Dinuclear and polymeric (μ-formato)nickel(II) complexes: Synthesis, structure, spectral and magnetic properties

Article abstract of DOI:10.1016/j.poly.2015.04.010

Two (μ-formato)nickel(II) complexes [Ni₂(HCOO)(bz)₈(H₂O)₂](HCOO)₃·4H₂O (1) and [Ni(tren)(HCOO)]ClO₄·H₂O (2) were synthesized and characterized by spectroscopic methods. The structure of complexes has been determined by X-ray crystallography. The formato ligand bridges the Ni(II) central atoms forming a dinuclear cation in 1 and a polymeric cationic chain in 2, respectively. The coordination environment of Ni(II) atom is nearly octahedral. Based upon the magnetic data, these two compounds display an exchange interaction of the antiferromagnetic nature along with the zero-field splitting. The results from magnetic analysis of 1 and 2, namely the isotropic exchange constants and the zero-field splitting parameters were further confirmed and studied by DFT method using at B3LYP/def2-TZVP and by CASSCF/NEVPT2, respectively.

Full text of DOI:10.1016/j.poly.2015.04.010

Polyhedron 95 (2015) 45–53
Contents lists available at ScienceDirect
Polyhedron
journal homepage: www.elsevier.com/locate/poly
Dinuclear and polymeric (
l-formato)nickel(II) complexes: Synthesis,
structure, spectral and magnetic properties
a
a,b
c
a
d
ˇ a
ˇ
ˇ
Kristína Matelková , Roman Boca , Lubor Dlhán , Radovan Herchel , Ján Moncol , Ingrid Svoboda ,
Anna Mašlejová a,
⇑
a Institute of Inorganic Chemistry, FCHPT, Slovak University of Technology, 812 37 Bratislava, Slovakia
b Department of Chemistry, FPV, University of SS Cyril and Methodius, 91701 Trnava, Slovakia
c Department of Inorganic Chemistry, Faculty of Science, Palacky University, 771 46 Olomouc, Czech Republic
d Material Science, Darmstadt University of Technology, 64287 Darmstadt, Germany
a r t i c l e i n f o
a b s t r a c t
Article history:
Two (
l
-formato)nickel(II) complexes [Ni2(HCOO)(bz)8(H2O)2](HCOO)3ꢀ4H2O (1) and [Ni(tren)(HCOO)]
Received 2 February 2015
Accepted 8 April 2015
Available online 16 April 2015
ClO4ꢀH2O (2) were synthesized and characterized by spectroscopic methods. The structure of complexes
has been determined by X-ray crystallography. The formato ligand bridges the Ni(II) central atoms
forming a dinuclear cation in 1 and a polymeric cationic chain in 2, respectively. The coordination
environment of Ni(II) atom is nearly octahedral. Based upon the magnetic data, these two compounds
display an exchange interaction of the antiferromagnetic nature along with the zero-field splitting. The
results from magnetic analysis of 1 and 2, namely the isotropic exchange constants and the zero-field
splitting parameters were further confirmed and studied by DFT method using at B3LYP/def2-TZVP
and by CASSCF/NEVPT2, respectively.
Keywords:
Formato-nickel(II) complexes
Crystal structures
Benzimidazole
Tren-complexes
Magnetism
Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction
also the development of new functional molecule based materials.
The rational design of these polymers remains to be one of
Different possible coordination of the carboxyl group leads to
the various crystal structures of coordination compounds
the major challenges. Depending on the geometrical properties of
formate and the transition metal atom, formato ligand can adopt
different bridging modes and they mediate ferro- or antiferromag-
netic exchange coupling between metal ions. Although a variety of
Mn(II), Mn(III), Co(II) and Cu(II) compounds containing formate as
the bridging ligand has been structurally characterized [10–17], a
few reports involved the magnetic studies of them. The most
extensively magnetic investigations have been focused to the
simply metal formate complexes M(HCOO)2ꢀ2H2O and their
anhydrous counterparts [18–20].
Previously we have reported studies on nickel(II) carboxylate
complexes including formate group [21]. In these papers we
reported structures, magnetic behavior and structural-magnetic
correlations of the mononuclear compounds. Some of these inves-
tigated complexes reveal formate group as uncoordinated anion
and also unidentate terminal ligand. To take this concept further
we decided to prepare polynuclear compounds with bulky and a
blocking ligands.
–
mononuclear, binuclear or polynuclear. Review papers of carboxy-
lato complexes deal mostly with acetato and trifluoroacetato
complexes [1]. Only little attention is paid to the formate ion as
a bridging ligand although as the smallest carboxylate it has
been reported to display not only monodentate but multiple
bridging modes. To our knowledge only a few formato-nickel(II)
complexes have been structurally characterized [2–6]. In a simple
formate Ni(HCOO)2(H2O)2 the formate ions are coordinated as
bridging bidentate ligands [7]. In a double formato complex
Ba2Ni(HCOO)6(H2O)2 three coordination modes of the formato
ligands were found: a monodentate, a bridging-bidentate, and a
monoatomic-bridging one [8]. A report about synthesis and spec-
tral characterization of seven new nickel(II)-formato-complexes
with imidazole ligands appeared recently [9].
Molecule-based magnetic polymers have attracted intense
interest in recent years, due to not only the fundamental research
of magnetic interaction and magnetostructural correlations, but
In the present communication the synthesis, structural and
spectroscopic characterization of a dinuclear complex [Ni2(HCOO)
(bz)8(H2O)2](HCOO)3ꢀ4H2O (1) and
a polynuclear compound
[Ni(tren)(HCOO)]ClO4ꢀH2O (2) is reported along with the magnetic
⇑
Corresponding author. Tel.: +421 2593 25 187; fax: +421 2524 93 198.
E-mail address: anna.maslejova@stuba.sk (A. Mašlejová).
and theoretical studies.
http://dx.doi.org/10.1016/j.poly.2015.04.010
0277-5387/Ó 2015 Elsevier Ltd. All rights reserved.

