ENDORENDORElectron Nuclear Double ResonanceElectron Nuclear Double Resonance

Professor P. T. ManoharanProfessor P. T. ManoharanDepartment of Chemistry and RSICDepartment of Chemistry and RSIC

Indian Institute of Technology MadrasIndian Institute of Technology MadrasChennai - 600 036, IndiaChennai - 600 036, India

G. Feher (1956) Phys. Rev. 103, 834 It complements the technique of EPR in identifying the

nuclei that are weakly interacting and allows the detailed mapping of the electron wave function.

EPR Hamiltonian

H = b B.g.S + S. D.S + ₢ Ii.. Ai. S + ₢ Ii. P. I i + ₢ bn B.gn.Iii i i

ENDOR

1 Solves the ambiguity in the assignment of hyperfine multiplets (i.e., correct identification of the nucleus)

2 Resolves the hyperfine lines, not resolved in EPR due to line broadening or complexity.

3 Gets more accurate values (PRECISION) for hyperfine coupling.

4 Measures nuclear quadrupole coupling constants (when I ³ 1)

Advantages: Sharper EPR lines/precise determination of hfc constants.

Two Related Techniques

ENDOR is EPR detected NMR

ENDOR ® Two frequencies irradiate the sample, a constant MW and a swept RF either by CW or pulsed mode

ESEEM ® Pulsed method ® irradiate the sample only by MW pulses.

S = , I = Case.

Isotropic spin Hamiltonian

H = g b B Sz - gn bnB Iz + A S. I

E = g b B ms – gn bn B mI + A ms mI

Transition probability is given by

Wif a | < f | v | i > |2

Let us say that the first EPR transition occurs at a field of Bk and second one at Bm, |Bk Bm| being the hyperfine coupling constant A/h and the centre of Bk and Bm defining the g value of the system.

CW ENDOR

1 The sample placed in a microwave cavity is subjected to a low microwave power and the magnetic field is placed at Bk. Optimize the parameter to get maximum amplitude of this signal

2 Achieve Partial saturation by increasing the microwave power (B1e) several

fold.

3 Now the sample is subjected to rf magnetic field (B1n) of wide range and

large power out put from an rf generator.

rf-frequency range will depend on Bk i.e microwave frequency and also the nn of

the concerned nucleus. [In the case of proton the range is 2 to 30 MHz since

proton NMR frequency corresponds to nn = gn bn Bk/h ]

The base line indicative of a constant EPR absorption (horizontal axis is that of n from rf generator) will have two absorptions at nn1 and nn2

± ?

(nn1 ± nn2) = nn = gn bn Bk/h º NMR frequency of the nucleide (bare) responsible for the hfc.

Also nn2 ± nn1 = A/h.

Upper sign ® | A | > 2nn

Lower sign ® | A | < 2nn

IMPLIES

Identification of the nucleus (gn with in 0.1% accuracy) Precise hfcc. Extremely low linewidth

Repeat the experiment at Bm to get another ENDOR spectrum.

This plot of rf frequency of changes in the EPR absorption intensity is called the ENDOR experiment

NOTE

1. The relative intensities of the two lines may not be same with the two

ENDOR spectra. Sometimes, one line may not even be detected, specially

when |A| = 2 nn.

2. ENDOR line typically represents a change with the EPR line intensity of

~1% of EPR line under non saturated conditions; hence a spectrometer of

high sensitivity is needed

3. Partial saturation is sufficient for the EPR; mostly saturations are

accomplished at ~ 4K. More complete saturation is needed for the NMR

transition.

4. ENDOR lines are relatively much narrower than EPR lines:

ENDOR » 3kHz to 1 MHz

EPR » 0.1mT » 2.80 MHz

Hence, the accuracy of splittings 10-3 %

5. Number of lines in an ENDOR spectrum is considerably less, i.e., greater

effective resolution and easier interpretation

6. Anisotropic hfc can be determined in solids by angular dependent

ENDOR

7. For I > one can determine e2qQ

8. Signs of A and e2qQ can also determined

(eg) diphenylanthracene (DPA) negative ion

All lines in this spectrum correspond to A/h < nn hfcs are ~ 0.6MHz , ~4MHz and ~7MHz.

