Organic spin clusters: Ferromagnetin spin coupling through a biphenyl unit in polyarylmethyl tri-, penta-, hepta-, and hexadecaradicals

Article abstract of DOI:10.1021/ja972378b

Polyarylmethyl high-spin polyradicals are designed to possess a structure corresponding to simple spin clusters, where component spins (S') arise from strong ferromagnetic coupling through 1,3-phenylene units and weak ferromagnetic spin coupling between t

Full text of DOI:10.1021/ja972378b

11674
J. Am. Chem. Soc. 1997, 119, 11674-11686
Organic Spin Clusters: Ferromagnetic Spin Coupling through a
Biphenyl Unit in Polyarylmethyl Tri-, Penta-, Hepta-, and
Hexadecaradicals
Andrzej Rajca,* Jirawat Wongsriratanakul, and Suchada Rajca
Contribution from the Department of Chemistry, UniVersity of Nebraska,
Lincoln, Nebraska 68588-0304
ReceiVed July 16, 1997X
Abstract: Polyarylmethyl high-spin polyradicals are designed to possess a structure corresponding to simple spin
clusters, where component spins (S′) arise from strong ferromagnetic coupling through 1,3-phenylene units and weak
ferromagnetic spin coupling between the component spins is mediated via 3,4′-biphenylene (or 3,5,4′-biphenylyne)
units. This rational design permits not only modular and highly convergent synthesis of very high-spin molecules
but also detailed analysis of their magnetic data. A series of polyether precursors for the corresponding polyarylmethyl
tri-, penta-, hepta-, and hexadecaradicals are prepared. The polyradicals are generated and characterized in frozen
tetrahydrofuran (or tetrahydrofuran-d8) solutions, using bulk magnetization studies. The measured values of S, from
fits of magnetization vs magnetic field data to Brillouin functions at low temperatures, indicate high-spin ground
states; e.g., S ) 7.2 vs theoretical S ) 8 for hexadecaradical. Estimated yields per site for generation of “unpaired”
electrons are as high as 98% for the best samples of penta-, hepta-, and hexadecaradicals. The magnetization vs
temperature data are fit to the Boltzman distribution of energy levels, obtained from Heisenberg Hamiltonian; the
fits produced ferromagnetic coupling constants (J/k) through 3,4′-biphenylene units. For tri- and pentaradical, for
which exact analytical solutions to the Heisenberg Hamiltonian can be obtained by the vector model, values of J/k
≈ 90 K are obtained. Hepta- and hexadecaradical, which could not be exactly solved by the vector model, are
5
5
5
approximated as a dimer of the S′ ) /2 and 1 component spins and a trimer of the S′ ) /2, 3 and /2 component
spins, respectively; the corresponding values of J/k, 13 and 4 K, are found to be scaled by the fraction of component
spin directly connected through the weak spin coupler (3,4′-biphenylene unit).
5
Introduction
dendrimers are drastically lower than expected (e.g., /2 rather
than 31/2); in contrast, those for macrocycles are close to the
expected values (e.g., 3.8 rather than 8/2).2a-c,3 Because the yield
for generation of “unpaired” electrons is finite in a multisite
polyradical, there will be sites with “unpaired” electrons missing.
We refer to such sites as defects. The most detrimental defects
are those that interrupt ferromagnetic coupling (π-conjugation)
between the remaining “unpaired” electrons in the polyradical,
leading to mixtures of spin systems with low values of S. The
key difference between dendrimers and macrocycles is revealed
by considering polyradicals with one defect. In dendrimers,
there are approximately 50% of the inner sites; a defect at one
of these sites would interrupt spin coupling. In macrocycles,
there is no such sites; i.e., a defect would lower the overall S
Very-high-spin organic molecules provide intellectual chal-
lenge and contribute to the understanding of organic magnetism.1
They pose fascinating problems involving synthesis of func-
tionalized mesoscopic-size molecules, attaining ferromagnetic
coupling between large number of “unpaired” electrons (i.e.,
very-high-spin) and informative magnetic characterization. High-
spin dendritic and macrocyclic polyradicals are two main classes
of such molecules.2-5 Dendritic and macrocyclic polyarylm-
ethyl polyradicals with up to 31 and 8 sites for “unpaired”
electrons, respectively, have been prepared.2,3 The S values for
X Abstract published in AdVance ACS Abstracts, November 15, 1997.
(1) For recent reviews on high-spin organic molecules, see: (a) Iwamura,
H. AdV. Phys. Org. Chem. 1990, 26, 179. (b) Dougherty, D. A. Acc. Chem.
Res. 1991, 24, 88. (c) Iwamura, H.; Koga, N. Acc. Chem. Res. 1993, 26,
346. (d) Rajca, A. Chem. ReV. 1994, 94, 871. (e) Miller, J. S.; Epstein, A.
J. Angew. Chem., Int. Ed. Engl. 1994, 33, 385. (f) Yoshizawa, K.; Hoffmann,
R. Chem. Eur. J. 1995, 1, 403.
(2) For high-spin polyarylmethyls, see: (dendritic) (a) Rajca, S.; Rajca,
A. In Polymeric Materials Encyclopedia; Salamone, J. C., Ed.; CRC: Boca
Raton, FL, 1996; pp 1830-1834. (b) Rajca, A. AdV. Mater. 1994, 6, 605.
(c) Rajca, A.; Utamapanya, S. J. Am. Chem. Soc. 1993, 115, 10688. (star-
branched) (d) Rajca, A.; Utamapanya, S.; Thayumanavan, S. J. Am. Chem.
Soc. 1992, 114, 1884.
(3) For macrocyclic polyarylmethyls, see: (a) Rajca, A.; Rajca, S.;
Padmakumar, Angew. Chem., Int. Ed. Engl. 1994, 33, 2091. (b) Rajca, A.;
Rajca, S.; Desai, S. R. J. Am. Chem. Soc. 1995, 117, 806.
by only /2.1d,3,6 However, the increased number of sites in
1
monomacrocyclic system is associated with greater probability
of encountering two or more defects, which may interrupt spin
coupling. Annelation of macrocyles significantly alleviates this
problem.1d,7 Recently, an annelated triple-calix[4]arene mac-
rocyclic polyarylmethyl polyradical with 14 sites for “unpaired”
electrons and S ) 6.2 has been prepared.8 Such a polyradical
not only requires an elaborate synthesis but also imposes
additional constraints on its stability and strength of ferromag-
netic coupling.8
(4) For high-spin polycarbenes, see: Nakamura, K.; Inoue, K.; Iwamura,
H. Angew. Chem. Int. Ed. Engl, 1993, 32, 872. Matsuda, K.; Nakamura,
N.; Takahashi, K.; Inoue, K.; Koga, N.; Iwamura, H. J. Am. Chem. Soc.
1995, 117, 5550. Matsuda, K.; Nakamura, N.; Inoue, K.; Koga, N.; Iwamura,
H. Chem. Eur. J. 1996, 2, 259. Matsuda, K.; Nakamura, N.; Inoue, K.;
Koga, N.; Iwamura, H. Bull. Chem. Soc. Jpn. 1996, 69, 1483.
(5) For a linear polymer with S ≈ 4, see: Murray, M. A.; Kaszynski,
P.; Kaisaki, D. A.; Chang, W.-H.; Dougherty, D. A. J. Am. Chem. Soc.
1994, 116, 8152.
(6) In principle, attaching sites with “unpaired” electrons to a chain as
pendants, should provide a polyradical with some resistance to defects.
However, only relatively low values of S could be attained with such systems
so far: Nishide, H.; Kaneko, T.; Nii, T.; Katoh, K.; Tsuchida, E.; Lahti, P.
M. J. Am. Chem. Soc. 1996, 118, 9695.
(7) Rajca, A. In Modular Chemistry; Michl, J., Ed.; Kluwer Academic
Publications: Dordrecht, The Netherlands, in press.
(8) Rajca, A.; Lu, K.; Rajca, S. J. Am. Chem. Soc. In press.
S0002-7863(97)02378-0 CCC: $14.00 © 1997 American Chemical Society

Organic Spin Clusters
J. Am. Chem. Soc., Vol. 119, No. 48, 1997 11675
All of the very-high-spin polyradicals, mentioned above, may
be viewed as ensembles of alternating sites for “unpaired”
electrons with 1,3-phenylenes (1,3,5-phenylynes), which func-
tion as strong ferromagnetic coupling units (strong FCUs).1b In
an alternative design, high-spin modules (component spins, S′)
are linked with weak FCUs to form simple spin clusters. In
such polyradicals, ferromagnetic coupling in high-spin modules
(intramodular ferromagnetic coupling, J′) is very strong, com-
pared to the interaction between the modules (intermodular
ferromagnetic coupling, J) and the thermal energy (kT) in the
applicable temperature range, i.e., J′ . J ≈ kT. An analogy
can be drawn to a high-spin transition metal cluster, with metal
ions corresponding to the modules.9
The spin cluster design is implemented with polyarylmethyl
polyradicals.1d Strong ferromagnetic coupling (J′) within the
modules is achieved by alternating triarylmethyl sites with 1,3-
phenylenes (or 1,3,5-phenylynes) as ferromagnetic coupling
units (FCUs). Weak ferromagnetic coupling (J) between the
modules is mediated with 3,4′-biphenylenes (or 3,5,4′-biphe-
1
nylynes) as FCUs.10,11 It is estimated that J/J′ ≈ /6, based upon
the available electron-proton spin couplings in triphenylmethyl
and 4-biphenyldiphenylmethyl monoradicals.12 Polyradicals
1-4 are designed as simple spin clusters (Figure 1).
The present design offers important advantages in approach
to very-high-spin organic polyradicals.
Exchange interactions, primarily responsible for ferromagnetic
coupling (J), should be adequately described by Heisenberg
Hamiltonian, H ) -2Σi>j JijSiSj, in organic polyradicals.1c,d
Because exact energy eigenvalues of Heisenberg Hamiltonian
for spin dimers and symmetrical trimers are readily available,
Figure 1. Triradical 1, pentaradical 2, heptaradical 3, hexadecaradical
4, and their representations as spin clusters.
more informative description of magnetic data is possible,
including temperature dependence for J ≈ kT.
(9) For a preliminary outline of the concept of organic spin clusters,
see: Rajca, A. In Proceedings from the 5th International Conference on
Molecule-Based Magnets; Osaka, Japan, 1996; Liq. Cryst. Mol. Cryst. In
press.
(10) For a 3,4′-biphenylene-based diarylmethyl, see: Rajca, A.; Rajca,
S. J. Am. Chem. Soc. 1996, 118, 8121.
(11) For 3,4′-biphenylene-linked dicarbene and dinitrene, see: Teki, Y.;
Fujita, I.; Takui, T.; Kinoshita, T.; Itoh, K. J. Am. Chem. Soc. 1994, 116,
11499. Minato, M.; Lahti, P. M.; van Willigen, H. J. Am. Chem. Soc. 1993,
115, 4532.
(12) Selected electron-proton spin coupling constants (in gauss, from
ENDOR experiments) are for triphenylmethyl, 1.143 (H3), 2.857 (H4), and,
for diphenylbiphenylmethyl, 0.193 (H3′), 0.487 (H4′): Maki, A. H.;
Allendoerfer, R. D.; Danner, J. C.; Keys, R. T. J. Am. Chem. Soc. 1968,
90, 4225.
Dendritic modules are designed to minimize the number of
the inner sites for “unpaired” electrons. Consequently, polyradi-
cals 1-3 possess only one site, where one defect may interrupt
spin coupling; hexadecaradical 4 has two such sites. Moreover,
4-biphenyl substituents at these sensitive sites should make the
radicals more stable.13 In particular, 3,4′-biphenyl-based triplet
diradical has been isolated as a solid, stable at ambient
temperature.10
(13) Tris(4-biphenyl)methyl does not dimerize in solution at ambient
temperature: Du¨nnebacke, D.; Neumann, W. P.; Penenory, A.; Stewen, U.
Chem. Ber. 1989, 122, 533.

