A R T I C L E S
Rajca et al.
alternative refinements but the results were inconclusive. It is
also possible that crystal structure is of the solid solution type.
The molecules of 1 are packed as “bilayers” with the upper
and lower rims of calix[4]arenes forming separate regions.
Within each layer, the other, nondimerized, diagonally posi-
tioned pair of nitroxides in 1 is involved in short intermolecular
contacts with the N‚‚‚O distances of about 4.0 Å between the
molecules translated along the b axis (Figure 5).26
Another set of lesser quality X-ray crystallographic data on
a different single crystal at 95 K (i.e., temperature near the
plateau in the øT vs T plot) supports the structural findings at
173 K, except for small differences in disorder and methanol
content.23b The distances (and mutual orientations) of the
nitroxide moieties in the intramolecular dimer and intermolecular
close contacts in both structures are compatible with relatively
strong and weak antiferromagnetic couplings, respectively.
Numerical fits to the øT vs T data (Figure 3) are based upon
the model of two diradicals with variable number of molar
equivalents (N1 and N2) and coupling constants (J1/k and J2/k),
describing the intramolecular dimer and intermolecular N‚‚‚O
contacts in 1, respectively (eq 1).
Figure 3. Plot of øT vs T for polycrystalline 1. The numerical fit (solid
line) to eq 1 has the following variable parameters (and their parameter
dependencies): J1/k ) -253 K (0.90), J2/k ) -1.5 K (0.34), N1 ) 0.649
(0.88), N2 ) 1.141 (0.54); R2 ) 0.9993.
increase |2D|, compared to the case of localization of spin
density on the NO moieties. For localized dinitroxides, in which
the intramolecular distances between the midpoints of the N-O
bonds were approximately 6.2 and 4.7 Å, |2D| ≈ 25 mT and
|2D| ≈ 40 mT were measured.22
Solid State Studies of 1. A plot of øT vs. T for the solid of
1 shows drastically different behavior compared to that found
in solution (Figure 3). The high-temperature slope and low
temperature downward turn in the øT vs T plot suggest the
presence of strong (|J/k| > 100 K) and weak (|J/k| < 10 K)
antiferromagnetic exchange interactions, respectively. When
heating and cooling at various rates (e2 K/min) within 2-300
and 90-370 K ranges, no hysteresis for øT vs T is detectable;
only slow decomposition of 1 above 300 K is found.
øT ) (1.118T/H)[N1F1 + N2F2]
(1)
Fn ) [2 sinh(a)]/[1 + 2 cosh(a) + exp((-2Jn/k)/T)];
n ) 1, 2
a ) 1.345(H/T)
Fitting with N1 * N2 indirectly accommodates tri- and dini-
troxide impurities and other structures in which nitroxides are
weakly coupled. The intradimer J1/k has a substantial range
(-200 to -300 K, 4 samples), which may in part have its origin
in the variable occupancies for the crystallographically disor-
dered major and minor positions of the nitroxide moieties of
the dimer in polycrystalline samples used for magnetic measure-
ments; the relatively shorter N‚‚‚O contacts (and smaller N-O-
N-O torsional angles) in the minor dimer are likely to be
associated with stronger antiferromagnetic couplings.
The correlation between the magnetic data on 10-mg powder
samples and structural data on single crystals is difficult; because
of solvent loss, only broad powder diffraction patterns were
obtained at room temperature. Therefore, a 0.5-mg batch of
single crystals was selected under polarizing microscope.
Following determination of full datasets for two crystals and
cell constants for additional three crystals at 153 K (Table 1s,
Supporting Information), the øT vs T plot, characteristic of
tetranitroxide 1, is obtained. These five datasets and the
previously discussed dataset at 173 K possess essentially
identical cell constants. (For the refined structures, small
differences in methanol content were observed.) This suggests
reproducibility of crystal structure for single crystals and, in
conjunction with the high-temperature slope (and low temper-
ature downward turn) in øT, confirms the presence of the
intramolecular nitroxide dimer.
To understand the origin of the strong exchange interactions
in the solid state, the structure of 1 is determined by X-ray
crystallography at 173 K (Figure 4).23a One of the two pairs of
diagonally positioned nitroxides is found in a pararellogram
arrangement with close intramolecular contacts in the 2.6-2.8
Å range, well within the N-O van der Waals contact of 3.07
Å.24 In this nitroxide dimer, the oxygens are disordered with
occupancies of approximately two-thirds and one-third for the
major (O2A and O2C) and minor (O2F and O2G) positions,
respectively (Figure 4). The N-O bond lengths in this intra-
molecular dimer are elongated by 0.2-0.3 Å compared to those
in the intermolecular dimers of nitroxides (and monomeric
arylalkylnitroxides).6,11-13 These disorder affected, elongated
N-O bond lengths may accommodate distortion to form the
intramolecular dimer or be associated with hydroxyamines.25
The latter, i.e., dimers of hydroxyamines, was explored in
(21) Eaton, S. S.; More, K. M.; Sawant, B. M.; Eaton, G. R. J. Am. Chem. Soc.
1983, 105, 6560-6567. The dependence of the spectral width (|2D|) on
the inter-dipole distance (r) is calculated according to the following
equation: |2D| ) 3gâ/r3 ) 2.78 × 103 (g/r3), where |D| is in mT and r is
in Å. The r ) 5 and 4 Å would correspond to |2D| of about 40 and 80 mT,
respectively, for a g ≈ 2 diradical.
(22) Rohde, O.; Van, S. P.; Kester, W. R.; Griffith, O. H. J. Am Chem. Soc.
1974, 96, 5311-5318.
(23) Crystallographic data for tetranitroxide 1: (a) at 173 K (dataset A),
C
88H112N4O8‚2.31CH3OH, red crystal (0.17 × 0.09 × 0.04 mm3), T ) 173
K, triclinic, P1h , a ) 10.2842(7) Å, b ) 13.0555(8) Å, c ) 33.167(2) Å,
R ) 95.779(1)°, â ) 96.733(1)°, γ ) 100.260(1)°, V ) 4318.0(5) Å3, Z )
2, µ ) 0.071 mm-1, R ) 0.0640, wR2 ) 0.1680, GoF ) 0.926 (F2, all
data). (b) at 95 K (dataset B), C88H112N4O8‚2CH3OH, orange crystal (cut,
0.05 × 0.05 × 0.005 mm3), T ) 95 K, triclinic, P1h , a ) 10.260(2) Å, b
) 13.106(4) Å, c ) 32.814(11) Å, R ) 95.487(9)°, â ) 90.497(15)°, γ )
100.881(15)°, V ) 4311(2) Å3, Z ) 2, µ ) 0.045 mm-1, R ) 0.1253, wR2
) 0.3164, GoF ) 1.082 (F2, all data).
Conclusion
One pair of diagonal nitroxides on the calix[4]arene upper
rim is found to form a strong antiferromagnetic, intramolecular
(24) For intermolecular nitroxide dimers, typical N‚‚‚O contacts and N-O bond
lengths are 2.28-2.37 and 1.28 Å, respectively (refs 6, 11, 12).
(25) Inoue, K.; Koga, N.; Iwamura, H. J. Am. Chem. Soc. 1991, 113, 9803-
9810.
(26) The oxygens of one of the nitroxides are also disordered over two positions
(63:37) introducing the negligible difference of 0.03 Å for the two 4.0 Å
N‚‚‚O contacts; the N-O bond lengths are normal 1.28 Å.
9
8536 J. AM. CHEM. SOC. VOL. 125, NO. 28, 2003