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4 Different Stages of Cycloaddition/Cycloreversion Reactions Within Confined Environments

4 Different Stages of Cycloaddition/Cycloreversion Reactions Within Confined Environments

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152



UNUSUAL STRUCTURES OF RADICAL IONS IN CARBON SKELETONS



FIGURE 7.11 A schematic representation of 4c–3e system geometries established within

hydrocarbon cages.



7.5 EXTENDING THE “CAGE CONCEPT”

In the above sections, it was shown that restricted carbon cages lead to unusual

structures of one-electron oxidized stages. This concept is extendable to molecular

skeletons comprising heteroatoms.

For, example, joining azo groups into are rigid carbon polycycle, such as in bis

(diazenes) N1 and N2. These proximate, parallel in-plane preoriented bis(diazenes)

were synthesized by the Prinzbach group are candidates for lacking N¼N/N¼N

photocycloadditions. The p–p distances (d) are equal to approximately 280 pm and the

nitrogen lone pairs are unable to interact because of steric reasons. On the other hand,

an efficient overlap of the pz orbitals is enforced.



153



EXTENDING THE “CAGE CONCEPT”



FIGURE 7.12 A schematic view of the “through-space” delocalization (as established for

N1 À and N2 À) and a scheme for a 4N/5e bonding. Only the interaction of the antibonding porbitals is displayed.

.



.



Oxidation of N1 and N2 cannot be established. However, one-electron reduction is

feasible in a straightforward way. Exposure with alkali-metal mirrors in THF or

dimethoxyethane under super dry conditions allows the detection of EPR spectra

attributable to the radical anions N1 À and N2 À. The 15 N hfc values of the pairwise

equivalent nitrogen nuclei are 0.420/0.394 and 0.430/0.340 mT, respectively. This is

approximately half the size of the corresponding values of (mono) diazenes and

reveals that the spin is (almost) evenly distributed between the virtually equivalent

nitrogen centers.

Are N1 À and N2 À really “through-space” delocalized radical anions as illustrated

in Fig. 7.12? A rather clear indication can be derived from the conspicuously large 1 H

hfc values of the g protons in N1 À and N2 À of 0.625 and 0.842 mT. This size can

only be rationalized by a dominating electron density between the formally nonbonded

diazene units and is in perfect agreement with density functional theory calculations.

In summary, the specific arrangement of the two diazene moieties allows an in-plane

delocalization of five (in-plane) p electrons within four almost coplanar nitrogen centers

(4N/5e bonding). This type of stabilization can even be extended to the corresponding

dianions (4N/6e bonding), which are remarkably persistent and can be characterized by

NMR spectroscopy. The unusual feature of these bonds is the fact that they are formed

by the interaction of antibonding pà orbitals (Fig. 7.12). The confinement of the

additional charge(s) to only four atoms causes intense ion pairing.31,32

.



.



.



.



.



.



154



UNUSUAL STRUCTURES OF RADICAL IONS IN CARBON SKELETONS



Oxidation of the four N atoms in N1 leads to trinitroxide NO1 and tetranitroxide

NO2. By comparison with spectra of the bis(nitroxide) radical cation, NO3 ỵ , it could

be concluded that in NO2 ỵ , a radical cation comprising all four NO moieties is

formed. This can be anticipated from the EPR spectrum (narrow, g factor ¼ 2.0061)

and the substantially lower oxidation potential of NO2 (1.37 V versus Ag/AgCl) in

comparison to NO1 and NO3 (1.65 V versus Ag/AgCl, both).; moreover, a characteristic absorption at 1020 nm was found for NO2 ỵ .33

.



.



.



Structurally related to bis(diazene) N2 are tetrazolidine N3 and N4, caged,

proximate syn periplanar bishydrazines. Their oxidation led to novel highly persistent

4N/7e radical cations with dominant electron delocalization along the cage bonds

mirrored by virtually identical EPR spectra dominated by a splitting by 4 equivalent

nitrogen nuclei with a 14 N hfc of 0.98 mT.34 A closely related 4c/7e bonding situation

was established in 1,3,6,8-tetraazatricyclo[4.4.1.13,8]dodecane (TTD). In TTD,

however, the nitrogen atoms are embedded in a more flexible skeleton and undergo

a more pronounced planarization upon oxidation. This leads to an attenuated s

character at the nitrogen centers and, consequently, a distinct decrease of the 14 N hfc

values (4 equivalent N atoms) to 0.343 mT.35



7.6 SUMMARY

Unusually persistent remarkable open-shell structures were discovered upon oneelectron oxidation/reduction of C4 and N4 fragments embedded into rigid carbon

skeletons. The thus generated radical ions reveal “electron deficient bonding.”

