Radicals in solution studied by endor and triple resonance spectroscopy

RADICALS IN SOLUTION STUDIED BY ENDOR AND TRIPLE RESONANCE SPECTROSCOPY

Klaus MOBIUS and Martin PLATO Institut für Molekülphysik, Freie Universität Berlin, West Germany and Wolfgang LUBITZ Institut für Organische Chemie, Freie Universität Berlin, West Germany

I

NORTH-HOLLAND PUBLISHING COMPANY - AMSTERDAM

PHYSICS REPORTS (Review Section of Physics Letters) 87, No. 4 (1982) 171—208. North-Holland Publishing Company

RADICALS IN SOLUTION STUDIED BY ENDOR AND TRIPLE RESONANCE SPECTROSCOPY Klaus MOBIUS and Martin PLATO Institutfür Molekulphysik, Freie Universität Berlin, West Germany

Wolfgang LUBITZ Inst instfür Organische Chemie, Freie Universität Berlin, West Germany Received March 1982 Contents: 1. Introduction 2. Principles of ENDOR and TRIPLE experiments 2.1. ENDOR 2.2. TRIPLE resonance as an extension of ENDOR 2.2.1. Special TRIPLE resonance 2.2.2. General TRIPLE resonance 3. Experimental arrangements 4. Density matrix treatment of magnetic multiresonance experiments 4.1. Basic relaxation theory 4.2. Molecular and experimental parameters governing ENDOR and TRIPLE experiments and their parametrization 4.3. Computational procedure 5. Comparison of experimental and theoretical ENDOR results 5.1. Influence of the molecular environment on the ENDOR effect 5.2. ENDOR effect of different nuclei in the same molecule

173 174 174 177 177 179 183 183 183

186 188 190

5.3. Special aspects 5.3.1. Cross-relaxation 5.3.2. Quadrupole effects 5.3.3. Internal motions 6. Applications to problems of chemical and biological interest 6.1. Hyperfine structure of low-symmetry radicals 6.2. ENDOR on organic radicals in liquid crystals 6.3. Hindered rotation of molecular fragments 6.4. ENDOR on ion pairs 6.5. Biochemical and biophysical applications 6.5.1. ENDOR on radicals derived from flavins 6.5.2. ENDOR on radical ions of photosynthetic pigments 7. Concluding remarks Acknowledgements References

190 191

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K Möbius eta!., Radicals in solution studied by ENDOR and TRIPLE resonance spectroscopy

173

1. Introduction For magnetic resonance studies of radicals in solution electron-spin-resonance (ESR) is a wellestablished spectroscopic method. However, when trying to elucidate the electronic structure of large and low-symmetry radicals, one is often hampered by problems of spectral resolution. It was as early as 1956 when Feher [1] demonstrated that by electron-nuclear-double-resonance (ENDOR) the spectral resolution can be greatly improved. This first ENDOR experiment was technically feasible only because the sample phosphorus doped silicon was studied at low temperature, where all the relaxation times are sufficiently long to easily obtain saturation. For radicals in liquid solution, however, these relaxation times are much shorter in the order of iO~—i0~ sec and, consequently, ENDOR-in-solution experiments are technically much more sophisticated, since much larger saturating microwave and rf fields have to be applied. This probably explains why the first ENDOR-in-solution experiments required many more years before they were successful. The pioneering work was performed by Cederquist [2] in 1963, who studied metal ammonia solutions, and by Hyde and Maki [3] in 1964, who investigated an organic radical in solution. The further development of ENDOR-in-solution spectroscopy was highly stimulated by Freed [4], whose general theory of saturation and double-resonance proved to be adequate in describing amplitude, width, and shape of ENDOR lines in great detail. Fig. 1 shows schematically, how ESR is extended to ENDOR. The sample in our case a fluid radical solution sits in a cavity/coil arrangement where it is simultaneously irradiated by microwave and rf fields. ENDOR signals are obtained by monitoring the changes of the amplitude of a saturated ESR line which occur when sweeping the frequency of the rf field through the nuclear resonance (NMR) region. —

—

—

—

—

—

mW power 0.01-lW (10 6Hz)

rf power 0.1-1kW (0.5-40 MHz)

lOG F.GERSON

cavity Fig. 1. Schematic drawing of microwave cavity with internal rf coil for broadband ENDOR and TRIPLE resonance experiments.

J.JACHIMOWICZ Switzerland

K MOBIUS

.

iS HYDE

0 SLENIART

15

R BIEHL Germany USA

20MHz

Fig. 2. High-resolution ESR and ENDOR half-spectra of the 2phenylcyclo[3.2.2]azine anion radical [101 (solvent: DME= 1,2dimethoxyethane, counterion: Na~,T = 210 K).

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K. Mdbius eta!., Radicals in solution studied by ENDOR and TRIPLE resonance spectroscopy

For ENDOR-in-solution in particular, we have to apply large rf powers in the order of 10 W to 1 kW together with microwave powers between 10 mW and 1 W. In an electron—nuclear—nuclear TRIPLE resonance experiment, two high-power rf sources are connected to the NMR coil. The advantages of this TRIPLE resonance are an enhanced sensitivity, resolution, and the possibility to directly determine relative signs of hyperfine couplings from line intensity variations. ENDOR and TRIPLE resonance have been successfully applied to organic mono-, bi-, and triradicals in solution [5,6] and recent review articles [7—9]cover the literature up to 1979. In this paper we will concentrate on monoradicals and will give examples of physical, chemical, and biological applications. In these examples. it will become obvious that ENDOR on non-proton nuclei is particularly important and, therefore, this aspect will be given a broader attention. Fig. 2 is intended to give a first impression of how drastic the gain in resolution can be when comparing ESR and ENDOR spectra of radicals in solution. This figure also indicates a positive side-effect of ENDOR: because of the complexity of the experiments, international cooperation is definitely encouraged [10]. In fig. 2 high-resolution ESR and ENDOR spectra of the phenylcyclazin anion radical in solution are compared. Assuming rapid rotation of the phenyl ring, one expects from symmetry considerations 9 proton hyperfine couplings (hfc’s) and a tenth coupling from the nitrogen. As a consequence, the ESR spectrum is overcrowded with inhomogeneously broadened lines, and there is little hope to analyse such an ESR spectrum in an unambiguous way. The ENDOR spectrum, on the other hand, contains much fewer lines, i.e. it is much better resolved, and from the proton line positions all 9 hfc’s can be immediately deduced. It is this improved spectral resolution which makes ENDOR so attractive for the spectroscopy of large molecules.

2. Principles of ENDOR and TRIPLE experiments 2.1. ENDOR To start this section, let us explain why ENDOR spectra are better resolved than ESR spectra. For this purpose we refer to fig. 3 which shows the energy level scheme of a radical (S = ~)containing 4 ms M1 -2 _____

ENDOR 1

Jil

~

ESR ii

___

ENDOR2 Fig. 3. Energy level diagram of a radical in solution with 4 equivalent protons in a high magnetic field. The total nuclear magnetic quantum number is given by M1 = ~ rn1. Five ESR lines but only 2 ENDOR lines appear.

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175

equivalent protons (I~= ~ for each of them) in a strong magnetic field. The interactions responsible for the various splittings are summarized in the following static spin Hamiltonian: ~

(1)

The leading term is the electronic Zeeman interaction, (gp8/h)H~followed by the nuclear Zeeman and hyperfine interactions, (g~~a~.Jh)B1 and a SI, respectively, summed over all nuclei. The hfc constant, a, is scalar as long as radicals in isotropic solutions are considered. In the strong field approximation with HIIz axis, the energy eigenvalues, classified by the magnetic spin quantum numbers, ms and m1, are given by 1-~msmiffl IL

— —

—~-—ssms gILB ~J

—

h

urn

giii/~K LI

1, ~

-~-

amsmi,

i.e. in a specific ms manifold the hyperfine levels are equidistant. In an ESR experiment, therefore, because of the selection rules, z~m~ = ±1,L~1m1~ = 0, five lines are observed (see fig. 3) with binomial intensity distribution owing to the transition frequency degeneracies for equivalent nuclei. In an ENDOR experiment, on the other hand, the sample is additionally irradiated with an rf field of varying frequency driving NMR transitions iXm1 = ±1of nuclei coupled to the unpaired electron. Thus, every group of equivalent nuclei no matter how many nuclei are involved and what their spin quantum number is contributes only two ENDOR lines due to the first order degeneracy of the NMR transitions (see fig. 3). Saturated ESR transitions can therefore be desaturated by NMR transitions, provided both transitions have energy levels in common. In an ENDOR spectrum the enhanced ESR signal intensity is recorded versus the NMR frequency showing that ENDOR is a variant of NMR, the unpaired electron serving as sensitive detector. Because of the pumping of the microwave transitions and the quantum transformation from rf to microwave quanta, ENDOR is much more sensitive than NMR, roughly by 5 orders of magnitude. Compared with ESR, however, one loses at least one order of magnitude in sensitivity. This is compensated by a gain in resolution: With increasing number of groups of nuclei the number of ENDOR lines increases only in an additive way, whereas the number of ESR lines increases in a multiplicative way. Consequently, for low-symmetry radicals the gain in spectral resolution is very drastic. In our phenylcyclazin example of fig. 2, the total number of lines per frequency extension of the spectrum is about 30 times larger for ESR than for ENDOR. This gain in resolution becomes particularly pronounced when nuclei with different magnetic moments are involved. Their ENDOR lines normally appear in different frequency ranges, and from their Larmor frequencies these nuclei can be immediately identified. In a doublet radical the two ENDOR lines occur to first order at —

—

VENDOR=

Ii.’~±a/2I

(3)

with the free nuclear Larmor frequency v~,= (gflp.KIh) H, i.e. they are symmetrically displayed about ti~ or ä/2, whichever is larger. We now turn to the ENDOR signal intensity. Conceptionally, the occurrence of an ENDOR enhancement of an ESR line can be best understood for the simplest case S = I = i.e. in a 4-level ~,

~,

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K Möbius eta!., Radicals in solution studied by ENDOR and TRIPLE resonance speciroscopy

diagram (see fig. 4). By wavy lines the various relaxation transition rates are indicated: W~describes the relaxation rate of the electron spins, W~that of the nuclear spins. W,~,and W,~2are cross-relaxation rates which describe the flip-flop and flop-flop processes of the coupled electron and nuclear spins. For isolated radicals in solution, the relaxation transitions are mainly induced by spin rotational interaction and by modulation of electronic Zeeman and electron—nuclear dipole interactions as a result of Brownian rotational tumbling. The corresponding time-dependent Hamiltonian will be discussed in section 4. In a phenomenological description, the ENDOR experiment, in which an ESR and an NMR transition are saturated simultaneously, can be visualized as the creation of an alternative relaxation path for the pumped electron spins, which is opened by driving the NMR transition, and which passes via We (1+ —)*--e.]— —)) and W,, (I— —>*-~—+)) — or even better via W~1(1+ —)*-~— +)). The extent to which this relaxation by-pass can compete with the direct W~route (J+ +)~-s.~— +)), determines the degree of desaturation of the ESR line and, therefore, determines the ENDOR signal intensity. The intensity pattern of ENDOR lines, therefore, does not generally reflect the number of contributing nuclei, in contrast to ESR and NMR. Obviously, good ENDOR signal-to-noise ratios require that this delicate interplay of the various induced and relaxation transition rates is carefully optimized. The parameters to be varied by the experimentalist are the radical concentration, the solvent viscosity, the temperature, and the microwave and rf field strengths. In order not to get lost in this multiparameter hide-and-seek play the experimentalist will appreciate some theoretical guidance: The simplest theoretical approach to predicting the magnitude of the ENDOR effect as a function of the various spin lattice relaxation rates Wa~of the spin system is to make use of an electric circuit analogy. This analogy can be established by regarding the various relaxation pathways a.r~~~13 as conductances proportional to ~ The ENDOR enhancement E is defined as the relative change of the ESR absorption signal during NMR irradiation. In the electric analogue this is equivalent to the relative change of the input conductance across the circuit branch belonging to the ESR transition after shortcircuiting all branches belonging to the resonant NMR transition (see fig. 5). This situation corresponds to the limit of high NMR saturation and to exact “on-resonance” conditions. By applying

N MR

-1/2 1 ~~-~.1/2

+

->

~We

~

~c:

:

E::e~.,~>©

S-1/2,

1-1/2,

0>0

VNDOR

-

Vn

+

Fig. 4. Four-level diagram of a system with S = 1/2, I = 1/2 with relaxation rates ~ For the phenomenological description of the ENDOR effect, see text.

