An ideal one-dimensional antiferromagnetic spin system observed in hydrogen-bonded naphth[2,3-d]imidazol-2-yl nitronyl nitroxide crystal: The role of the hydrogen bond

Article abstract of DOI:10.1021/jp035849r

A novel stable organic radical, 2-(naphth[2,3-d]imidazol-2-yl)-4,4,5,5- tetramethyl-4,5-dihydro-1H-imidazolyl-1-oxyl-3-oxide (4), has been designed, synthesized, and structurally characterized to examine the effects of ring extension on 2-(benzimidazol-2-yl)-4,4,5,5-tetramethyl-4,5-dihydro-1H- imidazolyl-1-oxyl-3-oxide (2). 4 forms four-centered intramolecular and intermolecular hydrogen bonds, and the hydrogen bonds are repeated along the c-axis to form a one-dimensional chain structure. This hydrogen-bonding motif contrasts that of 2, which forms three-centered intramolecular and intermolecular hydrogen bonds. The magnetic susceptibility measurement of 4 reveals that an antiferromagnetic interaction is dominant between spins, and the magnetic behavior is reproduced by the Bonner-Fisher model with J = -14 cm ^-1. Because each hydrogen-bonded chain is well isolated, a magnetic interaction pathway was thought to exist along the chain direction. Two interaction pathways have been assumed: (i) through-space interaction between the 0 atoms of the nitroxide and (ii) through die NH...ON intermolecular hydrogen bond. We have concluded that pathway (i) is predominant, by considering the identical magnetic data between the NH nondeuterated and deuterated samples. The hydrogen bond mainly has a role in crystal scaffolding.

Full text of DOI:10.1021/jp035849r

6144
J. Phys. Chem. B 2004, 108, 6144-6151
ARTICLES
An Ideal One-Dimensional Antiferromagnetic Spin System Observed in Hydrogen-Bonded
Naphth[2,3-d]imidazol-2-yl Nitronyl Nitroxide Crystal: The Role of the Hydrogen Bond
Hideaki Nagashima, Hidenari Inoue, and Naoki Yoshioka*
Department of Applied Chemistry, Faculty of Science and Technology, Keio UniVersity,
Kohoku-ku, Yokohama 223-8522, Japan
ReceiVed: June 28, 2003; In Final Form: February 23, 2004
A novel stable organic radical, 2-(naphth[2,3-d]imidazol-2-yl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazolyl-
1-oxyl-3-oxide (4), has been designed, synthesized, and structurally characterized to examine the effects of
ring extension on 2-(benzimidazol-2-yl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazolyl-1-oxyl-3-oxide (2).
4 forms four-centered intramolecular and intermolecular hydrogen bonds, and the hydrogen bonds are repeated
along the c-axis to form a one-dimensional chain structure. This hydrogen-bonding motif contrasts that of 2,
which forms three-centered intramolecular and intermolecular hydrogen bonds. The magnetic susceptibility
measurement of 4 reveals that an antiferromagnetic interaction is dominant between spins, and the magnetic
behavior is reproduced by the Bonner-Fisher model with J ) -14 cm-1. Because each hydrogen-bonded
chain is well isolated, a magnetic interaction pathway was thought to exist along the chain direction. Two
interaction pathways have been assumed: (i) through-space interaction between the O atoms of the nitroxide
and (ii) through the NH‚‚‚ON intermolecular hydrogen bond. We have concluded that pathway (i) is
predominant, by considering the identical magnetic data between the NH nondeuterated and deuterated samples.
The hydrogen bond mainly has a role in crystal scaffolding.
1. Introduction
whose hydrogen-bonding sites have high extensibility and
compare the similarities and/or differences in these radical
crystals.
One of the main topics of molecular magnetism is the con-
struction of a crystal system with a controlled dimensionality
of magnetic interactions, because the bulk magnetism of
molecular solids is closely correlated to the crystal structures.