For pagodane-related carbon skeletons 4C/3e radical cations with “tight” and

“extended” geometries could be established by spectroscopy (predominately EPR)

and quantum chemical calculations at the DFT level of theory. Such structures

resemble frozen stages of cycloadditions/cycloreversions on the hyper energy surface

of the hole-catalyzed cyclobutane formation.

Related unusual electron deficient bonds formed by the interaction of nonbonding

orbitals (4N/5e, 4N/7e) can also be established between azo, nitroxide, and amino

groups when they are appropriately arranged within a rather rigid molecular

framework.



REFERENCES



155



ACKNOWLEDGMENTS

The author thanks Professor Horst Prinzbach (University of Freiburg) for a longstanding very fruitful collaboration, a lot of fun, many beautiful molecules that we

have been investigating over the past 25 years and his suggestions for the manuscript.

The author is indebted to Professors Stephen Nelsen (Madison,Wisconsin) and Fred

Brouver (Amsterdam) for the joint investigations on TTD. The author also appreciates

the help of Professor Itzhak Bilkis (Hebrew University of Jerusalem) for his comments, and of Markus Griesser and Arnulf Rosspeintner (both Graz) for their keen eyes

for details.

REFERENCES

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Chem. B 2008, 112, 10045–10053.

3. Kirste, B.; Alder, R. W.; Sessions, R. B.; Bock, M.; Kurreck, H.; Nelsen, S. F. J. Am. Chem.

Soc. 1985, 107, 2635–2640.

4. Alder, R. W.; Sessions, R. B.; Symons, M. C. R. J. Chem. Res. Synop. 1981, 82–83.

5. Nelsen, S. F.; Alder, R. W.; Sessions, R. B.; Asmus, K. D.; Hiller, K. O.; Goebl, M. J. Am.

Chem. Soc. 1980, 102, 1429–1430.

6. Alder, R. W.; Sessions, R. B. J. Am. Chem. Soc. 1979, 101, 3651–3652.

7. Fourre, I.; Berges, J.; Braida, B.; Houee-Levin, C. Chem. Phys. Lett. 2008, 467,

164–169.

8. Joshi, R.; Ghanty, T. K.; Naumov, S.; Mukherjee, T. J. Phys. Chem. A 2007, 111,

2362–2367.

9. Asmus, K.-D. Nukleonika 2000, 45, 3–10.

10. Kishore, K.; Asmus, K. D. J. Phys. Chem. 1991, 95, 7233–7239.

11. Badger, B.; Brocklehurst, B. Trans. Faraday Soc. 1969, 65, 2582–2587.

12. Batsanov, A. S.; John, D. E.; Bryce, M. R.; Howard, J. A. K. Adv. Mater. 1998, 10,

1360–1363.

13. Fujitsuka, M.; Cho Dae, W.; Tojo, S.; Yamashiro, S.; Shinmyozu, T.; Majima, T. J Phys

Chem A 2006, 110, 5735–5739.

14. Ohya-Nishiguchi, H.; Terahara, A.; Hirota, N.; Sakata, Y.; Misumi, S. Bull. Chem. Soc. Jpn.

1982, 55, 1782–1789.

15. Roth, H. D.; Schilling, M. L. M.; Hutton, R. S.; Truesdale, E. A. J. Am. Chem. Soc. 1983,

105, 153–157.

16. Gerson, F. Acc. Chem. Res. 1994, 27, 63–69.

17. Knolle, W.; Janovsky, I.; Naumov, S.; Williams, F. J. Phys. Chem. A 2006, 110,

13816–13826.