W,2 ~We ~~2W3~e

E=i~I/I

2

W24rW.

Fig. 5. Electrical circuit analogy of the 4-level diagram of fig. 4. The ENDOR enhancement E is given by the relative change of the input current I when short-circuiting the branch 1,3 corresponding to an NMR transition.

K. Môbius eta!., Radicals in solution studied by ENDOR and TRIPLE resonance spectroscopy

177

the well-known rules for adding conductances in series or in parallel, one immediately finds for the simple case W~1= W,~2= 0: 1

E=2(2+b+b1)

(4)

where b = WnIWe. Not unexpectedly, the maximum of E is found for the “matching condition” b = 1, i.e. for W~.= W~.This optimum condition yields Emax = ~, showing that ENDOR signals are weaker than ESR signals by almost an order of magnitude in the absence of efficient cross-relaxation rates. Cross-relaxation rates become operative as soon as Wx exceeds the smaller of the two direct rates W~ or We. W~1,Wx2 0 always lead to an increased enhancement for both low- and high-frequency ENDOR lines, because these routes by-pass We and W~(see fig. 5). However, if W~1 W~2,which is the most frequent case (see section 4), the now unsymmetrical relaxation network will also produce unsymmetrical ENDOR line patterns. The largest ENDOR effect will obviously be observed for that NMR transition which forms a closed ioop with the ESR transition and the larger of the two W~rates. The observation of such unsymmetrical ENDOR line patterns not only provides clear evidence of particular dominant relaxation mechanisms, but also information about the relative signs of different isotropic coupling constants of a molecule (see section 6). We shall now look more closely at the temperature and solvent dependence of the ENDOR enhancement E by returning to the simpler situation where W~1= Wx2 = 0. According to eq. (4), E depends on the ratio WnI We. It will be shown in section 4 that W~and We usually depend differently on a rotational correlation time TR characteristic for the Brownian tumbling 1,which yields motion Wn/We of the ij. molecule Since TR in the liquidsection solution. In most~ cases ‘TR, of whereas W~ we r~obtain the important relation (see 4), where is the W,, viscosity the solvent, b = W~/We ~

(ijl T)2.

(5)

In the region b 4 1, i.e. W~4 W~,which is the most frequent situation for free radicals in solution at room temperature, we have from eq. (4) and eq. (5) E(b

~ 1) ~ (~/T)2.

(6)

Since ‘q/T strongly increases with decreasing temperature, mainly due to the strong temperature dependence of ~, the ENDOR effect can therefore be strongly enhanced by cooling the sample. Fairly seldomly, Wn ~ We at room temperature. For such cases, eq. (4) yields E(b~’1)cc (~/T)2

(7)

implying that the sample has to be heated to maximize the ENDOR effect. 2.2. TRIPLE

resonance as an extension of ENDOR

2.2.1. Special TRIPLE resonance Not for all systems an equalization of nuclear and electronic relaxation rates can be achieved by temperature and solvent selection. Then W~4 We, i.e. the slow W,, is the rate-determining step in the

178

K Möbius eta!., Radicals in solution studied byENDOR and TRIPLE resonance spectroscopy

relaxation by-pass. Consequently, in cases of vanishing cross-relaxation, Y/~acts like a bottle-neck for the ESR desaturation and limits the ENDOR signal intensity to less than one percent of the ESR intensity. There is an obvious way out of this dilemma by short-circuiting the W~bottle-neck by a second saturating rf field. In this electron—nuclear—nuclear triple resonance experiment, the two rf fields are tuned to drive both NMR transitions, ~ and v, of the same nucleus (see fig. 4) thereby enhancing the efficiency of the relaxation by-pass. As a consequence, one gains considerably in signal intensity. Such a TRIPLE resonance was theoretically proposed by Freed [111in 1969 and experimentally realized by Dinse et a!. [12]in 1974. Since both rf fields are applied at a frequency separation of the hyperfine constant of the same nucleus, this is a special version of TRIPLE resonance. The increased sensitivity is one important development. The second advantage of special TRIPLE resonance over ENDOR is that when both rf fields are sufficiently strong so that the induced transition rates become large compared with the relaxation rates W~ the ESR desaturation becomes independent of W~.As a consequence, the line intensities are no longer determined by the relaxation behaviour of the various nuclei, but rather reflect the number of nuclei involved in the transition [12]. TRIPLE lines can more easily be assigned to particular groups of nuclei in the molecule than can be done with ENDOR lines. Besides improved sensitivity and assignment capability, special TRIPLE resonance has also the advantage of higher resolution. Experiments and density matrix calculations [8, 11, 12] have shown that at a given power level, the effective NMR saturation, which determines the observed linewidth, is smaller in TRIPLE than in ENDOR. In fig. 6, the ENDOR and special TRIPLE spectra are shown for the 3-pyridyl-phenyl ketone anion radical as a representative example [13]. The spectra were recorded at a deliberately chosen high temperature, where the rings are rotating rapidly on the ESR time scale. At this temperature, however, W~4 We, and consequently the ENDOR signal-to-noise ratio is rather poor. Since the NMR transitions are already saturated at the applied field amplitude of 10 Grot (rotating frame), all the ENDOR lines show equal intensity within the noise limits. The special TRIPLE spectrum was obtained at the same —

—

15

20MHz

Special TRIPLE

0°

0

5MHz

Fig. 6. ENIDOR and Special TRIPLE resonance spectra of the 3-pyridyl-phenyl ketone anion radical (solvent: DME, counterion: Na~,T 240 K). Compare also fig. 20.

K Möbius eta!., Radicals in solution studied byENDOR and TRIPLE resonance spectroscopy

179

total rf power level and hence the rf field amplitudes per side band are reduced to (1/V’2). 10 Grot (for the generation of the two rf fields, see section 3). In qualitative accordance with the theoretical predictions, the signal-to-noise is increased in the TRIPLE spectrum. Furthermore, the intensity ratios 2: 1:2: 1: 1: 1: 1 of the TRIPLE lines reflect nicely the number of protons involved in the NMR transitions (the ortho and meta protons of the phenyl ring are equivalent). Finally, a reduction of the linewidth in the TRIPLE spectrum is also clearly visible.

2.2.2. General TRIPLE resonance Electron—nuclear—nuclear triple resonance can be generalized to include more than one nucleus, for example two inequivalent protons [14]. The first-order solution of the time independent spin Hamiltonian of eq. (1) for the simplest three-spin system S I~= ‘2 = ~leads to an eight-energy level scheme which can be characterized in the basis msmj1mi2), see fig. 7. From this figure it is obvious that we now =

can desaturate a pumped ESR transition by driving the NMR transitions of both nuclei. For the ESR transition shown in fig. 7 and neglecting cross-relaxation, this can be achieved, for instance, by driving the NMR transitions at uI and uI of nucleus 1 and 2, the relaxation by-pass being closed via We, Wni, Wn2. Because all the NMR transitions are doubly degenerate, there principally exist several of such closed relaxation by-passes involving tii and uI and, hence, a complete picture would be very confusing in such a two-dimensional representation of the energy levels. We, therefore, resort to a threedimensional representation of the eight-energy level scheme. As is depicted in fig. 7, the eight energy levels can be arranged to form the corners of a cube, in which the ESR transitions occur vertically, the NMR transitions horizontally. In which particular plane of the cube the NMR transitions occur, solely depends on the relative signs of the two hfc’s a, — and it is this sign-information which can additionally be obtained from a general TRIPLE resonance experiment. This will be explained with the aid of some topological games summarized in fig. 8. At the top of fig. 8, the energy level arrangement is depicted for the two different cases, a1, a2> 0 and a1 >0, a2 < 0. In S =1/2,I~=1/2,12 =1/2

Wn,~Wn2 ~

‘~,

_____

/

//

/

W~~2 ~ Wç~1 HL/=~We

/~

‘i,

,—i’

~ I\

H /1

~ 1m1m1m1>

fl~

V~

I

/

a2 >0

iiii

v~

v Vsn

H

t

~

v~ V2

1

I— — + >

I—+—>

v;

V~

l_++>

Fig. 7. General 1’RIPLE resonance on a radical with 2 inequivalent protons. All nuclear transitions are doubly degenerate in first order. A TRIPLE induced relaxation by-pass for the ESR transition shown, involving the high-frequency NMR transitions i4 and v~of both nuclei, can be achieved via the routes W~2, W~1, W~and W,,,, W~2, W~(cross-relaxation rates neglected). This situation can be more clearly visualized by a three-dimensional representation of the energy level scheme in form of a (distorted) cube.

180

K Mdbius et aL, Radicals in solution studied by ENDOR and TRIPLE resonance spectroscopy

ENDOR/TRIPLE

Topology

a~>0

~

NMR

~2,

02<0

___

ENDOR

TRIPLE(generat) (pyramid)

TRIPLE(special)

TRIPLE(general) (tetrahedron)

Fig. 8. Topology of ENDOR and TRIPLE resonance experiments for the three-spin system of fig. 7. The NMR transitions with their frequencies are given for the two cases of equal and opposite signs of the hyperfine couplings. For simplification, the ESR transitions are not distinguished.

the case that both coupling constants have the same sign, the doubly degenerate low-frequency NMR transitions, v~and v~,of both nuclei occur in one plane, the doubly degenerate high-frequency transitions, uI and uI, in the other. If the couplings have opposite signs, low- and high-frequency transitions of both nuclei occur in a mixed fashion in both planes. By now considering the level populations, the different multiple resonance experiments can be visualized by different geometrical figures which are derived from the cubes by contracting those corners that are connected by induced NMR transitions. This represents the limiting case of highly saturated NMR transitions, where the populations of the connected levels are equalized. In this representation, an ENDOR experiment, where only one of the doubly degenerate NMR transitions is saturated, for instance at u~(see fig. 7), forms a prism. Special TRIPLE, where v~and uI are driven simultaneously, forms a square. In general TRIPLE two different cases have to be distinguished: if all the NMR transitions are saturated in the same plane, because the coupling constants have the same sign, the 4 corners are contracted to a single point and a pyramid is formed. If, on the other hand, the NMR transitions for the two nuclei are saturated in both planes, because the coupling constants have opposite signs, a tetrahedron is formed. The impact of these topological games is shown in fig. 9 giving the result of an electric circuit analogy analysis of the relaxation networks of the various geometrical figures. The TRIPLE amplification factor V, which is plotted versus the ratio We/Wn, is defined as the ratio of TRIPLE and ENDOR line amplitudes. The analysis shows that the tetrahedron experiment always yields markedly larger TRIPLE line amplitudes than the pyramid experiment, and the difference between pyramid and tetrahedron becomes more pronounced in those cases, where We is much larger than W,,. This is frequently occurring for organic radicals in solution. Relative signs of coupling constants can therefore easily be determined from intensity changes in general TRIPLE spectra. As an example, fig. 10 shows ENDOR and general TRIPLE spectra of the fluorenone-sodium ion-pair in solution [15].The intensity of the low- and high-frequency ENDOR proton and sodium lines is the same, since experimentally almost constant transition moments over the whole frequency range

K Möbius et aL, Radicals in solution studied by ENDOR and TRIPLE resonance spectroscopy

100

—

YCTRIPLE)

—

Y)ENDOR)

181

spec. TRIPLE

pyramid 0.1

i

I

0.1

1

10

100

~We/Wn~

1000 (T/~)2

Fig. 9. TRIPLE amplification factor as function of the ratio WJ W~obtained by analysing the electrical circuit analogy of the various relaxation networks. The curves shown are valid for induced NI~4Rrates 100 times larger than W~cross-relaxation was neglected; for details see refs. [8,14].

