Preparation and characterization of dinuclear nickel(II) complexes containing N3Ni(μ1, 3-SO3R) 2(μ-RCN4)NiN3 cores: Crystal structures and magnetic properties

Article abstract of DOI:10.1002/zaac.201200501

The preparation and characterization of three new mixed ligand macrocyclic [Ni₂L2(L')]⁺ complexes are described, where (L2) ^2- represents a supporting macrocyclic hexaaza-bis(phenylsulfonato) ligand and L' a tetrazolato ligand. The complexes [Ni₂(L2)(CN ₄H)]BPh₄ (4), [Ni₂(L2)(CN₄Me)] BPh₄ (5), and [Ni₂(L2)(CN₄Ph)]BPh₄ (6) were synthesized by H₂O₂ oxidation of the corresponding [Ni₂(L1)(CN₄H)]BPh₄ (1), [Ni ₂(L1)(CN₄Me)]BPh₄ (2), and [Ni ₂(L1)(CN₄Ph)]BPh₄ (3) complexes supported by the corresponding hexaaza-bis(thiophenolate) macrocycle. The compounds were characterized by means of elemental analysis, mass spectrometry, IR, and UV/Vis spectroscopy. The crystal structures of compounds 4-6 show that the bridging thiophenolate functions in 1-3 are in all cases converted to μ _{1, 3}-bridging sulfonate groups to generate N₃Ni(μ _{1, 3}-SO₃R)₂(μ-RCN₄)NiN ₃ cores. The conversion to the phenylsulfonato groups is accompanied by a drastic increase of the Ni...Ni distances from 3.455(1) A in 1, 3.425(1) A in 2, and 3.443(1) A [3.450(1) A] in 3 to 4.2796(5) A [4.3375(6) A] in 4, 4.3402(6) A in 5, and 4.2607(4) A in 6. Upon oxidation the magnetic properties are affected. In contrast to 1-3, which exhibit an intramolecular ferromagnetic exchange interaction (S = 2 ground state), the spins of the nickel(II) (S_i = 1) ions in 4-6 are antiferromagnetically coupled, the coupling constants J being -1.39 cm ^-1 (4), -1.43 cm^-1 (5), and -1.60 cm^-1 (6) (H = -2JS₁S₂) to yield a diamagnetic S = 0 ground state. DFT (density functional theory) calculations were carried out to substantiate the experimental results. Copyright

Full text of DOI:10.1002/zaac.201200501

ARTICLE
DOI: 10.1002/zaac.201200501
Preparation and Characterization of Dinuclear Nickel(II) Complexes
Containing N3Ni(μ1,3-SO3R)2(μ-RCN4)NiN3 Cores: Crystal Structures and
Magnetic Properties
Jochen Lach,[a] Eva Perlt,[b] Barbara Kirchner,[b] and Berthold Kersting*[a]
Keywords: Macrocyclic ligand; Sulfonato donors; Nickel; Magnetic properties; Crystal structure; Tetrazolates; DFT calculations
Abstract. The preparation and characterization of three new mixed cases converted to μ1,3-bridging sulfonate groups to generate
ligand macrocyclic [Ni2L2(LЈ)]+ complexes are described, where
(L2)2– represents
supporting macrocyclic hexaaza-bis(phenyl-
sulfonato) ligand and LЈ tetrazolato ligand. The complexes
N3Ni(μ1,3-SO3R)2(μ-RCN4)NiN3 cores. The conversion to the phenyl-
sulfonato groups is accompanied by a drastic increase of the Ni···Ni
distances from 3.455(1) Å in 1, 3.425(1) Å in 2, and 3.443(1) Å
[3.450(1) Å] in 3 to 4.2796(5) Å [4.3375(6) Å] in 4, 4.3402(6) Å in 5,
and 4.2607(4) Å in 6. Upon oxidation the magnetic properties are af-
fected. In contrast to 1–3, which exhibit an intramolecular ferromag-
netic exchange interaction (S = 2 ground state), the spins of the
nickel(II) (Si = 1) ions in 4–6 are antiferromagnetically coupled, the
coupling constants J being –1.39 cm–1 (4), –1.43 cm–1 (5), and
–1.60 cm–1 (6) (H = –2JS1S2) to yield a diamagnetic S = 0 ground
state. DFT (density functional theory) calculations were carried out to
substantiate the experimental results.
a
a
[Ni2(L2)(CN4H)]BPh4 (4), [Ni2(L2)(CN4Me)]BPh4 (5), and
[Ni2(L2)(CN4Ph)]BPh4 (6) were synthesized by H2O2 oxidation of the
corresponding [Ni2(L1)(CN4H)]BPh4 (1), [Ni2(L1)(CN4Me)]BPh4 (2),
and [Ni2(L1)(CN4Ph)]BPh4 (3) complexes supported by the corre-
sponding hexaaza-bis(thiophenolate) macrocycle. The compounds
were characterized by means of elemental analysis, mass spectrometry,
IR, and UV/Vis spectroscopy. The crystal structures of compounds 4–
6 show that the bridging thiophenolate functions in 1–3 are in all
bridging thiophenolate to phenylsulfonate groups. On these
grounds we decided to prepare and characterize further exam-
ples of analogous complexes of the dinucleating macrocycles
(L1)2– and (L2)2–. In this study, we have selected the tetrazol-
Introduction
In the past several years we have characterized a number of
dinuclear transition metal complexes supported by the macro-
cyclic hexaaza-bis(thiophenolate) ligand H2L1.[1] With first
row transition metal ions such as Ni2+, Co2+, Fe2+, and Mn2+
the doubly deprotonated macrocycle (L1)2– invariably forms
mixed-ligand [M2(L1)(LЈ)]+ complexes with a bioctahedral
N3M(μ-SR)2(μ-LЈ)MN3 core structure, where LЈ represents a
bridging coligand (Scheme 1).[2–5] The complexes are distin-
guished by the bowl-shaped binding cavity that confers some
unusual properties on the complexes.[6] We have also investi-
gated the coordination chemistry of the hexaaza-disulfonate li-
gand H2L2, but to a lesser extent. Analogous pairs of dinuclear
[Ni2(L1)(LЈ)]+ and [Ni2(L2)(LЈ)]+ complexes have been re-
–
ates RCN4 (R = H, Me, Ph) as coligands.