18. Rideout, J.; Symons, M. C. R.; Swarts, S.; Besler, B.; Sevilla, M. D. J. Phys. Chem. 1985,

89, 5251–5255.

19. Roth, H. D. Electron Transfer in Chemistry; Balzani, V.,Ed.; Wiley-VCH, Weinheim,

2001; Vol 2, 55–132.



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UNUSUAL STRUCTURES OF RADICAL IONS IN CARBON SKELETONS



20. Garcia, H.; Roth, H. D. Chem. Rev. 2002, 102, 3947–4007.

21. Heller, C.; McConnell, H. M. J. Chem. Phys. 1960, 32, 1535.

22. Prinzbach, H.; Gescheidt, G.; Martin, H. D.; Herges, R.; Heinze, J.; Surya Prakash, G. K.;

Olah, G. A. Pure Appl. Chem. 1995, 67, 673–682.

23. Trifunac, A. D.; Werst, D. W.; Herges, R.; Neumann, H.; Prinzbach, H.; Etzkorn, M. J. Am.

Chem. Soc. 1996, 118, 9444–9445.

24. Wollenweber, M.; Etzkorn, M.; Reinbold, J.; Wahl, F.; Voss, T.; Melder, J.-P.; Grund, C.;

Pinkos, R.; Hunkler, D.; Keller, M.; Worth, J.; Knothe, L.; Prinzbach, H. Eur. J. Org. Chem.

2000, 3855–3886.

25. Gescheidt, G.; Herges, R.; Neumann, H.; Heinze, J.; Wollenweber, M.; Etzkorn, M.;

Prinzbach, H. Angew. Chem., Int. Ed. 1995, 34, 1016–1019.

26. Weber, K.; Prinzbach, H.; Schmidin, R.; Gerson, F.; Gescheidt, G. Angew. Chem., Int. Ed

1993, 32, 875–877.

27. Prinzbach, H.; Reinbold, J.; Bertau, M.; Voss, T.; Martin, H.-D.; Mayer, B.; Heinze, J.;

Neschchadin, D.; Gescheidt, G.; Prakash, G. K. S.; Olah, G. A. Angew. Chem., Int. Ed.

2001, 40, 911–914.

28. Fagnoni, M.; Dondi, D.; Ravelli, D.; Albini, A. Chem. Rev. 2007, 107, 2725–2756.

29. Etzkorn, M.; Wahl, F.; Keller, M.; Prinzbach, H.; Barbosa, F.; Peron, V.; Gescheidt, G.;

Heinze, J.; Herges, R. J. Org. Chem. 1998, 63, 6080–6081.

30. Gescheidt, G.; Prinzbach, H.; Davies, A. G.; Herges, R. Acta Chem. Scand. 1997, 51,

174–180.

31. Exner, K.; Hunkler, D.; Gescheidt, G.; Prinzbach, H. Angew. Chem., Int. Ed. 1998, 37,

1910–1913.

32. Exner, K.; Cullmann, O.; Voegtle, M.; Prinzbach, H.; Grossmann, B.; Heinze, J.; Liesum,

L.; Bachmann, R.; Schweiger, A.; Gescheidt, G. J. Am Chem Soc. 2000, 122,

10650–10660.

33. Exner, K.; Prinzbach, H.; Gescheidt, G.; Grossmann, B.; Heinze, J. J. Am. Chem. Soc.

1999, 121, 1964–1965.

34. Exner, K.; Gescheidt, G.; Grossmann, B.; Heinze, J.; Bednarek, P.; Bally, T.; Prinzbach, H.

Tetrahedron Lett. 2000, 41, 9595–9600.

35. Zwier, J. M.; Brouwer, A. M.; Keszthelyi, T.; Balakrishnan, G.; Offersgaard, J. F.;

Wilbrandt, R.; Barbosa, F.; Buser, U.; Amaudrut, J.; Gescheidt, G.; Nelsen, S. F.;

Little, C. D. J. Am Chem. Soc. 2002, 124, 159–167.