No®/THF VH

4

8

12

16MHz

Fig. 10. ENDOR and general TRIPLE resonance spectra of the fluorenone anion radical (solvent: tetrahydrofurane, counterion Na~).Note the inverted intensity ratio of the sodium lines around 3.7 MHz at 226 K and 172 K, see text.

182

K. Möbius eta!., Radicals in solution studied by ENDOR and TRIPLE resonance spectroscopy

have been provided. This symmetry of the ENDOR line intensities is lost in the TRIPLE spectra, where a second proton transition belonging to the largest hyperfine coupling is additionally pumped. For the protons with the two small couplings the high-frequency lines are enhanced compared with their low-frequency counterparts — thereby demonstrating that a tetrahedron experiment is performed with respect to the pumped transition. The largest and the two small coupling constants, therefore, must have opposite signs. For the next larger couplings it is just the other way round showing that a pyramid experiment is performed. One sees, how nicely also heteronuclear TRIPLE resonance works: when pumping a proton line, also the sodium line pair changes its intensity ratio. Between 226 K and 172 K this intensity ratio is even inverted, indicating that the sodium coupling constant has changed sign in this temperature range as a result of a change in the ion-pair conformation. The proton couplings, on the other hand, do not react likewise on this conformational change (see section 6).

I

mw bridge Variar, E 101

power meter Bird # 43 ~

lock-in Ithaco39lA TM

magnet AEG X20

110 cavity with NMR coil

-

Computer

xy recorder

hp 21 MX-E

hp 7004 B

poweramplifier 2x EN) A-300

I

10 kHz

1.

IL.

______________

power combir~1

5

EN) PM 400-4

—

fm oscillator Wovetek VCG Ill

6

I

I

--

10kHz pump OSCIII Wavetek 7000

2’~ -~‘

~

‘..~

,‘

I

____________

I

I idoub)e balanced Ii II L.,...J mixer i.~ I

digitol attenuator

scan oscilL hp 8660 C I

I

L

rf power control

_J it frequency

control

ANZAC MD 141

Fig. 11. Block diagram of the ENDOR/TRIPLE resonance spectrometer. The sample temperature can be varied by a N2 gas stream (AEG temperature control unit). The different modes of operation can be achieved by the following connections: ENDOR: conn. 1 open 2 open 3 open 4 open 5 open 6 closed

SpecialTRIPLE: conn. 1 open 2 open 3 closed 4 closed 5 closed 6 open

General TRIPLE: conn. 1 closed 2 closed 3 open 4 open 5 open 6 open

K. Mobius et al., Radicals in solution studied by ENDOR and TRIPLE resonance specmroscopy

183

3. Experimental arrangements The block-diagram of the most recent version of our multiple resonance spectrometer is depicted in fig. 11. The different modes of operation are explained in the figure caption. Conceptional details have been published previously [8]. The scan oscillator delivers the frequency modulated rf, whereas the pump oscillator is not modulated. In the special TRIPLE mode, the double balanced mixer produces the two side-band fields with the right modulation phase behaviour. This is achieved by setting the pump oscillator to the respective free nuclear Larmor frequency and mixing it with the scan oscillator frequency. In addition to data acquisition and handling, the computer is used to control the scan oscillator and to ensure approximately constant NMR power at the sample over a wide frequency range. Besides sample temperature, the most critical parameters of the experiment are the microwave and rf fields at the sample. Broadband ENDOR and TRIPLE experiments with sufficiently large microwave and rf field amplitudes are performed with the cavity/helix arrangement shown in fig. 12. This TM110 cavity is rather similar to that described earlier [8], the major improvement being the possibility to irradiate the sample with light in photolytic experiments. This is achieved by cutting two slits into the cylinder walls at the appropriate positions, where wall currents are least disturbed. The back slit is used to cool cavity and helix with a nitrogen gas stream. In the frequency range between 0.5 and 5 MHz, we use an NMR helix with 30 turns, in the range between 5 and 30 MHz one with 20 turns. With the two combined power amplifiers (600 W) the maximum rf fields obtained are 20 Grot (at 14 MHz) and 35 Grot (at 2 MHz). Sample

~NjI

Dewar

‘c.

magnetic

microwave field

electric

Fig. 12. Broadband ENDOR/TRIPLE cavity with internal NMR coil, Dewar line, and light irradiation slits. The microwave field configuration of the 1’M~0mode is also shown.

4. Density matrix treatment of magnetic muttiresonance experiments 4.1. Basic relaxation theory The principles of ENDOR and TRIPLE experiments have been described in section 2 in a phenomenological way on the basis of simple rate equations for the level populations. Although such an approach is very helpful in providing a first quick understanding of the basic idea underlying these experiments, it is hardly suited to explain the behaviour of an ENDOR spectrum in all its fine details,

K. Möbius eta!., Radicals in solution studied by ENDOR and TRIPLE resonance spectroscopy

184

such as the linewidths, the saturation behaviour, and special coherence effects caused by the presence of more than one radiation field. The most detailed theoretical treatment of steady state multiresonance experiments in the liquid phase has been carried out by Freed and co-workers in a series of papers [11,16a—d]. They use a density matrix method which, although rather complex, has proved to be extremely powerful in explaining even the finest details of multiresonance spectra. The density matrix method is essentially a variant of time dependent perturbation theory starting from the complete spin Hamiltonian of the paramagnetic molecule. Most generally, this Hamiltonian has the form = ~‘O+ ~‘

1(t) +

â(t)

(8)

where ~W0 is the time-independent part giving the zero-order energy levels and transition frequencies (compare eq. (1)), ~1(t) contains energy terms which are randomly time-modulated by environmental (lattice) effects, e.g. by the Brownian tumbling motion of the molecule in solution, and ê(t) represents the sum of the interactions of the spins with the external coherent radiation fields. In ENDOR (or TRIPLE) ê(t) contains the interaction of all electron and nuclear spins with one microwave and one (or two) ri radiation fields. The term of primary interest in eq. (8) regarding the behaviour of ENDOR and TRIPLE spectra is as it determines the magnitude of all spin lattice relaxation rates Wa~and linewidth parameters (1/T2)a,g between any two levels a, /9 of the spin system. Various types of interactions can contribute to ~‘1(t) for a doublet radical in liquid solution, e.g. 1. the coupling between the electron spin S and the rotational momentum J of the molecule: (9)

~1CsR/h—S~BJ;

2. the anisotropic electron Zeeman interaction between the magnetic moment of the electron g~1~ and the external magnetic field H due to spin-orbit coupling: (10) 3.

the anisotropic dipole—dipole hyperfine (END) interaction between the electron spin ~ and the nuclear spins I~: (11)

4.

the anisotropic quadrupolar hyperfine interaction of nuclei with L

>

(12) 5.

the isotropic electron—nuclear Fermi contact interaction ~ a~L;

(13)

K. Môbius eta!., Radicals in solution studied byENDOR and TRIPLE resonance spectroscopy

185

6. the isotropic electron Zeeman interaction (14)

~g/h = (g~~s~/h)H . S.

All interactions 1 to 6 are given in frequency units. The three quantities G, A1, and Qt are termed the (anisotropic) g-tensor, and the dipolar and quadrupolar hyperfine tensors, respectively. They are traceless second rank tensors which, in isotropic solutions, do not affect the positions of spectral lines. In order to contribute to ~t’1(t), any of the interactions listed above must be randomly time modulated by the rotational motion of the molecule in solution and/or internal molecular motions, such as rotation of groups of atoms (e.g. CH3) or vibrations. The last two interactions 5 and 6 can, obviously, only be affected by the latter type of motion since they are spatially isotropic. After having collected the various types of interactions which might possibly influence the intensity and width of ENDOR and TRIPLE lines, we proceed along the ideas of Freed and co-workers by writing down the “equation of motion” of the density matrix p(t): p = —i[~Co+ ê(t), p1

—

F(p po)

(15)

—

where [ ] represents the Poisson bracket over the enclosed operators [17]. Eq. (15) fully describes the time behaviour of the macroscopic ensemble of spins in the sample under the influence of â(t) and ~‘1(t). In the simplest system with two states a and /3, p,,,,,, and p,~represent the populations of these two states, and p,,,,~= P~adescribes the coherent mixing of the two states in the presence of an rf field having Ea~(t)~ 0. The expectation value of a quantum mechanical operator P is simply given by Trace (pP), P being the matrix representation of P. In ESR, ENDOR, or TRIPLE the signal amplitudes are proportional to the transversal component M5 of the magnetization, so that in this case P M5 NSF, where N is the number of radicals. All relaxation effects due to ~C1(t) are collected in the matrix F which is a function of p — Po, where Po is the density matrix in thermal or “Boltzmann equilibrium”. A matrix element of I’ between any pair of eigenstates a, a’ is given by faa

= — ~

Raa’~ti’(p— po)~,

(16)

where certain matrix elements of the “relaxation matrix” R are directly related to unsaturated linewidths and spin lattice relaxation rates, e.g. Rapap = (1/T2)ap and Raapp = Wad. The complete relaxation matrix R can be calculated tC from the spectral density functions j~(w)of the various time dependent terms j.~= 1,. , 6 of ~ 1(t) listed above. The selective action of a particular interaction ~ in creating only special relaxation paths, like We or W~,comes from the selection rules for the spin operators involved in that particular interaction. An important example is offered by the electron— nuclear dipole (END) hyperfine interaction (j~= 3), which, for a system with S = ~ and a single nucleus with I = ~, produces the following relaxation matrix elements (see fig. 4): . -

R1122 = W~= ~j(A)(We)

R2233 = Wx1 = 1J(A)(

R22~—— “a

R1212 —

1/T2e ——

2 ~(A) (0) _~j

o

1/T2~—

_~j

— —

D — ‘~‘ — “1144~ ~x2 —

121.(A)(~tunJ \

—

2)~4)~ i~We± Wfl)

‘~

—

—

~~2424 —

—

±

7 ~(A)

(0).