To construct such a system, intermolecular forces such as metal
coordination and hydrogen bonding have been introduced.1
Focusing on purely organic radical crystals, many organic radical
molecules that carry hydrogen-bonding sites have been reported
and characterized.2 Several quantum chemical calculations claim
the capability of a hydrogen bond to propagate magnetic
interaction,3 as well as to control the crystal packing. The
occurrence of magnetic interaction through the hydrogen bond
was recently reported, and it was confirmed by solution electron
spin resonance (ESR) spectra of tert-butyl nitroxide and poly-
(chloro)triphenylmethyl radicals.4 However, a complicated
problem is still present in the existing crystalline compounds:
because undesirable molecular contacts occur frequently, the
question of whether the hydrogen bond itself propagates
magnetic interaction or just has a role in crystal scaffolding is
not always clear. As a result, a magnetic structure does not
always correspond to the crystal structure controlled by a
hydrogen bond. To scrutinize the relationship between a
hydrogen bond and the magnetic properties of radical solids,
we must systematically study the organic radical molecules
Among the organic radical molecules that carry hydrogen-
bonding sites, we have been focusing on the nitronyl nitroxide
(NN) units that carry imidazole rings.5 From the standpoint of
crystal engineering, imidazole has a very interesting skeleton,
because it has both a proton-donor site and a proton-acceptor
site to form a hydrogen bond similar to a water molecule, and
the bond is reported to form a chain structure in the crystal.6
We have combined imidazole rings and NN units. As shown in
Figure 1, the derivatives have one NH proton-donor site (D)
and three proton-acceptor sites (one imine N atom (A1) and two
nitroxide O atoms (A2)), and their crystal structures are expected
to be controlled by hydrogen bonds. In the case of imidazol-
2-yl nitronyl nitroxide (1), a hydrogen bond chain of the type
D‚‚‚A1 is observed.5a In the case of benzimidazol-2-yl nitronyl
nitroxide (2), which exhibits intermolecular ferromagnetic
interaction with J ) +12 cm-1 in the crystal, however, A2 rather
than A1 participates in the intermolecular hydrogen bond. We
have also reported the magnetic properties of 4(5)-methylimid-
azol-2-yl nitronyl nitroxide (3).5b Judging from its magnetic
* Author to whom correspondence should be addressed. E-mail ad-
dress: yoshioka@applc.keio.ac.jp.
10.1021/jp035849r CCC: $27.50 © 2004 American Chemical Society
Published on Web 04/27/2004

Spin in H-Bonded Naphth[2,3-d]imidazol-2-yl NN
J. Phys. Chem. B, Vol. 108, No. 20, 2004 6145
2.2.3. 2-(Naphth[2,3-d]imidazol-2-yl)-4,4,5,5-tetramethyl-4,5-
dihydro-1H-imidazolyl-1-oxyl-3-oxide (4). To a solution of 6
(1.62 g, 8.24 mmol) in dry N-methyl-2-pyrrolidinone (NMP,
80 mL) was added 2,3-bis(hydroxyamino)-2,3-dimethylbutane8
(1.80 g, 12.4 mmol). The mixture was heated at 130 °C for 10
min and then stirred at room temperature for 48 h. The solution
was taken up in dichloromethane (300 mL), cooled to 0 °C,
and then sodium periodide (10.6 g, 49.4 mmol) in water (300
mL) was added with stirring. The organic layer was washed
with water, dried over anhydrous sodium sulfate, filtered, and
evaporated to dryness. Chromatography on silica gel with
chloroform as the eluent yielded 2-(naphth[2,3-d]imidazol-2-
yl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazolyl-1-oxyl-3-
oxide (4) (0.67 g, 25%), which was recrystallized in the form
of dark-green needles by slow evaporation from a dichloro-
methane/methanol solution. Mp: 229-230 °C (decomposition).
FAB-MS: observed 324 [M+1]+ (calculated for C18H19N4O2
) 323.37). Elemental analysis calculated for C18H19N4O2: C,
66.86; H, 5.92; N, 17.33. Found: C, 66.57; H, 6.08; N, 17.33.
Figure 1. Molecular design of imidazol-2-yl nitronyl nitroxide (NN)
derivatives.
data, 3 probably forms the same pattern of hydrogen bond as
2, although we have not succeeded in solving the crystal
structure yet. From these results, we have recognized that the
steric and/or electronic effects of substituents R and/or R′ of
the imidazole ring influence the crystal structure of the imidazol-
2-yl nitronyl nitroxide derivatives, and the skeleton is appropriate
for a systematic study of the effects of a hydrogen bond on the
intermolecular magnetic interaction. In this paper, we describe
the synthesis, crystal structure, and magnetic properties of newly
designed naphth[2,3-d]imidazol-2-yl nitronyl nitroxide (4) to
examine the effects of ring extension on the crystal packing
and magnetic behavior of 2.