11676 J. Am. Chem. Soc., Vol. 119, No. 48, 1997
Rajca et al.
Scheme 1. Synthesis of Modules and Their Assembly To Give Polyethers 1-(OMe)3, 2-(OMe)5, 3-(OMe)7, and 4-(OMe)16
Modular and highly convergent routes can be applied to the
synthesis of the polyarylmethyl polyether precursors to such
spin cluster polyradicals. 1,3-Phenylene-connected macro-
cyclic and/or dendritic modules can be connected via C(aryl)-
C(aryl) bond-forming reactions to produce 3,4′-biphenylene-
linked (or 3,5,4′-biphenylyne-linked) ensembles of modules; no
subsequent functionalizations of the triarylmethyl sites are
needed.10
8 (62%) or 9, respectively;15 etherification of triarylmethanol 9
with MeI gives ether 10 (86%).
Li/Br exchange of 10, followed by addition of 4-bromoben-
zoyl chloride, provides triarylmethanol 11; etherification with
MeI gives pentaether 12 (40%).
Modules 6, 8, 10, 12, and the previously prepared macro-
cyclic module 13 are used in the following synthetic steps.8
Dibromocalix[4]arene hexaether 13 is a single cis/trans isomer,
with no elements of symmetry on the NMR time scale.8
Suzuki coupling, without isolation of boronic acid derivatives,
is employed to connect the modules.16 For a pair of modules,
one of the modules is subjected to Li/Br exchange, followed
by addition of B(OMe)3, removal of the solvent under nitrogen
flow and vacuum, and heating with the other module in the
presence of Pd(Ph3P)4 and barium hydroxide in toluene/MeOH.
Results and Discussion
1. Synthesis of Polyethers. Modular and highly convergent
synthesis is employed to prepare polyethers 1-(OMe)3, 2-(OMe)5,
3-(OMe)7, and 4-(OMe)16. The synthesis is carried out in two
stages: (1) preparation of 1,3-phenylene-connected triarylmethyl
modules with 3- and 4-bromoaryl functional groups and (2)
linking the modules with 3,4′-biphenylene (or 3,5,4′-bipheny-
lyne) moieties (Scheme 1).
(14) Wakefield, B. J. The Chemistry of Organolithium Compounds;
Pergamon, Oxford, 1974; Chapter 4. For 4-bromophenyllithium, see:
Gilman, H.; Langham, W.; Moore, F. W. J. Am. Chem. Soc. 1940, 62, 2327.
For a derivative of module 6, without the tert-butyl substituent, see:
Hellwinkel, D.; Stahl, H.; Gaa, H. G. Angew. Chem., Int. Ed. Engl. 1987,
26, 794.
4-Bromophenyllithium, prepared by Li/Br exchange from 1,4-
dibromobenzene, is added to methyl 4-tert-butylbenzoate to give
triarylmethanol 5; etherification with MeI gives ether 6 in 63%
yield.14
(15) For an ethyl ether derivative of module 8, see: Rajca, A. J. Org.
Chem. 1991, 56, 3557.
(16) For a recent review on Suzuki coupling, see: Miyaura, N.; Suzuki,
A. Chem. ReV. 1995, 95, 2457. For the use of barium hydroxide and an in
situ procedure, see: Suzuki, A. Pure Appl. Chem. 1994, 66, 213. Maddaford,
S. P.; Keay, B. A. J. Org. Chem. 1994, 59, 6501.
Aryllithium, which is obtained via Li/Br exchange on
dibromoaryl compound 7,3a is either quenched with MeOH or
treated with 4,4′-di-tert-butylbenzophenone to give compound

Organic Spin Clusters
J. Am. Chem. Soc., Vol. 119, No. 48, 1997 11677
of 2 are associated with four 2-proton doublet and four 1-proton
triplet (J ) 2 Hz) resonances, corresponding to the four 1,3,5-
trisubstituted benzene rings of the dendritic branches. (Spectral
overlap in the 1D NMR spectrum does not permit unequivocal
assignment of one doublet/triplet pair.) The 12 “quadruplet”
peaks correlate 12 2-proton doublet (J ) 9 Hz) resonances,
corresponding to the 12 1,4-disubstituted benzene rings. The
2 groups of overlapped diagonal peaks (7.43-7.51, 7.18-7.26
ppm) must account for the remaining 1,4-disubstituted benzene
rings.
In the MeO group region, 9-11 singlets are resolved in the
293-348 K range (Table 1). The requirement for an even
number of resonances for the MeO groups in 4-(OMe)16
suggests at least one accidental isochrony in the best resolved
spectrum (at 328 K). Thus, the MeO groups should appear as
at least 12 singlets; i.e., eight 3 H and four 6 H resonances.
In the tert-butyl group region, 11-13 singlets are resolved
in the 293-348 K range (Table 1). In the best resolved
spectrum (at 293 K), isochronies involving two 1H singlet
resonances integrating to three and six tert-butyl groups must
be accidental. In conjunction with the requirement for an even
number of 1H resonances for the tert-butyl groups, the spectrum
at 293 K should contain at least 16 singlets; i.e., eight 9 H and
eight 18 H resonances.
Figure 2. FAB MS for 4-(OMe)16. (A) Partial low-resolution spectrum.
The most intense peak is at m/z 4607. (B) Spectrum for the (M -
OCH3)+ ion cluster from the high-resolution spectrum. (C) Calculated
spectrum for the (M - OCH3)+ ion cluster with formula C331H389O15
at natural isotopic abundance.
1H NMR spectra for hexadecaether 4-(OMe)16 in C6D6 are
compatible with a single cis/trans isomer of calix[4]arene ring,
lacking any elements of symmetry on the NMR time scale. The
two dendritic pentaether branches and their four diether sub-
branches are asynchronous. Each of the four diether sub-
branches contains two nonequivalent pairs of 4-tert-butylphenyl
groups; the other eight 4-tert-butylphenyl groups are nonequiva-
lent.
Isolated yields for 3,4′-biphenylene-linked polyethers are 51%
(1-(OMe)3), 47% (2-(OMe)5), 73% (3-(OMe)7), and 16% (4-
(OMe)16).
Polyethers 1-(OMe)3, 2-(OMe)5, 3-(OMe)7, and 4-(OMe)16
are characterized by FAB MS, IR, and NMR spectroscopies
and C/H elemental analyses.
All polyethers show expected (M - OCH3)+ cluster ions as
the most intense signals in the high mass range of FAB MS.
For the largest molecules studied, heptaether 3-(OMe)7 and
hexadecaether 4-(OMe)16, isotopic distributions for (M -
OCH3)+ were calculated and found in satisfactory agreement
with the experimental values. For 4-(OMe)16, the three most
intense isotopic peaks of (M - OCH3)+ possess the following
experimental m/z values and relative amplitudes (% RA): 4606.1
(84), 4607.1 (100), 4608.1 (86), vs calculated for C331H389O15,
4606.0 (80), 4607.0 (100), 4608.0 (94) (Figure 2).
2. Generation of Polyradicals and Quenching Studies.
Treatment of a polyether with an excess of Na/K alloy in
tetrahydrofuran (THF) or tetrahydrofuran-d8 (THF-d8) gives
purple-red solutions of the corresponding carbopolyanions
(Scheme 2).10 For tri- and pentaethers, the purple-red solution
is preceded by an incipient formation of blue-purple solution
of an intermediate carbanion; analogously, blue color is initially
observed for hepta- and hexadecaethers.
IR spectra for all polyethers show strong bands at ∼1600
and ∼1080 cm-1 corresponding to vibrational modes involving
benzene rings and ethereal linkages (C-O-C), respectively.
Synthetic intermediates, which posses hydroxyl group, have
Oxidation of the carbopolyanions with I2 at low temperatures
(168-178 K) gives the corresponding polyradicals in THF (or
THF-d8).10,18,19 The best results, as indicated by the magnitude
of S from magnetization studies, are achieved by addition of I2
in small portions (titrations). A sequence of color changes,
which is associated with oxidation of each carbopolyanion,
serves as an indicator, e.g., in oxidation leading to hexade-
caradical 4, initial purple-red color of carbopolyanion turns to
blue color, followed by green color, and, finally, yellow-brown
color of polyradical. The intermediate blue color appears when
most of I2 (80-90%) is added to the reaction mixture; probably,
at this stage of oxidation, the only carbanion sites left intact
are those two sites substituted with 4-biphenyl moiety. [It is
noted that triarylmethyl and 4-biphenyldiarylmethyl (aryl )
alkylphenyl) carbanions in THF are red (λmax ≈ 490 nm) and
blue (λmax ≈ 590 nm), respectively; the corresponding radicals
are yellow (λmax ≈ 350 nm) and orange-red (λmax ≈ 380 nm).]19
The green color appears when almost all I2 (95+%) is added to
the reaction mixture; at this stage of oxidation, only very small
amount 4-biphenyl-substituted carbanion is left. This sequence
of colors is exactly reversed when a polyradical is stirred with
alkali metal at low temperature (Scheme 2).
broad bands at ∼3600 cm-1
.
NMR spectra for triether 1-(OMe)3 and pentaether 2-(OMe)5
are straightforward. NMR spectra for more sterically hindered
heptaether 3-(OMe)7 are best interpreted in terms of three
nonequivalent sets of four 4-tert-butylphenyl groups; similarly,
synthetic precursors 11 and 12, possess two nonequivalent sets
of four 4-tert-butylphenyl groups.17
1H NMR spectra for hexadecaether 4-(OMe)16 in C6D6 are
obtained at 293, 328, and 348 K. Resonances in the aromatic,
MeO group, and 4-tert-butyl group regions are found (Figures
3 and 4).
Aromatic region of the spectrum is best resolved at 348 K.
COSY correlation shows 32 “singlet” off-diagonal peaks, 12
“quadruplet” off-diagonal peaks, and 2 groups of overlapped
off-diagonal peaks. The 32 “singlet” peaks are correlated within
4 sets of 6 and 4 sets of 2. The 4 sets of 6 are associated with
12 1-proton triplet (J ) 2 Hz) resonances, corresponding to the
four benzene rings of the calix[4]arene macrocycle. The 4 sets
(17) (a) For stereochemistry of propellers, see: Mislow, K. Acc. Chem.
Res. 1976, 9, 26. (b) For sterically hindered polyarylmethyl derivatives,
see: Rajca, A.; Janicki, S. J. Org. Chem. 1994, 59, 7099.
(18) Rajca, A. J. Am. Chem. Soc. 1990, 112, 5890.
(19) Rajca, S.; Rajca, A. J. Am. Chem. Soc. 1995, 117, 9172.

