Preparation and characterization of (CNSSS)2(A)2 (A = AsF6-, SbF6-, Sb2F 11-) containing the O2-like 5,5′-Bis(1,2,3,4-trithiazolium) dication: The second example of a simple nonsterically hindered main-group diradical that retains its paramagnetism in the solid state

Article abstract of DOI:10.1021/ic100760t

The reaction of NC-CN with a 1:1 mixture of S₄(MF ₆)₂ and S₈(MF₆)₂ (M = As, Sb) (stoichiometrically equivalent to four S₃MF ₆ units) results in the quantitative formation of S ₃NCCNS₃(MF₆)₂ [7(MF ₆)₂], which is the thermodynamic sink in this reaction. The Sb₂F₁₁^- salt 7(Sb₂F ₁₁)₂ is prepared by the addition of an excess of SbF ₅ to 7(AsF₆)₂. Crystal structure determinations for all three salts show that 7²⁺ can be viewed as two R-CNS ₃⁺ radical cations joined together by a C-C single bond. The two rings are coplanar and in a trans orientation due to electrostatic N^δ-...S^δ+ interactions. The classically bonded alternative (quinoidal structure), in which the octet rule is obeyed, is not observed and is much higher in energy based on calculated estimates and a simple comparison of π bond energies. Calculated molecular orbitals (MOs) support this, showing that the MO corresponding to the quinoidal structure lies higher in energy than the nearly degenerate singly occupied MOs of 7 ²⁺. The vibrational spectra of 7²⁺ in all salts were assigned based on a normal-coordinate analysis and theoretical vibrational frequencies calculated at the PBE0/6-31G* level. In the solid state, 7²⁺ is a planar disjoint diradical with essentially degenerate open-shell singlet and triplet states. The disjoint nature of the diradical cation 7²⁺ is established by magnetic susceptibility studies of the Sb₂F₁₁^- salt doped in an isomorphous diamagnetic host material (CNSNS)₂(Sb₂F₁₁) ₂ [10(Sb₂F₁₁)₂]. Intramolecular spin coupling is extremely weak corresponding to a singlet-triplet gap (δE_ST = 2J) of <±2 cm^-1. CASPT2[12,12]/6-311G* calculations support a triplet ground state with a small singlet-triplet gap. The single-crystal electron paramagnetic resonance (EPR) of 7(Sb₂F₁₁)₂ doped in 10(Sb ₂F₁₁)₂ is in agreement with the triplet state arising from the weak coupling between the unpaired electrons residing in p _π orbitals in each of the rings. Variable-temperature susceptibility data for bulk samples of 7(A)₂ (A = SbF ₆^-, AsF₆^-, Sb₂F ₁₁^-) are analyzed by employing both 1D chain and 2D sheet magnetic models. These studies reveal significant intermolecular exchange approximating that of a 1D chain for the SbF₆^- salt with |J| = 32 cm^-1. The exchange coupling is on the same order of magnitude as that for the AsF₆^- salt, although in this case it is likely that there are complex exchange pathways where no particular one is dominant. Intermolecular exchange in the Sb₂F ₁₁^- salt is an order of magnitude weaker. In solution, the EPR spectrum of 7²⁺ shows a broad triplet resonance as well as a sharp resonance that is tentatively attributed to a rotomer of the 7 ²⁺/anion pair, which is likely the origin of the green species given on dissolution of the red 7²⁺ salts in SO₂/AsF ₃/MF₅. We account for the many similarities between O ₂ and 7²⁺, which are the only simple nonsterically hindered nonmetal diradicals to retain their paramagnetism in the solid state. 7²⁺ is also the first isolable, essentially sulfur-based diradical as evidenced by calculated spin densities.

Full text of DOI:10.1021/ic100760t

Inorg. Chem. 2010, 49, 7861–7879 7861
DOI: 10.1021/ic100760t
-
-
-
Preparation and Characterization of (CNSSS)2(A)2 (A = AsF6 , SbF6 , Sb2F11
)
Containing the O2-like 5,50-Bis(1,2,3,4-trithiazolium) Dication: The Second Example
of a Simple Nonsterically Hindered Main-Group Diradical That Retains Its
Paramagnetism in the Solid State
T. Stanley Cameron,† Andreas Decken,‡ Friedrich Grein,‡ Carsten Knapp,‡,§ Jack Passmore,*,‡
J. Mikko Rautiainen,‡ Konstantin V. Shuvaev,‡,^ Robert C. Thompson,z and Dale J. Wood‡,||
†Department of Chemistry, Dalhousie University, Halifax, Nova Scotia B3H 4J3, Canada, ‡Department of Chemistry,
University of New Brunswick, Fredericton, New Brunswick E3B 5A3, Canada, and zDepartment of Chemistry,
University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada. § Current address: Institut fu€r
€
Anorganische and Analytische Chemie, Albert-Ludwigs-Universitat Freiburg, Albertstrasse 21, 79104 Freiburg
im Breisgau, Germany. ^ Current address: Department of Chemistry, Memorial University of Newfoundland,
St. John’s A1B 3X7, Canada. || Current address: Department of Chemistry, Bishop’s University, 2600 College
ꢀ
Street, Sherbrooke, Quebec J1M 1Z7, Canada.
Received April 20, 2010
The reaction of NC-CN with a 1:1 mixture of S4(MF6)2 and S8(MF6)2 (M=As, Sb) (stoichiometrically equivalent to four “S3MF6”
units) results in the quantitative formation of S3NCCNS3(MF6)2 [7(MF6)2], which is the thermodynamic sink in this reaction. The
Sb2F11- salt 7(Sb2F11)2 is prepared by the addition of an excess of SbF5 to 7(AsF6)2. Crystal structure determinations for all three
salts show that 72þ can be viewed as two R-CNS3þ radical cations joined together by a C-C single bond. The two rings are
coplanar and in a trans orientation due to electrostatic Nδ- Sδþ interactions. The classically bonded alternative (quinoidal
3 3 3
structure), in which the octet rule is obeyed, is not observed and is much higher in energy based on calculated estimates and a
simple comparison of π bond energies. Calculated molecular orbitals (MOs) support this, showing that the MO corresponding to
the quinoidal structure lies higher in energy than the nearly degenerate singly occupied MOs of 72þ. The vibrational spectra of 72þ
in all salts were assigned based on a normal-coordinate analysis and theoretical vibrational frequencies calculated at the PBE0/6-
31G* level. In the solid state, 72þ is a planar disjoint diradical with essentially degenerate open-shell singlet and triplet states. The
-
disjoint nature of the diradical cation 72þ is established by magnetic susceptibility studies of the Sb2F11 salt doped in an
isomorphous diamagnetic host material (CNSNS)2(Sb2F11)2 [10(Sb2F11)2]. Intramolecular spin coupling is extremely weak
corresponding to a singlet-triplet gap (ΔEST = 2J) of <(2 cm-1. CASPT2[12,12]/6-311G* calculations support a triplet ground
state with a small singlet-triplet gap. The single-crystal electron paramagnetic resonance (EPR) of 7(Sb2F11)2 doped in
10(Sb2F11)2 is in agreement with the triplet state arising from the weak coupling between the unpaired electrons residing in pπ
orbitals in each of the rings. Variable-temperature susceptibility data for bulk samples of 7(A)2 (A = SbF6-, AsF6-, Sb2F11-) are
analyzed by employing both 1D chain and 2D sheet magnetic models. These studies reveal significant intermolecular exchange
approximating that of a 1D chain for the SbF6- salt with |J|=32cm-1. The exchange coupling is on the same order of magnitude
as that for the AsF6- salt, although in this case it is likely that there are complex exchange pathways where no particular one is
dominant. Intermolecular exchange in the Sb2F11- salt is an order of magnitude weaker. In solution, the EPR spectrum of 72þ
shows a broad triplet resonance as well as a sharp resonance that is tentatively attributed to a rotomer of the 72þ/anion pair, which
is likely the origin of the green species given on dissolution of the red 72þ salts in SO2/AsF3/MF5. We account for the many
similarities between O2 and 72þ, which are the only simple nonsterically hindered nonmetal diradicals to retain their paramagnetism
in the solid state. 72þ is also the first isolable, essentially sulfur-based diradical as evidenced by calculated spin densities.
-
1. Introduction
gave the AsF6 salts of stable 7π radical cations
RCNSSS•þ [1•þ; R = F3C,1 Cl3C,2 F5C2,2 Cl,3a Br,3a I,3a
We have shown previously that the reaction of nitriles
R;CtN with a mixture of S4(AsF6)2 and S8(AsF6)2
(1) Cameron, T. S.; Haddon, R. C.; Mattar, S. M.; Parsons, S.; Passmore,
J. Inorg. Chem. 1992, 31, 2274.
*To whom correspondence should be addressed. E-mail: passmore@
unb.ca. Tel: 1-506-453-4821. Fax: 1-506-453-4981.
(2) Decken, A.; Mattar, S. M.; Passmore, J.; Shuvaev, K. V.; Thompson,
L. T. Inorg. Chem. 2006, 45, 3878.
r
2010 American Chemical Society
Published on Web 08/10/2010
pubs.acs.org/IC

7862 Inorganic Chemistry, Vol. 49, No. 17, 2010
Cameron et al.
Chart 1
paramagnetic, containing two unpaired electrons with only
weakantiferromagneticintramolecular coupling,4c and 72þ in
5
its various salts is the first example (other than O2 ) of a
simple nonsterically hindered main-group diradical to retain
its bulk paramagnetism in the solid state and to resemble O2
in many ways.
The diradical 72þ does not adopt the expected classically
bonded alternative (i.e., 62þ) in which the Lewis octet rule is
obeyed but rather contains two unpaired electrons per
molecule in the nonclassically bonded diradical structure 72þ
.
The related main-group diradicals 8,6 9,7 and 108 (Chart 1)
also do not adopt the expected quinoidal structures (e.g.,
those given in Chart 2 of ref 9), contrary to the situation
observed for 11-14 (Chart 1) and other related molecules.10
72þ, 8, 9, and 10 are members of a small subclass of isolable
nonsterically hindered main-group diradicals that are unique
inthattheycontaintwo radicalrings joinedby twoatomsand
yet do not adopt classical Lewis structures. However, all salts
of 72þ are paramagnetic in the solid state, whereas the neutral
diradicals 8 and 9 dimerize via π*-π* interaction and thus
are diamagnetic. A crystal structure of 10 was not obtained,
but the evidence implies that it exists in two forms, one
paramagnetic and the other diamagnetic, which becomes
paramagnetic upon grinding.8 The 1,10,5,50-tetramethyl-
6,60-dioxo-3,30-biverdazyl (15) is diamagnetic as a result of
substantial intramolecular antiferromagnetic coupling of the
unpaired electrons on each of the rings, leading to a singlet
ground state (singlet-triplet gap = -760 cm-1).11 Selected
other classes of diradicals include dinitroxides,12 triphenyl-
methyl diradicals,13 and other organic framework-based
(5) (a) To date six different phases of solid oxygen are known to exist. At
normal pressures, three phases exist. The R and β phases show antiferro-
magnetic behavior. The R phase exhibits long-range magnetic ordering,
while only short-range magnetic ordering is observed in the β phase. The
γ phase is paramagnetic. There is no conclusive evidence of the magnetic
behavior of the high-pressure phases δ-ζ of oxygen. However, it is believed
that the δ phase behaves similarly to the R phase and that the ε and ζ phases
are nonmagnetic because of magnetic collapse. (b) See: Freiman, Y. A.; Jodl,
H. J. Phys. Rep. 2004, 401, 1 and references cited therein.
C2F4(CNSSS•þ),3b C4F8(CNSSS•þ),3b C3F6(CNSSS•þ)3b] in
high yields (eq 1).
(6) (a) Bryan, C. D.; Cordes, A. W.; Haddon, R. C.; Hicks, R. G.; Oakley,
R. T.; Palstra, T. T. M.; Perel, A. J. J. Chem. Soc., Chem. Commun. 1994,
1447. (b) Bryan, C. D.; Cordes, A. W.; Goddard, J. D.; Haddon, R. C.; Hicks,
R. G.; MacKinnon, C. D.; Mawhinney, R. C.; Oakley, R. T.; Palstra, T. T. M.;
Perel, A. J. J. Am. Chem. Soc. 1996, 118, 330.
(7) (a) Cameron, T. S.; Lemaire, M. T.; Passmore, J.; Rawson, J. M.;
Shuvaev, K. V.; Thompson, L. K. Inorg. Chem. 2005, 44, 2576. (b) Decken,
A.; Cameron, T. S.; Passmore, J.; Rautiainen, J. M.; Reed, R. W.; Shuvaev, K. V.;
Thompson, L. K. Inorg. Chem. 2007, 46, 7436.
(8) Antorrena, G.; Brownridge, S.; Cameron, T. S.; Palacio, F.; Parsons,
S.; Passmore, J.; Thompson, L. K.; Zarlaida, F. Can. J. Chem. 2002, 80, 1568.
(9) Parsons, S.; Passmore, J.; White, P. S. J. Chem. Soc., Dalton Trans.
1993, 1499.
These molecules and 2þ (Chart 1) are members of a unique
class of stable, essentially sulfur-based main-group 7π radi-
cals and adopt a variety of solid-state structures ranging from
nearly diamagnetic dimers (e.g., R = Cl, Br, I),3a with
thermally accessible triplet states detected by electron para-
magnetic resonance (EPR) to paramagnetic weakly coupled
1D chains (R = CF3, CCl3, C2F5).1,2 Of these, the diradical
(CNSSS•þ)2, 72þ, reported by us in a series of preliminary
accounts,4 is particularly interesting. All salts of 72þ are
(10) (a) Barclay, T. M.; Cordes, A. W.; Oakley, R. T.; Preuss, K. E.; Reed,
R. W. Chem. Commun. 1998, 1039. (b) Barclay, T. M.; Beer, L.; Cordes, A. W.;
Haddon, R. C.; Itkis, M. I.; Oakley, R. T.; Preuss, K. E.; Reed, R. W. J. Am. Chem.
Soc. 1999, 121, 6657. (c) Ellern, A.; Bernstein, J.; Becker, J. Y.; Zamir, S.; Shahal,
L.; Cohen, S. Chem. Mater. 1994, 6, 1378. (d) Oakley, R. T.; Richardson, J. F.; v.
H. Spence, R. E. J. Chem. Soc., Chem. Commun. 1993, 1226. (e) Oakley, R. T.;
Richardson, J. F.; v. H. Spence, R. E. J. Org. Chem. 1994, 59, 2997. (f) Chu, S.-L.;
Wai, K.-F.; Lai, T.-F.; Sammes, M. P. Tetrahedron. Lett. 1993, 34, 847.
(g) Behringer, H.; Meinetsberger, E. Liebigs Ann. Chem. 1981, 1928.
(11) (a) Brook, D. J. R.; Fox, H. H.; Lynch, V.; Fox, M. A. J. Phys. Chem.
1996, 100, 2066. (b) Green, M. T.; McCornick, T. A. Inorg. Chem. 1999, 38,
3061.
(3) (a) Cameron, T. S.; Decken, A.; Kowalczyk, R. M.; McInnes, E. J. L.;
Passmore, J.; Rawson, J. M.; Shuvaev, K. V.; Thompson, L. K. Chem.
Commun. 2006, 2277. (b) Decken, A.; Ebdah, M.; Kowalczyk, R. M.; Landee,
C. P.; McInnes, E. J. L.; Passmore, J.; Shuvaev, K. V.; Thompson, L. K. Inorg.
Chem. 2007, 46, 7756.
(4) (a) Boyle, P. D.; Parsons, S.; Passmore, J.; Wood, D. J. J. Chem. Soc.,
Chem. Commun. 1993, 199. J. Chem. Soc., Chem. Commun. 1994, 676.
(b) Boyle, P. D.; Passmore, J.; Wood, D. J. Phosphorus, Sulfur, Silicon 1994,
93-94, 227. (c) Enright, G. D.; Morton, J. R.; Passmore, J.; Preston, K. F.;
Thompson, R. C.; Wood, D. J. J. Chem. Soc., Chem. Commun. 1996, 967.
(d) Berces, A.; Enright, G. D.; Morton, J. R.; Passmore, J.; Preston, K. F.;
Thompson, R. C.; Wood, D. J. Phosphorus, Sulfur, Silicon 1997, 124-125, 331.
(e) Boyle, P. D.; Cameron, T. S.; Decken, A.; Passmore, J.; Wood, D. J.
Phosphorus, Sulfur, Silicon 1997, 124-125, 549. (f) Berces, A.; Enright,
G. D.; Mclaurin, G. E.; Morton, J. R.; Preston, K. F.; Passmore, J.; Wood, D. J.
Magn. Reson. Chem. 1999, 37, 353.
(12) (a) Matsumoto, T.; Koga, N.; Iwamura, H. J. Am. Chem. Soc. 1992,
ꢁ
114, 5448. (b) Hernandez-Gasio, E.; Mas, M.; Molins, E.; Rovira, C.; Veciana, J.;
ꢀ
Borras-Almenar, J. J.; Coronado, E. Chem. Mater. 1994, 6, 2398. (c) Frank,
ꢀ
N. L.; Clerac, R.; Sutter, J.-P.; Daro, N.; Kahn, O.; Coulon, C.; Green, M. T.;
Golhen, S.; Ouahab, L. J. Am. Chem. Soc. 2000, 122, 2053. (d) Wautelet, P.; Le
Moigne, J.; Videva, V.; Turek, P. J. Org. Chem. 2003, 68, 8025.