2.3. X-ray Diffraction Analysis. A dark-green needlelike
crystal of 4 (0.55 mm × 0.20 mm × 0.20 mm) was measured
at a temperature of 297 K on a Rigaku four-circle AFC-7R
diffractometer with graphite monochromated Mo KR radiation
(λ ) 0.71073 Å). The data were collected using the θ-2θ scan
technique to a maximum 2θ value of 65.0°. The structure was
solved by a direct method (SIR92)9 and refined by SHELXL-
9710 on a Silicon Graphics O2 workstation with the program
system teXsan.11 Three standard reflections were measured every
150 reflections. Absorption correction was made by the Ψ scan
method. The positions of all H atoms were introduced by
difference Fourier maps. Non-H atoms were treated anisotro-
pically, and H atoms were treated isotropically. Because the
Flack parameter led to an inconclusive value, a Friedel pair was
merged before the final refinement, resulting in the absolute
direction of the polar axis being chosen arbitrarily.
2. Experimental Section
2.1. General Methods. Magnetic susceptibility measurements
were performed using a Quantum Design MPMS-5 SQUID
susceptometer that was working at the field strength of 0.5 T
in the temperature range of 1.8-300 K. ESR spectra were
recorded on a JEOL JES-RE3X X-band (9.4 GHz) spectrometer.
1H NMR spectra were obtained on a Varian MVX-300
spectrometer. Mass spectra were measured on a JEOL JMS-
DX302 mass spectrometer, using m-nitrobenzyl alcohol as a
matrix.
2.2. Syntheses. 2.2.1. Naphth[2,3-d]imidazole-2-carbalde-
hyde diethyl acetal (5). To a solution of sodium (1.20 g, 52.2
mmol) in dry ethanol (30 mL) were added 2,3-diaminonaph-
thalene (4.00 g, 25.3 mmol) and ethyl diethoxyacetate (5.35 g,
30.3 mmol). The mixture was refluxed for 24 h and cooled to
room temperature, and then the solvent was removed under
vacuum. The residue was dissolved in water, neutralized with
acetic acid, and extracted with ethyl acetate. The organic layer
was separated, dried over anhydrous sodium sulfate, and
evaporated to dryness. Chromatography on silica gel with
chloroform/ethyl acetate (1/1) as the eluent yielded naphth[2,3-
d]imidazole-2-carbaldehyde diethyl acetal (5) (3.31 g, 48%),
which was recrystallized as a white powder from an ethyl
acetate/n-hexane (1/1) solution. Mp: 214-215 °C [196-197
°C].7 1H NMR (DMSO-d6, 300 MHz): δ 8.17(s, 1H, Ar-H),
8.00(dd, 2H, Ar-H, J ) 2 and 7 Hz, Ar-H), 7.94(s, 1H, Ar-
H), 7.37(m, 2H, Ar-H), 5.77(s, 1H, CH), 3.70(m, 4H, 2 ×
CH2), 1.21(t, 6H, J ) 7 Hz, 2 × CH3). Fast atom bombard-
ment-mass spectroscopy (FAB-MS): observed 271 [M+1]+
(calculated for C16H18N2O2 ) 270.33). Elemental analysis
calculated for C16H18N2O2: C, 71.09; H, 6.71; N, 10.36.
Found: C, 70.98; H, 6.79; N, 10.38.
2.4. Computational Details. J values were calculated with
Gaussian 0312 at the UB3LYP13a,b or UBLYP13c/6-31G* levels
for a hydrogen-bonded dimeric coordinate extracted from X-ray
analysis. Spin annihilation was performed using the following
equation that was developed by Yamaguchi et al.14
E
LS - EHS
2 HS - S2 LS
J )
S
Tight convergence was used to discuss small energy differences
(10-8 au). Highest occupied molecular orbital-lowest-unoccupied
molecular orbital (HOMO-LUMO) mixed initial guesses were
created to estimate broken-symmetry singlet-state energies.