(17)

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K Mdbius et al., Radicals in solution studied by ENDOR and 1RIPLE resonance spectroscopy

+

Here the subscripts 1 to 4 refer to the four states +), +), 1+ —), and — —), respectively. If the Brownian tumbling motion is considered to be the only significant mechanism causing relaxation, the spectral density function j~(w)is given by j(A)(w)_

j_(TrA2)

—

(18)

1+~2~~1

where Tr A2 is the sum of diagonal elements (trace) of the squared dipolar hyperfine tensor A introduced in eq. (11), and TR is the rotational correlation time of the Brownian rotational diffusion. In order to discuss eqs. (17) on the basis of eq. (18) we assume the following conditions which are normally met in ENDOR and TRIPLE studies: tunTR 1, i.e. “fast tumbling limit” in the NMR frequency range, WeTR> 1, i.e. “slow tumbling limit” in the ESR frequency range. This yields W~ND c 1,W~ND= c2rR, W~ND= 6 W~ND= c 1.These relations are consistent with eqs. (5)—(7) in section 2.1r~ However, we 3r~ the proportionality constants c can now specifically calculate 1, c2, and c3 from the molecular property 2. Since W~ND> W~ND it also follows that the END interaction creates an unsymmetrical Tr A relaxation network giving rise to unsymmetrical ENDOR line patterns. However, this asymmetry decreases towards lower temperature, because both cross-relaxation rates “die out” with increasing TR in contrast to W~ND. After having set up the R-matrix from all relevant interactions contributing to ~~‘ 1(t), one can then work out steady-state solutions of eq. (15) for all non-vanishing diagonal and non-diagonal elements of p. This is done on a computer which also puts out the final ENDOR or TRIPLE spectrum for the specific conditions chosen in the experiment. The obvious advantage of such a rigorous theoretical approach to ENDOR and TRIPLE phenomena is that (i) the number of parameters determining the different spin lattice relaxation rates and unsaturated linewidths is reduced a relatively smallofnumber of independent fundamental molecular 2 and TR, andto(ii) the influence the microwave and rf fields is correctly taken parameters, e.g. Tr A account of at any power level. It also leads to a quantitative interpretation of all types of coherence effects typical for multiresonance experiments which show up as line distortions and sometimes even splittings. “~

4.2. Molecular and experimental parameters governing ENDOR and TRIPLE experiments and their parametrization

Recently [18], an attempt has been made to find as simple relations as possible between optimum ENDOR conditions, e.g. optimum temperature for a given solvent and microwave and rf fields, and a few of the most relevant molecular properties by employing the rigorous density matrix formalism described above. The aim of this study was to find a systematic approach to the ENDOR behaviour of different magnetic nuclei in different molecular environments and solvents. The following simplifying assumptions were made which are quite realistic for most organic doublet radicals in solution: (i) Brownian rotational diffusion is taken to be the dominant source of relaxation and can be described by a single rotational correlation time TR. This correlation time is related to molecular and solvent properties by the well-known Einstein—Debye relation TR

V~fffl/kT

(19)

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187

in which V~ffis the effective tumbling volume of the molecule, ~ the viscosity of the solvent, T the absolute solvent temperature, and k the Boltzmann constant. Under typical ENDOR conditions TR ranges between 5 x iO~ns and 5 ns. Values of ~/kT as function of temperature for a variety of solvents can be taken from fig. 1 in ref. [18]. (ii) Spin rotational coupling (eq. (9)) is the dominant source of nuclear spin independent relaxation. The corresponding matrix elements R ~ W~Rand —R ~a~/2 = 1/(2T~) between pairs of electron states a, /3 are parametrized with respect to TR as B/TR where B ranges typically between 10_6 and iO~.The value of B may be estimated from a semiempirical relation involving the deviation of the g-tensor components git from the free electron value g~[181: (20)

B=~~(ggj_ge)2.

The values of git are taken either from single crystal measurements or from theoretical estimates. (iii) The most important molecular parameters involving nuclear properties are the traces of the squared END hyperfine tensors, Tr A~,of the various magnetic nuclei in the molecule. In some cases, however, there can also be important contributions from quadrupolar interactions determined by Tr Q~. The magnitude of Tr A2 depends on the size of the magnetic moment ~,, of the particular nucleus and the unpaired electron spin distribution in its near vicinity, i.e. Tr A2 (r~)2.Typical ranges for Tr A2 in different types of radicals are given in fig. 13. The magnitude of Tr Q2 depends on the size of the quadrupole moment 0 of the nucleus multiplied by the electric field gradient at its position. This electric field gradient is produced by the electric charges of all electrons and nuclei in the molecule. Typical values of Tr Q2 in organic radicals are ca. 0.1 MHz2 for 2H, 1 to 10 MHz2 for 14N. For halogen nuclei, however, Tr Q2 can become as large as iO~to iO~MHz2. In these cases, relaxation will be predominantly determined by the quadrupolar interaction.

TrA2 (MHz2)

TPM

10

TPP

NB ‘lx

10

2

BCh)~

~

-

Rb~/D0MB

1o~f~j~

Alkali cohorts TPM BBP NB TPP TPO BChi DOMB Fi

triphenylmettiyl di - tert.. butyl benzoylphenox yl riitrobenzene Iripheriyl-phosphabeazene triphenyiphenoxyl loxydizing agent I bacteriochlorophyll di-ortho-mesiloylbenzene tiuore,,one

Fig. 13. Typical ranges of Tr A2 for different nuclei. Upper and lower limits are labeled by the names of the corresponding radicals or by the different possible positions a (directly bonded) or /3 (two bonds away) of the nucleus relative to the IT system.

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K. Mobius et al., Radicals in solution studied by ENDOR and

TRJPLE resonance spectroscopy

4.3. Computational procedure In the computational procedure which uses the rigorous density matrix approach, the parameters defined in (i)—(iii) are used as input data besides other data such as the number of nuclei, their spin, free Larmor frequencies and isotropic coupling constants as well as the measured strengths He and H~of the microwave and rf fields. Alternatively, in the procedure of optimizing the ENDOR effect, the values of He and H~(including hyperfine enhancement) are calculated so that they correspond to the constant saturation parameters 0e = 7~TieT2eHe2= 3 and o~= y~T1~T2~H~ = 1. The output of the computer program, which can be applied to any continuous wave magnetic resonance experiment with a maximum of two microwave and two rf radiation fields, are ENDOR or TRIPLE signal amplitudes, linewidths (actually the complete resonance line shapes), and the “optimum” microwave and rf field strengths H~~t and H~~t required to fulfill the saturation conditions given above. As an example, calculated ENDOR signal amplitudes are shown in fig. 14 as a function of the rotational correlation time ‘TR. These calculations were performed for a single nucleus with I = ~and for the stronger of the two ENDOR lines, 2profiting the cross-relaxation process W,2.BThe of the and thefrom spin-rotational relaxation constant aretrace treated as squared dipolar hyperfine tensor Tr A ‘t’E

TrA2~1OOOOMHz2

10~: _______________

‘t’~ ,~-2

TrA2~1DOOOMHz2

~ooD,~~B:xio5

E

2

2

IrA ~1DD0OMHz

~

_________________ 0.01

0.1

1.OTR(ns)

Fig. 14. ENDOR signal amplitudes for optimum rf modulation and fixed saturation conditions u,, = 3, o,, = 1 as a function of the rotational correlation time r~in the case of one nucleus with I = 1/2. The curves are parametrized by different values of Tr A2. Three sets of such curves are shown for different values of the spin rotational relaxation constant B (see text). The dashed lines show the i~dependence of the weaker of the two ENDOR lines for Tr A2 = 10 000 MHz2 and 1 MHz2 (shown only for the limiting values B = lx 106 and lx 10~).

K. Möbius eta!., Radicals in solution studied by ENDOR and TRIPLE resonance spectroscopy

189

parameters ranging from 1 to 10000 MHz2 and 10_6 to iO~,respectively. These ranges cover the majority of nuclei in organic free radicals. The curves YE(TR) for constant values of TrA2 and B have well-pronounced maxima at “optimum” values of ‘r~= r~. The steep rise and fall of YE(TR) on either side of r~ demonstrate how critically the various relaxation rates have to be balanced out by proper choice of solvent and temperature when performing ENDOR-in-solution work. It has to be remembered that TR is strongly dependent on temperature, mainly through the viscosity ~ of the solvent (see eq. (19)) which normally follows an exponential law of the form ~ exp(const/T). Evaluation of the computer results in the given ranges of B and Tr A2 (excluding Tr A2 = 10 000 MHz2 as a fairly seldom case) give [18] r0RPi

=

200(B/Tr A2)°44

(21)

where TR is in ns and Tr A2 in MHz2.t Eq. (21) fully includes cross-relaxation effects from the END interaction. The unsymmetrical effect of END cross-relaxation on the low- and high-frequency ENDOR line amplitudes for small values of TR(WCTR S 1) is also demonstrated in fig. 14. Qualitatively, eq. (21) implies that an increase (decrease) of the dipolar hyperfine coupling or a decrease (increase) of the spin rotational coupling require an increase (decrease) of the solvent temperature. The condition expressed by eq. (21) can often be fulfilled by convenient choice of solvent and/or temperature. A more restrictive condition is given by the computer result [18] PENDOR

H~°~t 100(B

X Tr

A2)”2

(22)

for the rf field H° (in t Gauss, rotating frame) required for maximum ENDOR signals. The factor 0~ ratio of the observed transition frequency of the observed nucleus and the free VENDOR/PH, being the proton frequency, takes account of the different magnetic nuclear moments and the enhancement or deenhancement of the rf field by the isotropic hyperfine interaction [19].The latter so-called hyperfine enhancement effect is of particular importance for nuclei which have VENDOR ~H inspite of a very small magnetic moment. A typical example is 14N with the ratio of Larmor frequencies VN/PH = 0.07, where the isotropic hyperfine coupling is often so large (>10 MHZ) that VENDOR v~at least for the high-frequency ENDOR line. Eq. (22) also shows that the product B x Tr A2 has to stay within reasonable limits for ENDOR still to be feasible. A practical upper limit for H~with present technical equipment lies around 30 Grot which implies a maximum value of B X Tr A2 in the order of 0.1 MHZ2 (in the absence of other nuclear spin relaxation processes than the END mechanism). However, ENDOR can often be observed with sufficient signal-to-noise ratio at rf fields significantly below the saturation condition implied by eq. (22) which means that the restrictions given above are not extremely severe. For the optimum microwave field one obtains H,,°~’t oc (B x Tr A2)112 in the limit of large values of Tr A2 similarly to eq. (22). This condition can in some cases be more restrictive than the condition for ~ since the ENDOR effect depends more strongly on He than on H~[18]. This is normally not critical for organic radicals, but can easily be fatal for transition metal complexes which mostly have large values of B X Tr A2 [20]. t For n equivalent nuclei with I = 1/2 Tr A2 in eq (21) has to be replaced by n Tr A2 For one nucleus with I 1(1 + 1). These modifications are first order corrections in the region where W,,/ W, < 1.