11678 J. Am. Chem. Soc., Vol. 119, No. 48, 1997
Rajca et al.
Figure 3. 1H NMR (500 MHz, C6D6) spectrum for 4-(OMe)16 at 348 K. Main plot: full spectrum, EM ) -1.5 Hz, GB ) 0.9 Hz. Peaks at 7.15
and 0.26 ppm correspond to residual less-than-fully deuterated benzene and water, respectively. Insert: 1H-1H COSY correlation in the aromatic
region. Two pairs of peaks, located near the diagonal, at (7.89, 7.84 ppm), (7.84, 7.89 ppm), (7.84, 7.80 ppm), (7.80, 7.84 ppm), and diagonal peak
at 7.75 ppm correspond to unknown impurities or instrumental artifacts.
A small portion of polyradical in THF (or THF-d8) is
transferred at low temperature to the quartz tube for magnetiza-
tion studies. Similarly prepared samples of 1 and 2, with
additional dilution with 2-methyltetrahydrofuran (2-MeTHF),
are employed for ESR spectroscopy. The remaining reaction
mixture is treated with Na/K alloy or Li at low temperature,
and, MeOH or MeOD is then added to produce hydrocarbons
1-(H)3, 2-(H)5, and 4-(H)16 and deuterated products 1-(D)3,
2-(D)5, 3-(D)7, and 4-(D)16, respectively (Scheme 2). [Hydro-
carbon 3-(H)7 is obtained by the MeOH quench of carbopolya-
nion, which is directly generated from 3-(OMe)7.]
In the FAB MS of hydrocarbons 1-(H)3, 2-(H)5, and 3-(H)7,
cluster ions corresponding to M+/(M - H)+ are observed; for
hydrocarbon 4-(H)16, isotopic peaks are not resolved and only
an average mass peak is found at m/z 4158. For deuterated
products 1-(D)3, 2-(D)5, 3-(D)7, and 4-(D)16, the peaks of
maximum amplitude in the isotopic cluster ions or average mass
peaks are shifted by 3, 5, 7, and 15 amu, relative to the
corresponding hydrocarbons.20
The 1H and 13C NMR spectra of the aromatic and tert-butyl
groups regions for hydrocarbons 1-(H)3, 2-(H)5, and 3-(H)7 and
their deuterated isotopomers are analogous to those for the
corresponding polyethers 1-(OMe)3, 2-(OMe)5, and 3-(OMe)7.
1
The H resonances of the triarylmethane protons appear as
singlets in the 5.52-5.20 ppm range. Their integration ratios
are 1:2 (1-(H)3), 1:4 (2-(H)5), and 2:4:1 (3-(H)7); the resonances
with integration of 1 H are assigned to the 4-biphenyl-substituted
1
sites. For deuterated isotopomers (1-(D)3, 2-(D)5, 3-(D)7), H
integrations suggest that overall deuterations at the triaryl-
methane sites are in the range of 96-97%; however, degree of
deuteration per site is typically less at the 4-biphenyl-substituted
sites (∼95%) compared to that of the other sites (∼97%).
The 1H NMR spectra for 4-(H)16 and 4-(D)16 consist of broad,
unresolved peaks at the chemical shifts corresponding to
aromatic, triarylmethane, and tert-butyl regions. Probably, these
two compounds are complex mixtures of cis/trans isomers. (For
Figure 4. Partial 1H NMR (500 MHz, C6D6) spectra for 4-(OMe)16 in
(20) Uncertainty about the relative contribution of the M+/(M - H)+
the C-OCH3 region. (A) 348 K, EM ) -1.5 Hz, GB ) 0.9 Hz. (B)
328 K, EM ) -1.5 Hz, GB ) 0.9 Hz. (C) 293 K, EM ) -1.6 Hz, GB
) 0.9 Hz.
and M+/(M - H)+/(M - D)+ ions to the isotopic clusters in 4-(H)16 and
the deuterated compounds complicates interpretation of the observed isotopic
shifts.

Organic Spin Clusters
J. Am. Chem. Soc., Vol. 119, No. 48, 1997 11679
1
Table 1. Relative Peak Integrations for the Partial H NMR in the
MeO- and t-Bu Group Regions for Hexadecaether 4-(OMe)16
density at the trityl carbon and the three adjacent benzene
rings.1d,12,21 Therefore, Heisenberg Hamiltonian, H ) -2Σi>j
JijSiSj, with ferromagnetic couplings (Jij > 0) between the
nearest-neighbor sites should be appropriate as starting point
for describing magnetism in such polyradicals.1cd,22,23 When
1-4 are considered as oligomers of spins 1/2, without any
assumptions about spin couplings, 1 (trimer) and 2 (pentamer)
are exactly solvable while 3 (heptamer) and 4 (hexadecamer)
are not solvable by the vector decoupling (Figure 5).9,24,25 When
J′ (1,3-phenylene) . J (3,4′-biphenylene) ≈ kT for 2 (pentamer),
inspection of the Heisenberg Hamiltonian eigenvalues implies
that the five highest in energy spin states are negligibly
populated (Figure 5). Therefore, pentaradical 2 is adequately
described by considering population of the five lowest in
energy spin states, which correspond to a trimer of the S′ ) 1,
1/2, and 1 component spins (Figure 1).9 When J′ . J for 3 and
4, exactly solvable spin dimer and trimer should provide useful
approximations (Figure 1). High-spin ground states are pre-
dicted for polyradicals 1-4 with ferromagnetic couplings J′, J
> 0.
T [K]
MeO groups
t-Bu groups
293 9 peaks; 1:1:2:6:2:1:1:1:1
13 peaks; 1:6:2:2:2:1:2:3:1:1:1:1:1
328 11 peaks; 1:1:1:1:2:4:2:1:1:1:1 12 peaks; 1:8:2:2:1:2:1:1:2:1:2:1
348 10 peaks; 1:1:1:1:2:6:1:1:1:1 11 peaks; 1:8:2:2:1:1:3:3:1:1:1
Scheme 2. Generation of Polyradicals 1-4 and Quenching
Studies
For both 1 and 2, considered as spin trimers, each pairwise
J-coupling between the component spins (S′) involves all
triarylmethyl spin sites associated with S′. However, for 3 and
4, only a fraction of the spin sites may be involved; i.e.,
only 1 out of 5 and 2 out of 6 spin sites participate in the
5
pairwise J-coupling of the terminal S′ ) /2 and the center S′
) 3 spins. Similarly to the case of dimer of S′ ) 1 spins for
S ) 2 tetraradical, studied by Dougherty and co-workers, values
for pairwise J-coupling between S′ spins in the dimer (3) and
the previously studied, more symmetrically substituted, mac-
rocyclic calix[4]arene hydrocarbons, cis/trans isomers could be
isolated or detected in comparable amounts.)3b Integration of
the triarylmethane region in 4-(D)16 gives ∼1 H (vs 16 H in
4-(H)16), which is within the error of integration for such
molecules with such large numbers of protons, appearing as
broad resonances. Therefore, the degree of deuteration for
1
1
trimer (4) should be scaled by
/
and (1/5)(2/6) ) /15,
5
respectively.9,26 Therefore, the relative values of J for spin
dimers and trimers corresponding to polyradicals 1-4 should
J
J
be J, J, /5, /15.
In a diradical, where two triarylmethyl sites are connected
through a 3,4′-biphenylene unit, a small thermal population of
the lowest excited state in the 1.8-160 K temperature range
was observed but it was insufficient for a reliable measurement
of J in frozen THF.10,27 Decreasing the energy gap between
the high-spin ground state and the lowest excited state, which
is 2J in the diradical, should increase thermal population of the
excited states.1d In polyradicals 1-4, the energy gaps are J, J,
(7/5)J, (6/15)J, with scaling factors for 3 and 4 included, i.e.,
significantly less than in the diradical.9
4. ESR Spectroscopy of Triradical 1 and Pentaradical 2.
X-Band (9.3 GHz) ESR spectra for 10-4 M 1 and 2 in
2-MeTHF/THF are obtained at 80 K. Line shape and intensity
distortions are found, especially for 2, even at the lowest
attainable microwave power settings at these experimental
conditions.
1
4-(D)16, based on both H NMR spectroscopy and FAB MS,20
is estimated only approximately in the D14-D16 range.
Incomplete deuterium incorporation may originate in proto-
nation of the initially formed carbanion by trace amounts of
proton sources (moisture, residual MeOH, etc.) in the reactants
and surface of the reaction vessel (with possible H/D KIE).
Slightly lesser degree of deuteration at the 4-biphenyl-substituted
sites compared to other sites correlates with initial formation
of 4-biphenyl-substituted carbanions, as deduced from color
changes at the early stages of reactions of both polyethers and
polyradicals with alkali metal (preceding text).
Isolation of both protonated and deuterated quenching
products confirms that the connectivity of the hydrocarbon
framework in polyradicals and the precursor polyethers is
identical. The high overall deuteration at the triarylmethane
sites only alludes to the possibility of high yield for generation
of “unpaired” electrons. In addition to incorporation of
hydrogens at triarylmethyl sites, other types of defects may
affect the yield for “unpaired” electrons such as formation of
dimers, addition of iodine to triarylmethyl sites (Ar3C-I), or
incomplete oxidation of carbopolyanion. All of the above
defects will affect the overall spin values for polyradicals and
introduce impurities with potentially different spin coupling
properties. However, only the defects involving incorporation
of hydrogens are detectable by the MeOH/MeOD quenching
experiments.
For 1, the ∆ms ) 1 region of the spectrum consists of five
equally spaced lines, of which the center line is relatively
intense. The spectral width is ∼70 G. The line spacing, relative
(21) For electron localization in 1,3-connected polyarylmethyls, see:
Utamapanya, S.; Rajca, A. J. Am. Chem. Soc. 1991, 113, 9242. Reference
19.
(22) Heisenberg, W. Z. Phys. 1926, 38, 441. Dirac, P. A. M. Proc. R.
Soc. 1926, 112A, 661. Heisenberg, W. Z. Phys. 1928, 49, 619.
(23) For valence bond calculations on polycarbenes, see: Teki, Y.; Takui,
T.; Kitano, M.; Itoh, K. Chem. Phys. Lett. 1987, 142, 181. Alexander, A.
A.; Klein, D. J. J. Am. Chem. Soc. 1988, 110, 3401.
(24) Belorizky, E.; Fries, P. H. J. Chim. Phys. (Paris) 1993, 90, 1077.
(25) For reviews on magnetism of polynuclear metal complexes, see:
Cairns, C. J.; Bush, D. H. Coord. Chem. ReV. 1986, 69, 1. Gatteshi, D.;
Caneshi, A.; Sessoli, R.; Cornia, A. Chem. Soc. ReV. 1996, 101.
(26) Itoh, K. Pure Appl. Chem. 1978, 50, 1251. Jacobs, S. J.; Schultz,
D. A.; Jain, R.; Novak, J.; Dougherty, D. A. J. Am. Chem. Soc. 1993, 115,
1744.
3. Spin Cluster Model. Magnetic interactions in isolated
organic polyradicals (e.g., as dilute solutions in diamagnetic
solvents) are expected to be dominated by isotropic exchange
interactions between “unpaired” electrons.1c,d In polyarylmethyl
high-spin polyradicals, “unpaired” electrons are localized at
triarylmethyl sites, with the comparable magnitude of spin
(27) Unpublished data from this laboratory.