Article
Inorganic Chemistry, Vol. 49, No. 17, 2010 7863
compounds.14 These and other related organic/main-group
diradicals and diradicaloids15-17 are not included in this
subclass because they do not conform to the aforementioned
criteria (i.e., the direct connection of sterically nonhindered
radical centers by two atoms).18 Salts of 72þ contain the first
examples of stable, isolable, almost completely sulfur-based
diradicals.
Hoffmann19 using extended Huckel calculations describing
€
72þ and related species as models for a ferromagnetic poly-
mer. Some of the earlier experimental work has been re-
peated, including the crystal structure of 7(SbF6)2 and red
7(Sb2F11)2 using modern state-of-the-art variable-tempera-
tureX-raymethods, leading us to concludethat thestructures
of the red and green crystals of 7(Sb2F11)2 are likely the same,
in contrast to previous claims that they are different.4e,20
Variable-temperature solid-state magnetic studies and other
bulk physical properties on single crystals of 7(MF6)2 will be
the subject of a separate publication.21
In this paper, we give a full account of the preparation of
7(A)2 [A = AsF6-, SbF6-, Sb2F11-] salts, their vibrational
spectra, structures, a variable-temperature magnetic study of
solid 7(Sb2F11)2 imbedded in a matrix of the isostructural
10(Sb2F11)2, and the electronic structure of 72þ with focus on
the characterization of 72þ in the gas, solution, and solid
states as a molecular species, and we account for the remark-
able similarities between it and O2 (see Figure 11). Parts of
this work were reported in 1993 and 1996 as preliminary com-
munications4a,c and later as three extended abstracts of con-
ference presentations.4b,d,e A single-crystal EPR study of
7(Sb2F11)2 in a matrix of the diamagnetic isostructural 10-
(Sb2F11)2 was published in J. Magn. Reson. Chem. in 1999.4f
However, numerous problems and questions remained. The
present, much more complete understanding of the system
was aided by a variable-temperature magnetic study of the
crystalline 7(Sb2F11)2 in a matrix of the diamagnetic iso-
structural 10(Sb2F11)2, which experimentally established the
2. Experimental Section
2.1. Materials. The preparation of 10(AsF6)29 and pale-green
rods of 7(Sb2F11)2 (5% by weight) imbedded in the solid matrix
of 10(Sb2F11)2 was carried out as previously described.4f The
mixture of S4(AsF6)2 and S8(AsF6)2 (1:1 ratio) was prepared by
condensing AsF5 and traces of Br2 onto S8 (vacuum-dried) in the
22
appropriate mole ratio in liquid SO2 and S4(AsF6)2 as pre-
viously described.23 S8 flowers (Anachemia) were vacuum-dried
prior to use. SO2 (Liquid Air), AsF3 (Ozark-Mahoning),
SO2ClF (Aldrich), and Br2 (Fisher) were stored over CaH2,
˚
NaF, a mixture of 3 and 5 A molecular sieves, and P4O10, res-
pectively. AsF5 was prepared according to reference 24. (CN)2
(Matheson) was used as received, and SbF5 (Ozark-Mahoning)
was distilled in vacuo prior to use.
triplet and singlet states to be identical in energy ( 2 cm-1
.
2.2. General Procedures. All reactions were performed in
two-bulb, two-valve Pyrex vessels incorporating 25 mL bulbs
and a medium sintered-glass frit using techniques that have been
previously described.25 Solid reagents and crystals were ma-
nipulated and handled under a nitrogen atmosphere in a drybox.
FT-IR spectra of Nujol mulls between KBr disks were recorded
at 293 K on a Bruker IFS66 FT-IR spectrometer at a resolution
of 2.0 cm-1. FT-Raman spectra were recorded at 120 K on a
Bruker IFS66 FT-IR spectrometer equipped with a Bruker
This simplified the analysis of the variable-temperature
magnetic data on 7(SbF6)2 and led to a reinterpretation of
the previously published data on 7(AsF6)2 and 7(Sb2F11)2.4c
Only in recent years have theoretical calculations that permit
the prediction of the lowest states of 72þ and vibrational
spectra in agreement with the experimental results become
feasible. This has allowed us to apply theoretical methods
to better understand 72þ in the gaseous, solution, and solid
phases. 72þ had been previously analyzed by Genin and
FRA106 FT-Raman accessory using
a Nd:YAG laser
(emission wavelength = 1064 nm; maximum laser power =
300 mW) in 5 mm Pyrex NMR tubes. Data were collected in the
backscattering mode (180ꢀ excitation; resolution 2.0 cm-1). A
UV/vis spectrum of 7(AsF6)2 in a SO2/AsF5 solution was
obtained on a Perkin-Elmer UV/vis spectrometer in a quartz
cell of 1 mm path length attached to a glass vessel fitted with a
Rotoflo valve. Elemental analyses of 7(AsF6)2, 7(Sb2F11)2, and
7(SbF6)2 were obtained from Mikroanalytisches Laboratorium
(13) (a) Veciana, J.; Rovira, C.; Crespo, M. I.; Armet, O.; Domingo,
V. M.; Palacio, F. J. Am. Chem. Soc. 1991, 113, 2552. (b) Veciana, J.; Rovira,
C.; Ventosa, N.; Crespo, M. I.; Palacio, F. J. Am. Chem. Soc. 1993, 115, 57.
(c) Ballester, M.; Pacual, I.; Carreras, C.; Vidal-Gancedo, J. J. Am. Chem. Soc.
ꢀ
1994, 116, 4205. (d) Viadel, L. I.; Carilla, J.; Labarta, A.; Julia, L. J. Mater.
ꢀ
Chem. 1998, 8, 1165. (e) Sedo, J.; Ventosa, N.; Ruiz-Molina, D.; Mas, M.;
€
Beller, Gottingen, Germany, and Galbraith Laboratories, Inc.,
Knoxville, TN.
Molins, E.; Rovira, C.; Veciana, J. Angew. Chem., Int. Ed. 1998, 37, 330.
(14) (a) Bock, H.; John, A.; Havlas, Z.; Bats, J. W. Angew. Chem., Int. Ed.
Engl. 1993, 32, 416. (b) Allinson, G.; Bushby, R. J.; Paillaud, J.-P. J. Am. Chem.
Soc. 1993, 115, 2062. (c) Stickley, K. R.; Blackstock, S. C. J. Am. Chem. Soc.
1994, 116, 11576. (d) Michinobu, T.; Takahashi, M.; Tsuchida, E.; Nishide, H.
Chem. Mater. 1999, 11, 1969. (e) Murata, H.; Takahashi, M.; Namba, K.;
Takahashi, N.; Nishide, H. J. Org. Chem. 2004, 69, 631.
2.3. Syntheses. 2.3.1. Preparation of 7(AsF6)2 from (CN)2
and a 1:1 Mixture of S8(AsF6)2 and S4(AsF6)2. Caution! Manip-
ulations with very poisonous cyanogen should be carried out in a
good vacuum line and very efficient fume hood. (CN)2 (0.490 g,
9.42 mmol) was condensed at 77 K into one bulb of a two-bulb
vessel and dissolved in ca. 10 mL of SO2. The solution was
poured into the second bulb containing a 1:1 mixture of S4-
(AsF6)2 and S8(AsF6)2, “S3AsF6” (3.78 g, 13.2 mmol), and the
mixture was stirred for 3 h to produce a brown precipitate under
a pale-green solution. The volatiles were removed to constant
weight, leaving 5.08 g of a dark-brown solid (calcd: 4.96 g based
€
(15) For main-group diradicals, see: (a) Grutzmacher, H.; Breher, F.
Angew. Chem., Int. Ed. 2002, 41, 4006. (b) Power, P. P. Chem. Rev. 2003, 103,
789. (c) Breher, F. Coord. Chem. Rev. 2007, 251, 1007. (d) Hicks, R. G. Org.
Biomol. Chem. 2007, 5, 1321.
(16) (a) Rajca, A. Chem. Rev. 1994, 94, 871. (b) Matasuda, K.; Iwamura, H.
Curr. Top. Solid State Mater. Sci. 1997, 2, 446.
(17) (a) Salem, L.; Rowland, C. Angew. Chem., Int. Ed. Engl. 1972, 11, 92.
(b) Borden, W. T. Diradicals. In Encyclopedia of Computational Chemistry;
Schleyer, P. v. R. , Ed.; Wiley-Interscience: New York, 1998; p 708.
(18) (a) Recently, examples of main-group diradicals that are paramag-
netic in the solid state have been reported, but as far as we are aware, they
either contain spacer groups between the radical centers, are stabilized bulky
groups, or are much more complicated than the systems in the subclass. For
examples, see: (b) Konarev, D. V.; Khasanov, S. S.; Otsuka, A.; Saito, G.;
Lyubovskaya, R. M. J. Am. Chem. Soc. 2006, 128, 9292. (c) Gilroy, J. B.;
McKinnon, S. D. J.; Kennepohl, P.; Zsombor, M. S.; Ferguson, M. J.; Thompson,
L. K.; Hicks, R. G. J. Org. Chem. 2007, 72, 8062. (d) Rajca, A.; Takahashi, M.;
Pink, M.; Spagnol, G.; Rajca, S. J. Am. Chem. Soc. 2007, 129, 10159. (e) Rajca,
A.; Shiraishi, K.; Rajca, S. Chem. Commun. 2009, 4372.
(20) Wood, D. Ph.D. Thesis, University of New Brunswick, Fredericton,
Canada, 2001.
(21) Scherer, W.; et al. Unpublished results.
(22) Gillespie, R. J.; Passmore, J.; Ummat, P. K.; Vaidya, O. Inorg. Chem.
1971, 10, 1327.
(23) Murchie, M. P.; Passmore, J.; Sutherland, G. W.; Kapoor, R.
J. Chem. Soc., Dalton Trans. 1992, 503.
(24) Aris, D. R.; Knapp, C.; Passmore, J.; Wang, X. J. Fluorine Chem.
2005, 126, 1368.
(25) (a) Murchie, M.; Passmore, J. Inorg. Synth. 1986, 24, 76. (b) Murchie,
M. P.; Kapoor, R.; Passmore, J.; Schatte, G.; Way, T. Inorg. Synth. 1997, 31, 102.
(19) Genin, H.; Hoffmann, R. Macromolecules 1998, 31, 444.