–
–
– [7,8]
ported with LЈ = Cl–, CH3CO2 , PhCO2 , 3-Cl–C6H4CO2 .
It was found that the structures and chemical properties are
strikingly different, a fact attributable to the conversion of the
* Prof. Dr. B. Kersting
E-Mail: b.kersting@uni-leipzig.de
[a] Institut für Anorganische Chemie
Scheme 1. Structures of [Ni2(L1)(CN4R)]BPh4 (1–3) and [Ni2(L2)-
(CN4R)]+ (4–6).
Universität Leipzig
Johannisallee 29
04103 Leipzig, Germany
[b] Wilhelm-Ostwald-Institut für Physikalische und Theoretische
Herein, we report on the preparation, structures, and
magnetic properties of the three tetrazolato-bridged
Chemie
Linnéstraße 2
[Ni2(L2)(CN4R)]+ complexes 4–6 (R
= H, Me, Ph)
04103 Leipzig, Germany
Supporting information for this article is available on the WWW
under http://dx.doi.org/10.1002/zaac.201200501 or from the au-
thor.
(Scheme 1). Their structures and magnetic properties are
discussed and compared with those of their reduced
524
© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Z. Anorg. Allg. Chem. 2013, 639, (3-4), 524–532

Dinuclear Nickel(II) Complexes with N3Ni(μ1,3-SO3R)2(μ-RCN4)NiN3 Cores
–
[Ni2(L1)(CN4R)]+ parents (1–3), which have been reported stretching vibration of sulfonate (RSO3 ) groups.[8,10,12,13] The
earlier.[3,4]
S–O frequencies resemble those of the Ni2 complexes [Ni2(L2)
(LЈ)] (LЈ = Cl–, O2CMe–, O2CPh–, O2C–C6H4–3Cl–) that were
–
investigated earlier, indicating that the RSO3 groups in 4–6
are also in a μ1,3-bridging mode.[7,8]
Results and Discussion
UV/Vis spectroscopic data of 4–6 were recorded from 190–
1600 nm in acetonitrile solution at room temperature with a
Jasco V-670 UV/Vis/NIR spectrophotometer. The most obvi-
ous spectral differences among the thiophenolate and phenyl-
sulfonate complexes occur in the UV/Vis region around
400 nm. The thiophenolato complexes display strong
thiolateǞNi2+ charge transfer transitions in this region.[4] The
phenylsulfonato complexes in 4–6 lack this transition, in
agreement with the conversion of the soft thiolate to hard
Syntheses of Metal Complexes
The route to the new compounds 4–6 used the complexes
1–3 as starting materials. These complexes were synthesized
according to published procedures, and subjected to direct oxi-
dations using excess of H2O2 as an oxidant.[4] This oxidant
converts thiophenolate complexes to sulfonate complexes.[9–11]
In previous work, we always used the perchlorate salts in such
oxidation reactions.[7] We now found that this method works
for the tetraphenylborate salts as well. Thus, the reaction of
green [Ni2(L1)(CN4H)][BPh4] (1) with an excess of
H2O2 in methanol solution provided the pale-green salt
[Ni2(L2)(CN4H)][BPh4] (4) in 67% yield. The tetraphenylbor-
ate salts 2 and 3 reacted in the same fashion yielding pale-
green 5 and 6 in reproducible yields as high as 63% and 64%,
respectively. All compounds are stable in air in the solid state
and in solution.
sulfonate groups. As
a consequence, the spin-allowed
3A2g(F)Ǟ3T1g(P) transition, which is expected for a Ni2+ ion
with octahedral coordination, but which is obscured in 1–3 by
strong RS–ǞNi2+ charge transfer transitions, can be detected
as a weak absorption band at 441–443 nm. The remaining
bands in the 630 nm and 1030 nm regions can be attributed
3
to the spin-allowed d–d transitions A2g(F)Ǟ3T1g(F) [ν2] and
3A2g(F)ǞT2g(F) [ν1] (for a NiII ion in a regular octahedral
environment).
Spectroscopic Characterization of Metal Complexes
Description of the Crystal Structures of Complexes 4, 5,
and 6
The composition of the compounds was confirmed by means
of elemental analysis, mass spectrometry, IR, and UV/Vis
spectroscopy. Selected analytical data are listed in Table 1. The
electrospray ionization mass spectra (ESI-MS) of dilute MeCN
solutions of 4–6 exhibit molecular ion peaks at m/z = 949.20,
m/z = 963.34, and m/z = 1025.36 with the correct isotopic dis-
tribution for the [Ni2(L2)(CN4R)]+ cations. Selected IR and
UV/Vis data for 4–6 are shown in Table 1. In the IR spectra
of 4–6 the most prominent features are the strong absorption
bands at ca. 1200 cm–1, which are attributable to the S–O
To unambiguously confirm the formulation of the com-
plexes and the coordination mode of the sulfonates and co-
ligands X-ray diffraction studies were carried out. Single-
crystals of 4·0.5MeCN·0.5H2O, 5·H2O, and 6·MeCN were ob-
tained from
a mixed MeOH/MeCN solution by slow
evaporation. All crystal structures consist of discrete
[Ni2(L2)(CN4R)]+ cations, tetraphenylborate anions, and solv-
ate molecules of the crystallization medium. Ortep plots of the
molecular structures of the cations in 4–6 are depicted in Fig-
ure 1, Figure 2, and Figure 3.[14] Selected bond lengths and
angles are summarized in Table 2 and Table 3. Structural pa-
rameters of 1–3 are also included in Table 2 and Table 3 for
comparative purposes.[4]
Table 1. Selected IR and UV/Vis analytical data for compounds 4–6.
Compound
IR bands /cm–1
UV/Vis λmax /nm (ε / m–1 cm–1)
–
4
5
6
1201 νs(RSO3 )
443 (19), 624 (14), 1030 (9)
442 (15), 630 (16), 1030 (11)
441 (19), 629 (17), 1030 (11)
–
1204 νs(RSO3 )
The six dinickel(II) complexes in 1–6 share a common
structural motif, where the dinickel(II) complex fragments
–
1203 νs(RSO3 )
Figure 1. Structure of the [Ni2(L2)(CN4H)]+ cation (left) and its core structure (right) in crystals of 4·0.5MeCN·0.5H2O with thermal ellipsoids
drawn at 25% probability. Hydrogen atoms are omitted for clarity.