11680 J. Am. Chem. Soc., Vol. 119, No. 48, 1997
Rajca et al.
1
Figure 5. Pentamer, heptamer, and hexadecamer of spins /2, corresponding to pentaradical 2, heptaradical 3, and hexadecaradical 4. Energy
eigenvalues from the Heisenberg Hamiltonian for pentaradical 2 are shown for J, J′ > 0 (both couplings ferromagnetic). J and J′ are spin coupling
through 3,4′-biphenylene and 1,3-phenylene units, respectively.
intensities, and approximate line shapes are compatible with
M vs T data at H ) 0.5 or 2.0 T for polyradicals are fit as
MT vs T to Heisenberg Hamiltonian-based spin cluster models
(eqs 1-4, Experimental Section). An initial fit may involve as
many as four variable parameters: J/k (spin coupling constant
in Kelvin), N (number of moles of polyradical), θ (mean field
parameter for small intermolecular magnetic interactions), and
Mdia (correction for diamagnetism). However, for samples with
satisfactory point-by-point correction for diamagnetism and
negligible intermolecular magnetic interactions, such as hexa-
decaradical 4, only two variable parameters, J/k and N, are
needed.
M vs H data at T ) 1.8, 3, and 5 K for tri- and pentaradicals
1 and 2 are fit to a Brillouin function with mean field parameter,
M vs H/(T - θ);32,33 θ is adjusted until the two variable
parameters, spin, S, and magnetization at saturation, Msat, are
identical for each T. Values of θ are similar but not identical
to those obtained from MT vs T fits. For hepta- and hexade-
caradicals 3 and 4, adequate fits to simple Brillouin functions,
M vs H/T, with two variable parameters, S and Msat, are
obtained.32
The use of Brillouin functions to describe magnetization at
low temperatures (1.8-5 K) is appropriate because of relatively
large values of ferromagnetic J/k for 1-4; that is, in this
temperature range, almost all spin systems are expected to be
in their high-spin ground states. For example, when M vs H
data are generated for hexadecaradical 4, using eq 4 (Experi-
mental Section) for M with J/k ) 4.2 K (see the following text),
excellent fits to simple Brillouin functions (M vs H/T) are
obtained with the following values of S: 8.00 (1.8 K), 8.00 (3
K), and 7.99 (5 K).
3
an S ) /2 state with the following zero field splitting (zfs)
parameters: |E/hc| ≈ 0 cm-1 and |D/hc| ≈ 0.0016 cm-1
0.004-0.006 cm-1, depending on conformation.28
.
Analogous 1,3-phenylene-based S ) 3/2 triradical has |D/hc| ≈
For 2, the ∆ms ) 1 region of the spectrum consists of seven
lines, with the 2:1:1:1:1:2 spacings and the relatively intense
center line. The spectral width is ∼140 G. The line spacing,
relative intensities, and approximate line shapes are compatible
with an S ) 5/2 state with |E/hc| ≈ 0 cm-1 and |D/hc| ≈ 0.0016
cm-1. The analogous 1,3-phenylene-based S ) 5/2 pentaradical
has |D/hc| ) 0.0027 cm-1 3b
.
Similar to the analogous 1,3-phenylene-based half-integral
spin tri- and pentaradicals, no resonances are detected in the
∆ms ) 2 regions for 1 and 2 at 80 K.3a,28 The experimental
difficulties are further compounded by relatively small values
of |D/hc| for 1 and 2.29
ESR spectra provide support for high-spin states of 1 and 2.
Their |D/hc| values are significantly decreased compared to
those of their 1,3-phenylene-based counterparts, as expected for
increased distances between triarylmethyl sites with “unpaired”
electrons.30 The decreased spectral resolution for 3,4′-biphe-
nylene-based polyradicals would severely limit any information
content of the ESR spectra for S > 3.31 Quantitative studies of
the ESR signal intensity (I) vs temperature (T), which could in
principle be used to determine J, are obstructed by the relatively
low softening point of 2-MeTHF matrix at <90 K, difficulties
in detecting ∆ms ) 2 signals, and microwave saturation in 1
and 2. In the relatively more favorable case of integral spin
3,4′-biphenylene-based diradical with |D/hc| ≈ 0.0025 cm-1
,
similar experimental limitations has provided only partial I vs
T determination.10 Bulk magnetization studies provide alterna-
tive technique for characterization and avoiding restrictions of
the ESR spectroscopy for spin-dilute polyradicals 1-4.
5. Magnetic Studies of Polyradicals 1-4. Magnetization
(M) is measured as a function of magnetic field (H ) 0-5.0 T)
and temperature (T ) 1.8-160 K) for frozen solutions of
polyradicals 1-3 in THF and 4 in THF-d8 (or THF) using a
SQUID magnetometer. Concentrations of polyradicals are in
the 10-3-10-5 M range, which translates to a typical “unpaired”
electron concentration in the 10-3 to 10-4 M range.
For triradical 1, J/k ) 90 ( 20 K, corresponding to a
ferromagnetic coupling through 3,4′-biphenylene moiety, is
obtained from a fit to a symmetrical trimer of the three S′ ) 1/2
component spins (Figure 6). The values of J/k and quality of
the fits are significantly sample-dependent, presumably, due to
presence of conformations, which possess different values of
J/k.28 Typical sample has S ≈ 1.3. Relatively large and
negative values for θ ) -0.60 - (-0.18) K, with |θ| decreasing
upon dilution with THF, suggest significant intermolecular
antiferromagnetic interactions for the triradical. Also, quality
of the M vs H/(T - θ) fits significantly improves for |θ| <
0.4.34
(28) Rajca, A.; Utamapanya, S. J. Am. Chem. Soc. 1993, 115, 2396.
(29) For smaller |D/hc|, intensity of the ∆ms ) 2 resonance, relative to
the ∆ms ) 1 region, is expected to decrease: Weissman, S. I.; Kothe, G.
J. Am. Chem. Soc. 1975, 97, 2537.
1
For pentaradical 2, fit to a pentamer of the five S′ ) /2
component spins gives J/k ) 90 ( 5 K and J′/k > 200 K,
(30) In the simplest model for interpreting relative values of triplet |D/
(32) Carlin, R. L. Magnetochemistry; Springer-Verlag: Berlin, 1986.
(33) Bino, A.; Johnston, D. C.; Goshorn, D. P.; Halbert, T. R.; Stiefel,
E. I. Science 1988, 241, 1479.
(34) For relatively large |θ| (compared to T), a self-consistent version
of the mean field approximation should be used for fitting M vs H data; for
a recent discussion, see: Veciana, J.; Rovira, C.; Ventosa, N.; Crespo, M.
I.; Palacio, F. J. Am. Chem. Soc. 1993, 115, 57 and references therein.
hc|
1/r3 (r ) distance between “unpaired” electrons), only dipolar
contributions to |D/hc| and localized “unpaired” electrons are assummed.
Eaton, S. S.; More, K. M.; Sawant, B. M.; Eaton, G. R. J. Am. Chem. Soc.
1983, 105, 6560.
(31) The problem of rapidly declining ESR spectral resolution for
homologous polyradicals with larger values of S is discussed in ref 3b.

Organic Spin Clusters
J. Am. Chem. Soc., Vol. 119, No. 48, 1997 11681
Figure 6. SQUID magnetometry (H ) 0-5.0 T) for triradical 1 in
THF. Main plot: M/Msat vs H/(T - θ), θ ) -0.42 K. Experimental
Figure 7. SQUID magnetometry (H ) 0-5.0 T) for pentaradical 2 in
THF. Main plot: M/Msat vs H/(T - θ), θ ) -0.025 K. Experimental
points at T ) 1.8, 3, and 5 K and Brillouin functions with S ) 3/2, 5/2,
7/2 are shown as symbols and lines, respectively. The fitting parameters
at T ) 1.8, 3, and 5 K are S ) 2.40 and Msat103 ) 8.90, 8.98, and 9.05
emu; the parameter dependence is 0.37, 0.59, and 0.86. Insert: MT vs
T at H ) 0.5 T. Open circles are the experimental points. The solid
3
points at T ) 1.8, 3, and 5 K and Brillouin functions with S ) 1, /2,
2 are shown, as symbols and lines, respectively. The fitting parameters
at T ) 1.8, 3, and 5 K are S ) 1.26 and Msat102 ) 1.02, 1.04, 1.06
emu; the parameter dependence is 0.59, 0.83, and 0.96. Insert: MT vs
T at H ) 1.0 T. Open circles are the experimental points. The solid
line is the numerical fit to the S′ ) 1/2, 1/2, 1/2 symmetrical trimer model
(eq 1). The fitting parameters and their parameter dependencies are
J/k ) 92 K (0.94), N ) 6.0 × 10-7 mol (0.86), θ ) -0.60 K (0.71),
and Mdia ) 1.4 × 10-5 emu (0.91). All experimental data are plotted
after both the point-by-point and the numerical corrections (Mdia ) 1.4
× 10-5 emu) for diamagnetism.
1
line is the numerical fit to the S′ ) /2 pentamer trimer model (eq 2),
with J′/k ) 500 K. The fitting parameters and their parameter
dependencies are J/k ) 89 K (0.94), N ) 3.2 × 10-7 mol (0.81), θ )
-0.093 K (0.66), and Mdia ) 4.0 × 10-5 emu (0.92). All experimental
data are plotted after both the point-by-point and the numerical
corrections (Mdia ) 4.0 × 10-5 emu) for diamagnetism.
corresponding to ferromagnetic couplings through 3,4′-biphe-
nylene and 1,3-phenylene moieties. Because the fits are
relatively insensitive to values of J′/k > 200 K and overparam-
etrized, J′/k ) 500 K . J/k ≈ T is set constant, eliminating
J′/k as variable parameter. Typical values of S are in the 2.3-
2.4 range. Values for |θ|, which are an order of magnitude
less than those for the triradical and decrease upon dilution with
THF, suggest only small intermolecular antiferromagnetic
interactions (θ < 0) for the pentaradical (Figure 7).
For heptaradical 3, fit to a dimer of the S′ ) 5/2, 1 component
spins give J/k ) 13 ( 2 K. Typical sample has S ) 3.3.
Intermolecular antiferromagnetic interactions are negligible (q
) 0 K) for the heptaradical (Figure 8).
For hexadecaradical 4, fit to a symmetrical trimer of the S′
5
5
) /2, 3, /2 component spins gives J/k ) 4 ( 1 K. Values of
S are in the 6.6-7.2 range; the lowest value of 6.6 is for the
most dilute sample; θ ) 0 K suggests negligible intermolecular
antiferromagnetic interactions for hexadecaradical (Figure 9).
6. Defects and Interpretation of Magnetic Data. Less than
perfect 100% yield for generation of “unpaired” electrons
implies presence of defects in polyradicals, as mentioned in the
preceding text.
Figure 8. SQUID magnetometry (H ) 0-5.0 T) for heptaradical 3 in
THF. Main plot: M/Msat vs H/T. Experimental points at T ) 1.8, 3,
5
7
9
and 5 K and Brillouin functions with S ) /2, /2, /2 are shown as
symbols and lines, respectively. The fitting parameters at T ) 1.8, 3,
and 5 K are S ) 3.28 and Msat103 ) 8.34, 8.33, and 9.31 emu; the
parameter dependence is 0.33, 0.50, and 0.78. Insert: MT vs T at H )
0.5 T. Open circles are the experimental points. The solid line is the
numerical fit to the S′ ) 5/2, 1 dimer model (eq 3). The fitting parameters
and their parameter dependencies are J/k ) 12 K (0.83), N ) 2.0 ×
10-7 mol (0.54), and Mdia ) 4.1 × 10-6 emu (0.80). All experimental
data are plotted after both the point-by-point and the numerical
corrections (Mdia ) 4.1 × 10-6 emu) for diamagnetism.
Interpretation of the M vs H data at low T in polyradicals
1-4 can be reduced to consideration of spin systems arising
from defects. (Thermal population effects, relevant to spin
coupling J, are negligible in these conditions.) Two types of
spin sites (triarylmethyl sites in 1-4) can be discerned,
depending on their impact on spin of polyradical. The first type,
which we refer to as “defect sensitive sites”, are those where
one defect interrupting π-conjugation will lead to a mixture of
spin systems, drastically lowering the overall value of S. The
second type, which we refer to as “defect insensitive sites”, are
those where one defect retains a single spin system, lowering
the 4-biphenyl-substituted sites and the other triarylmethyl sites,
respectively. A simple model is proposed for evaluation of
impact of defects on spin of polyradical. Parameter p is defined
as probability of finding an “unpaired” electron at spin site, for
1
its value of S by /2. In 1-4, these two types correspond to