3. Results
2.2.2. Naphth[2,3-d]imidazole-2-carbaldehyde (6). A solution
of 5 (4.10 g, 15.1 mmol) in 1M sulfuric acid (100 mL) was
stirred for 1 h at room temperature and then refluxed at 100 °C
for 10 min. After the solution was cooled to room temperature,
the pH was adjusted to ca. 10 with aqueous sodium carbonate
solution. The precipitate was filtered off, washed with water,
and dried under vacuum to yield naphth[2,3-d]imidazole-2-
carbaldehyde (6) (2.62 g, 88%) as a yellow powder. Mp: >
3.1. Syntheses. The synthetic route of 4 is shown in Scheme
1. 5 was synthesized by the cyclization reaction of 2,3-
diaminonaphthalene with ethyl diethoxyacetate under a strong
basic condition, using sodium ethoxide as described by Browne.15
5 was hydrolyzed using diluted sulfuric acid to yield the
corresponding aldehyde (6). 6 is not soluble in most organic
solvents, not even in dimethyl sulfoxide (DMSO) at room
temperature, which suggests the formation of the same dimeric
structure as reported for benzimidazole-2-carbaldehyde.16 The
condensation reaction of 6 with 2,3-bis(hydroxyamino)-2,3-
dimethylbutane was performed using NMP as a solvent, with
heating, followed by chemical oxidation using sodium periodide
to give 4 as a dark-green solid.17
1
300 °C. H NMR (DMSO-d6, 300 MHz at 80 °C): δ 10.07(s,
1H, CHO), 8.27(br-s, 2H, Ar-H), 8.04(br-s, 2H, Ar-H), 7.42-
(br-s, 2H, Ar-H). Elemental analysis calculated for C12H8-
N2O: C, 73.46; H, 4.11; N, 14.28. Found: C, 73.17; H, 4.35;
N, 14.18.

6146 J. Phys. Chem. B, Vol. 108, No. 20, 2004
Nagashima et al.
TABLE 1: Experimental and Calculated Hyperfine
SCHEME 1: Synthetic Route of 4
Coupling Constants (hfccs) of 4
hfcc (mT)
experimentala calculatedb
site
aN
aH
nitroxide N
naphthimidazole 1 N
naphthimidazole 3 N
0.739
0.013
0.042
(+)0.571, (+)0.437
(-)0.017
(-)0.081
methyl H
naphthimidazole 1 H
naphthimidazole 4 H
0.023
0.016
0.043
(+)0.014
(+)0.052
a 5 × 10-5M benzene/methanol (19/1) solution at room temperature.
b UB3LYP/EPR-II for experimental geometry.
solution, the nonequivalence disappeared, and the relative
intensity approached the ideal values, because of the coupling
of the unpaired electron with two equiValent nitrogen nuclei
(Figure 2). Each line exhibits a more-complex pattern, showing
the coupling of the unpaired electron with 12 hydrogen nuclei
3.2. Solution ESR Spectra. Solution ESR spectra of 4 were
measured at room temperature in 5 × 10-5M of benzene,
benzene/methanol (19/1), and benzene/methanol-d1 (19/1) solu-
tions. The spectrum of the benzene solution consists of typically
five lines, as usually shown in 2-aryl nitronyl nitroxides, but
the relative intensity (height of the first-derivative peaks) of
ca. 1:1.7:2:1.7:1 is clearly different from the expected intensity
of 1:2:3:2:1 (spectrum not shown). This is probably due to the
nonequivalence of the nitrogen nuclei (I ) 1) of the nitroxide
unit by forming an intramolecular N(H)‚‚‚O hydrogen bond.
Such nonequivalence of the nitrogen nuclei has also been
reported for intramolecular hydrogen-bonded 2-hydroxyphenyl
nitronyl nitroxides.18 When 5% methanol was added to the
1
(I ) /2) of four methyl groups and hydrogen and/or nitrogen
nuclei of the naphth[2,3-d]imidazole ring. When comparing the
spectra of the benzene/methanol and benzene/methanol-d1
solutions, we found that each complex pattern is different
(compare Figures 2 and 3). Hyperfine coupling constants (hfccs)
obtained by the curve-fitting technique19 are summarized in
Table 1. The spectrum of the benzene/methanol-d1 solution can
be nicely reproduced by the same hfccs for the benzene/
methanol solution, except for one hfcc for a proton. We assigned
the hfcc for the NH proton of the naphth[2,3-d]imidazole ring
by considering the proton exchange reaction between the
Figure 2. (a) Experimental and (b) simulated ESR spectra of 4 in a
benzene/methanol solution. Main figures correspond to the central
signals (MI ) 0).
Figure 3. (a) Experimental and (b) simulated ESR spectra of 4 in a
benzene/methanol-d1 solution. Main figures correspond to the central
signals (MI ) 0).