Z. Anorg. Allg. Chem. 2013, 524–532
© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
www.zaac.wiley-vch.de
525

J. Lach, E. Perlt, B. Kirchner, B. Kersting
ARTICLE
Figure 2. Structure of the [Ni2(L2)(CN4CH3)]+ cation (left) and its core structure (right) in crystals of 5·H2O with thermal ellipsoids drawn at
25% probability. Hydrogen atoms (and the Me group bonded to C39 in the right figure) are omitted for clarity.
Figure 3. Structure of the [Ni2(L2)(CN4Ph)]+ cation (left) and its core structure (right) in crystals of 6·MeCN with thermal ellipsoids drawn at
25% probability. Hydrogen atoms (and the Ph ring bonded to C39 in the right figure) are omitted for clarity.
Table 2. Selected bond lengths /Å of the complex cations in 1–6.
1
2
3Aa)
N7A,N8A N7B,N8B
3B
4Aa)
N7A, N8A N7B, N8B N7, N8
4B
5
6
X, Yb)
N7, N8
N7, N8
X, Yb)
N7,N8
Ni1–X
2.081(2)
2.319(2)
2.168(2)
2.227(2)
2.5152(7)
2.4626(7)
2.077(2)
2.237(2)
2.173(2)
2.311(2)
2.5194(9)
2.4509(6)
2.239(2)
2.079(2)
–
2.063(2)
2.306(2)
2.162(3)
2.232(3)
2.5044(8)
2.4664(8)
2.071(2)
2.204(2)
2.170(2)
2.324(2)
2.5012(8)
2.4699(8)
2.233(2)
2.067(2)
–
2.071(3)
2.346(3)
2.171(3)
2.207(3)
2.525(1)
2.431(1)
2.051(3)
2.205(3)
2.150(3)
2.332(3)
2.530(1)
2.450(1)
2.235(3)
2.061(3)
–
2.065(3)
2.317(3)
2.159(3)
2.221(3)
[2.532(1)
2.443(1)
2.055(3)
2.210(3)
2.154(3)
2.338(3)
2.515(1)
2.441(1)
2.233(3)
2.060(3)
–
Ni1–X
2.080(3)
2.251(3)
2.102(3)
2.237(2)
2.071(2)
2.084(2)
2.061(3)
2.394(3)
2.112(3)
2.254(3)
2.085(2)
2.066(2)
2.225(3)
2.071(3)
2.077(2)
–
2.079(3)
2.317(3)
2.128(3)
2.230(3)
2.072(2)
2.087(2)
2.072(3)
2.302(3)
2.120(3)
2.223(4)
2.097(2)
2.048(3)
2.220(3)
2.076(3)
2.076(2)
–
2.091(3)
2.272(2)
2.123(2)
2.206(3)
2.069(2)
2.093(2)
2.066(3)
2.250(3)
2.112(3)
2.322(2)
2.0645(19) 2.0756(15)
2.0936(19) 2.0580(14)
2.214(3)
2.079(3)
2.080(2)
–
2.0725(18)
2.2731(18)
2.1142(19)
2.231(2)
2.0658(16)
2.0822(17)
2.0802(19)
2.236(2)
Ni1–N1
Ni1–N2
Ni1–N3
Ni1–S1
Ni1–S2
Ni2–Y
Ni2–N4
Ni2–N5
Ni2–N6
Ni2–S1
Ni2–S2
Ni–Nc)
Ni–Nd)
Ni–Oc)
Ni–Sc)
Ni1–N1
Ni1–N2
Ni1–N3
Ni1–O1
Ni1–O5
Ni2–Y
Ni2–N4
Ni2–N5
Ni2–N6
Ni2–O2
Ni2–O4
Ni–Nc)
Ni–Nd)
Ni–Oc)
Ni–Sc)
2.125(2)
2.2387(18)
2.203(2)
2.076(2)
2.071(2)
–
2.4870(8)
2.4855(8)
2.484(1)
2.483(1)
C(4)···C(20) 9.4142(38) 9.2361(50) 9.2952(57) 9.2915(65)
C(4)···C(20) 8.1634(45) 8.1595(61) 8.1838(41) 8.5895(34)
Ni···Ni
3.455(1)
3.425(1)
3.443(1)
3.450(1)
Ni···Ni
4.2796(5) 4.3375(6)
4.3402(6) 4.2607(4)
N7–N8
N7–N9
N8–N10
C39–N9
C39–N10
1.367(2)
1.325(2)
1.317(2)
1.331(3)
1.341(3)
1.331(3)
1.330(3)
1.335(3)
1.333(4)
1.333(4)
1.346(4)
1.333(4)
1.328(4)
1.341(5)
1.347(5)
1.360(4)
1.320(4)
1.317(4)
1.347(5)
1.354(5)
N7–N8
N7–N9
N8–N10
C39–N9
C39–N10
1.345(3)
1.334(4)
1.328(4)
1.325(5)
1.330(4)
1.358(4)
1.327(4)
1.335(4)
1.326(4)
1.326(5)
1.375(4)
1.307(4)
1.316(4)
1.322(4)
1.325(5)
1.329(2)
1.336(3)
1.334(3)
1.326(3)
1.332(3)
a) There are two crystallographically independent molecules A and B in the unit cell. b) X and Y denote the donor atoms of the coligands. c)
Average values. d) Average Ni–N heterocycle distance.
526
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© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Z. Anorg. Allg. Chem. 2013, 524–532

Dinuclear Nickel(II) Complexes with N3Ni(μ1,3-SO3R)2(μ-RCN4)NiN3 Cores
Table 3. Selected bond angles /° of the complex cations in 1–6.