11682 J. Am. Chem. Soc., Vol. 119, No. 48, 1997
Rajca et al.
Figure 10. Enumeration of spin systems for hexadecaradical 4 with
one defect at the 4-biphenyl-substituted site. Yield per site for genera-
tion of “unpaired” electrons (100p %) is assummed identical for each
site.
Figure 9. SQUID magnetometry (H ) 0-5.0 T) for hexadecaradical
4 in THF-d8. Main plot: M/Msat vs H/T. Experimental points at T )
1.8, 3, and 5 K and Brillouin functions with S ) 6, 7, 8 are shown as
symbols and lines, respectively. The fitting parameters at T ) 1.8, 3,
and 5 K are S ) 7.16, 7.19, 7.14 and Msat102 ) 1.165, 1.164, and
1.161 emu; the parameter dependence is 0.27, 0.37, and 0.53. Insert:
MT vs T at H ) 0.5 T. Open circles are the experimental points. The
solid line is the numerical fit to the S′ ) /2, 3, /2 symmetrical trimer
model (eq 4). The fitting parameters are J/k ) 4.3 K and N ) 1.2 ×
10-7 mol, with parameter dependence of 0.57. Point-by-point correction
was used for all data to account for diamagnetism.
Table 2. Equations for Average Spin ( S ) As a Function of
Parameter p, Where 100p% Is Yield Per Site for Generation of
“Unpaired” Electrons in Polyradicals 1-4a
polyradical
S
S
p
5
5
1
2
3
4
1.5p/(2 - p)
2.5p/(2 - p)
3.5p/(3 - 2p)
8p/(5 - 4p)
2.40
3.28
7.2
0.98
0.98
0.98
a Estimated parameters p are from experimental values of S for the
best samples of 2-4 (Figures 7-9).
simplicity, it is assummed that p is identical for all sites.2c,35
The parameter p may be related to yield per site for generation
of “unpaired” electrons, 100p%. Spin systems, caused by
defects at the defect sensitive sites, are explicitly enumerated.
Defects at the defect insensitive sites are accounted for ap-
proximately, by scaling their contribution to spin with a factor
of p. In 4, the following spin systems, arising from defects at
the two 4-biphenyl-substituted sites, should be taken into
account: for no defects, one system with spin 1 + 7p; for one
defect, three systems with spin (1/2 + 5p), p, p; for two defects,
five systems with spin 3p, p, p, p, p. (Figure 10 shows spin
systems arising from one defect.) Equations for M, derived from
this model, are used for numerical fit of the M vs H/T data (eq
5 in the Experimental Section). The resultant values of p allow
for calculation of average spin S for a polyradical (Table 2,
eq 6 in the Experimental Section). For p’s near one in
polyradicals with connectivity of 1-4, S ≈ S within experi-
mental errors. Consequently, values of S from fits to the
variable spin Brillouin function (results section) may be used
to estimate p. Values of p, for polyradicals 2-4 range from
0.95 to 0.98, with the best samples for each polyradical attaining
0.98 (Table 2).35 Incidentally, sample of 4 with an excellent
yield per site, 100p% ) 98%, has S ) 7.2, which is 10% lower
than the theoretical value of S ) 8, and contains 100p16% )
72% of hexadecaradical with all 16 “unpaired” electrons intact.
This clearly illustrates the importance of the problem of defects
in very-high-spin polyradicals.
arises about the effect of such admixtures on the fitted values
of J/k. However, inclusion of variable parameter p would
overparametrize and/or severely complicate the MT vs T fits.
Thus, the impact of the fixed amounts of the spin impurities
are tested in the simplest polyradical, 1. For example, admixture
of 20% of an S ) 1/2 monoradical or 10% S ) 1 diradical (with
identical J/k) lowers value of J/k by only ∼3%.
Conclusions
Spin cluster approach to very-high-spin polyradicals provides
a series of adequately characterized polyradicals, including the
S ) 8 ground state hexadecaradical. Discriminating use of 3,4′-
biphenylene and 3,5,4′-biphenylyne ferromagnetic coupling units
in polyarylmethyl polyradicals allows for simplified modular
synthesis of their precursors, for attainment high yields for
generation of “unpaired” electrons, and for improved magnetic
characterization.
The next steps in design of very-high-spin polyradicals are
(1) use of larger number of modules, (2) increase in the number
of sites for “unpaired” electrons per module, and (3) use of only
macrocyclic modules.10 Such organic mesomolecules and
polymers hold a promise of greatly exceeding the present values
of S.
As far as the M vs T data for wide range of T are concerned,
the presence of defects implies that polyradicals 1-4 may
possess admixtures of uncoupled spins and spin clusters with
different energy levels and, in some cases, J/k, compared to
the spin clusters of the defect-free polyradicals. The question
Experimental Section
Materials and Special Procedures. Ether, tetrahydrofuran (THF),
and 2-methyltetrahydrofuran (2-MeTHF) for use on the vacuum line
were distilled from sodium/benzophenone in a nitrogen atmosphere.
Iodine (99.999%, resublimed crystals, ultradry) was obtained from
Johnson-Mathey. THF-d8 (99.95%D), which was obtained from
Cambridge Isotope Labs, was doubly vacuum transferred from sodium/
benzophenone prior to use. t-BuLi was obtained from either Aldrich
(1.7 M in pentane) or Across (1.5 M in pentane). Other major
(35) Assumptions of identical probability p for each site are common to
the simplest versions of percolation theories: Stauffer, D. Introduction to
Percolation Theory; Taylor and Francis: London, 1985.
(36) Estimate of p for triradical 1 is not reported because its relatively
large negative values of θ introduce significant error in values of S.34