Spin in H-Bonded Naphth[2,3-d]imidazol-2-yl NN
J. Phys. Chem. B, Vol. 108, No. 20, 2004 6147
TABLE 3: Crystal and Refinement Data of 4
parameter
TABLE 2: Calculated Spin Densities of 4a
atom
spin density
value
O1
O2
N3
N4
N5
N6
C7
C14
H5
H17
+0.382
+0.322
+0.249
+0.285
-0.006
-0.052
-0.203
+0.039
-0.001
+0.001
chemical formula
formula weight
crystal system
space group
lattice constants
a
b
c
C18H19N4O2
323.37
orthorhombic
Pca21 (No. 29)
13.515(3) Å
11.858(3) Å
10.593(3) Å
1697.6(8) Å3
4
volume, V
Z
calculated density, Dcalcd
µ
total reflections collected
independent reflections
reflections observed (I > 2σ(I))
number of parameters
Rint
1.265 g cm-3
0.085 mm-1
7114
a UB3LYP/EPR-II calculation for experimental geometry. See
ORTEP drawing for atom numbering.
3103
1407
293
0.0453
R (I > 2σ(I))
wR (all data)
0.041
0.082
goodness of fit
0.83
are summarized in Table 3. 4 crystallizes in the noncentrosym-
metric space group Pca21, with four molecules in a unit cell.
Figure 4 shows an ORTEP drawing of 4. The dihedral angle
between the best planes of the imidazole ring (N(5)-C(14)-
N(6)-C(16)-C(15)) and the O(1)-N(3)-C(7)-N(4)-O(2)
moiety is 12.4°; the coplanarity becomes higher when compared
to the corresponding angles of 48.4° for 1 and 24.3° for 2. The
crystal structure along the a- and c-axes is shown in Figure 5.
Short intermolecular distances of 3.12 Å between N(5)‚‚‚O(1)*
and 3.13 Å between N(5)‚‚‚N(6)* are found (symmetry code:
(*) -x + /2, y, z - /2), forming four-centered (trifurcated)
intramolecular and intermolecular hydrogen bonds between the
NH proton (D), the imine N atom (A1), and the nitroxide O
atoms (A2) (denoted by dashed lines).21 The hydrogen bonds
are repeated along the c-axis to form a one-dimensional chain
structure in edge-to-edge fashion. Along the hydrogen-bonded
chain, close contact between the O atoms of the nitroxide is
observed, and the distance of 2.99 Å between O(2)‚‚‚O(1)* is
slightly shorter than the sum of the van der Waals radii of the
two O atoms (3.04 Å).22 Judging from the distance, a strong
Figure 4. ORTEP drawing and atomic numbering of the molecular
structure of 4.
hydroxyl proton of methanol and the NH proton of the
naphthimidazole ring. Although the spectra were not sufficiently
resolved to assign hfccs for all the protons, the results showed
that spin densities are induced at least on the imidazole moiety,
which includes the NH proton-donor site.
Calculated hfccs (taken directly from calculated Fermi contact
terms), using Gaussian 03 at the UB3LYP/EPR-II20 level for
the experimental geometry, are compared with experimental hfcc
values in Table 1. Calculated Mulliken spin densities at the same
level are also summarized in Table 2. The experimental and
calculated results suggest that small spin densities are located
on the methyl groups and imidazole ring, although most of the
spin densities localized on the ONCNO moiety of the NN unit.
3.3. X-ray Analysis. A dark-green single crystal of 4 suitable
for X-ray analysis was obtained by slow evaporation from a
dichloromethane/methanol solution. Crystallographic data of 4
3
1
Figure 5. ORTEP drawings of the crystal structure of 4 along the a-axis (left) and along the c-axis (right). Dashed lines show intramolecular and
intermolecular hydrogen bonds.

6148 J. Phys. Chem. B, Vol. 108, No. 20, 2004
Nagashima et al.
Figure 7. Schematic drawing of intramolecular hydrogen bond (left)
and electrostatic repulsion (right).
Figure 6. øm-T and ømT-T (inset) plots of (O) 4 and (b) 4-d1. Solid
line is calculated using the Bonner-Fisher model with J ) -14 cm-1
.