1
2
3Aa)
3Ba)
4Aa)
4Ba)
5
6
X, Yb)
N7, N8
N7, N8
N7A, N8A N7B, N8B
X, Yb)
N7A, N8A N7B, N8B N7, N8
N7, N8
X–Ni1–N2
175.18(7) 176.67(9) 175.05(12) 175.52(11)
X–Ni1–N2
178.34(11) 172.46(12) 178.57(10) 177.89(8)
N1–Ni1–S2 169.73(5) 169.12(7) 167.52(8)
N3–Ni1–S1 170.64(4) 171.60(7) 171.91(9)
169.09(8)
171.21(8)
84.43(8)
87.29(9)
96.17(11)
95.87(11)
98.19(11)
90.46(8)
80.52(11)
98.20(8)
81.79(11)
96.74(8)
91.82(8)
79.43(3)
O5–Ni1–N1 167.42(9)
O1–Ni1–N3 167.95(9)
170.25(10) 167.05(9)
163.31(10) 167.68(11) 168.22(8)
167.64(7)
X–Ni1–S1
X–Ni1–S2
X–Ni1–N3
X–Ni1–N1
N1–Ni1–N3 98.48(6)
N1–Ni1–S1 90.85(5)
N2–Ni1–N1 80.23(6)
N2–Ni1–S1 97.97(6)
N2–Ni1–N3 82.93(7)
N2–Ni1–S2 96.95(5)
N3–Ni1–S2 90.92(5)
85.27(5)
87.12(5)
94.45(7)
96.21(6)
85.25(7)
87.78(6)
96.46(10) 94.45(12)
96.33(9)
97.98(9)
89.98(6)
80.96(9)
96.64(8)
83.92(9)
87.88(9)
X–Ni1–O1
X–Ni1–O5
X–Ni1–N3
X–Ni1–N1
94.04(9)
93.59(10)
91.94(10)
97.87(10)
91.98(10)
92.81(9)
94.18(8)
96.15(10)
95.54(9)
95.39(7)
95.36(7)
93.89(8)
93.97(7)
93.88(10)
96.68(10)
96.29(10)
97.11(11)
99.03(11)
89.04(8)
79.35(12)
99.40(9)
N1–Ni1–N3 99.80(9)
O1–Ni1–N1 84.44(9)
N2–Ni1–N1 84.64(10)
O1–Ni1–N2 84.67(9)
N2–Ni1–N3 84.51(10)
O5–Ni1–N2 85.03(10)
O5–Ni1–N3 86.31(9)
O5–Ni1–O1 87.49(8)
109.00(11) 102.93(10) 101.75(8)
82.57(9)
84.54(8)
83.03(10)
86.93(9)
84.32(10)
87.22(9)
84.49(10)
86.45(8)
84.85(6)
83.92(7)
84.62(7)
86.38(8)
86.75(7)
85.69(8)
86.22(6)
80.95(11)
88.10(10)
82.12(10)
95.46(10)
79.28(11)
88.27(10)
82.07(10) 82.77(12)
95.23(7)
91.54(6)
80.30(3)
96.29(9)
91.95(9)
80.08(3)
S1–Ni1–S2
Y–Ni2–N5
79.72(3)
175.33(6) 175.39(9) 175.56(12) 175.05(12)
Y–Ni2–N5
171.39(11) 178.56(13) 174.48(10) 178.68(8)
N4–Ni2–S1 171.30(4) 171.00(7) 171.28(9)
N6–Ni2–S2 169.16(4) 168.47(6) 169.34(8)
171.66(8)
168.92(8)
84.73(9)
87.19(9)
95.18(12)
96.15(11)
91.86(8)
89.96(8)
98.11(9)
97.29(9)
82.59(12)
79.85(11)
98.33(11)
79.80(3)
86.23(3)
89.86(3)
O2–Ni2–N4 169.94(9)
O4–Ni2–N6 164.05(9)
167.36(11) 163.12(12) 167.47(6)
167.70(12) 169.02(9)
165.61(7)
94.94(7)
95.87(7)
93.71(8)
95.87(7)
84.50(6)
85.11(6)
86.34(7)
83.89(7)
84.98(8)
84.55(7)
Y–Ni2–S1
Y–Ni2–S2
Y–Ni2–N4
Y–Ni2–N6
N4–Ni2–S2 91.53(5)
N6–Ni2–S1 90.01(4)
N5–Ni2–S1 98.04(4)
N5–Ni2–S2 97.04(5)
N5–Ni2–N4 81.69(6)
N5–Ni2–N6 80.46(6)
N4–Ni2–N6 98.50(6)
85.13(5)
86.86(5)
95.69(6)
96.17(6)
84.53(6)
87.61(7)
95.20(9)
97.02(9)
90.70(7)
89.61(6)
98.43(7)
96.35(7)
82.43(9)
79.53(9)
99.35(9)
80.29(3)
86.36(3)
85.07(9)
86.56(9)
96.14(12)
95.55(12)
91.81(9)
90.13(8)
97.23(9)
97.59(9)
82.17(12)
80.67(12)
98.33(11)
79.63(3)
85.87(4)
89.74(4)
Y–Ni2–O2
Y–Ni2–O4
Y–Ni2–N4
Y–Ni2–N6
94.30(9)
93.74(10)
93.59(11)
95.01(11)
96.74(12)
84.40(10)
86.71(11)
87.35(10)
85.55(12)
83.77(11)
84.24(13)
93.68(9)
93.18(9)
97.32(11)
93.39(9)
79.47(10)
83.61(8)
88.35(9)
92.05(9)
81.89(11)
81.72(9)
93.59(10)
90.63(10)
98.48(10)
O4–Ni2–N4 79.86(9)
O2–Ni2–N6 77.71(10)
O2–Ni2–N5 94.19(10)
O4–Ni2–N5 87.67(10)
N5–Ni2–N4 81.20(10)
N5–Ni2–N6 81.96(10)
N6–Ni2–N4 110.25(10) 101.28(12) 108.37(10) 103.00(7)
O2–Ni2–O4 91.06(9)
S1–Ni2–S2
Ni1–S1–Ni2 86.68(3)
79.86(2)
85.97(10)
87.19(8)
85.61(6)
Ni1–S1–Ni2
Ni1–S2–Ni2
Ph/Phc)
–
–
–
–
–
–
–
–
Ni1–S2–Ni2 89.378(2) 87.88(3)
Ph/Phc)
82.655(58) 77.998(82) 79.774(111) 80.507(120)
47.782(97) 47.827(110) 48.924(84) 56.547(72)
a) There are two crystallographically independent molecules A and B in the unit cell. b) X and Y denote the donor atoms of the coligands. c)
Angle between the normals of the planes of the aryl rings.