ENDOR experiment determines NMR transitions much better than an ordinary NMR experiment because of far greater ENDOR sensitivity due to:

1 EPR quantum >> NMR quantum (population differences higher)

2. dDE /dt is high at MW frequencies.

3. Effect of static field + Electron field helps alter the intensity of EPR

line during ENDOR (Enhancement)

Dynamics of ENDOR

Rearrangement of level populations from thermal equilibrium (Î = gbB/kT)

i. Boltzmann Population on the application of B.

ii. By pumping MW power on top of the EPR line;

(ii) Turning on the RF pump power;

(iii) Tracing out the ENDOR response on a recorder

± ?

Quadrupole Coupling Constant (QCC)

For spin I ³ 1, consider the quadrupole interaction terms. Due to the additional relaxation paths, more difficult to predict the intensity of the ENDOR lines.

In liquids isotropic hyperfine coupling

In solids, powders, frozen solution anisotropic information including QCC.

Applications F Centre in alkali Halides.

Anion vacancy in KBr.EPR line width 12.5 mT i.e., 125G due to a large number of unresolved lines.First shell and all other odd number shells have 39K (93.26%) or 41K(6.73%)Even numbered shells 79Br(50.69%) and 81Br(49.31%)

Six First shell and twelve 2nd neighbour shell nuclei give pj (2njI + 1) = 19x37 = 703

epr lines.ENDOR will be spread over a considerable range of frequency.Anisotropic and isotropic interactions will fall off with distance

All are of I = 3/2 i.e., hfcc + Qcc + differing gn

Hence EPR give no indication of any structure.

ENDOR 0.5 to 26 MHz

Narrowest line 10KHz

Quadrupolar contribution added

nn1 = |1/2[A|| + A^ (3cos2q - 1)] - gnbnB + 3P(3cos2q - 1) (MI - )|/h

nn2 = | - [A|| + A^ (3cos2q - 1)] - gnbnB + 3P(3cos2q - 1) (MI - )|/h

Where P = e2qQ/4I(2I 1)

Pulsed ENDOR

Uses pulsed MW and RF

In a pulsed ENDOR, the intensity of electron spin echo is measured as a

function of the radio frequency.

Advantages: (i) Entire sequence can be made short enough to exclude

unwanted and competing relaxation effects.

(ii) Pulsed ENDOR efficiency upto 100% while the

CWENDOR is only a few %

Mims-ENDOR

In 1965, Mims proposed the pulse ENDOR experiment shown in Figure 1. The original pulse scheme is based on the stimulated echo sequence with three non-selective mw pi/2 pulses. The first two mw pulses create a periodic polarization pattern across the inhomogeneously broadened EPR line. During the mixing period a selective rf pi pulse of variable frequency is applied. If the rf pulse is on-resonance with a NMR transition, the populations in this transition will be changed and consequently also the polarization pattern. This change is then measured as a function of the rf via the stimulated echo intensity created by the third non-selective pi/2 pulseIn a Mims-ENDOR experiment, the ENDOR signal intensity depends also on the hyperfine coupling constant A and on the time tau between the first two mw pulses. For certain values of tau, there is no ENDOR effect. Such blind spots are particularly troublesome in ENDOR spectra of disordered systems, where the knowledge of the proper line shape may be essential.

[1] W.B. Mims, "Pulsed endor experiments", Proc.R.Soc.London, 283, 452 (1965).

Davies-ENDOR

The pulse ENDOR scheme introduced by Davies [1] is based on selective mw pulses. A mw pulse is considered to be selective, if it only affects a single EPR line.Figure 1 shows the Davies-ENDOR pulse sequence. The selective mw pi pulse inverts the polarisation of an allowed EPR transition. During the mixing period, a selective rf pi puls is applied. If the rf pulse is on-resonance with a NMR transition, the polarization of this transition will be inverted and consequently, the polarization of the allowed EPR transitions will disappear. The change in the polarization of the EPR transition, selectively excited by the preparation pulse is then measured as a function of the rf via an echo created by two selective mw pulses.