Figure 8. Explanation drawing of the nature as an acid of imidazole
(top) and as an acid of the conjugated base (bottom).
magnetic interaction between the O atoms, which carry a large
positive spin density, is expected. On the other hand, the shortest
O‚‚‚O distance between hydrogen-bonded chains is 4.47 Å
twists the angles (Figure 7). Experimental pKa values of parent
heterocycles have been used to evaluate the electric charges of
D and A1, because pKa values are strongly affected by the atomic
charge distribution within the molecules. The pKa values of these
heterocycles, as an acid (Figure 8), are 14.2, 13.2, and 12.52
for imidazole, benzimidazole, and naphth[2,3-d]imidazole,
respectively,27 showing that the proton-donating character of
the NH protons increases in the following order: imidazole <
benzimidazole < naphth[2,3-d]imidazole. On the other hand,
the pKa values of conjugate acids of the parent heterocycles,
which correspond to the proton affinity of the A1 sites (Figure
8), are 6.95, 5.53, and 5.24 for imidazole, benzimidazole, and
naphth[2,3-d]imidazole, respectively, showing that the negative
charge of the N atom of the imine decreases in the following
order: imidazole > benzimidazole > naphth[2,3-d]imidazole.
In the case of 4, we considered that the hydrogen bond between
D and A2 is the strongest and that the electrostatic repulsion
between A1 and A2 is the weakest, resulting in the smallest
dihedral angle. The electronic effect of ring extension is due to
the fusion of the imidazole ring at the â-positions of the
naphthalene ring at which the electric charge densities are rather
lower than those at the R-positions. In addition to the former
two electrostatic forces, π-conjugation between the 2pz orbitals
of the naphthimidazole ring and the ONCNO moiety also
contribute to the planarity.
A schematic drawing of the hydrogen-bonded chain of 2 and
4 is shown in Figure 9. In the crystal of 2, D attracts two A2
sites to form three-centered (bifurcated) intramolecular and
intermolecular hydrogen bonds. The A2 site that does not
participate in the intermolecular hydrogen bond but does in the
intramolecular hydrogen bond approaches the sp2 C-atom of
the neighboring molecule. The σ-type orbital overlap between
the R-spin-carrying O atom and the â-spin-carrying sp2 C atom
enables the neighboring spins to couple ferromagnetically, based
on the McConnell I mechanism.28 A1 does not participate in
the intermolecular hydrogen bond. In the crystal of 4, on the
other hand, A1 does participate in the intermolecular hydrogen
bond to form four-centered (trifurcated) intramolecular and
intermolecular hydrogen bonds between D, A1, and A2. The
hydrogen bonds lead to an edge-to-edge molecular arrangement,
and the O‚‚‚C contact favorable to the occurrence of ferromag-
netic interaction is collapsed.
1
(O(1)‚‚‚O(2)**; symmetry code: (**) -x + 2, -y, z + /2).
The methyl groups of the NN units intervene between the O
atoms, and the large interchain orbital overlap seems to be
negligibly small.
3.4. Solid-State Magnetic Properties. The magnetic sus-
ceptibility measurement of a polycrystalline sample of 4 was
performed. The diamagnetic contribution was estimated using
the Pacault method.23 Figure 6 shows øm vs T and ømT vs T
(inset) plots for 4, where øm is the molar susceptibility and T is
the absolute temperature. At 300 K, ømT ) 0.36 emu K mol-1
,
which corresponds to the value expected for an isolated
monoradical (0.375 emu K mol-1). The value decreases slowly
as the temperature decreases, which suggests that an antiferro-
magnetic interaction is dominant between spins. Focusing on
the øm vs T plot, øm increases gradually as the temperature
decreases and has a broad maximum at 12 K. Solution ESR
spectra and density functional theory (DFT) calculations show
that most of the spin densities are concentrated on the ONCNO
moiety (see Tables 1 and 2), and the results are consistent with
reported polarized neutron diffraction (PND) studies for other
NN derivatives.24 When compared to the intrachain O‚‚‚O
distance of 2.99 Å, even the shortest interchain O‚‚‚O distance
of 4.47 Å is too long to affect the magnetic character. Therefore,
we consider that an ideal one-dimensional spin system is self-
assembled along the hydrogen-bonded direction. The magnetic
data can be nicely fit to the Heisenberg one-dimensional
antiferromagnetic chain model (the Bonner-Fisher model25),
using H ) -JS1‚S2 and the numerical expression26
NAg2µB
2
0.25 + 0.074975x + 0.075235x2
øm )
(
)
1.0 + 0.9931x + 0.172135x2 + 0.757825x3
kBT
where x ) |J|/(kBT). The best-fit parameter is J ) -14 cm-1
.