7864 Inorganic Chemistry, Vol. 49, No. 17, 2010
Cameron et al.
Scheme 1
7(Sb2F11)2 based on eq 8 in Scheme 1). The crystals of 7(Sb2F11)2
were grown from an SO2/SO2ClF mixture (2:1 mole ratio) by
slow evaporation of the solvent at room temperature, while the
collection bulb was held at 0 ꢀC. Dark-green crystalline rods
and some reddish-brown platelike crystals, visible under a
microscope, were obtained. Crystallization at a lower tempera-
ture seemed to increase the fraction of the red-brown phase.
The identity of both phases was confirmed by their X-ray struc-
tures.20 The X-ray structure reported below was obtained on a
red crystal stored for several years. It was red in transmitted
light but seemed green in reflected light. Some crystals were
coated in a green powder, which was removed when the crystals
were scratched. Elem anal. Obsd/calcd for C2N2S6Sb4F22: C,
2.04/2.09; N, 2.46/2.44; S, 15.60/16.74; Sb, 42.00/42.37; F,
37.90/36.37.
2.3.5. Preparation of (CNSNS)2(Sb2F11)2 [10(Sb2F11)2]. SO2
(18.3 g) and SbF5 (20.1 g, 92.7 mmol) were condensed onto
10(AsF6)2 (1.50 g, 2.56 mmol) at 77 K, giving a pale-yellow solu-
tion upon warming to room temperature. The mixture was
stirred for 3 days, and the volatiles were removed under a
dynamic vacuum to constant weight, leaving 2.86 g of a very
pale-yellow crystalline solid (calcd: 2.85 g based on eq 9 in
Scheme 1). 10(Sb2F11)2 was a pale-yellow solid that was indefi-
nitely stable under dry nitrogen at room temperature. The struc-
ture of 10(Sb2F11)2 was confirmed by X-ray diffraction, which
showed the dication 102þ to be structurally identical with that in
10(AsF6)2 reported previously.9 FT-Raman spectrum (cm-1):
[dication peaks]9 1499s, 1300vw, 1205w, 954 mw, 795s, 591 m,
540vw, 473s, 441mw, 292mw, 282mw, 219vs, 189vw, 154vs;
[Sb2F11- anion peaks] 684w, 646 m, 559vw, 354w.
on eq 2 in Scheme 1). Suitable single crystals of 7(AsF6)2 were
obtained as dark-red-brown plates from a AsF3 solution by the
slow removal of the solvent at 5 ꢀC over several days into a collection
bulb held at 0 ꢀC. Elem anal. Obsd/calcd for C2N2S6As2F12: C,
3.87/3.86; N, 4.48/4.52; S, 30.98/30.91; As, 23.92/24.08; F,
36.20/36.63. UV/vis (SO2/AsF5) λmax/nm (log ε/M-1 cm-1): 338
(2.5), 430 (1.4), 600 (0.4), 644 (0.5), 704 (0.3). The actual UV/vis
spectrum is shown in Figure S1 in the Supporting Information.
2.3.2. Preparation of 7(AsF6)2 from (CN)2 and S4(AsF6)2.
(CN)2 (0.345 g, 6.63 mmol) was condensed onto S4(AsF6)2
(3.42 g, 6.77 mmol) at 77 K in ca. 8 mL of SO2. The mixture
was warmed up to room temperature and stirred for 1 h to pro-
duce a pale-green solution over a dark-brown crystalline solid.
Removal of the volatiles left 2.56 g of reddish-brown crystalline
solid (calcd: 2.59 g based on eq 3 in Scheme 1). The FT-Raman
spectrum of the product was identical with that of 7(AsF6)2,
prepared as described in section 2.3.1. Elem anal. Obsd/calcd for
C2N2S6As2F12: C, 3.98/3.86; N, 4.63/4.52; S, 31.00/30.91; As,
24.22/24.08; F, 36.17/36.63.
2.3.6. Preparation of 7(Sb2F11)2 Imbedded in a Matrix of Iso-
morphous 10(Sb2F11)2. SO2 (10.8 g) was condensed at 77 K onto
a mixture of 10(Sb2F11)2 (0.893 g, 0.802 mmol) and 7(Sb2F11)2
(0.392 g, 0.341 mmol) to form a dark-green solution upon
warming to room temperature. The crystalline sample (large
pale-green rectangular rods) was prepared by slow evaporation
of the solvent with a temperature gradient of 5 ꢀC (collection
bulb, 0 ꢀC; bulb containing the mixture, 5 ꢀC) for 6 h. The cry-
stals were isolated by filtration. One of the crystals was exam-
ined by X-ray and found to have the same unit cell parameters as
those in 10(Sb2F11)2. These crystals were used to obtain vari-
able-temperature magnetic susceptibility measurements of 7-
(Sb2F11)2 diluted in a diamagnetic matrix of 10(Sb2F11)2, as
described in section 2.7. The slow removal of SO2 from the
supernatant solution produced smaller and darker-green rods,
which were not used for magnetic studies.
2.3.3. Preparation of 7(SbF6)2. SO2 (16.5 g), SbF5 (7.55 g,
34.8 mmol), and Br2 (∼15 mg) were condensed onto S8 (1.52 g,
5.93 mmol) to give a dark-blue solution over a colorless pre-
cipitate after 1 day. The dark-blue solution was filtered and the
precipitate washed several times with small portions of SO2. The
FT-Raman spectrum of the colorless solid (2.34 g) was consist-
ent with the presence of (SbF3)3SbF526 and/or (SbF3)6(SbF5)5,27
as well as some other unidentified material. (CN)2 (0.615 g, 11.8
mmol) was condensed onto the filtered blue solution at 77 K to
produce, upon warming to room temperature, a dark-green
solution over a reddish-brown precipitate. The mixture was
stirred for 3 days, and the volatiles were removed under a dyn-
amic vacuum, leaving 7.28 g of an inhomogeneous mixture of
reddish-brown shiny crystals (clean, no coated faces), reddish-
brown crystals coated by other solids, an amorphous-like brown
solid, and a small quantity of white solid (observed as small
specks throughout the brown solid). The X-ray crystal structure
of 7(SbF6)2 was determined using the well-shaped shiny crystals.
Variable-temperature magnetic, IR, and Raman measurements
were obtained on what appeared to be clean crystals separated
manually in the drybox. The X-ray structure reported below was
obtained from a crystal stored for several years.
2.3.7. Reduction of 7(AsF6)2. SO2 (10.6 g) was condensed at
77 K onto a mixture of 7(AsF6)2 (1.30 g, 2.08 mmol) and
Na2S2O4 (0.189 g, 1.09 mmol) into a vessel equipped with an
EPR tube to produce a yellow-brown solution over a black solid
upon warming to room temperature. A portion of the soluble
fraction was poured into an attached EPR tube, and an EPR
spectrum was obtained at 193 K (Figure S6 in the Supporting
Information). After 24 h, yellow crystals of S8 (FT-Raman) had
precipitated and continued to precipitate until the volatiles were
removed to constant weight, leaving after 3 days 1.39 g of an
inhomogeneous mixture of pale-yellow crystals of S8 (FT-
Raman), colorless crystals of NaAsF6 (X-ray), and a black
solid. The sulfur was extracted from the mixture using CS2
(10.5 g), leaving 1.25 g of NaAsF6 and the black solid (expected
total mass of NaAsF6 and proposed 7AsF6 is 1.34 g assuming a
quantitative reaction according to Scheme 1, eq 10). A small
amount of black solid was manually separated from the crystals
of NaAsF6, and the FT-Raman spectrum of the black solid was
obtained (Figure S5 in the Supporting Information). Attempts
to grow crystals of this material from SO2 were unsuccessful.
When a small amount of black solid was redissolved in SO2,
precipitation of sulfur crystals was observed after 10 min. The
soluble fraction was filtered and evaporated, producing the
2.3.4. Preparation of7(Sb2F11)2. SO2 (11.8g) andSbF5 (9.69 g,
44.7 mmol) were condensed at 77 K onto 7(AsF6)2 (1.70 g,
2.72 mmol), giving a dark-green solution upon warming to room
temperature. The mixture was stirred for 3 days, and the
volatiles were removed under a dynamic vacuum to constant
weight, leaving 3.13 g of a dark-green solid (calcd: 3.14 g of
(26) Nandana, W. A. S.; Passmore, J.; Swindells, D. C. N; Taylor, P.;
White, P. S.; Vekris, J. E. J. Chem. Soc., Dalton Trans. 1983, 619.
(27) Nandana, W. A. S.; Passmore, J.; White, P. S. J. Chem. Soc., Dalton
Trans. 1985, 1623.

Article
Inorganic Chemistry, Vol. 49, No. 17, 2010 7865
Chart 2
the Hall model32 for one-dimensional (1D) chains and the Lines
model33 for two-dimensional (2D) sheets.
2.8. Quantum-Chemical Calculations. The results for single-
reference density functional theory (DFT) calculations were
obtained using the Gaussian 03 suite of programs.34 The com-
monly used Pople split-valence double-ζ basis set, 6-31G*, was
employed in single-reference calculations. For DFT calcula-
tions, a hybrid functional by Perdew, Burke, and Ernzerhof
(PBE0),35 which has no thermodynamically fitted parameters,
was chosen. The geometry of 72þ was constrained to C2h sym-
metry in all cases, except when a relaxed potential energy scan
about the C-C bond was performed. The effects of other DFT
functionals (B3LYP and MPW1PW91) as well as inclusion of
extra polarization and diffuse functions and expansion of the
valence basis set to triple-ζ quality were tested and found to give
nearly identical results (Table S2 in the Supporting Informa-
black solid with no change in the FT-Raman spectrum. Upon
heating of this black solid at 100 ꢀC, a small amount of 1828
(Chart 2) sublimed out (X-ray). The FT-Raman spectrum of the
black residue was the same as that prior to heating.
2.4. Chemical Stability, Solubility, and Some Physical Prop-
erties of the Salts of 72þ. All of the salts of 72þ are indefinitely
stable under dry nitrogen at room temperature, but exposure to
moisture gives a white mist and a yellow solid (S8, FT-Raman).
Upon heating 7(MF6)2 to 200 ꢀC, sulfur is sublimed out. Heat-
ing of 7(Sb2F11)2 resulted in evolution of a white mist, which
condensed as colorless droplets (assumed to be SbF5). 7(MF6)2
is sparingly soluble in SO2 (M = As, 0.012 g mL-1; M = Sb,
0.027 g mL-1), while the solubility of 7(Sb2F11)2 in SO2 is greater
(0.057 g mL-1). All three salts are very soluble in the SO2/AsF5
mixture and pure AsF3. All solutions are green. When smeared
against a hard surface or ground using a mortar and pestle,
7(MF6)2 (M = As, Sb) changes color from red-brown to green.
The magnetic moment of 7(AsF6)2 increased from 2.62 to 3.33 μB
(determined by the Gouy method) for a sample ground for 1 h.
2.5. Crystal Structure Determinations. The measurements
were made on a Rigaku RAXIS diffractometer [7(SbF6)2 and
7(Sb2F11)2] and an Enraf Nonius CAD-4 diffractometer [10-
(Sb2F11)2]. The structures were solved by direct methods, and all
of the atoms were refined anisotropically.29 Data collection and
refinement parameters are listed in Table 1, except for 7(AsF6)2
[isomorphous to 7(SbF6)2], which was given in a preliminary
communication.4a Figures illustrating the crystal structures
were prepared using DIAMOND,30 which was also used to
determine all of the quoted intermolecular parameters.
tion). DFT calculations predicted a triplet ground state for 72þ
.
The “closed-shell” singlet state was found to be significantly
higher in energy than the triplet state. Because of the signifi-
cantly larger energy separation between the “closed-shell” sing-
let and triplet states compared to the experimental singlet-
triplet gap, symmetry-broken UPBE0 calculations were per-
formed to find a (“open-shell”) singlet diradical state.
The use of symmetry-broken methods provides only a quali-
tative description of the singlet diradical state. The proper treat-
ment of a static electron correlation in singlet diradical states
requires the use of multiconfigurational methods.36 The Molpro
program37 was employed for multiconfiguration calculations on
the lowest singlet and triplet states of 72þ. Geometry optimiza-
tions of 72þ were done using CASSCF38 with two different act-
ive spaces and Pople’s split-valence triple-ζ 6-311G* basis set.
The smaller active space consisted of eight electrons distributed
to the four highest occupied and lowest unoccupied orbitals of
the reference Hartree-Fock wave function constituting an [8, 8]
active space. The larger active space was augmented to include
two more occupied and unoccupied orbitals, leading to a [12, 12]
active space. The dynamical electron correlation to the
2.6. EPR Spectroscopy. All of the EPR spectra were obtained
using a modified Varian spectrometer. Samples for solution
EPR studies were prepared in a two-bulb vessel equipped with a
4 mm quartz tube. The following amounts were used: 7(AsF6)2,
0.161 g (0.259 mmol) in a SO2/AsF5 mixture (8.196/0.980 g);
7(SbF6)2, 0.251 g (0.351 mmol) in a SO2/AsF5 mixture (12.144/
1.437 g); 7(Sb2F11)2, 0.049 g (0.042 mmol) in a SO2/SbF5 mixture
(5.328/1.624 g). All solutions were dark green in color and
contained no insoluble material. Isotropic EPR spectra were
recorded at þ20 and -80 ꢀC; anisotropic frozen solution spectra
were recorded at -160 ꢀC. Single-crystal EPR studies of 7-
(Sb2F11)2 doped in a diamagnetic host have been described
elsewhere.4f
(34) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb,
M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.;
Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.;
Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakat-
suji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.;
Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li,
X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.;
Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.;
Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.;
Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich,
S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.;
Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.;
Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz,
P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.;
Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson,
B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision
C.02; Gaussian, Inc.: Wallingford, CT, 2004.
2.7. Magnetic Susceptibility Measurements. The variable-
temperature magnetic susceptibilities of red-brown 7(AsF6)2,
red-brown 7(SbF6)2, and light-green 7(Sb2F11)2 doped in dia-
magnetic 10(Sb2F11)2 were determined using a Quantum Design
(MPMS) SQUID magnetometer operating at a field of 1 T. The
actual numerical data are given in Table S1 in the Supporting
Information. The experimental magnetic data of 7(Sb2F11)2
diluted in a diamagnetic host were fitted by the Bleaney-Bowers
model,31 and those of 7(MF6)2 (M = As, Sb) were fitted by both
(35) (a) Perdew, J. P.; Ernzerhof, M.; Burke, K. J. Chem. Phys. 1996, 105,
9982. (b) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77,
3865–3868. Phys. Rev. Lett. 1997, 78, 1396.
(36) Bally, T.; Borden, W. T. Calculations on Open-Shell Molecules: A
Beginner’s Guide. In Reviews in Computational Chemistry; Lipkowitz, K. B.,
Boyd, D. B., Eds.; Wiley-VCH: New York, 1999; Vol. 13, pp 1-97.
€
(37) Werner, H.-J.; Knowles, P. J.; Lindh, R.; Manby, F. R.; Schutz, M.;
Celani, P.; Korona, T.; Mitrushenkov, A.; Rauhut, G.; Adler, T. B.; Amos,
R. D.; Bernhardsson, A.; Berning, A.; Cooper, D. L.; Deegan, M. J. O.;
Dobbyn, A. J.; Eckert, F.; Goll, E.; Hampel, C.; Hetzer, G.; Hrenar, T.;
(28) Underhill, A. E.; Hawkins, I.; Edge, S.; Wilkes, S. B.; Varma, K. S.;
Kobayashi, A.; Kobayashi, H. Synth. Met. 1993, 55-57, 1914.
(29) Sheldrick, G. M. SHELX-97, Program for the Refinement of Crystal
€
Knizia, G.; Koppl, C.; Liu, Y.; Lloyd, A. W.; Mata, R. A.; May, A. J.;
€
€
Structures; University of Gottingen: Gottingen, Germany, 1997.
(30) DIAMOND, version 3.2d; Crystal Impact: Bonn, Germany, 1997-2010.
(31) Bleany, B.; Bowers, K. D. Proc. R. Soc. London, Ser. A 1952, 214,
451.
McNicholas, S. J.; Meyer, W.; Mura, M. E.; Nicklass, A.; Palmieri, P.;
€
Pfluger, K.; Pitzer, R.; Reiher, M.; Schumann, U.; Stoll, H.; Stone, A. J.;
Tarroni, R.; Thorsteinsson, T.; Wang, M.; Wolf, A. MOLPRO, a package of
ab initio programs, version 2006.1; see http://www.molpro.net.
(38) (a) Werner, H.-J.; Knowles, P. J. J. Chem. Phys. 1985, 82, 5053.
(b) Knowles, P. J.; Werner, H.-J. Chem. Phys. Lett. 1985, 115, 259. (c) Busch, T.;
Degli Esposti, A.; Werner, H.-J. J. Chem. Phys. 1991, 94, 6708.
(32) (a) Estes, W. E.; Hatfield, W. E.; Van Ooijen, J. A. C.; Reedijk, J.
J. Chem. Soc., Dalton Trans. 1980, 2121. (b) Hall, J. W. Ph.D. Thesis, University
of North Carolina, Raleigh, NC, 1977.
(33) Lines, M. E. J. Phys. Chem. Solids 1970, 31, 101.