1 Tr A2 has to be multiplied by

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K. Möbius et al., Radicals in solution studied by ENDOR and TRIPLE resonance spectroscopy

Up to now, we have only discussed the role of intramolecular interactions on the magnitude of the ENDOR effect. The radical concentrations of ENDOR samples are, however, seldomly low enough to completely exclude exchange processes such as Heisenberg exchange or chemical exchange. The influence of the more important Heisenberg exchange will be considered in the application sections in terms of a parameter C which relates the exchange rate WHE to the correlation time by ~HE C/TR [181. This parameter is given by C 4NfVeff where N is the concentration of radicals and f takes account of intermolecular Coulombic effects in the case of charged radicals. For f 0.25 which is typical for radical ions, and Veff = 50oA~one obtains C 1 x icr5 for a radical concentration of c 1 x iO~M. Experiments and calculations show that at such concentrations Heisenberg exchange can already have a significant deenhancing effect on ENDOR signals. =

=

=

=

=

5. Comparison of experimental and theoretical ENDOR results

To start the application sections of this paper with the more physical aspects we present some experimental ENDOR results and discuss them on the basis of the foregoing theory. The discussion will be divided into the following parts: 1. the influence of molecular environment on the ENDOR effect of a particular nucleus, 2. the ENDOR effect of different nuclei in the same molecule, and 3. special aspects like cross-relaxation, quadrupole effects, and internal motions. 5.1.

Influence of the molecular environment on the ENDOR effect

In order to illustrate the different ENDOR behaviour of the same nucleus in different molecules we have chosen the ‘3C isotope in the radicals TPM ([a-t3C]triphenylmethyl-d fig. 15) in and BBP 3C],see fig. 16). Both radicals15, wereseedissolved toluene (2,3-di-tert-butyl-4-benzoylphenoxyl [carbonyl-’ with similar concentration of 3 x i0” M. In fig. 15 the ‘3C-ENDOR spectrum of TPM is depicted at the optimum temperature of 325 K, showing two 13C lines symmetrically spread around ~ai3c= 33.4 MHz in

~ji~i

.-L

325K

~

1PM 1

~O13C

35MHz’ 310

CICH)

205K

~O13C

ICH~CACP

165K~

ESR saturated ESRsatur~ed

310

VH

MHz

Fig. 15. ‘3C-ENDOR spectrum of [a-’3Cl triphenylmethyl-d, toluene, for details see text and ref. [21]. 5 in

~

10

I

15

20MHz

Fig. 16. ‘H- and ‘3C-ENDOR spectrum of 2,3-di-tert-butyl-43C]in toluene, for details see text and ref. benozylphenoxyl 122]. [carbonyl-’

K. Möbius eta!., Radicals in solution studied by ENDOR and TRIPLE resonance spectroscopy

191

a distance of twice the free ‘3C frequency (iA3c = 3.5 MHz). The 13C-ENDOR linewidth is as large as 500 kHz in the spectrum shown. The full saturation of nuclear transitions was not possible even when using rf fields up to 35 Grot. The different ‘3C line intensities at saturating either the high- or low-field ESR transition indicate dominant cross-relaxation effects (%I’52) [21]. In fig. 16 the complete ENDOR spectra of BBP are shown at 2 different temperatures. Besides the two ‘H-ENDOR line pairs, two 13C lines show up, centered around ~a’~c= 8.5 MHz. In contrast to TPM, the ‘3C-ENDOR lines are now detectable at low temperatures; at 165 K their intensity is even larger than that of the proton lines. The optimum temperature for ‘3C and ‘H is near 180 K. It should be noted that in these spectra the differences in low- and high-frequency 13C-ENDOR line intensities are caused by the hyperfine enhancement and not by cross-relaxation [22]. Saturation of nuclear transition was easily achieved; the saturated linewidth at 180 K was as low as 35 kHz. In table 1 those characteristic data of 13C-ENDOR in both radicals are collected which allow a comparison between theory and experiment. Table 1 Hyperfine and relaxation data for ‘3C in the radicals BBP~and 1PMb

BBP 1PM

V,ff

ai3c [NH.z]

TrA2’ [MHz2]

r~’t(theo)” Ens]

i-°~’(exp)’ Ens] [A3]

T~, [K]

~p~Pt(theo) [kFlz]

~i4~P’(exp) [kFlzI

H~’t(theo) [Groti

H~Pt(exp) [G, 01]

—17.1 +66.9

14 22000

1.2 0.025

2.0 0.03

180 325

20 1000

35±5 500±50

2.6 51

5±1 >35±5

500 315

3C]. 1PM:2,6-di-tert-butyl-4-benzoylphenoxyl[carbonyl-’ [a-’3C]triphenylmetbyl-dis. BBP: Anisotropic hf tensor calculated from IT-spin densities [181. liTheoretical -~ values taken from fig. 7b, ref. [181,using B = io~for spin rotation and C = iO~for Heisenberg exchange; aseparate calculation was necessary for 1PM. ‘Calculated from eq. (19), using T,,~ 1from ENDOR and V,~from independent relaxation measurements [21].Errors for r°~”(exp) are in the order of ±30%.

3C-p~spin density is quite large in TPM and vanishingly Signinand magnitude a’~ccalculated indicate thatvalues the ‘ of Tr A2 therefore differ by more than 3 orders of small BBP [21,22].ofThe magnitude, resulting in a correspondingly large difference in the theoretical optimum TR values, which are evaluated from fig. 7b in ref. [18] and using B = iO~for spin rotation and considering Heisenberg exchange for the actual radical concentration [18]. These TR values are in good agreement with those obtained by the Debye—Einstein relation using the optimum ENDOR temperature of the toluene solutions and radical volumes from independent measurements [18,21]. The comparison between calculated and experimental linewidths and saturating rf fields is also quite satisfying. For TPM the observed linewidth is somewhat smaller because rf saturation could not be achieved with the fields available in spite of the large hfs enhancement factor (PENDOR/P’~C 10). — The comparison between ‘3C-ENDOR in TPM and BBP clearly shows the influence of the different ‘3C hfs anisotropies arising from the different molecular environments. 5.2. ENDOR effect of different nuclei in the same molecule

As an example of ENDOR performed on different nuclei in the same molecule we chose the BPA radical ([a-13C]-bis-biphenylenallyl-d, 6) see fig. 17 [23]. A viscous mineral oil (Shell Ondina G17) was

192

K Möbius eta!., Radicals in solution studied by ENDOR and TRIPLE resonance spectroscopy

VD

BPA

~203c

‘/2

0H

I

I

I

P

I

I

I

0

5

10

15

20

25

30

35MHZ

Fig. 17. ENDOR spectrum of [a-’3Cl-bis-biphenylenallyl.d,sin mineral oil (Shell Ondina G 17), showing D, H, and ‘3C resonances; for details see text and ref. [231.

taken as solvent which allowed the detection of maximum ENDOR signals at elevated temperatures (>300 K). Higher temperatures are necessary because the BPA exists as a diamagnetic dimer at room temperature. In fig. 17 the multinuclear ENDOR spectrum of BPA at 360 K is depicted, showing almost equal ENDOR amplitudes for the deuterons, the proton, and carbon-13. In fig. 18 the solid lines represent the experimental ENDOR amplitudes vs. temperature for the ‘--S

2.5

/0

/

\

13k)

Q5~

‘I

overage

I exp. error

/

T 300

I

‘

340

380 K

Fig. 18. Experimental (solid lines) and calculated (dashed lines) temperature dependences of the first derivative ENDOR amplitudes Y~of the 3 high-frequency lines of D, H, and ‘3C in BPA (fig. 17). For the calculation a model radical has been chosen with one carbon-13, one hydrogen and one deuterium nucleus. The input parameters were: Tr A~= 370 (‘3C), 24 (‘H), 0.4 (D) MHz2 Tr G2 = 5 x iO~B = 106; C = 2 x i0~laboratory fields: He = 35 mOm,, H, = 10.5 (‘3C), 8 (H), 14 (D) G,; constant modulation amplitude 50 kH.z; a, = —34.03 (i3c) +36.55 (H), —0.84 (D) MHz; = 3.55 (‘3C), 14.00 (H), 2.15 (D) MHz. (END mixing terms between different nuclei have little influence on the results.)ESR position: exact centre of spectrum.

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193

3 high-frequency lines of D, H, and ‘3C. The dashed lines give the respective temperature dependences calculated by our computer program; the input parameters used are given in the figure caption. The temperature scale has been obtained by using the calculated TR values, an effective volume of 2000A~ from a molecular model, and a microscopic viscosity for the mineral oil of ~1micro = °.3flmacro. The correction factor of 0.3 was obtained by a one-point fit on the temperature scale, and is consistent with theoretical considerations [24]. A comparison between experimental and calculated optimum temperature yields 330 and 322 K for D, 340 and 324 K for ‘H, and 360 and 367 K for 13C, respectively. It should be noted that the calculation also correctly yields a common temperature (355 K) where the ENDOR amplitudes of all 3 nuclei are almost equal. This agrees nicely with the temperature of 360 K where the spectrum of fig. 17 was recorded. Furthermore, the relative magnitudes of ENDOR amplitudes for all nuclei are reproduced quite well over the whole temperature range even on a non-logarithmic scale. The same is true for ENDOR linewidths and saturating fields. 5.3. Special aspects 5.3.1. Cross-relaxation

In the examples discussed above we generally evaluated the largest ENDOR line of each pair. However, high- and low-frequency line intensities might be drastically different if cross-relaxation processes are present in the system, see fig. 14. Such effects are explicitly included in our computer program. Their evaluation might give a deeper insight into the relaxation characteristics of the system [21,25, 26]; furthermore, they provide a means to determine molecular parameters like ‘TR and V~

0[21]

or even the relative signs of hfc’s [26]. In fig. 19 the ESR and ENDOR spectra of the pyrazine radical anion, generated by sodium reduction in liquid ammonia, are depicted. By desaturating the central line (position A) in the ESR, a symmetrical ENDOR spectrum is obtained, exhibiting one proton and one nitrogen line pair. In the lower part of the figure (right) the experimental ENDOR spectra taken on ESR positions B and C are shown. They exhibit a significantly changed intensity pattern for both types of nuclei, as is indicated by dotted lines. From these spectra and similar experiments on the other positions in the ESR spectrum (e.g. M~’= 0, M~ 0) a dominant W,,2 process, originating in the nitrogen END term, is deduced. The existence of this process even at temperatures just above the freezing point of the solution can be explained by the fast tumbling of the quite small pyrazine molecule in the very low viscosity solvent liquid ammonia. The asymmetric intensity pattern observed for the nitrogen lines also shows up for the protons, which are relaxation-coupled thebenitrogen From the opposing patterns different of the 14Ntocan deducedsystem. in accordance with TRIPLEintensity experiments [26]. In fig. signs 19 (bottom, hfc’s for ‘H and left) the corresponding calculated ENDOR spectra are shown; the input parameters are listed in the figure caption. The shapes and amplitudes of all four lines have been calculated for ESR positions on the high- and low-field nitrogen hf component, yielding satisfying overall agreement. Remaining discrepancies concerning the relative magnitudes of ‘4N and ‘H line amplitudes might be due to simplifying model assumptions given in the figure caption. It has to be noted that the experimental (250 ± 10 kHz) and calculated (190—220 kHz) linewidths are also in satisfying agreement. —

5.3.2. Quadrupole effects ENDOR spectra with highly unsymmetrical intensity distributions have also been observed in the case of o-dimesitoyl-benzene (DOMB) alkali metal radical complexes in solution. These effects