4. Discussion
4.1. Effects of Ring Extension on Molecular Structure and
Crystal Structure. The dihedral angles between the best planes
of the imidazole rings and the ONCNO moieties of 1, 2, and 4
are 48.4°, 24.3°, and 12.4°, respectively. These dihedral angles
are determined by the balance of two electrostatic forces: an
intramolecular hydrogen bond between the NH proton (D) and
the O atom of the nitroxide (A2), which retains high coplanarity,
and electrostatic repulsion between the lone pairs of the N atom
of the imine (A1) and the O atom of the nitroxide (A2), which
4.2. Spin Density Induced on the NH Proton Donor Site.
Spin-density distribution within a molecule is significantly
important when intermolecular magnetic interaction is examined
by applying the McConnell I mechanism for close contact
between the molecules. We are especially interested in the sign

Spin in H-Bonded Naphth[2,3-d]imidazol-2-yl NN
J. Phys. Chem. B, Vol. 108, No. 20, 2004 6149
Figure 10. Schematic drawing of spin polarization mechanism of 4.
Figure 9. Schematic drawing of the hydrogen-bonding motifs of 2
(left) and 4 (right). Dashed lines show intramolecular and intermolecular
hydrogen bonds.
TABLE 4: Calculated Spin Densities on Each Basis
Function and Fermi Contact at the NH Proton (H5) of 4a
spin density
1s
2s
0.00000
0.00001
3s
4s
5px
5py
0.00010
-0.00080
-0.00002
-0.00001
-0.00007
-0.00078
5pz
Figure 11. Plausible magnetic coupling mechanism of 4 along the
total Mulliken spin density
hydrogen-bonded direction.
Fermi contact term
(+)0.01378 mT
a UB3LYP/EPR-II calculation for experimental geometry.
the nuclei, are not always a good representation of the spin
densities on the entire atoms.18
and magnitude of the spin density on the NH proton of 4,
because the hydrogen bond could become a magnetic interaction
pathway. Solution ESR spectra clearly showed that spin densities
are induced on the NH proton donor site, although we could
not determine the sign. To support this result, we used the
calculated hfccs and spin densities of 4 (see Tables 1 and 2).
Interestingly, the UB3LYP/EPR-II single point calculation for
the X-ray analysis structure shows that the Mulliken spin density
of the NH proton is negative and that the Fermi contact term
of the proton is positive: the signs are opposite. In the case of
2-tert-butylaminoxylbenzimidazole,29 the same signs of spin
density and the Fermi contact term were calculated for the
corresponding NH proton (-0.00195 and -0.612 G at a
UBLYP/cc-pVDZ level, respectively). Therefore, the conflict
observed in 4 may not be due to the electronic structure of the
imidazole skeleton itself. The spin densities of each of the basis
sets of 4 summarized in Table 4 show that positive spin densities
are induced on the inner shells (1s, 2s, 3s) and that negative
spin densities are induced on the outer shells (4s, 5p). This result
could be interpreted as follows: spin densities on inner shells
are induced through a covalent bond and those on outer shells
are induced through an intramolecular hydrogen bond, as shown
in Figure 10.30 In summary, small negative spin densities were
calculated on the NH proton-donor site. This suggests that the
Fermi contact terms, which reflect only the spin densities on
4.3. Magnetic Interaction Pathway. It is quite natural for 4
to assume a magnetic interaction pathway along the hydrogen-
bonded chain direction by taking into account the magnetic
character that is reproducible by the one-dimensional chain
model. We have assumed two plausible interaction pathways
along the chain direction, as described in Figure 11: (i) through-
space interaction between the O atoms of the nitroxide, which
causes antiferromagnetic interaction; (ii) through the NH‚‚‚ON
intermolecular hydrogen bond, which causes ferromagnetic
interaction. Experimental results showed that the antiferromag-
netic interaction is dominant between spins and that pathway
(i) must be the main mechanism of the interaction. To examine
the contribution of pathway (ii), we prepared 4-d1, in which
the NH hydrogen was replaced by deuterium. If pathway (ii)
contributes greatly to the magnetic interaction, a noticeable
change would be expected, as shown in the crystal of RSNN
that was reported by Sugawara et al.2e 4-d1 was prepared by
recrystallization from dichloromethane/methanol-d1 solution.
The ND stretching appears at 2432 cm-1, as expected, by
applying Hooke’s law to the NH stretching of 3253 cm-1 for
4, and the percentage of deuteration was estimated to be ca.