[Ni2(L2)]2+ and [Ni2(L1)]2+ adopt a conical “calixarene-like” changes in the shape of the cavity.[7,8] These changes can be
conformation that gives rise to a hydrophobic cavity.[15] In expressed by the intramolecular distance between the two aryl
each case the two nickel(II) ions are coordinated in a square- carbon atoms C(4) and C(20) and the angle between the nor-
pyramidal fashion either by a fac-N3(μ-S)2 {in [Ni2(L1)]2+} or mals of the planes that are generated by the phenyl rings of
a fac-N3O2 donorset {in [Ni2(L2)]2+}. Together with the μ2,3
-
the macrocycle. While the angles between the Ph rings in 1–3
bridging tetrazolato coligands each of the nickel(II) atoms are all greater than 77°, the corresponding values in 4–6 are
reaches a distorted octahedral coordination environment. In all all significantly smaller (below 57°). The C(4)···C(20) dis-
cases the tetrazolate units are effectively planar and bridge the tances are thus shortened by 0.7–1.3 Å, a fact that results in a
NiII ions in a symmetrical fashion through their two ring nitro- more “cleft”-like rather than a “cone”-like binding pocket.
gen atoms N(7) and N(8). With 2.060(3)–2.079(3) Å the
average Ni–Nhet bond length is very similar in all six com-
plexes. The N–N and C–N bond lengths of the coordinated
tetrazolates however differ significantly from those of the free
Magnetic Measurements
tetrazoles. This is in agreement with the fact that upon removal
To examine their electronic structures, measurements of the
of the proton the nitrogen atoms N7, N8 and N9, N10 become temperature dependent magnetic susceptibility of the sulfonato
equivalent.[16] It can be noted that the N(7)–N(8) bonds in 4– complexes 4–6 were carried out on powdered samples at an
6 show an average bond length of 1.352(3) Å, which is much applied external field of 0.5 T in the temperature range be-
longer than the 1.295(3) Å and 1.285(3) Å found in 1-H-tetra- tween 2 and 330 K with a MPMS 7XL SQUID (Quantum De-
zole and 5-methyltetrazole.[17,18] As one might expect the sign) magnetometer. The temperature dependencies of the mo-
Ni···Ni distances in the oxidized complexes are significantly lar magnetic susceptibility (per dinuclear complex) of the com-
longer (0.81–0.91 Å) than the corresponding distances in their plexes 4–6 are shown in Figure 4 in the form of χMT vs. T
reduced counterparts in order to accommodate the coordinating plots. The susceptibility data of their parent complexes 1–3 are
sulfonate oxygen atoms. That of course leads to drastic shown for comparative purposes.[3]
Z. Anorg. Allg. Chem. 2013, 524–532
© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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527

J. Lach, E. Perlt, B. Kirchner, B. Kersting
ARTICLE
cally very similar it can be concluded that this difference solely
originates from the oxidation of the supporting ligand.
In order to quantify the magnitude of the magnetic exchange
interaction and to determine the g values of the complexes 4–
6 the experimental χMT vs. T data were analyzed using the
spin Hamiltonian [Equation (1)], including the isotropic Hei-
senberg-Dirac-van-Vleck (HDvV) exchange, the single-ion
zero-field splitting and the single-ion Zeeman interactions
using a full-matrix diagonalization approach.[19,20]
(1)
The experimental data of 4–6 were fitted to Equation (1)
over the full temperature range, assuming identical g values
for the two NiII ions. The parameters of 4–6 leading to the best
fits are listed in Table 4 together with the parameters deter-
mined earlier for 1–3.[3] The parameters determined for 4 were
J = –1.39 cm–1 and g = 2.22. In the case of 5 the best fit to
the experimental data yielded J = –1.43 cm–1 and g = 2.24.
The best fit parameters for 6 were J = –1.60 cm–1 and g =
Figure 4. The temperature dependencies of the molar magnetic suscep-
tibility (per dinuclear complex) of the complexes 4–6 and their parent
complexes 1–3[3] in the form of χMT vs. T plots. The full lines repre-
sent the best theoretical fits to Equation (1).
The χMT values of 4 slowly decrease from 2.53 cm3·K·mol–1 2.26. In the case of 1–3 the inclusion of the zero-field splitting
(4.49 μB) at 330 K to 0.54 cm3·K·mol–1 (2.08 μB) at 2 K. This parameter improved the quality of the fit. In the case of 4–6,
is in contrast to 1, where the values increase with decreasing however, the fit was found to be quite insensitive to the value
temperature from 2.77 cm3·K·mol–1 (4.71 μB) at 300 K to a of D. Therefore D was fixed to zero in this case. It should be
maximum of 3.92 cm3·K·mol–1 (5.60 μB) at 14 K. A similar mentioned in this respect that magnetic susceptibility measure-
behavior can be noted for the other two complex pairs 2/5 and ments are not very suitable for the determination of the D pa-
3/6. Thus, for 5 the χMT data decreases from 2.54 cm3·K·mol–1 rameter,[21] and so these values should be taken indicative than
(4.51 μB) at 330 K to 0.60 cm3·K·mol–1 (2.20 μB) at 2 K. In definite. A previous high-field EPR study has shown that the
the parent complex 2 the product χMT gradually increases from D values for NiII complexes supported by the N6S2
2
2.71 cm3·K·mol–1 (4.66 μB) at 300 K to a maximum of macrocycle have a negative sign and are on the order of
3.58 cm3·K·mol–1 (5.35 μB) at 22 K. Further lowering of the 0.5–1.0 cm–1.[22] Nevertheless, the value of J is unambiguous
temperature is accompanied by a rapid decrease of χMT, being and represents an accurate measure of the magnetic coupling
2.19 cm3·K·mol–1 (4.18 μB) at 2 K. Again, for 6 the χMT values in these complexes.
decrease from 2.54 cm3·K·mol–1 (4.51 μB) at 330 K to
The change of the sign of J is presumably associated with a
0.51 cm3·K·mol–1 (2.02 μB) at 2 K. For 3, on the other hand, change of the angle between the magnetic orbitals of the two
the product χMT gradually increases again from NiII ions. It should be noted in this respect that there is a large
2.65 cm3·K·mol–1 (4.60 μB) at 300 K to a maximum of increase of the angle between the N2NiS2 and N2Ni(Osulfonato
)
2
3.51 cm3·K·mol–1 (5.30 μB) at 22 K. Further decrease in tem- planes upon going from the thiophenolato-bridged compounds
perature is accompanied by a rapid decrease of χMT, being 1–3 to the sulfonato-bridged species 4–6. Thus, the angles be-
2.36 cm3·K·mol–1 (4.35 μB) at 2 K. Thus oxidation of the tween the normals of the planes through the S1S2N6N4 and
thiophenolato complexes is in all cases accompanied by a S1S2N1N3 planes in the former are all Ͻ 48° {1: 46.87(3)°, 2:
change of the exchange coupling between the electron spins of 46.67(4)°, 3: 47.16 (6)° [47.14(5)°]}, whereas the angles be-
the NiII ions from ferromagnetic in 1–3 to antiferromagnetic tween the normals of the planes through the O4O2N6N4 and
in 4–6. Thus, 4–6 exhibit an S = 0 spin ground state and 1–3 O5O1N1N3 planes in the latter series are all at Ͼ 87° {4:
have an S = 2 spin ground state. Since the coligands are chemi- 87.71(5)° [88.57(7)°], 5: 87.56(6)°, 6: 89.35(4)°}. Further it
Table 4. Magnetic parameters for 1–6 resulting from analysis of temperature dependent magnetic susceptibility data and from DFT calculations.