8

MAGNETIC FIELD EFFECTS ON

RADICAL PAIRS IN HOMOGENEOUS

SOLUTION

JONATHAN. R. WOODWARD

Chemical Resources Laboratory, Tokyo Institute of Technology, Midori-ku, Yokohama, Japan



8.1 INTRODUCTION

The idea that the application of a magnetic field might alter the course of a chemical

reaction is a tantalizing one that was, however, considered by physicists for a long time

to be unlikely due to the very small magnitude of the interaction of molecules with

magnetic fields relative to the thermal energy and typical reaction barriers of most

reactions. However, the development of the radical pair mechanism (RPM) in the

1960s1–3 led to the prediction that chemical reactions proceeding through radical pair

(RP) intermediates might show sensitivity to externally applied magnetic fields. The

first experimental verifications of this prediction followed in the 1970s. Buchachenko

et al. demonstrated a magnetic field effect (MFE) on the reaction of substituted benzyl

chlorides with n-butyl lithium,4,* and Brocklehurst et al. showed MFEs on the

fluorescence and absorption intensities in the pulse radiolysis of fluorene in squalene. 7

Research in this field flourished and soon overwhelming evidence was amassed

confirming that indeed both the rate and yield of RP reactions could be controlled by

the application of magnetic fields easily generated by common permanent and

Ã

This experiment was carefully repeated more recently by Hayashi et al., 5,6 who were unable to reproduce

the effect, although the experimental conditions varied slightly from the original work.



Carbon-Centered Free Radicals and Radical Cations, Edited by Malcolm D. E. Forbes

Copyright Ó 2010 John Wiley & Sons, Inc.



157



158



MAGNETIC FIELD EFFECTS ON RADICAL PAIRS IN HOMOGENEOUS SOLUTION



electromagnets. Alongside theoretical treatments,8–10 these experiments showed that

RP reactions show a complex dependence on magnetic field strength that could be used

to gain insight into the dynamic processes involved. A comprehensive and seminal

review of the first 15 years of MFE studies was written by Steiner and Ulrich11 and is

essential reading for those with an interest in this field.



8.2 THE SPIN-CORRELATED RADICAL PAIR

Central to the magnetic field sensitivity of chemical reactions is the spin-correlated

radical pair (SCRP).12,13 The creation of free radicals from neutral molecules requires

the separation of two electrons and thus always results in the formation of a pair of

radicals. Furthermore, the spin states of the unpaired electrons on the two radicals are

correlated and defined by the multiplicity of the precursor molecule (Fig. 8.1).

Typically, RPs generated in thermal reactions will be born from singlet-state (S)

precursors and thus are generated in a pure singlet state, whereas for photochemical

reactions, both singlet and triplet (T) RPs can be prepared. Generation of a triplet RP

represents an unusual chemical scenario. The excess energy supplied to generate the

original triplet molecule through absorption of a photon is rapidly removed from the

newly born RP through collisions with the surrounding solvent. This now leaves two

reactive radical species next to one another in solution, but unable to react together as

the spin states of the two electrons prevent them from entering the same molecular

orbital due to the restrictions imposed by the Pauli principle. As the first triplet excited

state of the molecule is usually energetically inaccessible, this means that for neutral

free radicals in solution, triplet-correlated RPs are nonreactive. For reaction to take

place between the two radicals, the RP must first undergo spin-state interconversion to



FIGURE 8.1 The formation and subsequent recombination of S and T RPs from closed shell,

neutral molecules with conservation of spin state. Examples of the three most common methods

of RP formation are illustrated.



THE SPIN-CORRELATED RADICAL PAIR



159



a singlet state. The key to the magnetic field sensitivity of RPs is that the process of

conversion of a triplet RP to and from a singlet one (referred to as S–T state mixing) is

driven by weak magnetic interactions in the radicals and can be influenced by the

presence of an external magnetic field.

8.2.1 Radical Pair Interactions

RP reactions have been found to be well described by the application of a spin

Hamiltonian,14 a common approach used in the field of magnetic resonance, which

reduces the full Hamiltonian to one that contains only spin-dependent terms. The

interactions capable of influencing spin-state mixing processes in RPs are concisely

introduced in the expression for the spin Hamiltonian of a RP, which can be written as a

sum of interradical, intraradical, and external interactions.

^ inter ỵ H

^ intra ỵ H

^ ext

^ RP ẳ H

H



8:1ị



The intraradical interactions provide the mechanism for coherent spin-state mixing

and the interradical interactions act contrary to this process.