194

K. Möbius eta!., Radicals in solution studied by ENDOR and TRIPLE resonance spectroscopy

A

:~L~~H

~N)

ESR 10

calculated

~

15 MHz

experimental

VH

VH

j~)~~high~field ESR

~

B

-field ESR suIt

ui,Iis,uI

10 15 20MHz ‘4N-ENDOR spectra (top, bottom right) of pyrazine

1H. and Fig. 19. Experimental taken at different positions in the ESR spectrum shown (positions A: M

iii

10

15MHz

radical anion in liquid ammonia (sodium reduction) at 205 K

1N = Ml~= 0; B: M~= —2, M~= 0; C: M~= +2; M~= 0). The calculated 4N), 100 (H) TrG2=5X106, C=l05, ,r,=3, a’~=+20.34, r*s~were: 1.01, ENDOR spectra (bottom left) MHz2 have been obtained for a B=105, model radical containing one H,=6.2Gm,; nitrogen and two proton nuclei.aH=—7.6OMHz; The input parameters TrA~=850(‘ vH = 13.93 MHz; v, = 9.30Hz, constant modulation amplitude: 50 kHz. The calculations shown were performed for the ESR high-field (Ml~ = —1, M~’= 0) and low-field (M~= +1, M~= 0) components for all four complete ENDOR lines in 10 kHz steps in order to “simulate” the experimental spectra.

appeared particularly pronounced for the RB-DOMB complex. In a combined ENDOR and electron— electron-double resonance (ELDOR) study [27] on this complex, these effects were found to originate from a mutual action of quadrupolar and dipolar relaxation both caused by the rotational molecular motion. The alternative explanation by a cross-relaxation process, as it might have been produced by modulation of the isotropic Rb hfc, could be definitely ruled out by the ELDOR results. ENDOR measurements alone are generally not able to discriminate between these two possible causes unless very subtle second order effects are analysed. In terms of the general relaxation theory described in section 4, it is an additional term proportional to m 5 Tr(AQ) contained in W~,which either increases or decreases W~depending on the sign of the electron spin state m5 = + or On account of the large quadrupole coupling of Rb in the complex, these differences in W,, are sufficiently large to produce the observed strong intensity differences in the low- and high-frequency Rb ENDOR lines. The combined ENDOR and ELDOR results yield a variety of interesting information on the structure of the Rb complex. From the ENDOR results the sign of the Rb hyperfine coupling could be deduced with high certainty to be positive [27]. —~.

K. Möbius eta!., Radicals in solution studied by ENDOR and TRIPLE resonance spectroscopy

195

5.3.3. Internal motions

So far we have only considered the rotational motion of the whole molecule as source of relaxation. However, there are also certain internal motions which might have the appropriate frequency spectrum to cause electron/nuclear relaxation and therefore influence the ENDOR linewidths and amplitudes. Such effects can also be analysed by our computer program. The most important of these effects is the modulation of isotropic hfc’s by internal motions [7,28], which is described by ~‘a(t) = a(t) S. I (see interaction number 5 in section 4). Such a relaxation mechanism causes a W,,, process which might become dominant and is then very efficient for the ENDOR enhancement (see fig. 4). This electron— nuclear flip-flop relaxation process influences the relative intensities of high- and low-frequency ENDOR lines in an opposite way as a dominant W,,2 process from the END interaction does. An illustrative example is provided by the cyclohexyl substituted phenoxyl radical which has been described by Atherton and Day [28]. 6. Applications to problems of chemical and biological interest Typical applications of solution ENDOR and TRIPLE resonance in chemistry and biology cover as diverse subjects as for instance hyperfine structure of low symmetry radicals [10], structures, and geometries of radicals [29]; chemical reaction products (solvent substitutions [30], radical rearrangements [31,32], electron/proton transfer [26],and dimerization [26]);test of MO theories (spin density distributions [10,38], IT — U delocalization [33], lifting of orbital degeneracies by substitution [34]), coherence effects in multiresonance experiments [16c,35]; studies of internal dynamics like hindered rotation [36,37], ion pairing [15,38], and chemical exchange [39]; ligand hyperfine structure in metal complexes [20]; radicals in liquid crystals, e.g. for determining quadrupole couplings [40,41]; biologically important quinones [42], flavins [43], and photosynthetic pigments [44]; and polyradicals [6], e.g. biradicals [5]. From this variety of applications we have chosen a number of examples which are illustrative to demonstrate the power of the methods. It should be pointed out, however, that despite the efficiency of the multiresonance methods in determining hyperfine couplings, ambiguities remain in the assignment of these hfc’s to particular molecular positions. The first example will illustrate this point. Such problems can ultimately only be solved by chemical assistance, like specific isotopic labelling. —

6.1. Hyperfine structure of low-symmetry radicals ENDOR and TRIPLE methods were applied to a series of 3 radicals, the 2-, 3-, and 4-pyridyl-phenyl ketone anions (2-, 3-, and 4-PPK, see fig. 20) in order to unravel their complex hyperfine structure [13]. The radical anions were generated by sodium reduction in 1,2-dimethoxyethane (DME). The ESR spectra of these systems are extremely difficult to interpret. However, ‘H-ENDOR yields well resolved spectra, the extracted hfc’s are collected in table 2 together with their signs, which were determined by general TRIPLE experiments. From symmetry considerations, a maximum number of 9 proton hfc’s is expected for each radical. Since only 6 to 7 ENDOR line pairs could be resolved, accidental equivalencies of hfc’s are present. These were easily determined by special TRIPLE resonance, the corresponding spectra are shown in fig. 20. The nitrogen ENDOR transitions are expected to appear at quite low frequencies. Nevertheless, they could also be measured, see table 2. It is well-known that benzophenone ketyl forms contact ion pairs with sodium in ethereal solutions [45]. We could indeed

196

K Möbius era!., Radicals in solution studied by ENDOR and TRIPLE resonance spectroscopy

2-PPK

I

I4~f~

3-PPK

ESR

3-PPK

exPerimental

J~J~i~N

~Tulate~~Ø~

~T~1~eN

0

5MHz

10

Fig. 20. Special TRIPLE resonance spectra of 2-, 3-, and 4-pyridyl phenyl ketyl (Na/DME) at 220, 240, 200 K, respectively (see table 2); the carrier frequency was set to p~= 14 Mlix, H, = 2)< 7.10,,,, C01fl pare fig. 6.

Fig. 21. Experimental and computer simulated ESR half spectrum of 2-PPK (see fig. 20) by using hfc’s and multiplicities given in table 2.

Table 2 Hyperfine data for 2-, 3- and 4-pyridyl phenyl ketyl (Na/DME)

nucleus

2-PPK’, 220K a, [MHzl

3-PPK~,240 K a, [MHzl

4-PPK~,200 K a, [MHzl

‘H ‘H ‘H ‘H ‘H ‘H

—0.92 (1) +1.65(2) +2.10 (1) —4.23(2) —5.21(2) —12.78(1)

+2.24(2) +2.77(1) —6.19(2) —6.78 (1) —7.96(1) —9.39(1) —12.61 (1) 2.24(1) 3.17(1)

0.08(1) +0.92(1) +1.71(2) —4.62(2) —5.66(1) —7.76(1) —9.03(1) 8.69(1) 1.26(1)

4N ‘ ~Na

—

7.90 (1) 1.54(1)

‘Hfc’s from ESR fits and ENDORJspecial TRIPLE, signs from general TRIPLE, the number of nuclei belonging to one hfc are given in brackets, it was derived from special TRIPLE and ESR simulations.

K. Mdbius eta!., Radicals in solution studied by ENDOR and TRIPLE resonance spectroscopy

197

detect the 23Na-ENDOR lines around ~23Na = 3.7 MHz for all three radicals, the corresponding hfc’s are also collected in table 2. Using the hfc’s for the protons, nitrogen, and sodium together with the number of contributing nuclei given in table 2, each ESR spectrum could be computer simulated in all details. As an example, the experimental and computed ESR half-spectrum of 2-PPK is shown in fig. 21. The ESR spectrum is composed of 2592 hyperfine lines, whereas the ENDOR only yields 6 proton line pairs, and one nitrogen and one sodium line pair in quite different frequency regions. Assignments of the hfc’s to molecular positions was attempted [13]on the basis of the ENDOR and TRIPLE data. The result was, however, not unambiguous in all cases. Furthermore, a comparison with MO calculations, e.g. of the INDO type, was even more hampered by the unknown twist angle of the two aromatic rings and, last not least, by the formation of a tight ion pair with the sodium counter ion. As is known from the literature [38,45] and will also be shown in this paper, ion pairing might result in a considerable alteration of hfc’s, especially for heteronuclei in the radical. Thus, unequivocal assignments will only be possible with the aid of selectively deuterated radicals.

6.2. ENDOR on organic radicals in liquid crystals Up to this point, we have only discussed ENDOR spectra of radicals dissolved in isotropic solution. In such solutions traceless parts of the static Hamiltonian, like the electron—nuclear-dipole and quadrupole interactions, are averaged out because of rapid molecular tumbling. The use of liquid crystals as anisotropic solvents can retain information about anisotropic interactions. In external fields of some kilogauss nematic solvents and solute molecules can be partially aligned along the field directions [461.As a consequence, line shifts and splittings occur when going from the isotropic to the nematic phase of the solvent. They depend on the degree of ordering achieved at a particular temperature and on the magnitude of the anisotropic interactions. The first determination of ‘4N quadrupole couplings in an organic radical was achieved by ENDOR in liquid crystals [40]. During the last few years a number of ENDOR studies in liquid crystals has been performed by two groups at Berlin [23,40, 41, 47]. As an example we review the first determination of deuterium quadrupole couplings in an organic radical [41]. The system studied was the partially deuterated perinaphthenyl radical (PNT) in the nematic liquid crystal “Phase IV” (Merck), see fig. 22. In the upper part of fig. 22 the ENDOR spectrum in the isotropic solution is depicted, showing pairs of proton and deuterium lines around ~H and i’D, respectively. When cooling the sample down into the nematic phase of the liquid crystal, the shift L~a= anem — a, 50 of the proton coupling can be used for measuring the temperature dependent degree of ordering of the PNT in the mesophase. For an axially symmetric molecular, like PNT, this shift is given by [41] z~a(T)=A2~O~2(T) where O~.and A0~are the components along the axis of highest symmetry of the traceless ordering and hyperfine tensors. If A00 is known, ~ can be determined, or vice versa. For nuclei with I > ~ it is now possible to determine components of the quadrupole tensor by ENDOR. For small quadrupole couplings, ENDOR is the only method of choice, since it is basically an NMR experiment. ESR is not suitable in this respect since, to first order, the quadrupole interaction shifts all levels equally which are connected by ESR transitions. In the lower part of fig. 22 the quadrupole splitting of the two low-frequency D-ENDOR lines of

198

K. Möbius eta!., Radicals in solution studied by ENDOR and TRIPLE resonance spectroscopy

0

//

5

\

6v

} I

0.75

0

10

15 MHz

5v0 onisotropic solution

I

085

I

1.65

1.75 MHz

Fig. 22. Top: D- and H-ENDOR spectrum of the partially deuterated perinaphthenyl radical shown in mineral oil (Shell Ondina 017) at 293 K. Bottom: Splitting S~of the two low-frequency D-ENDOR lines in the nematic phase IV (Merck) at 293 K caused by the quadrupole interaction under changed experimental conditions (compare refs. [321 and [411). On the right hand side the molecular axis system used isdepicted. The labels I and 2 refer to the symmetry equivalent molecular sites.