a)
a)
a)
c)
c)
c)
Complex
J
/cm–1
g
D
/cm–1
J(1) /cm–1
J(2) /cm–1
J(3) /cm–1
Exp.
Exp.
Exp
B3LYP
B3LYP
B3LYP
1
2
3
4
5
6
+13.50b)
+20.00b)
+19.20b)
–1.39
–1.43
–1.60
2.28b)
2.20b)
2.17b)
2.22
2.24
2.26
0.98b)
28.38
26.03
27.71
–2.84
–2.39
–2.94
18.92
17.35
18.47
–1.89
–1.59
–1.96
28.36
26.02
27.70
–2.84
–2.39
–2.94
8.10b)
5.85b)
0 (fixed)
0 (fixed)
0 (fixed)
a) Parameters resultant from least-squares fit to the χMT data under the spin Hamiltonian in Equation (1), J = coupling constant (H = –2JS1S2),
g = g value, D = zero-field-splitting parameter. b) Parameters from Ref. [3]. c) Parameters obtained from calculations with the ORCA program.
528
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Dinuclear Nickel(II) Complexes with N3Ni(μ1,3-SO3R)2(μ-RCN4)NiN3 Cores
can be noted that the absolute value of the exchange interaction mental data. This is in agreement with a study of Soda and
in 4–6 compared to that in 1–3 is smaller by an order of magni- co-workers who found the B3LYP functional to overestimate
tude. This observation may be explained with the increased coupling constants especially at incomplete basis sets. Further-
Ni···Ni distance and therefore increased length of the coupling more, the observed numbers of J(1) and J(3) do not differ
path upon oxidation.
significantly, as is predicted to be the case for weak coupling
as present in the investigated complexes.
The observation of ferromagnetic exchange interactions in
1–3, for which the Ni–S–Ni angles are close 90° is in good
agreement with earlier studies,[3,29] and accords to the An-
derson[30,31] and Goodenough-Kanamori rules.[32–34]. The oc-
currence of antiferromagnetic coupling in 4–6 is caused by the
alteration of the electronic structure of the complexes upon the
change of the coordination sphere around each NiII ion from
N4S2 to N4O2. Due to the replacement of the soft sulfur donor
atoms by hard oxygen atoms the degeneracy of the magnetic
orbitals is lost and the antiferromagnetic singlet term is stabi-
lized.[20] The observed antiferromagnetic behavior is in ac-
cordance with the Hay-Thibeault-Hoffmann model[35] and fits
the results given in the literature.[8] As illustrated for 1 and 4
in Figure 5 the difference of alpha and beta electron density of
complexes 1–6 shows positive values indicating an excess of
alpha electrons at the nickel atoms. Interestingly, for 1–3 cou-
pling of these electrons is mediated mainly across the sulfur
atoms leading to ferromagnetic coupling (90° Ni–S–Ni angle),
while for 4–6 an antiferromagnetic coupling pathway is medi-
ated mainly via the bridging tetrazolato coligands. Graphical
representations of the coupling pathways and spin densities of
the other compounds are available as Supporting Information.
Theoretical Calculations
The results of the DFT calculations for 1–6 are summarized
in Table 4. As shown by Equation (2), Equation (3), and Equa-
tion (4), there are three formulations available for the evalu-
ation of the magnetic coupling constants.[23–27]
EBS – EHS
J(1) =
(2)
2
Smax
EBS – EHS
J(2) =
J(3) =
(3)
(4)
Smax·(Smax + 1)
EBS – EHS
(ϽS2ϾHS – ϽS2ϾBS
)
Herein, the formulations according to Noodleman,
J(1)[23–25] and J(2)[26] are valid for weak and strong coupling,
respectively, whereas J(3) as published by Yamaguchi et al.[27]
holds for the whole range of coupling strengths and reduces to
J(1) or J(2), respectively, in either of the edge cases.[28] Re-
gardless of the chosen formulation, the calculations reproduce
the correct sign of J. The experimental exchange coupling con-
stants seem to be very closely resembled by the DFT calcula-
tions using the formulation J(2) by Bencini. Nevertheless, as-
suming the formulation according to Yamaguchi et al. [J(3)] to
Conclusions
The
oxidation
of
dinuclear
nickel
complexes
be the most reasonable, it turns out that the calculated coupling [Ni2(L1)(LЈ)]BPh4 [LЈ = CN4H– (1), CN4Me– (2), and CN4Ph–
constants overestimate the magnitude as compared to experi- (3)] supported by the hexaaza bis(thiophenolate) ligand (L1)2–
Figure 5. Top: Graphical representation of the spin densities of compounds 1 (left) and 4 (right) at an isovalue of 0.025. Bottom: Ferromagnetic
coupling pathway across the sulfur atoms in 1 (left) and antiferromagnetic coupling pathway across the bridging coligand in 4 (right).