7866 Inorganic Chemistry, Vol. 49, No. 17, 2010
Cameron et al.
Table 1. Crystal Data and Structure Refinement Details for 7(SbF6)2, 7(Sb2F11)2, and 10(Sb2F11 2
)
a
7(SbF6)2
7(Sb2F11)2
7(Sb2F11)2
10(Sb2F11)2
empirical formula
fw
temperature (K)
λ (A)
space group
CNSSbF6
357.9
173
0.710 73
P1
triclinic
dark red, block
5.6403(12)
7.9108(18)
9.2776(16)
98.550(9)
92.427(7)
103.476(12)
396.81(14)
2
CNSSb2F11
574.68
296
0.710 70
P1
triclinic
dark red, block
8.4380(14)
8.9554(12)
10.5349(8)
103.31(3)
101.40(3)
118.68(3)
633.84(36)
2
C2N2S6Sb4F22
1149.36
123
0.710 73
P1
triclinic
dark red, block
8.4307(11)
8.7468(11)
10.2677(11)
100.978(3)
101.941(1)
118.442(3)
613.5(2)
1
C2N2S6Sb4F22
1113.3
293
0.710 73
P1
triclinic
˚
cryst syst
color and habit
pale yellow, parallelepipeds
˚
a (A)
8.171(3)
8.616(2)
10.333(3)
102.30(2)
101.50(3)
117.76(2)
590.3(3)
1
˚
b (A)
˚
c (A)
R (deg)
β (deg)
γ (deg)
3
˚
volume (A )
Z
density (g cm-3
)
2.996
4.307
3.011
4.863
3.111
5.025
3.132
5.056
μ (mm-1
)
reflns collected
indep reflns
R1b, wR2c
13 447
1614
0.0681, 0.2156
28 552
5455
0.0376, 0.0480
13 806
2654
0.0346, 0.0418
3865
3341
0.0392, 0.0957
P
P
P
P
a From ref 20. b R1 = ||Fo| - |Fc||/ |Fo|. c wR2 = { [w(Fo2 - Fc2)2]/ [Fo4]}1/2
.
CASSCF state energies was included in a perturbational manner
using the CASPT2 method.39
Both products have been shown to be identical by ele-
mental analysis and vibrational spectroscopy. 7(AsF6)2
can also be obtained by the reactions of (CN)2 and
“S10(AsF6)2” and “S16(AsF6)2” (Scheme 1, eqs 4 and 5,
respectively).20 The FT-Raman spectra of the products
from the latter two reactions show peaks attributable to
7(AsF6)2 and sulfur, but the observed weight changes and
the in situ EPR spectra of these reactions (see section 3.6)
indicate also the presence of other species.
[12,12]-CASSCF-optimized geometries of the triplet and
singlet electronic states of 72þ and PBE0-optimized geometries
of the triplet and closed-shell singlet states are included in Table 4.
The harmonic vibrational frequencies of the PBE0-optimized
triplet and open-shell singlet states of 72þ are listed in Table 5.
The vibrational modes were assigned by normal-coordinate
analysis and visualization of the calculated frequencies. For
the normal-coordinate analysis, Cartesian force constants cal-
culated for a PBE0/TZVPP-optimized structure35,40 were trans-
formed into more descriptive internal coordinates using the
Turbomole program.41 Descriptions of the internal coordinates
and assignment of calculated normal modes to internal coordi-
nates have been presented in Tables S3 and S4 in the Supporting
Information. The rotational profile about the C-C bond was
examined by performing a UPBE0 relaxed potential energy scan
by varying the N-C-C-N dihedral angle from 0 to 180ꢀ. The
effect of solvent SO2 on the rotational profile was examined by
repeating the scan using the IEFPCM solvent model.42 Di-
The synthesis of 7(SbF6)2 (Scheme 1, eq 7) was carried
out similarly to 7(AsF6)2 but using SbF5 instead of AsF5
(Scheme 1, eq 6). We note that S4(SbF6)2 and S8(SbF6)2
have not yet been isolated in the solid state, and we do not
suggest that these species are actually formed. The pro-
duct obtained from reaction (7) appears as an inhomoge-
neous mixture of highly crystalline red 7(SbF6)2 (X-ray
crystal structure) and small amounts of a colorless solid
(reduced antimony fluorides).26,27 The clean red crystals
were manually separated from the product mixture under
the microscope, and the FT-Raman spectrum (Figure S2
in the Supporting Information) obtained on these crystals
showed two peaks at 654 and 651 cm-1, which could not
be assigned to either the dication or the SbF6- anion but
which matched very well with the most intense peak (653
cm-1) observed in the FT-Raman spectrum of the re-
duced antimony fluorides isolated from reaction (6).
The preparation of 7(Sb2F11)2 was carried out by re-
acting pure 7(AsF6)2 with a large molar excess of SbF5
(Scheme 1, eq 8). After removal of the excess SbF5 in a
vacuum, pure 7(Sb2F11)2 (IR, Raman, elemental analysis)
was obtained in an almost quantitative yield. This salt was
used for cocrystallization with 10(Sb2F11)2 (prepared
analogously, Scheme 1, eq 9) to obtain the sample of
72þ “diluted” in a diamagnetic host studied by magnetic
susceptibility measurements.
˚
electric constant 14.0 and solvent radius 2.032 A were applied
for the SO2 solvent.
3. Results and Discussion
-
3.1. Syntheses of (CNSSS)2(A)2 (A = AsF6-, SbF6
,
Sb2F11-) and 10(Sb2F11)2. The reaction of an excess of
(CN)2 and a 1:1 mixture of S4(AsF6)2 and S8(AsF6)2
proceeded to produce the reddish-brown pure 7(AsF6)2
(IR, Raman, and elemental analysis) in an almost quan-
titative yield (Scheme 1, eq 2).
The same reddish-brown solid was obtained from the
reaction between (CN)2 and S4(AsF6)2 (Scheme 1, eq 3).
(39) (a) Werner, H.-J. Mol. Phys. 1996, 89, 645. (b) Celani, P.; Werner, H.-J.
J. Chem. Phys. 2000, 112, 5546.
(40) (a) Weigend, F.; Ahlrichs, R. Phys. Chem. Chem. Phys. 2005, 7, 3297.
(b) Metz, B.; Stoll, H.; Dolg, M. J. Chem. Phys. 2000, 113, 2563.
(41) (a) TURBOMOLE, Program Package for ab initio Electronic
Structure Calculations, version 5.10; TURBOMOLE GmbH: Karlsruhe,
3.2. Reduction of 72þ. Evidence for the Radical Cation 7þ.
Reduction experiments of 7(AsF6)2 (Scheme 1, eq 10) were
performed to prepare the monoradical monocation 7•þ,
which potentially could form a structure with stronger inter-
actions between the heterocyclic rings, leading to interesting
€
€
€
Germany, 2008. (b) Ahlrichs, R.; Bar, M.; Haser, M.; Horn, H.; Kolmel, C.
Chem. Phys. Lett. 1989, 162, 165.
ꢁ
(42) (a) Cances, E.; Mennucci, B.; Tomasi, J. J. Chem. Phys. 1997, 107,
3032. (b) Cossi, M.; Barone, V.; Mennucci, B.; Tomasi, J. Chem. Phys. Lett.
1998, 286, 253.

Article
Inorganic Chemistry, Vol. 49, No. 17, 2010 7867
bulk properties. Herein we present some spectroscopic
evidence for the formation of a solid containing 7(AsF6),
but the X-ray structure could not be obtained.
Reaction (10) (Scheme 1) proceeded to form an inho-
mogeneous mixture of S8, NaAsF6, and a black solid
proposed to be 7(AsF6). Notably, the FT-Raman and IR
spectra (see Figure S5 in the Supporting Information and
ref 20) of this product were similar to that of 7(AsF6)2,
except that the majority of the peaks were shifted to
significantly lower wavenumbers (e.g., the CdN stretch
at 1513 cm-1 in 7(AsF6)2 and 1417 cm-1 in the black solid
and the S-N stretch at 911 and 876 cm-1, respectively).
This observation is consistent with the weakening of the
bonds within the rings arising from the addition of an
electron to the π* singly occupied molecular orbital
(SOMO) of 72þ (see Figure 5). The C-C stretching fre-
quencies (1192 cm-1 in 7(AsF6)2 and 1190 cm-1 in the
black solid) remained essentially unchanged, consistent
with the nodal properties of SOMOs at the two C atoms.
The reduction of 72þ with Na2S2O4 was monitored in
situ by EPR. The recorded spectra showed two resonan-
Figure 1. Depiction of 72þ [as visualized from the structure of 7(SbF6)2].
Thermal ellipsoids drawn at 50% probability.
The observed coordination numbers about each dication
and anion in 7(MF6)2 (M = As, Sb) are 12 and 6, respec-
tively. The analogous coordination numbers in 7(Sb2F11)2
are 10 and 5 (Figure S10 in the Supporting Information).
We find that these observed arrangements fit the radius
ratio rule for predicting coordination numbers based on
the sizes of the cations and anions (see Table S7 in the
Supporting Information).44 Cation-anion contacts in
the structures of 72þ (confined exclusively to S F con-
3 3 3
tacts)45 were used to calculate the corresponding valency
units by applying Brown’s approach, which estimates an
effective positive charge on each S atom in the dication
assuming that the interaction is ionic.46 The calculated
values are listed in Table 3, where they are compared with
the gas-phase natural bond orbital (NBO) atomic charges
computed by a DFT method. The sum of the valency
units for the three S atoms is close to unity, consistent
with a charge of 1þ on each of the -CNSSS•þ rings, as is
expected for an ionic structure.
ces: a singlet with g = 2.0155, attributed to the starting 72þ
,
and a pentet with g = 2.0132 and a coupling constant
aN = 2.0 G (Figure S6 in the Supporting Information).
The pentet almost certainly arises from the coupling of an
unpaired electron to two equivalent N atoms, which could
be the case for 7•þ, assuming that the unpaired electron is
delocalized over both rings. Examination of the molecu-
lar structure of 7•þ in the gas phase optimized at the
UPBE0/6-31G* level of theory (Ci symmetry, true mini-
mum) shows two slightly nonplanar equivalent -CNSSS
rings with nitrogen hyperfine coupling constants of 1.0 G
(Figure S7 in the Supporting Information). The puckered
nature of the two rings indicates that the stabilizing π
delocalization is reduced by the addition of the eighth π
electron, and thus 7•þ is expected to be considerably less
stable that the perfectly planar dication. The putative
7(AsF6) redissolved in SO2 appeared to gradually decom-
pose, losing elemental sulfur with the subsequent forma-
tion of unidentified products. The only identified product
was 18 (Chart 2), obtained upon sublimation of the black
residue given by evaporation of a filtrate separated from
the elemental sulfur.
The observed trans-planar geometry (C2h symmetry) of
72þ is stabilized by inter-ring Sδþ Nδ- electrostatic
3 3 3
interactions (NBO charges listed in Table 3) and is the
most stable of all of the other possible molecular arrange-
ments (see computational analysis section 3.5). The dica-
tion consists of two 7π CNSSS•þ rings joined by a C-C
2
2
˚
˚
single bond (1.462 A, cf. 1.46 A for a sp -sp single bond
distance).47 The experimental geometrical parameters of
72þ are in good agreement with those predicted at the
PBE0/6-31G* and [12,12]-CASSCF/6-311G* levels of
theory (Table 4). The calculated geometries of both triplet
and open-shell singlet states are almost identical, imply-
ing very weak or even negligible interaction between the
unpaired electrons. The calculated atomic spin densities
of the triplet state show that the spin density lies almost
completely on the S atoms (Table 3) in a fashion similar to
that of other trithiazolium radicals.2,3 Thus, the two rings
in the dication can be viewed as two independent mono-
cations joined by a C-C single bond (albeit their elec-
trons are very weakly interacting). This view is strongly
3.3. Crystal Structures of 7(SbF6)2 and 7(Sb2F11)2. The
structure of red 7(SbF6)2 is isomorphous to red 7(AsF6)2,
which was reported in a preliminary communication.4a
Therefore, the following discussion of the structural fea-
tures (including packing motifs) of 7(SbF6)2 is also rele-
vant for 7(AsF6)2.
The dication 72þ is shown in Figure 1. The internal
structural parameters of centrosymmetric 72þ (Table 2)
are not statistically different in 7(MF6)2 (M = As, Sb)
and 7(Sb2F11)2 and are similar to those of the other salts
of RCNSSS•þ reported previously.1-3 SbF6- has a distorted
Oh symmetry (see Figure S8 in the Supporting Information).
The symmetrically cis-fluorine-bridged [—(SbFSb) = 148.1-
(2)ꢀ] Sb2F11- structure is ordered at -150 ꢀC (see Figure S9
in the Supporting Information) and is similar to that pre-
viously reported in Ir4(CO)8(μ-F)2(Sb2F11)2.43 The increase
in disorder with temperature is discussed in the Supporting
Information.
(44) Huheey, J. E.; Keiter, E. A.; Keiter, R. L. Inorganic Chemistry:
Principles of Structure and Reactivity; 4th ed.; Harper Collins: New York, 1993.
(45) Contacts were only considered if their distances fell within the sum of
˚
the van der Waals radii of the atoms in question (C-F = 3.05 A, N-F =
˚
˚
2.90 A, and S-F = 3.50 A). There were no C-F and N-F contacts found
that were less than these values in any of the salts. The value for the S-F
˚
contacts was increased from 3.20 to 3.50 A, reflecting the fact that the radius
of sulfur is anisotropic.
(46) Valency units were calculated using Brown’s relationship. The con-
tacts of sulfur have been defined as s = (R/R0)-N or s = exp[(R0 - R)/B],
where R is the observed distance, R0 is the value of the bond length with the
unit bond valence, and N and B are constants. The constants are available
from http://ftp.ccp14.dl.ac.uk/ccp/web-mirrors/i_d_brown/bond_valence_-
param/ (Brown, I. D. The Chemical Bond in Inorganic Chemistry;The Bond
Valence Model; Oxford University Press: Oxford, U.K., 2002).
(47) Gleiter, R. Angew. Chem., Int. Ed. 1981, 20, 444.
(43) Hwang, I.-C.; Seppelt, K. Inorg. Chem. 2003, 42, 7116.