[1] E. R. Davies, "A new pulse ENDOR technique", Phys. Lett. , 47A, 1 (1974).

Chirp Time-Domain ENDOR Spectroscopy

Conventional ENDOR methods observe the nuclear frequencies during radio frequency (rf) irradiation which leads to power broadening. It was first proposed by Hoefer et al. to use time-domain observation for the elimination of this broadening mechanism [1]. However, time-domain ENDOR poses the technical problem of exciting nuclear transitions in a frequency band of about 20 MHz width. This can be done by using chirp pulses instead of the usual monochromatic irradiation, i.e., by sweeping the rf linearly through the required frequency range during the pulse [95.6]. It can be shown that the optimum flip angle of the chirp pulse for the single transitions is smaller than pi/2 and that it can be achieved for typical systems with standard pulse ENDOR instrumentation. Because of the multiplex advantage, chirp time-domain ENDOR features higher sensitivity than established pulse ENDOR experiments, in particular if only a few ENDOR lines are spread over a broad frequency band. Another advantage is that concepts from ESEEM can easily be adapted to time-domain ENDOR, e.g. the ENDOR analogon to HYSCORE [2] is obtained just by introducing a pi pulse into the sequence.

[1] P. Höfer, A. Grupp, and M. Mehring, "High-resolution time-domain electron-nuclear-sublevel spectroscopy by pulsed coherence transfer", Phys. Rev. A 33, 3519 (1986) [2] P. Höfer, A. Grupp, H. Nebenführ, and M. Mehring, "Hyperfine sublevel correlation (HYSCORE) spectroscopy: A 2D ESR investigation of the squaric acid radical", Chem. Phys.

Lett. 132, 279 (1986)

Comparison of Davies- and Chirp ENDOR spectra of bis(glycinato)copper(II)

2D Chirp ENDOR of bis(glycinato)copper(II)

Comparison of ENDOR and ESEEM experiments

23Na ENDOR spectrum of the Fe(CN)63- complex in NaCl, for four different

orientations. The contribution of the nuclear Zeeman interaction (around 80 MHz) is subtracted. FIR (ESR) frequency 244.996GHz.

ENDOR spectrum of the Fe(CN)63- complex in NaCl in the 18-27 MHz

range.B||[100] = 6.0017 Tesla. FIR (ESR) frequency 244.996 GHz.

EPR spectrum of 2,2,6,6-tetramethyl-1-piperidinyl-oxy (TEMPO) in toluene-d8 + 10% dimethylformamide-d7 at 285.135GHz and 40K. The spectrum is

fitted with the g-values gzz = 2.00214(4), gyy = 2.00620(4) and gxx = 2.00972(4).

The hyperfine splitting due to the nitrogen nucleus is only visible along the z-direction (93.5MHz).

ENDOR spectra of 2,2,6,6-tetramethyl-1-piperidinyl-oxy (TEMPO) in toluene-d8 + 10% dimethylformamide-d7 at 285.135GHz and 3.0K. The

magnetic field varies from 10.132(top) to 10.176(bottom) in 2mT steps.

Example 1: EPR and corresponding ENDOR spectrum (recorded at 4K) of a Cu doped MgO catalyst. The ENDOR spectrum clearly reveals the coordination environment of the Cu2+ ions, which are surrounded by 5 distinct OH groups. The weak interactions between the Cu2+ ion and the proton are clearly not visible in the EPR spectrum.

ENDOR spectrum

Example 2: EPR and ENDOR spectrum (100K) of a surface defect center (an FS

+(H) colour center) on a polycrystalline oxide surface. The ENDOR

spectrum clearly shows the magnitude of the coupling between the surface trapped electron and a nearby proton. Despite the complex heterogeneous nature of the polycrystalline oxide sample, the resolution of the ENDOR signals is excellent.

EPR spectrum ENDOR spectrum

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