, D. B. Goodin, and S. Un, Multifrequency High-Field EPR Study of the Tryptophanyl and Tyrosyl Radical Intermediates in Wild-Type and the W191G Mutant of Cytochrome c Peroxidase J. Am. Chem. Soc. 2001, 123, 5050-5058

Multi-frequency EPR spectra of Tryptophanyland Tyrosyl Radical Intermediates

Incremento de la sensitividadLa diferencia de población de Boltzmann entre 2 estados

energéticos depende de la diferencia de energía y de la

temperatura:

BgE;en

nB

kTE m

Para g = 2, y T = 300 K, y enresonancia:

n½/n-½ = 1 en 1000 para banda X; n½/n-½ = 1 en 100 para banda W.

Esta es una de las principales razones para ir a altas frecuencias en EPR.

A. Solano-Peralta et al., Dalton Trans., 2009, 1668-1674

Multi-frequency EPR spectra of a complex of HS Fe(III)

Multi-frequency EPR spectra of a complex of Fe(III), d5 HS. g = 2.0884, D = 0.1730 cm-1, E = 0.0 cm-1



0 1 2 3 4 5 6 7 8

G-Band

W-Band

Q-Band

X-Band

Magnetic field (T)

Multi-frequency EPR spectra of a complex of Fe(III), d5 HS. g = 2.0884, D = 0.1730 cm-1, E = 0.0 cm-1

HF- EPR (94 GHz) spectra and angular variation diagram of [Fe(DMSO)6](NO3)3 at Room Temperature



Experimental

Simulated

g = 2.010

D = 0.173 cm-1

E = 0.0 cm-1

B = 19 mT

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

0

10

20

30

40

50

60

70

80

90

Eule

r angle

(°)

Magnetic field (T)

0.0 0.5 1.0 1.5 2.0 2.5

x 50

P. M.H. Kroneckl, et al, FEBS, 1990, 268, 274


G. Strzelczak,, et al, Radiation research 155, 619 (2001)


A. Engalytcheff, et al, Free Radical Research, 38, 59 (2004)

Multi-frequency EPR spectra of Radicals Produced in Irradiated β-Blockers

A. Szyczewski, et al., J. Alloys and Compounds 451 (2008) 182–185

Multi-frequency EPR spectra of Gadolinium(III) cryptates

Analysis of the EPR spectra of the Gd(III)/hexa(diphenylphosphinoxide)-cyclotriphosphazene complex, carried out at X- and W-band (9.4 and 94 GHz) frequencies, provided information on the phase transition near 5.4K and information on the time durability of the Gd/PNPcomplexes immobilized in the SiO2 xerogel matrix.

Estudio de sistemas de espín alto y entero

J. Krzystek, et. al, Inorg. Chem. 2002, 41, 4478

J. Krzystek, A. Ozarowski, S. A. Zvyagin,

and J. Telser, High Spin Co(I): High-

Frequency and -Field EPR Spectroscopy

of CoX(PPh3)3 (X = Cl, Br), Inorg. Chem.

2012, 51, 4954

Estudio de sistemas de espín alto y entero

A. Gunn, , Elucidation of Bioinorganic Chemical Structures by Electron Paramagnetic Resonance Spectroscopy at Multiple Frequencies, Thesis (Ph.D.), University of California, Davis, 2012, 207 pages (http://gradworks.umi.com/35/40/3540511.html )

Multi-frequency EPR spectra of some metalloenzymes

“Multifrequency electron paramagnetic resonance (EPR) spectroscopy is a powerful tool that allows us to probe molecular structure and magnetic interactions of paramagnetic systems. By expanding from traditional X-band EPR into higher microwave frequencies, the terms of the spin Hamiltonian can be resolved and distinguished. Many complex and important paramagnetic systems are found in biology. Molecules of interest include metalloenzymesand proteins with organic radicals”

http://gradworks.umi.com/35/40/3540511.html

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