7868 Inorganic Chemistry, Vol. 49, No. 17, 2010
Cameron et al.
-
Table 2. Compilation of Structural Parameters and Pauling Bond Orders a of 72þ in the MF6 (M = As, Sb) and Sb2F11- Salts
7(AsF6)24a (295 K)
7(SbF6)2 (173 K)
7(Sb2F11)2 (296 K)
7(Sb2F11)2 (123 K)
˚
Bond Distances (A)/Pauling Bond Orders
C-C
1.462(5)/0.99
1.471(6)/0.96
1.281(7)/1.85
1.609(4)/1.53
2.077(2)/0.92
2.021(2)/1.10
1.746(5)/1.27
6.7
1.469(4)/0.97
1.288(4)/1.80
1.601(3)/1.57
2.062(2)/0.96
2.014(2)/1.12
1.746(4)/1.27
6.7
1.475(6)/0.95
1.291(6)/1.79
1.616(3)/1.50
2.074(2)/0.93
2.028(2)/1.07
1.747(5)/1.27
6.6
C-N
1.284(3)/1.83
1.600(2)/1.58
2.070(1)/0.94
2.018(1)/1.11
1.748(3)/1.26
6.7
N-S1
S1-S2
S2-S3
C-S3
sum of the BOs in the ring
Selected Angles (deg)
C-C-N
120.3(2)
121.3(2)
101.0(1)
97.5(4)
96.8(9)
116.6(2)
120.1(4)
120.8(4)
101.2(2)
97.23(7)
97.1(2)
119.5(2)
120.8(2)
101.4(1)
97.53(5)
97.0(1)
119.3(3)
120.7(3)
101.2(2)
97.45(7)
97.0(1)
C-N-S1
N-S1-S2
S1-S2-S3
S2-S3-C
S3-C-C
116.2(3)
117.4(2)
117.1(3)
a Calculated using the following relation: log(BO) = (D1 - Dn)/0.71, where BO = bond order, D1 = distance of a single bond [standard values
2
3
3
3
3
˚
(hybridization): C-C 1.46 (sp ), C-N = 1.47 (sp ), C-S = 1.82 (sp ), N-S = 1.74 (sp ), S-S = 2.05 (sp ) A], and Dn = observed bond distance.
Table 3. Valency Units46 Calculated for the S F Contacts in the Structures of 7(AsF6)2, 7(SbF6)2, and 7(Sb2F11)2, Corresponding NBO Charges of 72þ in Different Spin
3 3 3
States and Calculated Spin Densities of the Triplet State of 72þ [Calculated at the PBE0/6-31G* Level of Theory]
valency units
NBO charges
open-shell singlet
7(AsF6)2
7(SbF6)2
7(Sb2F11)2
closed-shell singlet
triplet
spin density triplet
C
N
S1
S2
S3
total
0.00
-0.55
0.85
0.25
0.45
0.01
-0.56
0.77
0.28
0.50
0.01
-0.56
0.78
0.28
0.50
-0.01
0.01
0.30
0.40
0.30
1.00
0.31
0.40
0.27
0.98
0.32
0.37
0.22
0.91
0.38
0.31
0.31
1.00
1.00
1.00
1.00
Table 4. Calculateda and Experimental (X-ray) Bond Distances of 72þ
PBE0
CAS
7(SbF6)2
tripletb
open-shell singlet
closed-shell singlet
rotomer, triplet
tripletb
singlet
C-C
1.471(6)
1.281(7)
1.746(5)
1.609(4)
2.077(2)
2.021(2)
1.469
1.284
1.769
1.611
2.108
2.039
1.470
1.284
1.769
1.612
2.108
2.039
1.445
1.300
1.785
1.583
2.086
2.063
1.485
1.281
1.774
1.603
2.119
2.035
1.472
1.266
1.754
1.637
2.044
2.039
1.474
1.264
1.757
1.639
2.044
2.038
C-N
C-S3
N-S1
S1-S2
S2-S3
a Corresponding to fully optimized true minima. Bond distances calculated with the HF, B3LYP, and MPW1PW91 functionals are given in the
Supporting Information. bAbbreviations PBE0 and CAS stand for PBE0/6-31G* and CASSCF[12,12]/6-311G* levels of theory, respectively.
supported by the results of an EPR study as well as mag-
netic susceptibility measurements of 72þ “diluted” in a
diamagnetic host (see sections 3.6 and 3.7).
The perpendicular distances between cations (with re-
spect to the planes of the cations) within stacks along the a
-
axis are 3.69(3) A [AsF6 ] and 3.50(3) A [SbF6-]. The
˚
˚
Valence bond and molecular orbital (MO) descriptions
of the structure of 72þ predict that the sum of the bond
orders within each CNSSS•þ ring should be 6.5 with five σ
bonds, two π bonds, a nonbonding electron pair, and the
seventh π electron in a π* orbital. The sum of the
calculated Pauling bond orders (Table 2) within the
isolated ring is in general agreement with this description.
3.3.1. Packing Motifs of 7(MF6)2 (M = As, Sb) and
7(Sb2F11)2. The isomorphous 7(MF6)2 structures contain
alternating sheets of MF6- anions and planar 72þ in the
bc plane (see Figures 2a and S11 in the Supporting
Information for more packing views), with each dication
inclined at angles of 39.92(1)ꢀ [AsF6-] and 40.62(2)ꢀ
[SbF6-] with respect to the bc plane. There are stacks of
dications down the a and b axes, as illustrated in Figure 2a.
corresponding distances in the stacks along the b axis are
48
4.35(3) and 4.65(3) A. The a stacks are slipped (i.e.,
˚
equivalent atoms in adjacent cations do not coincide with
the normal of the plane of the cations) by 40.26(1) and
38.36(2)ꢀ and the b stacks by 34.63(3) and 36.04(3)ꢀ in
AsF6- and SbF6- salts, respectively, in order to minimize
the electrostatic repulsion between positively charged S
atoms. The cation-cation contacts in the approximate
plane through the plane of the cations (the angle between
the approximate and actual planes of one particular
-
-
cation is 5ꢀ in the AsF6 salt and 6ꢀ in the SbF6 salt)
(48) The slipping angle is defined as the angle between the normal of the
plane through all atoms of one cation and the vector through one atom of the
same cation and the equivalent atom in a neighboring cation in the stack.

Article
Inorganic Chemistry, Vol. 49, No. 17, 2010 7869
Figure 2. (a) Crystal packing of 7(MF6)2 (M = As, Sb) along the c axis showing alternating sheets of dications and anions lying in the bc plane. (b) 72þ
interlayer and interstack S-S dication contacts in 7(MF6)2 (MF6- anions have been removed for clarity). Values given for 7(SbF6)2 with those for 7(AsF6)2
in brackets (std. of S-S contacts, 0.002). Cations belonging to the same approximate plane through the plane of the cations are indicated with an asterisk.
Thermal ellipsoids are drawn at 50% probability.
are shorter than those in the stack along the a axis for the
AsF6 salt, while the opposite is true in the case of
Figure S12 in the Supporting Information and Figure 3b,
respectively). The nearest intercationic contacts are illu-
strated in Figure 3b, the shortest of which connect 72þ via
S(3)-S(3) into a 1D strand. A discussion of temperature-
dependent disorder of some of the Sb2F11- F atoms and
-
7(SbF6)2 (see Figure 2b). This difference may be the origin
of the dramatic difference seen in the magnetic properties
of single crystals of these isostructural salts, which will
be discussed in an upcoming paper.21 Nonbonded radii,
defined as twice the van der Waals radius of sp2-hybri-
dized sulfur perpendicular and parallel to the plane,
the strength of the corresponding S F contacts is given
3 3 3
in the Supporting Information.
3.3.2. Are the Structures of the Red and Green 7-
(Sb2F11)2 Crystals the Same? The red compound in all
of the structures obtained at -150 to þ73 ꢀC has the same
crystal packing, modified only by the increasing disorder
of the F(8)-F(11) equatorial group around the Sb(2)
atom (see Figure S12 in the Supporting Information).
Thus, they all have the same structures with no phase
change over the whole temperature range. The atomic
parameters of the green compound from the structure
determined at þ23 ꢀC are identical,20 within experimental
error, to those of the red compound also determined at
þ23 ꢀC. Thus, all five structures represent the same
crystal packing of the same ion pairs. However, some
cautionary comments are included in the Supporting
Information for those attempting to repeat the experi-
mental work.
49
˚
are 4.06 and 3.20 A, respectively. The dications are
therefore almost, but not completely, isolated from one
another.
The packing in 7(Sb2F11)2 is similar to that of 7(MF6)2,
but intercationic distances are longer and the dications
are more effectively separated by intervening anions (see
Figure 3a). Note that the low-temperature structure is
illustrated as the anion is ordered at -150 ꢀC but becomes
increasingly partially disordered upon an increase of the
temperature (see the Supporting Information for further
discussion). As shown in Figure 3a, the dications stack
down the a axis inclined at an angle of 19.59(1)ꢀ to the bc
plane with a slip angle of 54.93(2)ꢀ. However, there is no
direct contact between cations in the stacks because the
perpendicular distance between the planes of the dica-
tions is 6.90(2) A and the closest distances between atoms
3.4. Vibrational Spectra of the Salts of 72þ. The C2h
symmetry of 72þ leads to 12 IR-active and 12 Raman-active
vibrational modes (mutually exclusive rule).50 The actual
spectra (Figures S2 and S3 in the Supporting Informa-
tion) contain more than 24 peaks including the vibrational
˚
˚
in the neighboring cations in the stack are 7.250(5) A
˚
for S(3)-N(1) and 7.282(2) A for S(3)-S(3) (shown in
(49) Nyburg, S. C.; Faerman, C. H. Acta Crystallogr. 1985, B41, 274.

7870 Inorganic Chemistry, Vol. 49, No. 17, 2010
Cameron et al.
Figure 3. (a) Crystal packing view of 7(Sb2F11)2 (at -150 ꢀC) along the a axis. (b) Illustration of the shortest S-S contacts between cations in 7(Sb2F11)2 (std.
of S-S contacts, 0.002). Cations belonging to different strands are indicated with different letters (bold). Thermal ellipsoids are drawn at 50% probability.
modes of anions. The experimental and calculated vibra-
tional frequencies of 72þ are in good agreement (Table 5).
The assignment of calculated normal modes was carried
out by a normal-coordinate analysis (see Tables S3 and S4
in the Supporting Information for details). The assign-
ment shows that apart from the normal modes corre-
sponding to the CdN and S-S stretching frequencies
most of the normal modes involve several different inter-
nal coordinates, i.e., are mixed.
The CdN vibrational region is very complex, contain-
ing no less than nine vibrations between 1481 and 1607
cm-1 in the FT-Raman spectrum of 7(AsF6)2 at 120 K.
The most intense Raman band at ca. 1510 cm-1 is
attributed to the symmetric CdN vibration, and the weak
bands between 1470 and 1490 cm-1 are attributed to the
13C and 15N isotopomers. Peaks at the higher wavenum-
bers could be due to overtones or combination bands. We
note that peaks found above the region of the Raman-
active CdN stretch are also observed in the FT-Raman
spectra of 10(AsF6)2,8 10(Sb2F11)2, and 10,8 as well as in
some RCNS3•þ radical cations.2 These features are likely
an inherent property of CNS-containing five-membered
heterocycles. The FT-Raman spectrum of 7(Sb2F11)2 in a
SO2 solution (see Figure S4 in the Supporting In-
formation) does not show a similar pattern, but the peaks
are much less intense than they are in the solid state. The
room temperature FT-Raman spectra of the solids are
less resolved than the spectra taken at 120 K but, none-
theless, contain the same features as those observed in the
low-temperature spectra. This implies that the additional
complexity of the vibrational spectra is likely not due to a
phase change at low temperatures.
Although the ν2 vibrational mode [1192 cm-1 in 7(AsF6)2]
corresponding to C-C stretching shows some mixing with
other internal coordinates, it clearly indicates that the C-C
bond is closer to a single bond (cf. the inter-ring C-C stretch
in biphenyl, 1275 cm )
-1 51 than a double bond (e.g., C2H4,
1622.6 cm-1).52 Furthermore, comparison of the stretching
force constants derived from calculated normal modes
showed the C-C bond order to be 1.1 (see Supporting
Information for details). In addition the bond orders for
the S(1)-S(2) and S(2)-S(3) bonds were estimated using a
stretching frequency bond order relationship developed
earlier53 and comparing calculated force constants. Both
(51) (a) Katon, J. E.; Lippincott, E. R. Spectrochim. Acta 1959, 627.
(b) Steele, D.; Lippincott, E. R. J. Mol. Spectrosc. 1961, 6, 238.
(52) Shimanouchi, T. Tables of Molecular Vibrational Frequencies
Consolidated Vol. I; National Standards Reference Data Series 39; NBS:
Washington, DC, 1972.
(50) Nakamoto, K. Infrared and Raman Spectra of Inorganic and Co-
ordination compounds, 4th ed.; Wiley-Interscience: Toronto, 1986.