50%, based on the intensities of the solid-state IR spectra. The
øm vs T and ømT vs T plots of 4-d1 are shown in Figure 6, with
the result for 4 for comparison. The maximum øm values of 4
and 4-d1 are both 0.0109 emu mol-1 at 12 K, which suggests

6150 J. Phys. Chem. B, Vol. 108, No. 20, 2004
Nagashima et al.
hydrogen bond) have been assumed, we have concluded that
pathway (i) is predominant and that the hydrogen bond mainly
has a role in crystal scaffolding.
Acknowledgment. This work was partly supported by a
Grant-in-Aid for Scientific Research (B) 15310094 from the
Ministry of Education, Culture, Sports, Science, and Technol-
ogy, Japan. H. N. thanks financial supports from Keio University
(Keio Leading-edge Laboratory of Science and Technology) and
the 21st Century COE program “KEIO Life Conjugate Chem-
istry” from the Ministry of Education, Culture, Sports, Science,
and Technology, Japan.
Supporting Information Available: Variation of Fermi
contact terms and Mulliken spin densities of H atoms, as a
function of the dihedral angle between the aryl rings and the
ONCNO moeities (Figure 1S); angular dependence of calculated
J values for rotation of the naphthimidazole ring (Figure 2S)
and the NN unit (Figure 3S). (PDF and CIF data.) This material
is available free of charge via the Internet at http://pubs.acs.org.
References and Notes
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Figure 12. Schematic drawing of a canted orbital overlap of 4.
that the effect of deuteration on the magnetic interaction is
negligible and that pathway (i) is predominant. The hydrogen
bond mainly has a role in crystal scaffolding. Even though a
small spin density is induced on the NH proton and pathway
(ii) might exist in the crystal, the magnitude is much smaller
than that of pathway (i), and the observed magnetic interaction
of -14 cm-1 is mainly propagated by pathway (i).31
As mentioned previously, the O‚‚‚O distance of the nitroxide
units along the hydrogen-bonded chain direction is 2.99 Å.
Judging from the O‚‚‚O distance and the spin densities carried
by the O atoms of the nitroxide, the experimental J value of
-14 cm-1 is much smaller than that which is expected. This
can be explained by the canted overlap between the pz orbitals
(Figure 12). Spin densities are located in the pz orbitals
perpendicular to the ONCNO mean planes, and a strong
antiferromagnetic interaction is expected when a perfect anti-
parallel orbital overlap is realized, as shown in crystals such as
1 or 4-azaindol-2-yl nitronyl nitroxides.32 In the case of 4,
however, the dihedral angle between the best planes of
neighboring ONCNO moieties along the hydrogen-bonded chain
is 68.3°, and the overlap between the pz orbitals is incomplete,
resulting in a weaker antiferromagnetic interaction than ex-
pected.
J values calculated for the coordinate of a hydrogen-bonded
dimer at the UB3LYP/6-31G* and UBLYP/6-31G* levels are
-1.0 and -17.7 cm-1, respectively, qualitatively reproducing
the experimentally obtained J value of -14 cm-1. The strong
functional dependency might due to limitations of the density
functional calculation in the present case.
5. Summary
The one-dimensional hydrogen-bonded chain observed in the
crystal of 2-(naphth[2,3-d]imidazol-2-yl)-4,4,5,5-tetramethyl-4,5-
dihydro-1H-imidazolyl-1-oxyl-3-oxide (4) can be recognized as
an ideal one-dimensional spin system because each chain is well-
isolated by the steric effects of the naphth[2,3-d]imidazole ring
and four methyl groups. Although two magnetic interaction
pathways ((i) through-space interaction between the O atoms
of the nitroxide and (ii) through the NH‚‚‚ON intermolecular
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Spin in H-Bonded Naphth[2,3-d]imidazol-2-yl NN
J. Phys. Chem. B, Vol. 108, No. 20, 2004 6151
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NH proton changes while changing the angle, although that of Fermi contacts
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corresponds to the experimental geometry). The rotation of the naphthimi-
dazole ring does not affect the J values very much, whereas rotation of the
NN unit does affect the J values significantly, showing that the close contact
between the nitroxide O atoms induced by the intermolecular hydrogen
bond, rather than the intermolecular NH‚‚‚ON hydrogen bond, is responsible
for the antiferromagnetic character. In Figure 2S in the Supporting
Information, the maximum J value appears at 0°, which implies that the
NH‚‚‚ON hydrogen bond is a ferromagnetic interaction pathway. See
Supporting Information (Figures 2S and 3S) for more details.
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