PNT in the nematic phase is shown. For both lines the splitting is 2q = ~000e 00QIh

&‘~=

42.2 kHz at 20°C.From [41]

the 2q component of the quadrupole coupling along the z-axis (fig. 22) could be determined to be e 000/h = —(94±3)kHz (0~~ = —(0.300±0.005) at 20°C [41]). The sign has been measured by TRIPLE-induced ESR [41].Assuming 2qCDQ/h = +188 kHz. an axially symmetric quadrupole tensor, its component along the C—D is eobtained for PNT was used to test the reliability of the semiempirical molecular orbital Thebond result method INDO in predicting electric field gradients in free radicals. The charge density matrix P for the whole molecule including off-diagonal elements was used in order to avoid additional approximations. The matrix of the field gradient operator was also fully calculated by including all multicenter integrals. This was achieved by using an expansion of the Slater orbitals employed in the INDO method into several (up to 6) Gaussian orbitals [48]. By this method, all integrals can be reduced to analytical expressions which are handled very fast by the computer. In an intermediate step, the INDO charge density matrix P had to be transformed back to the non-orthogonal basis by the Löwdin transformation S”2PS1’2 in which S is the overlap matrix. The computation yielded e2qCDQIh +289 kHz, ,~= 0.04, for the standard CD distance r~ = 1.08 A (+233 kHz, ~ = 0.04, for rco = 1.12 A) independent of the position of D in the molecule within ±2kHz. Although correct in sign and order of magnitude this value =

K Möbius eta!., Radicals in solution studied by ENDOR and TRIPLE resonance spectroscopy

199

differs from the experimental value of +188 kHz by 60%, showing that improved MO methods are definitely called for. Similar observations have been made in the case of nitrogen quadrupole couplings in triplet states [49].The independence of the calculated D quadrupole coupling of the position of D in the molecule with its strongly differing IT spin densities shows that the single unpaired electron has only little effect on the total electronic charge distribution in such large aromatic systems. This is consistent with the observation of very similar D quadrupole couplings found in singlet ground and excited ir triplet states of aromatic molecules [50,51]. By an unfortunate coincidence, the out-of-plane component of the D quadrupole tensor in planar ir systems, which is normally measured in nematic liquid crystals, has practically no contributions from the ir charge density at all, so that this component alone is not a very sensitive probe even of large changes in the ir charge density. In the meantime, Kurreck and collaborators succeeded in orienting the PNT system in liquid crystals with respect to a second axis by use of polar substituents like chlorine [52].For 2-chloro-PNT, for example, they determined e2qCDQ/h = 174 ± 10 kHz, ~ = 0.08 ±0.04. The same authors extended the ENDOR studies to smectic mesophases [23,47, 52, 53] and showed that even ion radicals can be dissolved and oriented in liquid crystals with the aid of crown ether complexation [54]. 6.3. Hindered rotation of molecular fragments Hindered rotation of molecular fragments in organic radicals has been paid much attention to in ENDOR spectroscopy [7,29, 36, 37, 42]. As a representative example we choose the ortho-tetraphenyl radical anion [36]. Fig. 23 (left) shows ENDOR spectra of this system at different temperatures. The fast jump Av,.6v,~/4k~

VH

—

-t’—-.J”--..N’--.

—

I

240 1< 220 210

coalescence point”

200

\fl

ôvo 0~c,.-k

190

T

180

~/7’\,/”\\~V

160 K

slow jump

~vo.2k,

I

6 •oo exchange

11

J’1’\._

1111111

1

15

:::

2 ~

/~1~vOkTrO

20MHz

Fig. 23. Left: H-ENDOR spectra of ortho-terphenyl radical anion at different temperatures, the marks 0 and x refer to those lines which are influenced by hindered rotation. Right: This side shows the equations governing the different regions of exchange (“two-jump process”) and the corresponding behaviour of the spectral lines. Ai.5 and ~v are the unperturbed and perturbed linewidths, respectively; the temperature dependent exchange rate kT increases from bottom to top.

200

K Möbius eta!., Radicals in solution studied byENDOR and TRIPLE resonance specrroscopy

analysis of the corresponding ESR spectra is very difficult, while ENDOR directly yields the desired information, i.e. the temperature dependence of particular line positions (marked by 0, x): Two pairs of lines obviously show a temperature behaviour characteristic for nuclear spins jumping between magnetically inequivalent sites. This jump process is attributed to hindered rotation of the two ortho-phenyl rings. At sufficiently low temperatures this results in an inequivalency of the respective ortho and meta protons of these rings. In fig. 23 (right) the basic equations for describing the different ranges of a two-jump process are given. In the slow-jump region, for example, the rate constant k~of this process can be determined from the separation öv of the two ENDOR lines. The whole range can be handled by using modified Bloch equations for the line shape analysis [55].From the Arrhenius plot ln kT f(1/T) the activation energy Ea and the pre-exponential factor k0 is available according to =

kT =

k0exp(—E,/kT).

For the ortho-tetraphenyl anion, Ea = 0.286 ±3% eV and k0 10u2205) s’ were determined. The Ea value could be interpreted as the molecular potential barrier for the hindered rotation [36]. From a comparison with MO calculations and assuming a fully correlated jump of the 2 phenyl rings, an equilibrium phenyl twist angle of 65° was obtained. Using this angle, reasonable agreement of experimental and calculated hfc data was achieved. 6.4. ENDOR on ion pairs As was already mentioned in section 2 (fig. 10), ENDOR signals could be detected also from alkali counterions which are in close contact with anion radicals. Fig. 24 shows ENDOR spectra of fluorenone ketyl with different alkali cations in DME. Besides the 4 pairs of proton lines, expected from symmetry

V7L.

VH

~

V133c

7’~j~l2

~e1~

I

5MHz

10

15

20

Fig. 24. Alkali- and H-ENDOR spectra of fluorenone ketyl at 200K in DME generated with different alkali metals, see ref. [381.

K. Möbius~eta!., Radicals in solution studied by ENDOR and TRIPLE resonance spectroscopy

201

considerations, alkali line pairs show up around the respective Larmor frequencies. ENDOR and TRIPLE experiments make it possible to study ion pairs in greater detail than by ESR, e.g. their structure, dynamics, and equilibria as function of counterion, solvent, and temperature. In this respect, we were interested to see how far the spin density distribution in the fluorenone radical anion is affected by the counterion and/or solvent. In table 3 the complete set of hfc data (1H, alkali, carbonyl-13C and -‘TO) is given, demonstrating that there exist systematic changes of all hfc’s with the type of counterion. These changes show certain regularities which are best reflected in diagrams correlating hfc’s or spin densities with intrinsic properties of the alkali ions, such as electron affinities or reciprocal radii (figs. 12 to 15 in ref. [38]). The final result is that all counterions form contact ion pairs, the electrostatic interaction with the alkali ion determining all the details of the spin density redistribution in the anion. The temperature dependence of all hfc data [38] indicates that in ethereal solvents even at 300 K no conversion into “solvated ion pairs” or “free ions” occurs. Such species can, however, be observed in the solvent HMPA (hexamethyl-phosphortriamid) [38].

Table 3 Experimental hyperfine couplings in MHz for fluorenone ketyl in DME with different counterions at 200 K ‘H 1,8

‘H 2,7

‘H 3,6

‘H 4,5

‘3C 9

‘~O 10

+0.60 +0.37 +0.26 +0.22

—9.03 —8.88 —8.80 —8.77

+1.93 +1.87 +1.85 +1.84

+15.98 +12.41 +11.14 + 10.67

—24.17 —25.18 —25.52 —25.71

—0.37 +0.15

85pj~~Rb

—6.36 —5.93 —5.75 —5.68

‘33Cs TBA’

—5.65 —5.54

+0.20 <+0.1

—8.74 —8.73

+1.83 +1.81

+10.31 +8.42

—25.77 —26.51

+0.23

counterion 6Li ~Na

nucleus pos.

metal

(±

+0.09, +0.22 004)b —

All data taken from ENDOR except those for ‘~owhich are taken from ESR; sign information obtained from general TRIPLE (‘H, metal) or ESR linewidth effects (‘3C, ‘TO). ‘3C- and ‘70-data were measured on compounds which were isotopically enriched in the carbonyl group [38].For the position numbering see fig. 24. ‘TEA: tetra-n-butylammonium cation (electrolytic reduction). b This value was deduced from a diagram correlating metal spin densities and cation electron affinities [38].

In order to get a better insight into the structure of the ion pairs, INDO calculations were performed on the Li-fluorenone ketyl. The best agreement with experiment was achieved for a Li position 2.18 A above the carbonyl group (see fig. 25). However, we have been unable to reproduce consistently the temperature dependence of the complete set of hfc’s by altering the Li position. This led us to introduce one solvent molecule (DME) explicitly into the calculation. In table 4 the experimental hfc’s for 300 K and 200 K are given (note sign change of 7Li hfc, which has directly been determined by general TRIPLE, compare fig. 10). These data are consistent with the following model: at high temperatures, the solvation is less pronounced, the complex is described by the calculation of Li-fluorenone; at low temperature the DME is chelating the counterion and the complex is described by the Li-fluorenoneDME calculation. In this model, the relative changes ~a/IaI of all hfc’s including their signs are satisfactorily reproduced. Concluding this part, we want to mention that the investigation of ion pairs is not only of academic interest. The existence of such species in many ionic reactions influence the reaction time, the yield, and sometimes even the direction and stereochemistry of the specific chemical reaction.

202

K. Möbius er al., Radicals in solution studied by ENDOR and TRIPLE resonance spectroscopy

:A

9.:

F LUO RE NONE

Fig. 25. View of the geometry used in the calculation of the Li-fluorenone ion pair including one solvent (DME) molecule; for details see ref. [38].

Table 4 Comparison between experimental and calculated hfc’s in MHz for Li-fluorenone ketyl in DME Experiment

INDO calculation

nucleus

pos.

300K

200K

i~a/~aanI’ Li-Fl’

Li-Fl/DME’

~a/Pau.piJ’

‘H ‘H ‘H ‘H

1,8 2,7 3,6 4,5 9 10

—6.50 +0.73 —8.97 +1.88 +17.81 —23.45 +0.20

—6.36 +0.60 —9.30 +1.93 +15.98 —24.17 —0.37

—0.02 +0.18 +0.04 —0.03 +0.10 +0.03 +2.85

—4.66 +1.95 —5.34 +2.73 +14.91 —32.10 —1.20 -0.006

—0.01 +0.06 +0.03 —0.02 +0.16 +0.10 +2.10

‘3c ‘~o 7Li ‘H

—4.69 +2.08 —5.18 +2.67 +17.67 —29.28

+0.32

(J)~4E)d

‘Calculated for Li-fluorenone (Li-Fl) using the same coordinates as in fig. 25. b Li-Fl with one DME solvent molecule, for coordinates see fig. 25. ‘Shift of hfc’s relative to the high temperature situations (see text). d largest ‘H-hfc of the solvent (methyl groups).