Article
Inorganic Chemistry, Vol. 49, No. 17, 2010 7871
Table 5. Compilation of Experimental and Calculated [PBE0/6-31G*] Vibrational Frequencies of the Salts of 72þ a
calculated for 72þ b
7(AsF6)2
7(SbF6)2
Raman
7(Sb2F11)2
IR
Raman
IR
IR
Raman
triplet
BS singlet
assignments c
1624 (1)
1628 (1)
1620 (14) 1626 (1)
1579 (<1)
1558 (2)
1539 (1)
1528 (sh)
1514 (100)
1515 (2)
1484 (1)
1634 (37) 1624 (1)
2ν18
1581 (<1)
1558 (2)
1542 (1)
1526 (sh)
1513 (100)
ν18 þ ν19
ν3 þ ν4
2ν19
ν2 þ ν8
1555 (2)
1537 (2)
1515 (sh)
1504 (100) 1608 (0/100) 1612 (0/100) ν1 [νs( CdN)]
1512 (5)
1508 (6)
1614 (14/0)
1617 (14/0)
ν17 [νas(CdN)]
1486 (<1)
1481 (<1)
1230 (1)
1192 (2)
911 (4)
1474 (1)
13C isotopomer of ν1
15N isotopomer of ν1
2ν20
1231 (<1)
1191 (2)
908 (7)
1223 (<1)
1186 (2)
909 (6)
1229 (0/9)
937 (0/7)
1224 (0/9)
933 (0/9)
ν2 [mainly ν(C-C)d]
ν3 [mainly νs(S(1)-N)d]
ν1-ν20
907 (4)
901 (2)
811 (29)
772 (14)
810 (100)
767 (40)
642 (2)
810 (100)
764 (9)
836 (100/0)
779 (68/0)
657 (0/1)
650 (0/0)
638 (52/0)
547 (4/0)
542 (0/2)
490 (12/0)
836 (100/0)
778 (68/0)
656 (0/1)
650 (0/0)
637 (56/0)
548 (4/0)
542 (0/2)
491 (12/0)
ν
ν
18 [νas(S(1)-N)]
19 [mainly νas(S(3)-C)d]
647 (2)
643 (<1)
529 (2)
ν4 [mixed νs(S(3)-C) and δs ring (ip)]
ν
ν
ν
14 [C-C bend (oop)]
20 [mixed δas ring (ip) and νas(S(3)-C)]
21 [νas(S(2)-S(3))]
626 (100)
534 (2)
627 (62)
533 (1)
531 (1)
478 (15)
625 (11)
527 (4)
535 (3)
530 (3)
ν5 [νs(S(2)-S(3))]
477 (3)
474 (61)
454 (1)
ν10 [mixed δs ring (oop) and
C-C bend (oop)]
464 (3)
457 (2)
418 (3)
373 (1)
335 (2)
297 (<1)
225 (1)
459 (2)
447 (2)
416 (1)
468 (1)
441 (0/1)
436 (12/0)
430 (0/2)
404 (5/0)
334 (0/>1)
294 (0/<1)
220 (0/<1)
167 (6/0)
117 (0/0)
91 (3/0)
438 (0/1)
437 (14/0)
430 (0/1)
404 (5/0)
330 (0/1)
293 (0/<1)
219 (0/<1)
167 (6/0)
117 (0/0)
91 (3/0)
ν6 [mainly νs(S(1)-S(2)) d]
ν
22 [νas(S(1)-S(2))]
ν7 [mainly δs ring (ip)d]
23 [δas ring (ip)]
ν8 [F ring (ip)]
15 [δas ring (oop)]
ν9 (ring breathing)
417 (3)
372 s
ν
337 (<1)
297 (<1)
225 (1)
335 (<1)
ν
ν11 [δs ring (oop)]
ν16 [δas ring (oop)]
ν24 (ring scissoring)
ν12 [C-C bend (oop)]
ν13 (τ ring)
78 (2/0)
48 (0/0)
78 (2/0)
45 (0/0)
a Anion frequencies and assignmentsare included in Tables S5and S6in theSupporting Information.b Calculated intensities are listed as (IR/Raman), and
the values are scaled to the most intense band in the spectrum, which is given a value of 100. Peak areas were approximated assuming triangular peaks and a
flat baseline. cAbbreviations: sh, shoulder; ν, stretching; δ, deformation; τ, twisting; F, rocking; ip, in plane; oop, out of plane, s, symmetric; as, asymmetric;
with respect to different rings of the cation. d Small contributions from other normal modes are not shown. See the Supporting Information for details.
•
methods gave estimated bond orders of 0.7 and 1.1 for the
S(1)-S(2) and S(2)-S(3) bonds, respectively, which are in
reasonable agreement with those calculated from bond
distances (see Table 2).
C5H5-, the five constituent atoms of the CNSSS•þ
monomer give rise to five π MOs (designated as π1-π5
in Figure 4). However, the degeneracy of the π2/π3 (filled)
and π4/π5 (empty) couples in C5H5- is lifted in •CNSSS•þ
because of the differences in electronegativity and mis-
match in energies of the constituent C, N, and S atoms. A
similar MO description for bonding in the CNSSSþ ring
in the HCNSSSþ derivative has been given previously at
the ROHF/3-21G* level of theory.1
The vibrational spectra of the anions were assigned by
comparison to spectra of species where the anions have high
symmetry, i.e., Oh symmetry for MF6- (M = As, Sb) and
- 54
D4h symmetry for trans-fluorine-bridged Sb2F11
.
The
observed spectra were more complex than the reference
spectra, consistent with the lower symmetry of anions
The two •CNSSS•þ monomers, each containing five π
orbitals occupied by seven electrons, generate 10 π orbi-
tals for 72þ (designated as Π1-Π10 in Figure 4). The
nearly degenerate Π7 and Π8 (ΔE = 0.07 eV), which
represent the two SOMOs of 72þ, arise from a linear
combination of the two half-filled π4 orbitals of
•CNSSS•þ. Notably, the orbitals Π7 and Π8 are essentially
nonbonding with respect to the C-C bond, thus account-
observed in the crystal structures of 72þ salts, e.g., approxi-
-
mate C2 symmetry for the cis-fluorine-bridged Sb2F11
.
Details of the assignment of the anion frequencies are
presented in the Supporting Information (Tables S5 and S6).
3.5. Computational and Theoretical Analysis of MOs
and the Electronic Structure of 72þ. Following Hoff-
mann’s approach,19 we constructed MOs of 72þ from
the linear combination of the corresponding MOs of the
•CNSSS•þ fragment, which can be formally derived from
72þ by breaking the C-C single bond. This generates an
unpaired electron in the C σ orbital. By analogy with
ing for the observed diradical nature of 72þ
.
The delocalized triplet-state SOMOs of 72þ are almost
but not completely sulfur-based (sum of the SOMO S
atom occupancies Π7 0.94 and Π8, 0.88; almost 100% of
the calculated spin density on the S atoms; see Table 3)
and equivalent to the localized SOMOs calculated using
a symmetry-broken formalism (Figure 5). The SOMO
atom occupancies give a picture similar to that of
calculated spin densities (Table 3) but imply slightly
€
(53) Brownridge, S.; Cameron, T. S.; Du, H.; Knapp, C.; Koppe, R.;
€
Passmore, J.; Rautiainen, J. M.; Schnockel, H. Inorg. Chem. 2005, 44, 1660.
(54) (a) Begun, G. M.; Rutenberg, A. C. Inorg. Chem. 1967, 6, 2212.
(b) Willner, H.; Schaebs, J.; Hwang, G.; Mistry, F.; Jones, R.; Trotter, J.; Aubke, F.
J. Am. Chem. Soc. 1992, 114, 8972.

7872 Inorganic Chemistry, Vol. 49, No. 17, 2010
Cameron et al.
Figure 4. Diagram illustrating the formation of MOs of •þSSSNC-CNSSS•þ from the two •CNSSSþ• fragments. Note that π refers to the monomer-
based π orbitals, while Π refers to the MOs of 72þ; unlabeled orbitals are of the σ type. Monomer SOMOs refer to the unpaired electron on the π4 orbital and
in the dangling σ bond, respectively. Orbitals drawn at isosurface 0.05 au.
Figure 5. (A) Two SOMOs of the triplet state of 72þ. (B) Two SOMOs for the symmetry-broken singlet state of 72þ. Drawn at isosurface 0.05 au.
stronger interaction between the unpaired electrons (as
indicated by the small occupancies on the C atoms). The
spin-paired quinoidal structure 62þ (Chart 1) with a
CdC double bond, which would have been expected

Article
Inorganic Chemistry, Vol. 49, No. 17, 2010 7873
Figure 6. Calculated [PBE0/6-31G*] dependence of the energy of 72þ in its triplet state on the N-C-C-N dihedral angle between the two -CNSSS•þ
rings.
based on a simple Lewis model, is not observed for 72þ
.
Table 6. Singlet-Triplet Gap ΔEST (cm-1)a of 72þ Calculated at the UPBE0 and
CASPT2 Levels of Theory
The MO Π9 represents the C-C π bond corresponding
to the quinoidal structure. Depending on the energies
of the nearly degenerate MOs Π7 and Π8 relative to that
of Π9, a diradical ground state, as in 72þ, or a closed-shell
singlet ground state, as in 11-14, is observed. In the case
of 72þ, Π9 lies much higher in energy (by about 1.56 eV).
The geometry of the calculated closed-shell singlet
(Table 4) is close to the triplet-state geometry. Thus, the
closed-shell singlet corresponds to a double occu-
pancy of the Π7 orbital and not the quinoidal struc-
ture, which would be adopted if Π9 were lower in energy
than Π7 and Π8. No minimum corresponding to the
quinoidal structure 62þ with a short C-C bond was
found for 72þ, in contrast to 10,8 where such a minimum
was obtained. Partial optimization of 72þ by constrain-
ing the C-C bond to an approximate double-bond dis-
72þ
broken symmetry UPBE0
CASPT2[8,8]
CASPT2[12,12]
þ125
þ217
þ264
a The positive sign of ΔEST means that the triplet state is the ground
state (1 cm-1 = 1.1963 ꢀ 10-2 kJ mol-1).
3.5.1. Theoretical Determination of the Ground State of
72þ. The theoretical singlet-triplet gap of 72þ was deter-
mined using single-configuration broken-symmetry UPBE0
and multiconfiguration CASPT2 methods. The results
are given in Table 6. All calculations assign the triplet
state as the ground state of 72þ. The calculated singlet-
triplet gap is small (þ217 and þ264 cm-1 at the CASPT2-
[8,8] and CASPT2[12,12] levels, respectively). The calcu-
lated triplet ground state is consistent with the pseudo-
disjoint nature of the highest occupied MOs Π7 and Π8.
A comparison with related 8-10 neutral species (see
Table S8 in the Supporting Information for results and
discussion) showed singlet diradical ground states for 8
and 9 and only a very weak ferromagnetic coupling of
electrons in 10; i.e., theory predicts that 72þ is the most
likely of these radicals to form a triplet state consistent
with the experimental findings.4,6-8 The calculation re-
sults are also consistent with the lack of features attribu-
table to exchange interaction between radical centers in
the EPR of 108 and the onset of exchange interactions in
the EPR spectrum of 8 observed at higher temperatures
(303 K).6b
˚
tance (1.334 A) approximating the quinoidal struc-
ture gave a structure that was 99 kJ mol-1 higher in
energy than the optimized 72þ structure (see Figure 11).
The experimentally observed trans-planar geometry of
the C2h symmetry (with a 180ꢀ dihedral angle) that
maximizes intramolecular Nδ- Sδþ electrostatic in-
3 3 3
teractions is the most stable conformation in the gas
phase according to the results of the potential energy
scan calculations about the C-C bond (Figure 6).
However, there is a second minimum corresponding to
ca. a 40ꢀ dihedral angle (C2 symmetry) between the two
rings. Both stationary points found at 180ꢀ and 40ꢀ are
true minima, as indicated by the absence of imaginary
frequencies. The cis conformation at 0ꢀ, with the two
repulsive Sδþ Sδþ and Nδ- Nδ- interactions, can
3 3 3
3 3 3
also be optimized; however, it is, in fact, a first-order
saddle point, as indicated by the vibrational frequency
analysis. In a SO2 solution, a similar rotational profile of
72þ was calculated but with the barriers decreased by
However, because of the relatively small singlet-triplet
gap, the ground-state assignment of 72þ should be treated
with some caution because CASPT2 calculations have
been reported to have difficulty in accurately describing
the singlet-triplet gaps of systems where the magnetic
about 3 kJ mol-1
.

7874 Inorganic Chemistry, Vol. 49, No. 17, 2010
Cameron et al.
electrons are only weakly coupled.55 For an accurate
description, even more rigorous methods are required,
e.g., difference-dedicated configuration interaction cal-
culations.56 However, these calculations have not been
attempted. Furthermore, it should be noted that, because
of the similarities of the singlet- and triplet-state energies,
the solid-state effects to the structures (e.g., dipole inter-
actions from other ions) could influence the energy
ordering of the states. This can lead to differences be-
tween theoretically determined and experimentally ob-
served ground states. The experimental determination of
the ground state of 72þ from magnetic measurements is
presented in the following section.
3.6. Magnetic Properties of the Salts of 72þ. Measure-
ments at room temperature of the magnetic susceptibil-
ities of the two salts of 7(A)2 (A = AsF6, SbF6) show the
essential paramagnetism of the diradical dication. The
magnetic moment values at 300 K for 7(A)2, where A =
AsF6 and SbF6, are 2.36 and 2.51 μB, respectively, con-
sistent with the presence of two unpaired electrons per
Figure 7. Measured signal times temperature (EMUmesT) vs tempera-
ture plot for the dilute sample of 7(Sb2F11)2.
SQUID measurements were collected over the tempe-
rature range 2-300 K at an applied field of 10 000 G on
a 0.1011 g sample of 7(Sb2F11)2 doped into 10(Sb2F11)2.
dication and the disjoint nature of 72þ (theoretical μeff
=
2.45 μB). Variable-temperature magnetic susceptibility
studies on samples of 7(A)2 (A = AsF6, Sb2F11)4c and
on 7(SbF6)2, as reported here, give evidence for weak
antiferromagnetic exchange in the solid state in all three
materials. Previously reported20 variable-temperature
susceptibility measurements of 7(AsF6)2 in a SO2/AsF5
solution obtained using Evan’s method are consistent
with the solid-state results given here.
Theoretical as well as experimental EPR studies, given
elsewhere in this report, support the picture of a diradical
in which the two electrons are, at most, very weakly
coupled to each other within the molecular diradical unit.
In an attempt to determine whether the apparent antiferro-
magnetic behavior observed in the magnetic susceptibility
studies of the 72þ salts arises from such intramolecular ex-
change, from intermolecular interactions in the crystal
lattice, orboth, magneticsusceptibility measurementswere
performed on a sample of 7(Sb2F11)2 doped into a dia-
magnetic host 10(Sb2F11)2. Significantly, this experiment
was possible because 7(Sb2F11)2 is isomorphous with the
diamagnetic material 10(Sb2F11)2. By diluting 72þ in a
diamagnetic host, we aimed at eliminating any intermo-
lecular interactions between dications to ensure that all
variation of the magnetic susceptibility with temperature
is due to intramolecular interactions. Both 7(Sb2F11)2 and
10(Sb2F11)2 contain dications that are next-but-one
neighbors in the ionic array, weakly connected by two
A plot of the product of the measured signal (EMUmes
)
times T versus T is shown in Figure 7. Analysis required
that we first use the data to determine the weight fraction, f,
of the diradical in the sample. This was accomplished by
using the data obtained at temperatures above 70 K,
where the plot is linear.
The linear portion above 70 K was analyzed as a straight
line (solid line in Figure 7) with slope -0.000 149 9 (EMU)
and intercept 0.1148 (EMU K). The overall measured
signal is a composite of that due to the temperature-
dependent paramagnetic signal from the diradical
(EMUdirad) and the temperature-independent diamag-
netic signal from all atoms (EMUdia) as well as any
temperature-independent paramagnetic (TIP) signal pre-
sent (EMUTIP). Assuming that any exchange coupling
between the electrons in the diradical is indeed small, as
indicated earlier, and can be ignored above 70 K (the
region of linearity of the graph), the intercept will corre-
spond to EMUdiradT and the slope to EMUdia þ EMUTIP
.
Magnetic susceptibilities for the diradical, χdirad, are
obtained from
χdiradT ¼ ðEMUdiradTMWÞ=ðf ꢀ mass ꢀ HÞ
ð11Þ
where MW is the molecular weight of 7(Sb2F11)2, f is its
mass fraction in the doped sample, and H is the applied
field. Employing the value 0.7505 as the χdiradT value for
two unpaired and uncoupled electrons yields 0.174 for the
value of f.
S
S [7(Sb2F11)2] and S N [7(Sb2F11)2] interactions.
3 3 3
3 3 3
Replacement of 102þ by 72þ would favor 72þ 102þ
2þ3 3 3
interactions (S S and S N) rather than 7
72þ
3 3 3 3 3 3
3 3 3
At all temperatures over the range 2-300 K, the value
of EMUdirad can be obtained from
(two S S) interactions. Thus, 72þ 72þ as neighbors is
3 3 3
3 3 3
not favored and, on general statistical grounds, will lead
to 72þ likely being homogeneously distributed in the host
matrix of 10(Sb2F11)2. This is strongly supported by the
single-crystal EPR studies that showed the material to
contain essentially isolated 72þ dications.4f
EMUdirad ¼ EMUmes - ð - 0:0001499Þ
ð12Þ
Employing eq 12 with a value 0.174 for f, the values of
χdirad can be calculated for all temperatures, as can μeff
values for the diradical.
(55) Queralt, N.; Taratiel, D.; de Graaf, C.; Caballol, R.; Cimiraglia, R.;
Angeli, C. J. Comput. Chem. 2008, 29, 994.
(56) (a) Miralles, J.; Daudey, J.-P.; Caballol, R. Chem. Phys. Lett. 1992,
198, 555. (b) Miralles, J.; Castell, O.; Caballol, R.; Malrieu, J.-P. Chem. Phys.
1993, 172, 33.
For curve-fitting purposes, we halved the χdirad values
obtained above for the doped sample to obtain values for
the monoradicals, χmonorad and, hence, μeff values for the
monoradicals. These are plotted as a function of the