Organic Spin Clusters
J. Am. Chem. Soc., Vol. 119, No. 48, 1997 11683
commercially available chemicals, including MeOD (99.5+% D), were
obtained from Aldrich. Preparations of 7 and dibromocalix[4]arene
hexaether (13) have been described.3,8
Module 8. t-BuLi (4.40 mL of 1.7 M solution in pentane, 7.48
mmol) was added to a solution of 7 (2.00 g, 3.68 mmol) in ether (65
mL) at -78 °C. After 3.5 h, the reaction was quenched with MeOH
(1 mL) at -78 °C and warmed to ambient temperature for 30 min.
The reaction mixture was washed with 100 mL of water and extracted
with ether (3 × 50 mL); the combined organic layer was washed with
brine (25 mL) and dried over MgSO4. Concentration in vacuo gave
1.625 g of clear viscous liquid. Separation by column chromatography
(230-400 mesh silica gel, 10% benzene in hexane) gave 1.056 g of
white solid (62%). Recrystallization of 150 mg of this white solid
with MeOH/ether gave 100 mg of white crystals, mp 124-126 °C. 1H
NMR (500 MHz, EM ) -1.6, GB ) 0.9, CDCl3): δ 7.685 (t, J ≈ 2,
1 H), 7.351 (dt, J ) 8, J ≈ 2, 1 H), 7.326 (dt, J ) 8, J ≈ 2, 1 H),
7.306, 7.293 (AB, J ) 9, 8 H), 3.026 (s, 3 H), 1.307 (s, 18 H). 13C-
{1H}DEPT(135°)NMR (125 MHz, CDCl3): δ aromatic quaternary
region, expected, 4 resonances; found, 4 resonances at 150.0 (q), 148.0
(q), 139.9 (q), 122.0 (q); aromatic nonquaternary region, expected, 6
resonances; found, 6 resonances at 131.0, 129.7, 129.2, 128.7, 127.1,
124.7; aliphatic region, resonances at 86.4 (q), 52.0, 34.4 (q), 31.3. CI
GC-MS: m/z (%RA for m/z ) 50-500) at (M - OCH3)+ 433 (47),
435 (47) and at (M - C10H13)•+ 331 (100), 333 (93).
For preparation of polyradicals, solutions of carbopolyanions in THF
(or THF-d8) were prepared in argon-filled Vacuum Atmospheres or
M. Braun gloveboxes or a 10-3 Torr vacuum line. In selected
preparations, starting from polyethers 1-(OMe)3, 2-(OMe)5, and
3-(OMe)7, all glassware and metalware were heated in the Braun
glovebox antechamber to 180 °C under 10-3 Torr vacuum overnight.
In all preparations, starting from hexadecaether 4-(OMe)16, vacuum
line was used; the vessel and the procedures are described elsewhere.8
All polyethers were heated under 10-3 Torr vacuum in the 50-70 °C
mineral oil bath overnight, prior to their use in preparation of
carbopolyanions.
NMR Spectroscopy and Other Analyses. NMR spectra were
obtained using Omega spectrometer (1H, 500 MHz) in CDCl3, benzene-
d6, THF-d8; the chemical shift references were 1H, TMS, 0.0 ppm,
benzene-d5, 7.15 ppm, acetone-d5, 2.04 ppm, THF-d7, 3.48 ppm, and
13C, CDCl3, 77.0 ppm, THF-d8, 67.45 ppm. Coupling constants (J)
are reported in hertz. Typical 1D FID was subjected to exponential
1
multiplication with an exponent of 0.1 Hz (for H) and 1.0-2.0 Hz
(for 13C); for selected spectra, both exponential and gaussian multiplica-
tions (EM and GB, respectively) were used, with exponents indicated
as EM and GB for each applicable spectrum. IR spectra were obtained
as described previously.2c ESR spectra are acquired, using a liquid
nitrogen dewar, as described elsewhere.3b GC MS analyses were carried
out using Hewlett-Packard 5890/5972 instrument equipped with a 30
m × 0.25 mm DB-5 capillary column. Typical oven temperatures were
stepped up from 100 to 280 °C at a rate of 20 °C/min. FAB MS
analyses were carried out at the Nebraska Center for Mass Spectrometry.
Module 10. t-BuLi (27.0 mL of 1.5 M solution in pentane, 40.5
mmol) was added to a solution of 7 (10.91 g, 20.05 mmol) in THF
(180 mL) at -78 °C over the period of 10 min. After 1 h, 4,4′-di-
tert-butylbenzophenone (5.89 g, 20.05 mmol) was added under nitrogen
flow at -78 °C. The reaction mixture was allowed to warm to ambient
temperature for 1 day; the reaction mixture was quenched with
water (300 mL). After extraction with ether (2 × 200 mL), the
combined organic layer was dried over MgSO4. Concentration in
vacuo gave 16.04 g of light yellow viscous liquid, which is triaryl-
methanol 9, suitable for use in the next step in the synthesis. 1H NMR
(500 MHz, CDCl3): δ 7.590 (t, J ≈ 2, 1 H), 7.429 (t, J ≈ 2, 1 H),
7.265, 7.084 (AB, J ) 9, 4 H), 7.221 (t, J ≈ 2, 1 H), 7.243, 7.186
(AB, J ) 9, 4 H), 2.931 (s, 3 H), 2.576 (s, 1 H), 1.305 (s, 18 H), 1.302
(s, 18 H).
Elemental analyses were completed by M-H-W Laboratories, P.O.
Box 15149, Phoenix, AZ 85060.
Etherification of Triarylmethanols.17b General Procedure.
A
round bottom flask with sidearm was charged with NaH (60%
dispersion in mineral oil, 3-20 equiv based on triarylmethanol). After
mineral oil was removed with pentane under nitrogen flow, THF was
added, and during cooling with an ice bath, triarylmethanol (1 equiv)
in THF was then added. (The concentration of triarylmethanol in the
reaction mixture was 0.01-0.05 M). The resultant suspension was
stirred for 1-4 h during which time the temperature of cooling bath
was allowed to reach ambient temperature. After the bath was recooled
to 0 °C, MeI (1.5-3 equiv based on NaH) was added. Following 4-19
h of stirring at ambient temperature, aqueous workup was carried out.
The ether extract was dried over MgSO4 and, then, concentrated in
vacuo to give crude modules 6, 10, and 12.
Etherification of 9 (16.04 g, 21.13 mmol), according to the general
procedure, followed by recrystallization from MeOH/ether afforded
14.09 g (86%) of white solid, mp 206-208 °C. 1H NMR (500 MHz,
CDCl3): δ 7.580 (d, J ≈ 2, 2 H), 7.301 (t, J ≈ 2, 1 H), 7.245, 7.179
(AB, J ) 9, 16 H), 2.943 (s, 3 H), 1.305 (s, 36 H). 13C{1H}DEPT-
(135°)NMR (125 MHz, CDCl3): δ aromatic quaternary region,
expected, 4 resonances; found, 4 resonances at 149.8 (q), 146.5 (q),
140.2 (q), 121.9 (q) ; aromatic nonquaternary region, expected, 4
resonances; found, 4 resonances at 128.6, 128.5, 128.4, 124.5; aliphatic
region, resonances at 86.5 (q), 52.0, 34.4 (q), 31.4.
Module 6. n-BuLi (34.0 mL of 2.5 M solution in hexane, 85 mmol)
was added to a solution of 1,4-dibromobenzene (20.0 g, 84.8 mmol)
in ether (300 mL) at -78 °C. After 2.5 h, methyl 4-tert-butylbenzoate
(7.36 g, 38.3 mmol) was added as liquid by syringe under nitrogen
flow at -78 °C. The reaction mixture was allowed to warm to ambient
temperature for 1 day, and the reaction mixture was quenched with
water (300 mL). After extraction with ether (2 × 150 mL), the
combined organic layer was dried over MgSO4. Concentration in vacuo
gave 17.99 g of light yellow viscous liquid, which is triarylmethanol
5, suitable for use in the next step in the synthesis. 1H NMR (500
MHz, CDCl3): δ 7.434, 7.167 (AB, J ) 8, 8 H), 7.327, 7.110 (AB, J
) 9, 4 H), 2.713 (s, 1 H), 1.309 (s, 9 H).
Etherification of 5 (0.921 g, 1.942 mmol), according to the general
procedure, gave 1.04 g of light yellow viscous liquid. Separation by
column chromatography with (TLC grade silica gel, hexane to 1% ether/
hexane) gave 0.594 g of white solid (63%), mp 110-112 °C. 1H NMR
(500 MHz, EM ) -1.2, GB ) 0.9, CDCl3): δ 7.416, 7.298 (AB, J )
9, 8 H), 7.307, 7.245 (AB, J ) 9, 4 H), 3.024 (s, 3 H), 1.302 (s, 9 H).
13C{1H}DEPT(135°)NMR (125 MHz, CDCl3): δ aromatic quaternary
region, expected, 4 resonances; found, 4 resonances at 150.4 (q), 143.3
(q), 139.1 (q), 121.2 (q); aromatic nonquaternary region, expected, 4
resonances; found, 4 resonances at 131.0, 130.2, 128.6, 124.9; aliphatic
region, 82.4 (q), 52.1, 34.5 (q), 31.3. CI GC-MS: m/z (%RA for m/z
) 50-500) at (M - OCH3)+ 455 (15), 457 (30), 459 (15) and at (M
- C10H13)•+ 331 (100), 333 (97).
Module 12. t-BuLi (9.50 mL of 1.5 M solution in pentane, 14.3
mmol) was added to a solution of 10 (5.248 g, 6.79 mmol) in THF (60
mL) at -78 °C. After 2.5 h, the temperature in the cooling bath was
allowed to warm to -20 °C over a period of 20 min; subsequently,
4-bromobenzoyl chloride (0.675 g, 3.08 mmol) was added under
nitrogen flow at -20 °C. After 2 h at -20 °C, the reaction mixture
was allowed to warm to ambient temperature overnight. The reaction
mixture was quenched with water (200 mL). After extraction with
ether (2 × 200 mL), the combined organic layer was dried over MgSO4.
Concentration in vacuo gave 5.55 g of light yellow viscous liquid.
Column chromatography (TLC grade silica gel, 10% ether in hexane)
afforded triarylmethanol 11 (1.70 g, 35%), which is suitable for use in
the next step in the synthesis. 1H NMR (500 MHz, EM ) -1.2, GB
) 0.85, CDCl3): δ 7.28-7.24 (m, 8 H), 7.163, 7.108 (AB, J ) 9, 16
H), 7.160, 7.106 (AB, J ) 9, 16 H), 6.930 (d, J ) 8, 2 H), 2.778 (s,
1 H, exch. D2O), 2.731 (s, 12 H), 1.265 (s, 72 H). 13C{1H}DEPT-
(135°)NMR (125 MHz, CDCl3 ): aromatic quaternary region, expected,
8 resonances; found, 8 resonances at 149.38 (q), 149.35 (q), 146.3 (q),
145.5 (q), 143.2 (q), 141.13 (q), 141.09 (q), 120.8 (q); aromatic
nonquaternary region, expected, 8 resonances; found, 7 resonances at
130.5, 130.0, 129.4, 128.47, 128.41, 125.5, 124.3; aliphatic region, 86.8
(q), 82.2 (q), 51.9, 34.3 (q), 31.4. FABMS (3-NBA) cluster: m/z (%RA
for m/z ) 340-1800) at (M - OCH3)+ 1539.9 (80), 1540.9 (87), 1541.9
(100), 1542.9 (84), 1543.9 (49). IR (cm-1): 3600 (O-H), 1593 (Ar),
1081 (C-O-C).