Z. Anorg. Allg. Chem. 2013, 524–532
© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
www.zaac.wiley-vch.de
529

J. Lach, E. Perlt, B. Kirchner, B. Kersting
ARTICLE
[Ni2(L2)(CN4Ph)]BPh4 (6): This compound was prepared from
[Ni2(L1)(CN4Ph)][BPh4] (3) (100 mg, 0.08 mmol) in a manner analo-
gous to 4. Yield: 69 mg (0.07 mmol, 64%). C69H89BN10Ni2O6S2
(1346.84): calcd. C 61.53; H 6.66; N 10.40%; found C 60.76, H 6.66,
N 10.09%. IR (KBr): ν˜ = 3455 (m), 3055 (w), 3032 (w), 2999 (w),
2964 (s), 2869 (w), 1601 (m), 1580 (w), 1478 (w), 1450 (s), 1429 (w),
1411 (w), 1397 (w), 1366 (m), 1268 (w), 1250 (w), 1203 (s), 1150
(w), 1132 (w), 1090 (s), 1059 (w), 1043 (w), 1032 (m), 1012 (w), 999
(w), 974 (w), 913 (w), 893 (m), 831 (w), 821 (s), 750 (w), 733 (s),
705 (s), 667 (s), 640 (w), 630 (m), 612 (m), 598 (w), 562 (w), 548
with H2O2 produces the corresponding complexes 4–6 of the
disulfonate macrocycle [Ni2(L2)(LЈ)]BPh4. While the overall
structures of the complexes remain constant, the magnetic
properties change significantly. Upon oxidation the intramolec-
ular magnetic exchange interaction between the electron spins
of the NiII ions changes from ferromagnetic to antiferromag-
netic due to replacement of a bridging thiophenolate to a bridg-
ing sulfonate moiety in the coupling path. The magnetic prop-
erties, however, were not markedly influenced by the size of
the functional group R of the 5-R-tetrazolates. The J values (w) cm–1. ESI-MS+ (MeCN): m/z = 1025.36 [C45H69N10Ni2O6S2]+.
UV/Vis (CH3CN): λmax (ε, m–1 cm–1) = 382 (42), 441 (19), 629 (17),
1030 (11) nm.
that were obtained by DFT calculations are in good agreement
with the experimentally determined values. The calculations
also shed light on the way the magnetic exchange interactions
are propagated between the two metal atoms in the two com-
plex types.
Crystal Structure Determinations: The X-ray diffraction data were
collected at 183 K with a IPDS-1T (STOE) or a IPDS-2T (STOE)
diffractometer using graphite monochromated Mo-Kα radiation (λ =
0.71073 Å). The intensity data were processed with the program STOE
X-AREA.[36] The crystal structures were solved by direct methods and
refined by full-matrix least-squares on the basis of all data against
Experimental Section
F2 using SHELXL-97.[37] Diamond 3.2g was used for the creation of
artwork.[14] Unless otherwise noted non-hydrogen atoms were refined
anisotropically whereas the coordinates of the hydrogen atoms were
calculated for idealized positions with isotropic displacement param-
eters. Selected crystallographic data are tabulated in Table 5.
General Remarks: Solvents and reagents were of reagent grade qual-
ity and used as received unless otherwise specified. Infrared spectra
were recorded with a Bruker Vector 27 FT-IR spectrometer. Electronic
absorption spectra were taken with a JASCO V-670 UV/Vis/NIR spec-
trophotometer, elemental analyses with a VARIO EL – elemental ana-
lyzer. Temperature-dependent magnetic susceptibility measurements
on powdered solid samples were carried out with a MPMS 7XL
SQUID magnetometer (Quantum Design). The observed susceptibility
data were corrected for underlying diamagnetism.
In the crystal structure of 4·0.5MeCN·0.5H2O the water solvate mole-
cules were refined isotropically. The bond lengths[38] of the acetonitrile
molecules were constrained to C–C = 1.470 Å and C–N = 1.136 Å
using the DFIX command implemented in the SHELXL program suite.
Furthermore one of the tert-butyl groups was found to be rotationally
disordered. The disorder was refined applying a split model using the
PART command yielding an occupancy factor of 0.76/0.24. In the crys-
tal structure of 5·H2O one of the tert-butyl groups and the atoms C13
and C24 were found to be disordered. The two disorders were found
to have similar occupancy factors and a split model with an occupancy
factor of 0.68/0.32 was applied. In the crystal structure of 6·MeCN
rotational disorder occurred at one of the tert-butyl groups and at the
phenyl ring of the coligand. Hence split models had to be applied
yielding occupancy factors of 0.57/0.43 and 0.64/0.36 respectively.
[Ni2(L2)(CN4H)]BPh4 (4): To a solution of [Ni2(L1)(CN4H)]BPh4 (1)
(100 mg, 0.09 mmol) in methanol (60 mL) was added hydrogen perox-
ide (2 mL, 50 wt% solution in water, 35.19 mmol). Refluxing the reac-
tion mixture for 10 h yielded a pale green solution. After cooling to
room temperature the solution was filtered, and a solution of NaBPh4
(146 mg, 0.43 mmol) in ethanol (10 mL) was added to the filtrate. The
amount of solvent was reduced to about 10 mL under reduced pressure
to precipitate the pale-green microcrystalline tetraphenylborate salt 4,
which was isolated by filtration, thoroughly washed with cold
ethanol and dried in vacuo. Yield: 73 mg (0.06 mmol, 67%).
C63H85BN10Ni2O6S2 (1270.74): calcd. C 59.55, H 6.74, N 11.02%;
found C 59.57, H 6.84, N 11.11%. IR (KBr): ν˜ = 3448 (m), 3054 (w),
3031 (w), 2999 (w), 2982 (w), 2964 (s), 2906 (w), 2868 (m), 1631
(w), 1601 (m), 1581 (w), 1478 (s), 1429 (w), 1411 (w), 1396 (w), 1367
(m), 1309 (w), 1301 (w), 1270 (w), 1258 (w), 1241 (w), 1201 (s), 1157
(w), 1091 (s), 1062 (w), 1044 (w), 1031 (m), 1016 (w), 1007 (w), 976
(w), 916 (w), 890 (m), 851 (w), 832 (w), 821 (m), 802 (w), 744 (w),
734 (s), 711 (w), 705 (s), 668 (m), 640 (w), 629 (w), 614 (w), 606
(m), 596 (w), 561 (w), 548 (w) cm–1. ESI-MS+ (MeCN): m/z = 949.20
[C39H65N10Ni2O6S2]+. UV/Vis (CH3CN): λmax (ε, m–1 cm–1) = 383
(38), 443 (19), 624 (14), 1030 (9) nm.
Crystallographic data (excluding structure factors) for the structures in
this paper have been deposited with the Cambridge Crystallographic
Data Centre, CCDC, 12 Union Road, Cambridge CB21EZ, UK. Copies
of the data can be obtained free of charge on quoting the depository
numbers CCDC-901287 (4·0.5MeCN·0.5H2O), CCDC-901288
(5·H2O), and CCDC-901289 (6·MeCN) (Fax: +44-1223-336-033;
E-Mail: deposit@ccdc.cam.ac.uk, http://www.ccdc.cam.ac.uk).