6.5. Biochemical and biophysical applications In the last decade ENDOR has found increasing interest also in the fields of biophysics and biochemistry. Most of these studies have been performed at low temperatures (100 K—2 K) in the solid state, dealing with paramagnetic species of photosynthetic pigments [44,56, 57], flavoproteins [58], cobalamin [59],hemoglobin, and other metallo proteins [60].However, it is clearly desirable to study biological systems at physiological conditions, i.e. in their natural environments in water at room temperature. This implies that ENDOR-in-solution techniques should be applied to biomolecular systems. This might be extremely difficult when transition metal ions are involved [20]. There exist, however, a large variety of biologically important metallo porphyrins, quinones, and hetero aromatic molecules whose oxidized or reduced species essentially behave like organic IT radicals. For them ENDOR-in-solution is feasible; and we restrict ourselves to the discussion of such species. The examples chosen are flavins and photosynthetic pigments.

K. Möbius et aL, Radicals in solution studied byENDOR and TRIPLE resonance spectroscopy

203

6.5.1. ENDOR on radicals derivedfrom flavins It is a well-known fact that paramagnetic species are involved in biocatalysis mediated by flavoenzymes [61].Such flavin radicals play a vital role in mitochondrial respiration and in a variety of other biological redox processes [62].In the past, the application of ENDOR experiments has been restricted to solid state work, yielding hfc data only for methyl groups [58]. Recently, Kurreck and coworkers started to investigate flavin radicals by ENDOR-in-solution. Proton and nitrogen ENDOR transitions could be detected from which hfc’s including their signs (from general TRIPLE) were determined for a variety of cationic, anionic, and neutral flavin radicals [43]. As an example, the ENDOR spectrum of the riboflavin (vitamin B2) radical cation is presented in fig. 26. Since there is almost no spin density in the pyrimidyl part of flavin radicals, the detected 6 proton5 and nitrogen representin the complete 4N (positions and2 10), and hfc’s the protons a-(6, 9) and set of couplings which are expected for ‘ f3-position (7, 8, 10) to the ir-electron delocalization pathway. CH 2OH ICHOHI3

toluene/CF3COOHINO2S2O4 ,260 K

CM2 H

0N 1“2 N2

1‘2

1

A

VH

CH3~~.~_MyN~o CH3~N~~y~

~

H

Rad~aICation of I

Riboflavin

I

I

I I

I

I

I

I

I

I

I

I

I

I

I

I

I

IVitomin B2)

I

I

3 6 9 12 15 18 21 24 27 MHz 4N- and H-ENDOR spectrum of the riboflavin radical cation at 265 K (CF Fig. 26. ‘ 3COOH/toluene, sodium dithionite reduction); for further details see ref. [43].

6.5.2. ENDOR on radical ions of photosynthetic pigments Photosynthesis in green plants and photosynthetic bacteria demands the presence of chlorophylls (Chl) or bacteriochlorophylls (BCh1) (fig. 27). The majority of these species function as light harvesting pigments and only few of them are involved in primary photochemistry. In photosynthesis, the incident light photons are funneled to a “reaction centre” where the light-induced charge separation occurs [63]. This results in the formation of cation and anion radicals of the tetrapyrrole pigments, followed by fast electron transfer to secondary acceptors, and the generation of a membrane potential by which the subsequent biochemical reactions are driven. In purple bacteria, which use only one photosystem, the primary donor is believed to be a “special pair” of BCh1 molecules, whereas the array of electron acceptors involves bacteriopheophytin (BPh), the free base of BChI, eventually monomeric BChl (“voyeur”), an iron quinone complex, quinone (0)

204

K Möbius et aL, Radicals in solution studied by ENDOR and TRIPLE resonance spectroscopy

H\

2b

O6~~...CH3

CH ~

H_Cr

~H

4b~3

2b

j

H

0

H3C ~

30CH3

C H2

H3d

)~._N\ ,.N~ Hi

i~ N

~

)__N\

p—H

,~

N ~\

H3C~”.. 8 IV17~

H—<~ 8o

CH3

i1611~)

H3C&.

H~’ V HC~CH2O2~~!oO

R

Ig

1V17

N

~‘~‘~)

H”~’ ~

CH ,

~

i~ 8

,l~1:~

N

~ 0~

/

R

lOb

Bacteriochiorophyll a

i~\

CH3

V

HC__CH2 °2~1Oa

0t

I

1H3

Oi

,03 CH lOb

Ch Iorophy(l a

Fig. 27. Molecular structures of bacteriochlorophyll a (BChl a) and chlorophyll a (Chi a). The aliphatic side chain usually is phytyl (C~H~), some bacteria have geranyl geranyl (C~H 33),see ref. [441.

and finally a “quinone pool”: —3ps

(BChl)~~

—200ps )

BPh(BCh1)

)

—O.lms

QaF~

> Qb

Q-pool.

In green plants and algae two photosystems are involved. In photosystem 1 the electron is donated from a monomeric Chl species to an intermediate acceptor, which is believed to be monomeric Chl, and then to iron-sulfur-proteins. The constitution of the primary donor in photosystem 2, monomeric or dimeric Chi, is still under discussion, the sequence of electron acceptors involves pheophytin Ph and different quinones [64]. In the past 10 years a large amount of our knowledge about these paramagnetic species, in vitro or in vivo, has been deduced from ESR and from ENDOR with its much higher resolution [44a]. Highly relevant work has been performed in particular by the groups of Feher [56], Norris [57],and Fajer [44b]. Recently, it has been demonstrated in this laboratory that for protons and nitrogens an almost complete set of hfc’s, including their signs, can be determined by applying ENDOR and TRIPLE resonance to the in vitro prepared radical cation of BChl a [65]and [66],and 4N andthe 1Hradical nuclei anions in BChlof aBChI andaBPh a is BPh a [67].An example of the type of spectra obtained for ‘ given in fig. 28. Although the ESR spectra are very similar, a distinction of these species is clearly possible by their ENDOR and TRIPLE spectra. A first assignment of hfc’s to molecular positions was achieved by the signs of hfc’s (from general TRIPLE), relative signal intensities (from special TRIPLE), simulations of ESR spectra, and specific relaxation behaviour of the different types of protons in the system [66, 67]. For all the species studied, very recent ab initio calculations are available from Petke et

K Möbius et aL, Radicals in solution studied by ENDOR and TRIPLE resonance spectroscopy

14N-ENDOR

205

‘H-Special TRIPLE ESR

l/2QN2~

g.20032

::

I

I

I

I

I

1

2

3

4

5MHz

III

0 1 2 3

II

1.

5MHz

Fig. 28. ESR (293 K), ‘4N-ENDOR (280 K), and H-Special TRIPLE spectra (255K) from BChl a and BPh a anion radical. For further details see refs. [661and [67].

at. [68].A comparison between calculated and experimental hfc’s strongly supports the above assignment and, even quantitatively, often yields satisfying agreement. We are currently studying the anion and cation radical of Chl a [69]where proton and nitrogen couplings including signs could be detected. All this work performed on the in vitro pigment radicals will help to identify the in vivo systems. Furthermore, it should be possible to detect structure and local geometry alterations which are caused by the environment (proteins, neighbouring pigments, and membranes). In the past, ENDOR investigations of oxidized and illuminated intact photosynthetic entities, like whole cells, chromatophores, and reaction centres, have been restricted to frozen solutions at low temperatures [44,56, 57]. In such spectra dipolar broadening mostly prevents the detection of hfc’s other than those from methyl protons. Nevertheless, these investigations strongly supported the “special pair” model for the primary donor, which was originally proposed from ESR data [57].One disadvantage of these measurements lies in the unknown effect of sample freezing on the protein structure which contains the photosynthetic pigments. In cooperation with H. Scheer (München) we have very recently performed an ENDOR experiment on the in situ light-induced radical cation of the primary donor in reaction centre/LDAO (lauryldimethylaminoxid) preparations of Rp. sphaeroides R-26 in water at 25°C[70]. The reversible appearance of the ESR signal (fig. 29) is accompanied by the bleaching of the band at 870 nm, which has been checked by optical spectroscopy. The ENDOR and general and special TRIPLE spectra are shown in fig. 29. They are identical with those obtained by chemical oxidation of reaction centres. Seven proton hfc’s could be deduced, all of them being positive. A comparison with those obtained from the monomeric BCh1 a cation [65]shows that the signs of the hfc’s are the same, but their magnitudes are —

206

K. Möbius eta!., Radicals in solution studied by ENDOR and TRIPLE resonance spectroscopy

7~EJ~fl II

800

~25I

~AL •234~6

/.OOnm

0

2

1

A

7

6MHz B

Reaction centres Rp, sphaeroides R-26 illuminated in situ

‘“~\\ I

I

5

H

2o/ 25°C

~pumped

A

Special TRIPLE ~

B

ENDOR

C General TRIPLE

C

~ V + +

I

8

I

+~j++++ I

12

I

I

16

I

20MHz

Fig. 29. H-Special TRIPLE, ENDOR, and General TRIPLE spectra of the light-induced cation of the primary electron donor in reaction centres of Rp. sphaeroidesR-26 (°°3 x iO~M, 0.01 MTris buffer, pH 7.5, 0.1% LDAO) at 25°C.The ESR and part of the VIS spectrum (dark and actinic light) are shown as insert. For details refer to ref. [70].

reduced in the in vivo system. However, the hfc’s are not scaled down by a constant factor of 2 as proclaimed in the first order “special pair” model for the primary donor cation. These data indicate that the special pair structure might be more complicated than hitherto assumed. We are currently trying to assign the hfc’s to molecular positions by studying selectively deuterated reaction centres.

7. Concluding remarks In this article we have tried to demonstrate the great diversity of possible applications of multiple electron resonance spectroscopy in the fields of physics, chemistry, and biology. By the recent extension of ENDOR to electron—nuclear—nuclear TRIPLE resonance significant progress has been made with regard to spectral resolution, sensitivity, and sign information of hyperfine interaction parameters, thus improving the elucidation of the electronic structure of complex molecular systems. This has become particularly evident in the case of biomolecules. Viewing the ENDOR literature of recent years, one can firmly state that electron—nuclear-multiple resonance in solution is a strongly expanding field. Besides protons a large number of other nuclei has become accessible, and further nuclei will undoubtedly serve as probes in ENDOR spectroscopy in the future. Admittedly, ENDOR requires an intricate multi-parameter adjustment for its optimization in particular for nuclei other than protons.

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Fortunately, however, the theory of multiple electron resonance in solution is so highly developed by now that this problem can be approached in a systematic manner by employing only a small number of fundamental molecular and solvent properties.

Acknowledgements The authors are grateful to the following collaborators who have contributed to the completion of this article: F. Lendzian (this laboratory) built the version of the spectrometer described in section 3 and collaborated in the photosynthesis experiments; K. Heumos (this laboratory) investigated the pyridylphenyl ketyls; Dr. A.J. Hoff (University of Leiden) and Dr. H. Scheer (University of Munich) participated in the in vitro and in vivo experiments on the chlorophylls. Skilfull synthetic work on isotopically labelled compounds was performed by Dr. H. Kurreck and his coworkers (Free University of Berlin) and H. Zimmermann (Max-Planck-Institut, Heidelberg). We also acknowledge competent assistance of the following colleagues of this institute: J. Claus and W. Schmidt who built the multiple resonance cavities, Mrs. B. Rottger and H. Seidel who prepared the numerous drawings, and Mrs. H. Reeck who typed the manuscript in its different stages of development. Financial support by the Deutsche Forschungsgemeinschaft (5th 161) is gratefully acknowledged.

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