11684 J. Am. Chem. Soc., Vol. 119, No. 48, 1997
Rajca et al.
Etherification of 11 (1.59 g, 1.01 mmol), according to the general
procedure, gave 1.63 g of light yellow viscous liquid. Filtration through
flash silica with 5% ether in hexane and recrystallization from MeOH/
ether afforded 1.40 g (87%) of white solid, mp 134-136 °C. 1H NMR
(500 MHz, EM ) -0.90, GB ) 0.80, CDCl3): δ 7.300 (d, J ) 2, 4
H), 7.245 (t, J ) 2, 2 H), 7.234, 7.042 (AB, J ) 8, 4 H), 7.161, 7.115
(AB, J ) 8, 16 H), 7.161, 7.111 (AB, J ) 8, 16 H), 2.779 (s, 12 H),
2.748 (s, 3 H), 1.522 (s, 72 H). 13C{1H}DEPT(135°)NMR (125 MHz,
CDCl3): δ aromatic quaternary region, expected, 8 resonances; found,
7 resonances at 149.3 (q), 143.6(q), 142.6 (q), 142.2 (q), 141.28 (q),
141.25 (q), 120.5 (q); aromatic nonquaternary region, expected, 8
resonances; found, 6 resonances at 130.48, 130.45, 129.3, 128.3, 127.1,
124.3; aliphatic region, 87.2 (q), 86.8 (q), 52.04, 51.97, 34.3 (q), 31.4.
FABMS (3-NBA) cluster: m/z (%RA for m/z ) 340-1800) at (M -
OCH3)+ 1153.9 (85), 1154.9 (82), 1155.9 (100), 1156.9 (81), 1157.9
(50). IR (cm-1): 1593 (Ar), 1082 (C-O-C). Anal. Calcd for
(q), 149.5 (q), 144.2 (q), 143.1 (q), 141.0 (q), 140.6 (q), 139.9 (q),
139.5 (q); aromatic nonquaternary region, expected, 8 resonances; found
7 resonances at 129.0, 128.6, 128.5, 126.5, 124.67, 124.63, 124.4;
aliphatic region, 86.9 (q), 86.7 (q), 52.08, 52.02, 34.4 (q), 31.4, 31.3.
FABMS (3-NBA) cluster: m/z (% RA for m/z ) 400-2000) at (M -
OCH3)+ 1682.0 (18), 1683.0 (23), 1684.0 (83), 1685.0 (100), 1686.0
(68), 1687.0 (32), 1688.0 (14). IR (cm-1): 1595 (Ar), 1081 (C-O-C).
Anal. Calcd for C124H146O35: C, 87.77; H, 8.57. Found: C, 86.70, H,
8.44.
3-(OMe)7. Following the general procedure for Suzuki coupling,
starting from 10 (0.146 g, 0.189 mmol) and 12 (0.202 g, 0.127 mmol),
reflux for 1 day in toluene/MeOH (8 mL) gave a the crude product as
a light yellow viscous solid. Column chromatography (TLC grade silica
gel, 5% ether in hexane) and recrystallization from MeOH gave 0.204
g of white solid (73%), mp 168-172 °C. 1H NMR (500 MHz, EM )
-1.40, GB ) 0.90, CDCl3, 1H-1H COSY cross-peaks in the aromatic
region): δ 7.714 (d, J ) 2, 2 H, 7.311), 7.399 (d, J ) 8, 2 H, 7.195),
7.350 (d, J ) 2, 4 H, 7.206), 7.311 (t, J ) 2, 1 H, 7.714), 7.235 (s, 16
H), 7.195 (d, J ) 8, 2 H, 7.399), 7.206 (t, J ) 2, 2 H, 7.350), 7.148 (d,
J ) 9, 16 H), 7.126 (d, J ) 9, 8 H), 7.121 (d, J ) 9, 8 H), 2.989 (s,
6 H), 2.798 (s, 3 H), 2.760 (s, 12 H), 1.291 (s, 36 H), 1.232 (s, 72 H).
13C{1H}DEPT(135°)NMR (125 MHz, CDCl3): δ aromatic quaternary
region, expected, 12 resonances; found, 11 resonances at 149.5 (q),
149.1 (q), 144.3 (q), 143.0 (q), 142.8 (q), 142.3 (q), 141.44 (q), 141.41
(q), 141.0 (q), 139.5 (q), 139.4 (q); aromatic nonquaternary region,
expected, 12 resonances; found 9 resonances at 129.3,128.7, 128.4,
128.3, 127.0, 126.0, 124.4, 124.3, 124.0; aliphatic region, 86.86 (q),
86.83 (q), 52.08, 51.98, 51.95, 34.4 (q), 34.3 (q), 31.4. FABMS (3-
NBA) cluster: m/z (% RA for m/z ) 400-2320) at (M - OCH3)+
2166.5 (16), 2167.5 (24), 2168.5 (72), 2169.5 (100), 2170.5 (84), 2171.5
(43), 2172.5 (21); calcd for C157H187O6 (M - OCH3)+ 2168.4 (56),
2169.4 (100), 2170.4 (89), 2171.4 (53), 2172.4 (24). IR (cm-1): 1594
(Ar), 1081 (C-O-C). Anal. Calcd for C158H190O7 : C, 86.21; H,
8.70. Found: C, 86.06; H, 8.90.
C108H129O5Br: C, 81.58; H, 8.37. Found: C, 81.18; H, 7.95.
General Procedure for Polyethers 1-(OMe)3, 2-(OMe)5, 3-(OMe)7,
and 4-(OMe)16 (Suzuki Coupling).16 t-BuLi (1.5 or 1.7 M solution
in pentane, 2.1 equiv) was added to the first module (1 equiv) 0.02-
0.06 M in THF at -78 °C. After 2-3 h, the reaction mixture was
allowed to warm to -20 to -30 °C for 10-15 min and, then, B(OMe)3
(1.1-1.25 equiv) was added to the reaction mixture. After warming
to ambient temperature overnight, the reaction mixture was dried under
N2 flow and, then, evacuated. Subsequently, the following components
were added to the reaction mixture: the second module (neat, under
N2 flow), Ba(OH)2‚8H2O (0.6-1.0 equiv, neat, under N2 flow), Pd-
(PPh3)4 (0.03-0.05 equiv per CC bond, either neat in an N2 glovebag
or 0.01-0.02 M in degassed toluene), and toluene/MeOH (1:1, degassed
by N2 bubbling). The reaction mixture was allowed to reflux under
N2 atmosphere for 1-3 days. After extraction with ether, the ether
layer was dried over MgSO4, filtered, and concentrated in vacuo to
give a crude product.
1-(OMe)3. Following the general procedure for Suzuki coupling,
starting from 8 (0.302 g, 0.648 mmol) and 6 (0.143 g, 0.293 mmol),
reflux for 3 days in toluene/MeOH (30 mL) gave the crude product as
a clear oil. Separation by column chromatography with (TLC grade
silica gel, 5% ether in hexane), followed by recrystallization from
MeOH gave 0.130 g of white solid (51%), mp 164-166 °C. 1H NMR
(500 MHz, EM ) -1.2, GB ) 0.6, CDCl3): δ 7.733 (t, J ) 2, 2 H),
7.491 (s, 8 H), 7.438 (dt, J ) 8, J ) 2, 2H), 7.400 (dt, J ) 8, J ) 2,
2 H), 7.37-7.28 (m, 22 H), 3.090 (s, 3 H), 3.057 (s, 6 H), 1.304 (s, 9
H), 1.298 (s, 36 H). 1H NMR (500 MHz, EM ) -1.2, GB ) 0.85,
4-(OMe)16. Following the general procedure for Suzuki coupling,
starting from 12 (0.200 g, 0.126 mmol) and 13 (0.052 g, 0.029 mmol,
reflux for 2 days in toluene/MeOH (8 mL) gave the crude product as
a clear oil. Column chromatography (TLC grade silica gel, 7% ether
in hexane), preparative TLC (7% ether in hexane with repeated
developments), and treatment with boiling MeOH gave 19.9 mg of
white glassy solid (15%). 1H NMR (500 MHz, EM ) -1.60, GB )
0.90, C6D6, 293 K): δ 8.180-7.080 (m, 128 H), 3.180 (s, 3 H), 2.999
(s, 3 H), 2.956 (s, 6 H), 2.936 (s, 18 H), 2.927 (s, 6 H), 2.921 (s, 3 H),
2.913 (s, 3 H), 2.886 (s, 3 H), 2.860 (s, 3 H), 1.238 (s, 9 H), 1.228 (s,
54 H), 1.226 (s, 18 H), 1.218 (s, 18 H), 1.215 (s, 18 H), 1.206 (s, 9 H),
1.200 (s, 18 H), 1.187 (s, 27 H), 1.180 (s, 9 H), 1.176 (s, 9 H), 1.172
(s, 9 H), 1.163 (s, 9 H), 1.151 (s, 9 H). 1H NMR (500 MHz, EM )
-1.50, GB ) 0.90, C6D6, 328 K): δ 8.150-7.050 (m, 128 H), 3.168
(s, 3 H), 2.997 (s, 3 H), 2.990 (s, 3 H), 2.968 (s, 3 H), 2.955 (s, 6 H),
2.944 (s, 12 H), 2.941 (s, 6 H), 2.935 (s, 3 H), 2.931 (s, 3 H), 2.883 (s,
3 H), 2.875, (s, 3 H), 1.234 (s, 9 H), 1.228 (s, 72 H), 1.221 (s, 18 H),
1.219 (s, 18 H), 1.215 (s, 9 H), 1.195 (s, 18 H), 1.192 (s, 9 H), 1.191
(s, 9 H), 1.188 (s, 18 H), 1.184 (s, 9 H), 1.176 (s, 18 H), 1.159 (s, 9
H). 1H NMR (500 MHz, EM ) -1.50, GB ) 0.90, C6D6, 348 K,
1H-1H COSY cross-peaks in aromatic region): δ 8.102 (t, J ) 2, 1
H, 7.869, 7.561), 7.921 (t, J ) 2, 1 H, 7.815, 7.484), 7.918 (t, J ) 2,
1 H, 7.865, 7.795), 7.869 (t, J ) 2, 1 H, 8.102, 7.561), 7.865 (t, J )
2, 1 H, 7.918, 7.795), 7.846 (d, J ) 2, 2 H, 7.672), 7.839 (d, J ) 2, 2
H, 7.680), 7.815 (t, J ) 2, 1 H, 7.921, 7.484), 7.803 (d, J ) 2, 2 H,
7.656), 7.795 (t, J ) 2, 1 H, 7.918, 7.865), 7.736 (t, J ) 2, 1 H, 7.684,
7.586), 7.684 (t, J ) 2, 1 H, 7.736, 7.586), 7.680 (t, J ) 2, 1 H, 7.839),
7.672 (t, J ) 2, 1 H, 7.846), 7.656 (t, J ) 2, 1 H, 7.803), 7.636 (d, J
) 9, 2 H, 7.283), 7.586 (t, J ) 2, 1 H, 7.736, 7.684), 7.561 (t, J ) 2,
1 H, 8.102, 7.869), 7.43-7.51 (overlapped, 7.18-7.26), 7.503 (t or d,
J ) 2, 1 H or 2 H, 7.243), 7.484 (t, J ) 2, 1 H, 7.921, 7.815), 7.464
(d, J ) 9, 2 H, 7.283), 7.429 (d, J ) 9, 2 H, 7.402), 7.404 (d, J ) 9,
2 H, 7.362), 7.402 (d, J ) 9, 2 H, 7.429), 7.362 (d, J ) 9, 2 H, 7.404),
7.350 (d, J ) 9, 2 H, 7.169), 7.342 (d, J ) 9, 2 H, 7.127), 7.18-7.26
(overlapped, 7.43-7.51), 7.283 (d, J ) 9, 2 H, 7.636), 7.283 (d, J )
9, 2 H, 7.464), 7.243 (d or t, J ) 2, 2 H or 1 H, 7.503), 7.169 (d, J )
9, 2 H, 7.350), 7.127 (d, J ) 9, 2 H, 7.342), 3.166 (s, 3 H), 3.017 (s,
3 H), 2.999 (s, 3 H), 2.981 (s, 3 H), 2.958 (s, 6 H), 2.952 (s, 18 H),
1
C6D6, H-1H COSY cross-peaks in the aromatic region): δ 8.190 (t,
J ) 2, 2 H, 7.598, 7.375), 7.623 (d, J ) 9, 8 H, 7.242), 7.598 (dt, J1
) 8, J2 ) 2, 2 H, 8.190, 7.180), 7.544 (d, J ) 9, 4 H, 7.482), 7.544 (d,
J ) 8, 2 H, 7.289), 7.482 (d, J ) 9, 4 H, 7.544), 7.375 (dt, J1 ) 8, J2
) 2, 2 H, 8.190, 7.180), 7.289 (d, J ) 8, 2 H, 7.544), 7.242 (d, J ) 9,
8 H, 7.623), 7.180 (t, J ) 8, 2 H, 7.598, 7.375), 3.112 (s, 6 H), 3.045
(s, 3 H), 1.219 (s, 9 H), 1.166 (s, 36 H). [Note: 1H-1H COSY cross-
peak a between resonances at 7.598 and 7.375 ppm was not detected.]
13C{1H}DEPT(135°)NMR (125 MHz, CDCl3): δ aromatic quaternary
region, expected, 8 resonances; found, 8 resonances at 149.8 (q), 149.6
(q), 145.5 (q), 143.3 (q), 140.7 (q), 140.4 (q), 140.0 (q), 139.7 (q);
aromatic nonquaternary region, expected, 10 resonances; found, 10
resonances at 129.0, 128.7, 128.6, 128.1, 127.5, 127.1, 126.5, 125.3,
124.7, 124.6; aliphatic region, 86.8 (q), 86.7 (q), 52.1, 52.0, 34.4 (q),
31.4. FABMS (3-NBA) cluster: m/z (% RA for m/z ) 350-1240) at
(M - OCH3)+, 1065.8 (16), 1066.8 (15), 1067.8 (100), 1068.8 (84),
1069.8 (37), 1070.8 (12). IR (cm -1): 1602 (Ar), 1079 (C-O-C). Anal.
Calcd for C80H90O3: C, 87.39; H, 8.25. Found: C, 87.61; H, 8.08.
2-(OMe)5. Following the general procedure for Suzuki coupling,
starting from 10 (0.503 g, 0.650 mmol) and 6 (0.143 g, 0.293 mmol),
reflux for 2 days in toluene/MeOH (30 mL) gave the crude product as
a clear oil. Column chromatography with (TLC grade silica gel,
benzene/hexane, 2:1) and recrystallization from MeOH gave 0.235 g
of white solid (47%), mp 184-186 °C. 1H NMR (500 MHz, EM )
-1.2, GB ) 1.2, CDCl3): δ 7.647 (d, J ) 2, 4 H), 7.481, 7.458 (AB,
J ) 9, 8 H), 7.363 (t, J ) 2, 2 H), 7.336, 7.295 (AB, J ) 8, 2 H),
7.239 (s, 32 H), 3.074 (s, 3 H), 2.979 (s, 12 H), 1.298 (s, 72 H), 1.294
(s, 9 H). 13C{1H}DEPT(135°)NMR (125 MHz, CDCl3): δ aromatic
quaternary region, expected, 8 resonances; found, 8 resonances at 149.7