The spin state of a given radical is commonly and simply described by a spin vector

operator

^ẳ^

Sy j ỵ ^

Sz k

8:2ị

S

Sx i þ ^

Where i, j, and k are unit vectors along the x, y, and z directions. The expectation value

of this operator is the electron spin magnetization vector, which describes the bulk

electron spin state for a given radical.

D E      

^ ẳ ^

Sy j ỵ ^Sz k

S

Sx i ỵ ^



8:3ị



8.2.2 Intraradical Interactions

Electrons possess the properties of charge and spin angular momentum and thus

possess a magnetic moment (e.g., Ref. 15 and references therein). This magnetic

moment is capable of interacting with other magnetic moments in its vicinity. For an

isolated free radical, the only other source of magnetic moments is those generated by

the nuclei in the molecule with nonzero spin quantum numbers. The coupling between

electron and nuclear magnetic moments is known as the hyperfine interaction15 and

has two components. The first is the direct, through-space dipolar interaction between

the electron and a given nucleus. This interaction is anisotropic and for radicals in a

homogeneous solution, rapid tumbling serves to average this interaction to zero. An

isotropic interaction between electron and nuclear magnetic moments exists only

when the electron penetrates inside a nucleus. This is only possible for s-orbitals or

orbitals that possess some s-character. Being isotropic, it is not influenced by the

relative orientation of electron and nuclear spins. It is usually written as

^ Á ^Ii

^ hfi ¼ ai S

H



ð8:4Þ



160



MAGNETIC FIELD EFFECTS ON RADICAL PAIRS IN HOMOGENEOUS SOLUTION



where ai is the isotropic hyperfine coupling constant (HFC) for the interaction between

electron spin S and nuclear spin Ii. Thus, for the RP, we must consider the total set of

electron–nuclear spin interactions for each electron (i.e., one on each radical, labeled 1

and 2) with all the nuclear spins in the given radical.

^ intra ẳ

H



X

i



^1 ^I1i ỵ

ai S



X



^2 ^I2i

ak S



ð8:5Þ



k



Unlike a free electron, an electron in a molecule also experiences a complex

interaction between spin and orbital angular momentum, spin–orbit coupling.

These interactions are described in terms of a tensor, g.15,16 EPR spectroscopy is

the most common method for determining g-tensors. Indeed, g-tensor analysis in

complex biomolecules can give important orientational information on paramagnetic centers.16,17 For radicals free to tumble in isotropic solution, the EPR

spectra reveal a reduction to an isotropic g-value. For typical small organic free

radicals, this g-value is very similar to the value for a free electron (ge ¼ 2.0023)

but can differ much more substantially (0–6) for species such as transition metal

ions.

8.2.3 Interradical Interactions

The Hamiltonian for interradical interactions can be decomposed into two terms

corresponding to the electron exchange interaction and the electron dipolar interaction

^ inter ẳ H

^ exchange ỵ H

^D

H



8:6ị



The electron exchange interaction is critical to the magnetic field sensitivity of

reactions. It is a purely quantum mechanical effect arising from the fact that the

wavefunction of indistinguishable particles (in this case electrons) is subject to

exchange symmetry as defined by the Pauli principle. It results in an energy separation

between S and T RP states as the radicals approach close enough for the electrons to

become correlated and bonding begins to occur.

Figure 8.2a shows a diagrammatic representation of the orbital energies for a pair of

hydrogen atoms as a function of the separation of these two radicals. For separations of

greater than about 1 nm, the S and T states have equal energy, as the two electrons are

uncorrelated. For shorter distances, bonding can occur for the singlet state but not for

the triplet state. The energy separation between the two is the electron exchange

interaction and rises very rapidly for close RPs. At these short RP separations, the

exchange interaction dominates the spin Hamiltonian and serves to halt S–T state

mixing. This is significant because it means that when radicals approach one another

close enough to react, the ability to undergo spin-state interconversion is lost. Thus, for

a RP originally born in a triplet state, no interconversion to singlet, and thus no reaction

can occur until the radicals diffuse apart sufficiently that the exchange interaction no

longer swamps the hyperfine interaction. The exchange interaction is typically

included in the spin Hamiltonian in the following form, where J is the value of the