Article
Inorganic Chemistry, Vol. 49, No. 17, 2010 7875
Figure 8. μeff vs T plot for the dilute sample of 7(Sb2F11)2.
temperature in Figure 8. The decrease in the moment
observed at low temperatures suggests some form of
antiferromagnetic interaction. We analyzed the suscept-
ibility data employing the Bleany-Bowers equation31 in
which J is the intramolecular coupling constant and g was
set at 2.00 in all analyses presented here. Allowing J to
vary produced the best fit, shown as the solid line in the
figure, for a value of J = -1.23 cm-1. Visual inspection
shows that this analysis fails to reproduce the general
shape of the experimental curve at low temperatures. In
spite of the fact that intermolecular interactions are anti-
cipated to be negligible in a dilute sample, we analyzed the
susceptibility data by employing the Bleany-Bowers
equation in a form that includes, in addition to J for
intramolecular exchange, a Weiss θ term (employing the
T-θ form of the Curie-Weiss law) to allow for inter-
molecular exchange. Allowing both J and θ to vary and
plotting the best-fit curve as the magnetic moment versus
temperature gave the dashed line shown in Figure 8 for
values of J = þ0.56 cm-1 and θ = -2.29 K. The agree-
ment between the theory and experiment is much im-
proved in this case. An equally good fit is obtained
assuming simple Curie-Weiss behavior. This is shown
as a dotted line in Figure 8, where θ has the best-fit value
of -1.77 K. For the diluted sample, we conclude that,
while there is measurable overall antiferromagnetic ex-
change present, it is extremely weak. Importantly, for this
study, the magnitude of intramolecular exchange in the
Figure 9. Temperature dependence of χ of (a) 7(SbF6)2 and (b) 7-
(AsF6)2. Open circles present experimental data, and lines indicate
theoretical fits (see text). In all cases, values of χ are quoted per radical
center (i.e., half a diradical). Fitting parameters are given in Table 7.
netic susceptibilities (on a per monoradical basis, i.e.,
χmonoradical as described above) are plotted versus T for
7(SbF6)2 and 7(AsF6)2 (data for 7(Sb2F11)2 are presented
in Figure S13 in the Supporting Information). The data
are new for 7(SbF6)2 and those published earlier4c for
7(AsF6)2 [and 7(Sb2F11)2]. The earlier analysis of the data
for the AsF6- and Sb2F11- salts, employing the Bleany-
Bowers equation, is not appropriate given the study
described above on the diluted sample of 72þ that revealed
that intramolecular exchange is negligible. In the present
work, we analyze the data for these salts as well as the new
data for the SbF6- salt under the assumption that intra-
molecular exchange can be ignored.
For 7(AsF6)2 and 7(SbF6)2, the presence of broad
maxima in the susceptibility (at ca. 60 K) suggests a
low-dimensional nature of magnetic intermolecular inter-
actions between diradical centers. Accordingly, we have
examined fits of the data for these salts to two published
models for antiferromagnetic exchange interactions in
extended systems: one for infinite 1D chains, which we
will term the Hall model,32 and the other for infinite 2D
sheets, termed the Lines model33 here. It is important to
72þ dication, as measured by J, is small with | J| < 1 cm-1
.
The results are not inconsistent with the presence of a
diradical species in which there is, at most, a small sepa-
ration between the singlet and triplet states, a situation
suggested elsewhere in this report by EPR and theoretical
calculations.
In our earlier communication, we analyzed the mag-
netic susceptibility data obtained for nondiluted samples
of 7(AsF6)2 and 7(Sb2F11)2 using the Bleany-Bowers
equation for pairs of interacting S = 1/2 magnetic cen-
ters.4c This yielded rather poor fits; importantly though,
the study led to the conclusion that, at most, only very
weak antiferromagnetic exchange was present in the two
compounds, with the strength of the exchange being
much weaker in the latter. In Figure 9, measured mag-
note that, whereas the Hamiltonian employed in the Hall
model takes the form H = 2J Si Sj, that for the Lines
P
3
P
model is of the form H = J Si Sj. Hence, a direct
3
comparison of the J values between the models requires

7876 Inorganic Chemistry, Vol. 49, No. 17, 2010
Cameron et al.
Table 7. Fitted Magnetic Parametersa for 7(SbF6)2 and 7(AsF6)2
7(SbF6)2
7(AsF6)2
Hall
Lines
Hall
Lines
2-300 K
40-300 K
2-300 K
40-300 K
2-300 K
40-300 K
2-300 K
40-300 K
|J|/cm-1
θ/K
31.6(0.9)
14(2)
194(29)
0.2 (0.04)
32.2(0.1)
4.1(0.3)
266(2)
51.4(2)
-15(1)
447(37)
0 (fixed)
40.7(0.3)
8(1)
278(7)
0 (fixed)
42.0(1)
1(3)
112(30)
0.07 (0.04)
45.0(0.1)
-25.9(0.6)
240(3)
61.8(1)
-20(1)
268(23)
0 (fixed)
57.2(0.1)
-15.6(0.3)
242(2)
TIP/106 cm-1
% P b
0 (fixed)
0 (fixed)
0 (fixed)
a g was fixed at 2.0 for all analyses. The numbers shown in brackets are standard deviations. b % P values were fixed at zero for all 40-300 K data
analyses and for some 2-300 K data analyses where inclusion generated unrealistic negative values.
that the Lines J values be halved. The equations given for
these two models were both modified slightly to include a
contribution to the susceptibility from TIP and a Weiss θ
to allow for any additional interactions that may be
indicated, in addition to those measured by J in the
models. The susceptibility data for these salts show a
sharp increase on cooling below approximately 20 K
because of, we conclude, paramagnetic impurity. Ac-
cordingly, the equations were also modified to include a
fraction P of paramagnetic impurity, itself modeled as a
coupled with a coupling strength corresponding to |J|
= 32.2 cm-1. Deviation from pure single-chain behavior
is measured by the Weiss constant θ of 4.1 K. In effect, the
smaller the θ is, the closer the behavior is to that of
isolated chains. This analysis suggests that there are
higher-dimensional interactions than 1D in the com-
pound. The fit to the 2D Lines model is actually slightly
worse, suggesting that this is not modeling the data and
that the magnetic properties of 7(SbF6)2 are best descri-
bed as consistent with the presence of antiferromagneti-
cally coupled chains with additional, weaker, interchain
interactions. The presence of multiple pathways for ex-
change coupling is not unexpected given the complex
extended molecular structure exhibited by this com-
pound. It should be noted too that the θ value of 4.1 K
(2.85 cm-1), which is taken as a measure of the secondary
interactions, generated in the Hall fit, is an order of
magnitude weaker than the primary intrachain interac-
tions as measured by |J| = 32.2 cm-1. This supports the
conclusion that the Hall model is providing a reasonable
description of the magnetic properties of the compound.
In the case of the Lines model fit, the θ value of 8 K (5.56
cm-1) is proportionally larger in comparison to |J|,
consistent with the conclusion that this model is in-
appropriate.
The 40-300 K data for 7(AsF6)2 are reproduced rea-
sonably well by both the 1D and 2D models, although the
quality of the fit is slightly better for the 2D Lines model in
this case. Importantly, however, the θ “correction” factor
is substantial in both instances (Table 7), indicating that
neither model is providing an appropriate description of
the exchange interactions in the compound. We conclude
that in the case of 7(AsF6)2 no particular chain or sheet
pathway dominates.
Calculated DFT coupling constants support (see the
Supporting Information for details) the 1D chain model
for magnetic behavior of 7(SbF6)2, consistent with the
magnetic data analysis. Although the magnetic analysis
was inconclusive regarding the dimensionality of the
exchange of 7(AsF6)2, the DFT calculations support 2D
behavior. Calculations suggest that the cation stacks in
both salts form an important antiferromagnetic pathway.
In addition to intrastack interaction, 7(AsF6)2 appears to
exhibit significant interstack antiferromagnetic interac-
1
simple S = /2, g = 2.0 component. “Fits” of the ex-
perimental susceptibility values to calculated values,
over the temperature range 2-300 K, were exami-
ned for both salts using both models, and the resulting
“best fits” are shown in Figure 9a,b as solid black lines
for the Hall model and solid gray lines for the Lines
model. The corresponding fit parameters are given in
Table 7. In the curve fitting done in this study, the value
of g was fixed at 2.0, consistent with the EPR studies
reported herein. While the calculated curves generally
follow the trend of the experimental data, clearly the
“fit” is not good in any of the cases. In particular, it is
difficult to model the relatively sharp decline in the
susceptibility at temperatures just below the maximum
as well as the relatively sharp increase in the suscept-
ibility observed upon cooling at the lowest temperatures.
Accordingly, we focused our attention on the tempera-
ture region from just below the susceptibility maximum
to room temperature (40-300 K), a region where the
effects of paramagnetic impurities are minimized. In
each of these analyses, the value of P was fixed at zero.
The best-fit calculated susceptibilities are shown as filled
circles in the figures, filled black for the Hall model fit and
gray for the Lines model fit. The corresponding best-fit
parameters are given in Table 7. We now examine the
40-300 K fits for 7(AsF6)2 and 7(SbF6)2 in detail and
consider the significance of the parameter values gener-
ated in this process.
The 40-300 K data for 7(SbF6)2 are modeled best over
this temperature range by the 1D-chain Hall model. The
2D-sheet Lines model does not produce the experimental
data well near the susceptibility maximum. In both cases,
the fitting required the inclusion of a Weiss θ parameter of
4.1 K for the Hall fit and 8 K for the Lines fit. This
parameter serves to account for any factors, such as addi-
tional magnetic interactions, not specifically modeled.
For example, in the analysis of the data using the Hall
model, the magnetic behavior of the compound can be
˚
tion (via 4.113 A S S contact; see Figure 2b).
3 3 3
An analysis of the analogous 7(Sb2F11)2 data (given in
the Supporting Information) shows the presence of only
weak antiferromagnetic coupling (an order of magnitude
smaller than that observed for the other two salts) con-
sistent with the much larger intercationic contacts.
described as following, approximately, that of an ex-
tended chain of S =
1
/ spins, antiferromagnetically
2

Article
Inorganic Chemistry, Vol. 49, No. 17, 2010 7877
Table 8. Experimental Spin-Hamiltonian Parameters of 7(Sb2F11)2 Doped in a Crystal of 10(Sb2F11 2
)
4f and Simulated Spin-Hamiltonian Parameters of 7(AsF6)2 in a Frozen
SO2/AsF5 Solution4c,d
g principal values
D principal values
xx
yy
zz
xx
177.00
yy
zz
single crystal4f
2.017 082
2.002 206
2.027 133
218.03
-395.03
D = -592.5 ( 2.9; E = 20.5 ( 2.0 MHz
D = -555; E = 54 MHz (solution 1)a
D = -555; E = 22 MHz (solution 2)a
frozen solution4c,d
2.0096
2.0198
1.9943
1.9844
2.0210
2.0211
a Two different solutions gave almost identical simulated spectra, both in good agreement with the experimentally observed spectrum. The results for
solution 2 are in slightly better agreement with those of the single crystal.
In summary, variable-temperature (2-300 K) magnetic
susceptibility studies on a sample of 7(Sb2F11)2 doped
into the isomorphous diamagnetic host material, 10-
(Sb2F11)2, revealed that the magnitude of intramolecular
exchange in the 72þ dication, as measured by J, is small,
with | J| < 1 cm-1 corresponding to a singlet-triplet gap
of <(2 cm-1. The overall antiferromagnetic behaviors
observed for nondiluted samples of the 7(A)2 salts, as
Figure 10. Orientations of g components with respect to the plane of
the molecule.
evidenced by decreasing moments with temperature in all
three salts and the appearance of susceptibility maxima
near 60 K in the MF6- (M = As, Sb) salts, arise mostly
from intermolecular exchange interactions. Attempts to
quantify the magnitude of the exchange interactions and
establish the dimensionality of exchange in 7(MF6)2 by
fitting the susceptibility data to known magnetic models
for antiferromagnetic exchange in 1D-chain and 2D-sheet
extended systems were partly successful. Analyzing the
40-300 K data for 7(SbF6)2 gave the best fit for the 1D
model with |J| = 32 cm-1. Importantly, however, while
7(SbF6)2 shows dominant 1D-chain behavior, the neces-
sity of including a small θ value in the analysis suggests
the existence of additional exchange pathway(s). In the
case of 7(AsF6)2, magnetic modeling attempts showed the
neither 1D nor 2D models were appropriate for the
compound, suggesting the existence of complex exchange
pathways where no particular one dominates.
3.7. EPR Spectra of 7(MF6)2 (M = As, Sb) and 7-
(Sb2F11)2. The EPR spectra of 7(AsF6)2, 7(SbF6)2, and
7(Sb2F11)2 in a SO2/MF5 solution (M = As, Sb) were
measured at þ20, -80, and -160 ꢀC (frozen solution).
The spectra of 7(AsF6)2 are given in Figure 1 of ref 4c
and compared with those of the other similar salts in the
Supporting Information (Figures S14-S16). The simu-
lated EPR parameters obtained for the frozen-solution
spectra of 7(AsF6)24c,d and those for 7(Sb2F11)2 in a host
single crystal of 10(Sb2F11)24f are given in Table 8.
The solution EPR spectra of all three salts contain two
resonances: a narrow resonance superimposed onto a
broader peak with essentially identical g values [7(AsF6)2,
2.0162; 7(SbF6)2, 2.0127; 7(Sb2F11)2, 2.0143], none of
which shows any 14N hyperfine splitting, and the g values,
peak widths, and intensities varysignificantly from one salt
to another. The broader of the two resonances is attributed
to the triplet state (S = 1) of 72þ. The observation of the
triplet state in solution is characteristic of diradicals with
weakly coupled electrons.57
components, and an additional resonance is observed at
half-field (Δms = (2), confirming the presence of triplet-
state species (see Figure S17 in the Supporting Infor-
mation). The frozen-solution spectra of the three salts of 72þ
have very similar spectroscopic features, with the
separation between the outermost splitting lines corre-
sponding to D (the axial zero-field-splitting parameter, a
measure of the effect of the magnetic field of one unpaired
electron onto another) of 555 ( 10 MHz. The spectra
were simulated by two similar sets of data,4c,d and the
principal values of g were typical of a 7π radical, in which
gmin (=gyy) is just less than ge and is perpendicular to the
molecular plane (Figure 10). The largest component of
the dipole tensor Dzz lies in the molecular plane, and
assuming a point dipole approximation, we calculated
58
˚
the separation between “point electrons” as ca. 5.2 A,
which is in good agreement with quantum-chemical cal-
culations that place almost all of the spin density on S
atoms (Table 3). The small value of D is consistent with
very weak coupling between the unpaired spins and a very
small singlet-triplet energy gap, conforming to the vari-
able-temperature magnetic susceptibility measurements
and the quantum-chemical calculations.
The parameters extracted from single-crystal EPR
measurements4f (Table 8) are in better agreement with
the corresponding parameters of the frozen solution 2
than those of solution 1. Notably, the value of gyy is very
close to that of the free spin, as expected for a π radical
with the unpaired electron in a pπ orbital perpendicular to
the plane of the molecule. Therefore, the description of
72þ as a diradical with two weakly interacting unpaired
electrons is consistent with the observed EPR spectra.
The origin of the narrower resonance located in the
middle of the solution EPR spectra (see Figures S14-S16
in the Supporting Information) is controversial. The width
of this resonance is unaffected by differences in the MF5
(M = As, Sb) concentration, suggesting that it arises from
Freezing the solutions to -160 ꢀC causes the broader of
the two resonances to split into six zero-field-splitting
1
a doublet species (S = /2), in which relaxations are less
(57) Atherton, N. M. Electron Spin Resonance: Theory and Applications;
Wiley: New York, 1973.
(58) The distance between the two spin centers has been calculated by R0 =
(0.65g2/D)1/3
.