Organic Spin Clusters
J. Am. Chem. Soc., Vol. 119, No. 48, 1997 11685
a ) (1.345H)/(T - θ)
2.942 (s, 3 H), 2.940 (s, 3 H), 2.889 (s, 3 H), 2.886 (s, 3 H), 1.237 (s,
9 H), 1.233 (s, 72 H), 1.227 (s, 18 H), 1.226 (s, 18 H), 1.223 (s, 9 H),
1.202 (s, 9 H), 1.199 (s, 27 H), 1.195 (s, 27 H), 1.187 (s, 9 H), 1.182
(s, 9 H), 1.171 (s, 9 H). FABMS (3-NBA) cluster: m/z (% RA for
m/z ) 800-4800) at (M - OCH3)+ 4604.1 (41), 4605.1 (79), 4606.1
(84), 4607.1 (100), 4608.1 (86), 4609.1 (64), 4610.1 (45); calcd for
ck ) 1 + 2
cosh(ia); k ) 1, 2, ..., S; for integral S
∑
i)1-k
ck ) 2
cosh(ia/2); k ) 1, 3, ..., 2S; for half-integral S
331H389O15 (M - OCH3)+ 4604.0 (11), 4605.0 (42), 4606.0 (80),
∑
C
i)1-k,odd
4607.0 (100), 4608.0 (94), 4609.0 (71), 4610.0 (44), 4611.0 (24). IR
(cm-1): 1593 (Ar), 1083 (C-O-C). Anal. Calcd for C332H392O16:
C, 85.96; H, 8.52. Found: C, 85.08; H, 8.41.
Reactions of Heptaether 3-(OMe)7 with Na/K and MeOH
Quenching Product 3-(H)7. A drop of Na/K alloy (multimolar excess)
was added to a stirred polyether (15.2 mg) in THF (0.5 mL). After 3
days of stirring, MeOH (a few drops) was added. The usual aqueous
workup with ether gave the crude product. Preparative TLC (2.5%
ether in hexane) gave a clear oil (11.3 mg). Treatment with boiling
ether/MeOH afforded a white solid (8.2 mg).37
sk )
sk )
i(sinh(ia)); k ) 1, 2, ..., S; for integral S
∑
i)1-k
(i/2)(sinh(ia/2)); k ) 1, 3, ..., 2S; for half-integral S
∑
i)1-k,odd
em ) exp(-mb)/T; m ) integer; b ) J/k
em′ ) exp(-mb′)/T; m ) integer; b′ ) J′/k ) 500 K
Equations for M for polyradicals 1-4 are as follows:
1 as S′ ) 1/2, 1/2, 1/2 trimer
Preparation of Polyradicals for SQUID Magnetometry, ESR
Spectroscopy, and Quenching Studies with MeOH and MeOD.3b
Polyether (7-16 mg) was stirred for several days with excess Li metal
(for 1-(OMe)3, 2-(OMe)5, 3-(OMe)7) or Na/K alloy (for 2-(OMe)5,
3-(OMe)7, 4-(OMe)16) in THF or THF-d8 (0.5 mL). For 1-(OMe)3,
2-(OMe)5, and 3-(OMe)7, carbopolyanions in THF were obtained in
an argon-filled glovebox and, then, transferred to an oxidation vessel,
which was modified by the replacement of the 4 mm with 5 mm o.d.
quartz tube.27 For 4-(OMe)16, carbopolyanions in THF-d8 (or THF)
were prepared directly in a multicompartment oxidation vessel, as
described elsewhere.8 Addition of I2, either as crystals under stream
of argon or through vacuum transfer at low temperatures (168-178
K) gave the corresponding polyradicals in THF (or THF-d8). A small
portion of polyradical in THF (or THF-d8) was transferred at low
temperature to a 5 mm quartz tube. The tube possessed a thin flat
bottom, located ca. 60 mm from the end of the tube.8 The tube was
flame sealed and stored in liquid nitrogen for magnetization studies.
Samples of tri- and pentaradicals 1 and 2 for ESR spectroscopy were
diluted with 2-MeTHF several-fold prior to transfer to a 4 mm quartz
tube. The remaining reaction mixture was treated with Na/K alloy or
Li at 168-178 K for several hours and, then, at 195 K for several
days. Subsequent addition of MeOD or MeOH was followed with usual
aqueous workup. Separation by PTLC, 2.5% ether in hexane (2.0%
ether in hexane for 4-(H)16 and 4-(D)16) gave clear oils of hydrocarbons
1-(H)3, 2-(H)5, and 4-(H)16 and deuterated products 1-(D)3, 2-(D)5,
3-(D)7, and 4-(D)16.37
M ) (2(11180)NF1) + Mdia; S ) 3/2 (1)
where
F1 ) [s3 + s1(e3 + e1)]/[c3 + c1(e3 + e1)]
2 as S′ ) 1/2, pentamer
M ) (2(11180)NF2) + Mdia; S ) 5/2 (2)
where
F2 ) {s5 + s3[e5 + e1 + (2e2′e1)] + s1[e4 + e2 + (2e2′e4) +
(e4′e2)]}/{c5 + c3[e5 + e1 + (2e2′e1)] + c1[e4 + e2 + (2e2′e4) +
(e4′ e2)]}
3 as S′ ) 5/2, 1/2, dimer
M ) (2(11180)NF3) + Mdia; S ) 7/2 (3)
where
SQUID Magnetometry. Quantum Design (San Diego, CA)
MPMS5S was used. The sample tubes were inserted to the magne-
tometer at low temperature under helium atmosphere and, then,
evacuated and purged with helium, as described elsewhere. Following
the measurements, sample tubes were stored at ambient temperature
for several weeks, until their magnetic moments were negligible. Such
samples were carefully reinserted to the magnetometer, with the sample
chamber at 200 K, and subjected to the identical sequence of
measurements as the original sample. Such data were used for the
point-by-point correction for diamagnetism.
F3 ) [s7 + s5e7 + s3e12]/[c7 + c5e7 + c3e12]
4 as S′ ) 5/2, 3, 5/2 trimer
M ) (2(11180)NF4) + Mdia; S ) 8 (4)
where
F4 ) [s8 + s7(e16 + e6) + s6(e30 + e20 + e12) + s5(e42 + e32
+
e24 + e18) + s4(e52 + e42 + e34 + e28 + e24) + s3(e60 + e50
+
Numerical Curve Fitting. The SigmaPlot for Windows software
package was used for numerical curve fitting. The reliability of a fit
is measured by the parameter dependence, which is defined as
follows: dependence ) 1 - ((variance of the parameter, other
parameters constant)/(variance of the parameter, other parameters
changing)). Values close to 1 indicate overparametrized fit. Up to
four variable parameters, J/k (spin coupling constant in Kelvin), N
(number of moles of polyradical), θ (mean field parameter for small
intermolecular magnetic interactions), Mdia (correction for diamagne-
tism) are used for fitting MT vs T data over wide range of T. For
selected samples, accurate point-by-point correction for diamagnetism
and/or negligible intermolecular magnetic interactions may eliminate
Mdia and/or θ as variable parameters.
e42 + e36 + e32 + e30) + s2(e66 + e56 + e48 + e42 + e38) +
s1(e60 + e52 + e46)]/[c8 + c7(e16 + e6) + c6(e30 + e20 + e12) +
c5(e42 + e32 + e24 + e18) + c4(e52 + e42 + e34 + e28 + e24) +
c3(e60 + e50 + e42 + e36 + e32 + e30) + c2(e66 + e56 + e48 + e42
+
e38) + c1(e60 + e52 + e46) + e54]
Using Mdia from the MT vs T fit and/or point-by-point correction
for diamagnetism, M vs H data at low temperatures (T ) 1.8, 3, 5 K)
were corrected for diamagnetism. For tri- and pentaradicals 1 and 2,
fitting to a Brillouin function with mean field parameter, M vs H/(T -
θ) were carried out;32,33 θ was adjusted until the two variable parameters,
spin, S, and magnetization at saturation, Msat, were identical for each
T. For hepta- and hexadecaradicals 3 and 4, θ ) 0 from the MT vs T
fit, providing adequate fits to simple Brillouin function, M vs H/T, with
two variable parameters, S and Msat.32 Alternative procedure for 4,
involve fitting the M vs H/T data to a sum of Brillouin functions (B(Si))
weighted with fractions (xi) of spin systems with spin Si in the sample
Equations for magnetization, M(T,H), are obtained using the standard
statistical mechanical procedures on energy eigenvalues, derived from
the Heisenberg Hamiltonian. The following definitions are introduced
for notation of all equations for M:
(37) See the Supporting Information.

11686 J. Am. Chem. Soc., Vol. 119, No. 48, 1997
Rajca et al.
of polyradical with 0-2 defects at the two 4-biphenyl-substituted sites
(eq 5). Variable parameters are p and Msat.
research (CHE-9510096) and The Camille and Henry Dreyfus
Teacher-Scholar Award Program (1991-1996). We thank Dr.
Ronald Cerny of the Nebraska Center for Mass Spectrometry
for mass spectral determinations and Dr. Richard Schoemaker
for two-dimensional NMR spectra. We thank Dr. Shailesh Desai
for the help with the synthesis.
M/Msat
)
B(Si)xi/
(5)
∑
∑
i
i
For 4, the following parameters are used: xi ) p2, 2p(1 - p), (1 - p)2,
4[p(1 - p) + (1 - p)2] and Si ) 1 + 7p, 0.5 + 5p, 3p, p, where i )
1-4. Average spin S is defined as follows (eq 6, Table 2):
Supporting Information Available: A listing of NMR, MS,
and IR data for hydrocarbons 1-(H)3, 2-(H)5, 3-(H)7, and 4-(H)16
and deuterated products 1-(D)3, 2-(D)5, 3-(D)7, 4-(D)16 (4 pages).
See any current masthead page for ordering and Internet access
instructions.
S )
Sixi/ xi
(6)
∑ ∑
i
i
Acknowledgment. We gratefully acknowledge the National
Science Foundation, Chemistry Division for the support of this
JA972378B