Electronic Structure Calculations: All density functional theory
(DFT) calculations were performed applying the Kohn-Sham density
functional theory (KS-DFT) in conjunction with the def2-TZVP basis
set[39,40] using the ORCA program.[41] The investigated geometries
were obtained from X-ray diffraction studies. No further geometry op-
timizations were carried out in order to get results resembling the mo-
lecular geometry in the crystal structures. We employed the hybrid
functional B3LYP.[42–46] Coupling constants were evaluated by broken
symmetry calculations using the FlipSpin feature of ORCA. Graphical
representations of spin density and of the HOMOs and LUMOs were
created using the visual molecular dynamics (VMD) software.[47]
[Ni2(L2)(CN4Me)]BPh4 (5): This compound was prepared from
[Ni2(L1)(CN4Me)][BPh4] (2) (100 mg, 0.08 mmol) in a manner analo-
gous to 4. Yield: 68 mg (0.05 mmol, 63%). C64H87BN10Ni2O6S2
(1284.77) calcd. C 59.83; H 6.83; N 10.90%; found C 58.86, H 6.96,
N 10.40%. IR (KBr): ν˜ = 3597 (w), 3379 (w), 3057 (w), 3039 (w),
3002 (w), 2968 (m), 2869 (w), 1602 (w), 1581 (w), 1480 (s), 1428
(w), 1412 (w), 1397 (w), 1367 (w), 1270 (w), 1231 (w), 1204 (s), 1151
(w), 1091 (m), 1060 (w), 1045 (w), 1032 (m), 1002 (w), 978 (w), 916
(w), 893 (m), 821 (m), 803 (w), 741 (m), 735 (w), 709 (s), 668 (m),
639 (w), 631 (w), 611 (m), 597 (w), 562 (w), 548 (w) cm–1. ESI-MS+ Supporting Information (see footnote on the first page of this article):
(MeCN): m/z = 963.34 [C40H67N10Ni2O6S2]+. UV/Vis (CH3CN): λmax Experimental and calculated susceptibility data for complexes 1–6 and
(ε, m–1 cm–1) = 378 (40), 442 (15), 630 (16), 1030 (11) nm.
graphical representations of coupling pathways and spin densities.
530 www.zaac.wiley-vch.de
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Z. Anorg. Allg. Chem. 2013, 524–532

Dinuclear Nickel(II) Complexes with N3Ni(μ1,3-SO3R)2(μ-RCN4)NiN3 Cores
Table 5. Selected crystallographic data for compounds 4·0.5MeCN·0.5H2O, 5·H2O, and 6·MeCN.
4·0.5MeCN·0.5H2O
5·H2O
6·MeCN
Formula
C64H86.50BN10.50Ni2O6.50S2
1299.29
P21/a
14.2594(5)
50.4554(17)
18.7925(7)
90
C64H87BN10Ni2O7S2
1300.79
C2/c
21.5600(8)
19.1490(6)
31.3230(12)
90
C71H92BN11Ni2O6S2
1387.91
P21/c
12.9343(6)
34.3993(9)
15.7358(7)
90
M /g·mol-1
Space group
a /Å
b /Å
c /Å
α /°
β /°
110.670(3)
90
12650.2(8)
8
93.069(5)
90
12913.2(8)
8
97.145(3)
90
6947.0(5)
4
γ /°
V /Å3
Z
ρcalcd /g·cm–3
Crystal size /mm3
μ (Mo-Kα) /mm–1
θ limits /°
Measured refl.
Independent refl.
Observed refl.a)
No. parameters
1.364
0.18ϫ0.14ϫ0.11
0.71073
1.2–28.1
54592
24361
13886
1569
0.046 /(0.092)
0.100/(0.109)
0.61/–0.79
1.338
1.327
0.16ϫ0.14ϫ0.11
0.71073
2.4–28.1
43988
11187
7520
0.17ϫ0.15ϫ0.10
0.71073
1.4–27.2
52392
15330
10685
795
913
b)
R1 (R1all data)
0.040/(0.062)
0.093/(0.098)
0.79/–0.65
0.040/(0.065)
0.095/(0.103)
0.59/–0.95
wR2c)/(wR2 all data)
Δρfin (max, min) /e·Å–3
2
2 2
2 2
a) Observation criterion: I Ͼ 2σ(I). b) R1 = ∑||Fo|–|Fc||/w∑|Fo|. c) wR2 = {w∑[w(Fo –Fc ) ]/∑[w(Fo ) ]}1/2
.
[10] V. E. Kaasjager, E. Bouwman, S. Gorter, J. Reedijk, C. A. Grap-
perhaus, J. H. Reibenspies, J. J. Smee, M. Y. Darensbourg, A. De-
recskei-Kovacs, L. M. Thomson, Inorg. Chem. 2002, 41, 1837–
1844.
[11] C. A. Grapperhaus, M. Y. Darensbourg, Acc. Chem. Res. 1998,
31, 451–459.
[12] R. K. Henderson, E. Bouwman, A. L. Spek, J. Reedijk, Inorg.
Chem. 1997, 36, 4616–4617.
[13] K. Nakamoto, Infrared and Raman Spectra of Inorganic and
Coordination Compounds, Part B: Applications in Coordination,
Organometallic, and Bioinorganic Chemistry, 6th ed., Wiley, Ho-
boken, N. J 2009.
Acknowledgements
We are grateful to Prof. Dr. H. Krautscheid for providing facilities for
X-ray crystallographic measurements. This work was supported by the
Deutsche Forschungsgemeinschaft DFG-FOR 1154 “Towards molecu-
lar spintronics” and the University of Leipzig. Calculations were per-
formed within the Cluster of Excellence “Structure Design of Novel
High-Performance Materials via Atomic Design and Defect Engineer-
ing (ADDE)” that is financially supported by the European Union
(European regional development fund) and by the Ministry of Science
and Art of Saxony (SMWK). Computer time from the computer center
at the University of Leipzig is gratefully acknowledged. We thank
the ZIH Dresden for providing computational resources and support.
J. Lach and E. Perlt thank the SAB for ESF grants.
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Received: November 16, 2012
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