7878 Inorganic Chemistry, Vol. 49, No. 17, 2010
Cameron et al.
Figure 11. Comparison of the electronic states of O2 and planar 72þ 62
.
Structures of (O2)2, quinoidal 72þ, and a dimer of 72þ have been obtained by partial
optimization by constraining the middle O-O bond (1.50 A), the CdC bond (1.334 A), and the intradimer S-S bond (2.10 A), respectively.63 Energy
differences are given per monomer. The three electron bond descriptions for oxygen have been adopted from ref 64: [a] experimental energies from ref 65; [b]
calculated at the CCSD(t)/6-311G* level: [c] calculated at the PBE0/6-311G* level.
˚
˚
˚
drastically affected by the solvent.57 However, it seems
unlikely that it arises from a reduced species, e.g., 7•þ,
because of the presence of an excess of oxidizing agent
(see section 3.2). The g values of the broad and narrow
resonances are essentially identical (within experimental
error), implying that the two arise from species with very
similar structures. The high purity of 7(AsF6)2 (elemental
analysis and vibrational spectra) precludes the presence
of an impurity giving rise to such an intense signal. It also
has to be noted that the EPR spectrum of a single crystal
of 7(Sb2F11)2 doped into 10(Sb2F11)2 did not contain such
a narrow resonance. Previously, the narrower resonance
in solution spectra of 72þ was proposed to arise from a
metastable rotomer obtained by rotation about the C-C
single bond.4c,d Indeed, such a rotomer was found in the
gas phase as a minimum corresponding to the twisted
conformation with a N-C-C-N dihedral angle of 40ꢀ
(Figure 6). The π-orbital overlap in the rotomer would be
minimal because of breaking of the coplanarity of the rings
and an increased distance between unpaired spins, leading
to an EPR spectrum of a doublet state rather than a triplet
state. However, thecalculatedenergydifferenceofca. 33kJ
mol-1 (30kJmol-1 in a SO2 solution; Figure 6) impliesthat
a significant population of this rotomer conformation is
unlikely. Careful simulations of all observed solution EPR
spectra did not reveal any correlation between the ratios of
tripletand singletstatesandthe temperature. Instead, these
ratios seemed to depend more on the anion. It is possible
rarely given. The most common proposal is that the sharp
central resonance is due to monoradical impurities;13b,d,59
however, in our case, the S = 1/2 monoradical 7•þ can be
excluded in the presence of an excess of oxidizing agent
MF5. The radical trication 73þ could be a possibility, but
our quantum-chemical calculations [MPW1PW91/6-
31G*] predict that the oxidation of 72þ to 73þ by AsF5 is
endothermic by about 2479 kJ mol-1 in the gas phase, and
experimental attempts to prepare 73þ failed. In some cases
in the literature, an alternative explanation of the central
peak was an isomeric diradical form13c or chemical ex-
change-narrowing effects.60 In our situation, the origin of
the narrow resonance is most likely due to a rotomer 72þ
stabilized by ion-pairing effects. All salts of 72þ dissolve in
SO2, AsF3, SO2/MF5, and AsF3/SO2/MF5 mixtures togive
green solutions. It is likely that this green color is due to the
72þ/anion ion pair. The green surface of the red 7(Sb2F11)2
-
could arise from this or a related 72þ/Sb2F11 ion pair.
However, the origin of the green color in the crystals of
7(Sb2F11)2 remains an open question.
4. Conclusions and Comparison of 72þ with O2
The reaction of NC-CN with a 1:1 mixture of S4(MF6)2
and S8(MF6)2 (M = As, Sb) (stoichiometrically equivalent to
four “S3MF6” units) results in the quantitative formation of
red 7(MF6)2 (eqs 2 and 7) in one-step reactions. Other stoi-
chiometries also resulted in the formation of 72þ, the thermo-
dynamically favored product in this reaction. 7(Sb2F11)2 was
that 72þ forms an ion pair 72þ MF6-/Sb2F11 with
-
3 3 3
Sδþ Fδ- interactions that replace the Sδþ Nδ- con-
3 3 3
3 3 3
(59) Selected examples: (a) Spagnol, G.; Shiraishi, K.; Rajca, S.; Rajca, A.
Chem. Commun. 2005, 5047. (b) Sato, K.; Sawai, T.; Shiomi, D.; Takui, T.;
Wang, Q.; Wang, J.-S.; Li, Y.; Wu, G.-S. Synth. Met. 2003, 137, 1197. (c) Rajca,
A.; Rajca, S.; Wongsriratanakul, J. Chem. Commun. 2000, 1021. (d) Bushby,
R. J.; McGill, D. R.; Ng, K. M.; Taylor, N. J. Chem. Soc., Perkin Trans. 2 1997,
1405.
tacts in the planar conformation and stabilize the rotomer
configuration. As noted above, the ring rotation likely
leads to decoupling of the unpaired electrons in 72þ
.
Interestingly, many of the published EPR spectra of
triplets in the literature also contain an additional narrow
resonance in the center, but satisfying explanations are
€
(60) Ziessel, R.; Stroh, C.; Heise, H.; Kohler, F. H.; Turek, P.; Claiser, N.;
Souhassou, M.; Lecomte, C. J. A. Chem. Soc. 2004, 126, 12604.

Article
Inorganic Chemistry, Vol. 49, No. 17, 2010 7879
prepared by the reaction of 7(AsF6)2 with an excess SbF5.
7(AsF6)2 and 7(Sb2F11)2 gave excellent elemental analyses,
while 7(SbF6)2 contained some diamagnetic (SbF3)3SbF5. All
salts were characterized by X-ray structure determinations,
rigorous assignment of vibrational spectra including a normal-
coordinate analysis, variable-temperature magnetic suscept-
ibility measurements, and EPR spectroscopy. Evidence was
presented for 7þ given by the reduction of 7(AsF6)2 in liquid
SO2. 72þ was also investigatedby several theoretical methods.
The X-ray structures of red 7(Sb2F11)2 and green 7(Sb2F11)2
previously reported as different4e,20 have been shown to likely
be the same. All results show that 72þ contains two CNSSS•þ
radical cations joined by a single C-C bond in a trans-planar
centrosymmetric arrangement due to intracationic electro-
electrostatic repulsion and positive charge localization in the
dimer. At very low temperatures, the magnetic susceptibilities
of both solid O2 and salts of 72þ decrease because of
5
antiferromagnetic intermolecular coupling of unpaired elec-
trons. For salts of 72þ, antiferromagnetic intermolecular
coupling decreases with an increase in the size of the anion,
and we note that different structural forms of O2 have dif-
ferent magnetic properties.5 Thus, there are significant simi-
larities between O2 and 72þ in the gas phase and in its various
salts. Notwithstanding some definite differences, i.e., un-
paired electrons are parallel to one another and very weakly
coupled in 72þ, whereas those in O2 are perpendicular and
strongly coupled, 72þ has an isomeric rotomer that cannot
exist for O2, 72þ can be said to be O2-like even though it is
sulfur-based. It is the first example of an essentially sulfur-
based diradical, as evidenced by calculated spin densities. As
far as we are aware, O2 and the salts of 72þ are the only simple
nonsterically hindered main-group isolated compounds to
show paramagnetism in the solid state. In this paper, we
focused on the molecular properties of 72þ and its relation-
ship to O2. Further studies on intriguing variable-tempera-
ture magnetic and other bulk physical properties of single
crystals of 7(MF6)2 are in progress.21
static Nδ- Sδþ interactions. EPR studies in solution give a
3 3 3
broad peak that we attribute to the triplet-state 72þ in
equilibrium with a sharp singlet peak, which is likely a 72þ
rotomer/anion ion pair. Our previous EPR studies4f of single
crystals of 7(Sb2F11)2 diluted in isomorphous diamagnetic
host 10(Sb2F11)2 unambiguously demonstrated 72þ to exhibit
a triplet state arising from interaction of the unpaired
electrons in pπ orbitals (largely sulfur) in each of the rings
(see Figures 5 and 11). In this work, we report that variable-
temperature magnetic studies on this material give an energy
difference between the open-shell singlet and triplet states of
less than (2 cm-1; i.e., they are essentially degenerate.
Therefore, 72þ can be seen to be similar to O2 in that they
are both triplet-state molecules and do not adopt classical
Acknowledgment. We thank the Natural Sciences and
Engineering Research Council (NSERC) of Canada for
funding (T.S.C. and J.P.), the Alexander von Humboldt
Foundation in Germany for providing a Feodor-Lynen
Fellowship (C.K.), the Ministry of Education in Finland
and Helsingin Sanomat Foundation for providing finan-
cial support (J.M.R.), Dr. Sandra Altmannshofer and
Prof. Dr. Wolfgang Scherer, University of Augsburg,
Augsburg, Germany, for unpublished crystallographic
data on 7(SbF6)2, Prof. Dr. Scherer and Dr. Ernst-
Wilhelm Scheidt (Augsburg) for helpful comments on
the interpretation of the magnetic data, Dr. Scott Brown-
ridge for the FT-Raman measurements, Rod McGregor
for collaboration with EPR spectroscopy, Dr. Gilles
Villemure for assistance with UV/vis spectroscopy, and
1
electron-paired structures of quinoidal 62þ and singlet Δg
O2, which are about 100 kJ mol-1 higher in energy (see
Figure 11). The higher energy of the 62þ isomer is attributed
to the loss in π bond energy61 and positive charge localization
relative to 72þ. In contrast to 72þ, with essentially degenerate
open-shell singlet and triplet states, the unpaired electrons of
O2 are strongly coupled and the observed singlet state of O2
lies much higher in energy than the O2 triplet state (see
Figure 11). Furthermore, the unpaired electrons in O2 and
72þ do not pair in the solid state to form chemically bonded
dimers or polymers. Figure 11 illustrates the energetically
unfavorable formation of dimers of O2 and 72þ. Dimeriza-
€
€
€
€
Dr. Heikki Tuononen, University of Jyvaskyla, Jyvaskyla,
Finland, for his help with the MCSCF calculations and
normal-coordinate analysis.
tion of O2 results in the loss of a strong π bond (352 kJ mol-1
)
and the gain of a weaker σ bond (142 kJ mol-1).44 Dimeriza-
tion of 72þ can be regarded to occur with the loss of a S-S π
bond (199 kJ mol-1) and the gain of the related σ bond of
similar strength (226 kJ mol-1) but is strongly disfavored by
Supporting Information Available: X-ray crystallographic
data in CIF format for 7(SbF6)2 and 7(Sb2F11)2 at different
temperatures, UV/vis spectrum of 7(AsF6)2 in a SO2/AsF5
solution, FT-Raman and IR spectra of 72þ species, results of
normal-coordinate analysis of 72þ, assignment of anionic vibra-
tional frequencies, predicted and observed coordination in 72þ
salts, packing of 7(MF6)2 (M = As, Sb), structural depictions of
anions in 72þ salts, cautionary comments on the effect that the
measurement temperature has on observed reduced cell para-
(61) Sum of the π bond energies in observed delocalized geometry:
2E(CdN) þ 2E(SdS) = 2 ꢀ 322 þ 2 ꢀ 152 = 949 kJ mol-1. Sum of the
π bond energies in the quinoidal structure: E(CdC) þ 2E(NdS) = 266 þ 2 ꢀ
204 = 674 kJ mol-1. Thus, the observed structure is favored by 274 kJ mol-1
with respect to the quinoidal structure based on π bond energies and further
stabilized by resonance and charge delocalization. Bond energies are taken
from ref 44.
-
meters of 7(Sb2F11)2, relation of disorder in Sb2F11 to the
S
(62) Note that there is also a rotomer of 72þ that has been observed in
equilibrium with the planar triplet state 72þ in solution.
F contact strength and temperature, in situ EPR spectrum
3 3 3
of the reduction of 7(AsF6)2 with Na2S2O4 in SO2, EPR spectra
of 72þ salts in a SO2/AsF5 solution, magnetic susceptibility data
of 72þ salts, discussion on the magnetic properties of 7(Sb2F11)2,
optimized structural parameters of 72þ at different levels of
theory, comparison of lowest states of 72þ with related main-
group radicals, and calculated magnetic coupling pathways in
crystals of 72þ salts. This material is available free of charge via
the Internet at http://pubs.acs.org.
(63) The partially optimized structure of 72þ is only a rough approxima-
tion of a true quinoidal structure because the strength of the C-N bonding
tends to make the C-N bonds shorter than normal C-N single bonds and,
in turn, the S-N bonds longer than double bonds.
(64) Pauling, L. The Nature of the Chemical Bond, 3rd ed.; Cornell
University: Ithaca, NY, 1960.
(65) Herzberg, G. Spectra of Diatomic Molecules; Van Nostrand Reinhold:
New York, 1950.