THE SPIN-CORRELATED RADICAL PAIR



161



FIGURE 8.2 (a) Variation of RP energy with interradical separation exemplified by a pair of

hydrogen atoms. The difference in energy between the S and T states is given by the electron

exchange interaction and falls rapidly as the radicals become separated. (b) Variation of RP

energy with applied external magnetic field strength due to the electron Zeeman effect. The

S and T0 states remain unchanged, their separation determined by the interradical separation

(see (a)).



exchange integral between the two electron spins, r is the separation of the radicals,

and rJ and J0 are both empirically determined parameters.





1

^

ỵ 2S1 S2

H exchange ẳ Jrị

2



8:7ị



Jrị ẳ J0 e r=rJ



ð8:8Þ



The exchange interaction typically drops to magnitudes of the same order as

hyperfine couplings within a single diffusive step.18–20 For neutral RPs, the exchange

interaction is always negative, but positive J has been proposed and observed in some

radical ion pairs (RIPs).21–24

The dipolar interaction is a direct interaction between the magnetic dipoles of the

electrons on the two radicals.





2

^1 Á S

^2 À 3 ðS1 rịS2 rị

^ D ẳ m 0 m B g1 g2 S

H

4ph2 r3

r2



ð8:9Þ



where g1 and g2 are the isotropic g-values of radicals A and B and r is the vector

separation of the two radicals, usually defined to be between the centers of the relevant

electron orbitals. The dipolar interaction has a shallower distance dependence than the

exchange interaction and is capable of retarding spin-state interconversion at larger

radical separations. The significance of the dipolar interaction in differing field

strengths is discussed later, but in general, for RP reactions in homogeneous solution,



162



MAGNETIC FIELD EFFECTS ON RADICAL PAIRS IN HOMOGENEOUS SOLUTION



the dipolar interaction is neglected and the total spin Hamiltonian for a RP in zero

magnetic eld is usually given as



 X

X

^1 ^I1i ỵ

^2 ^I2k

^ RP; Bẳ0 ẳ Jrị 1 ỵ 2S1 S2 ỵ

ai S

ak S

H

2

i

k



8:10ị



8.3 APPLICATION OF A MAGNETIC FIELD

Application of an external magnetic field alters the nature of some of the magnetic

interactions in a RP and also leads to additional terms in the spin Hamiltonian through

the electron Zeeman interaction.

8.3.1 The Zeeman Effect

The Zeeman effect is the name given to the interaction between an electron and an

external magnetic field.15 For a radical tumbling freely in solution, it can be written as

^ B ẳ gm Sz B

^ Zeeman ẳ gmB S

H

B



8:11ị



where g is the g value of the radical concerned and mB is the Bohr magneton. It causes

the two possible spin states (ms ẳ ỵ 1, a and ms ẳ 1, b) to become nondegenerate;

their energy separation increasing linearly with the strength of the applied magnetic

field. EPR spectroscopy is based on using resonant microwave radiation to cause

transitions between these two spin states.

For a pair of radicals, the Zeeman effect serves to energetically separate the triplet

RP into three sublevels, written as T þ 1, T0, and TÀ1. The energy of the T þ 1 state

increases, while that of the TÀ1 state is reduced by an equal amount. The S and T0 states

possess no magnetic moment in the direction of the applied field and thus are

unaffected. This is illustrated in Fig. 8.2b.

The effect of the application of an external field on an electron is well described in

many EPR texts, for example, Ref. 15. A vector picture is often used that, while

approximate, describes the interaction sufficiently for most situations. The electron

magnetic moment experiences a torque that causes it to precess around the direction of

the applied magnetic eld at the Larmor frequency.

wẳ



gmB Blocal

h



8:12ị



Figure 8.3 shows vector pictures for the four RP spin states in an external magnetic

field. A static image is insufficient to visualize this model, and we must remember that

all the electron magnetic moments are in constant precession about the direction of the

magnetic field at their respective Larmor frequencies.

The orientation of electron spins in this manner influences the electron–electron

dipolar interaction described above. For strong magnetic fields, the diffusive



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