46
K. Matelková et al. / Polyhedron 95 (2015) 45–53
Table 1
2. Experimental
2.1. Synthesis
Crystallographic data for 1 and 2.
Chemical formula
C57H53N16Ni2O4 (HCO2)3 C7H19N4NiO2ꢀ(ClO4)ꢀ(H2O)
4H2Oa
Mr
1374.10b
Monoclinic
P21/c
367.44
Monoclinic
P21/n
Ethanol and methanol were purified before use by standard
methods. Nickel(II) formate, as a hydrate was synthesized by
slowly adding the stoichiometric amount of the nickel(II)-carbon-
ate to the aqueous-ethanol solution of the formic acid in excess.
All other chemicals were purchased commercially and used
without further purification.
Crystal system
Space group
T (K)
a (Å)
b (Å)
300(1)
95(1)
16.680(2)
24.021(2)
17.071(2)
90
12.7790(10)
7.5944(4)
15.6210(10)
90
c (Å)
a
(°)
The complex [Ni2(HCOO)(bz)8(H2O)2](HCOO)3ꢀ4H2O (1) was
prepared by reaction of benzimidazole (2.5 g) with Ni(HCOO)2ꢀ
2H2O (1 g) in molar ratio 4:1 in warm dried ethanol under reflux
conditions for 4 h. After a few days of slow evaporation the solid
substances were filtered off. Within several days small turquoise
crystals suitable for X-ray crystallographic studies had formed.
Found: N, 16.7; C, 53.2; H, 4.97; Ni, 9.0. [Ni2(HCOO)(bz)8(H2O)2]
(HCOO)3ꢀ4H2O requires N, 16.6; C, 53.4; H, 4.78; Ni, 8.7%.
From water–methanol solution the compound of composition
[Ni(tren)(HCOO)]ClO4ꢀH2O (2) has been prepared. To dissolved
Ni(ClO4)2ꢀ6H2O (0.50 g) in 10 cm3 of methanol in the first beaker
tris(2-aminoethyl)amine (tren, 0.40 g) has been added producing
a purple solution. The solution consisting of Ni(HCOO)2ꢀ2H2O
(0.25 g) and distilled water (20 cm3) was prepared in the second
beaker and combined with the first one. After a few minutes of stir-
ring 10 cm3 of methanol was added and then 30 cm3 of distilled
water. The mixture was stirred ca one and half h. and fine precip-
itate was filtered off. The clear solution was allowed to stand for
two months while violet crystals crystallized. Found: N, 15.25; C,
22.88; H, 5.76; Ni, 15.97. [Ni(tren)(HCOO)]ClO4ꢀH2O requires N,
15.26; C, 23.01; H, 5.68; Ni, 16.00%.
b (°)
98.67
90
6775.76
4
0.71037
1.13
109.724(9)
90
1427.06
4
0.71037
1.583
c
(°)
V (Å3)
Z
k (Mo K
a
)/Å
l
(mmꢁ1
)
Crystal size (mm)
0.44 ꢂ 0.28 ꢂ 0.20
0.20 ꢂ 0.14 ꢂ 0.06
qcalc (g cm–3
)
1.121
1.710
S
0.984
1.184
0.0584
0.1484
R1 [I > 2
wR2 [all data]
r(I)]
0.1138
0.3426
0.74, ꢁ0.49
1005076
D
CCDC
imax
;
D
imin (e Åꢁ3
)
0.83, ꢁ0.50
1005077
a
The solvent water molecule content was estimated from the electron density
attributed to the disordered solvent contribution by SQUEEZE
The molecular weight was calculated using disordered solvent and anion
molecules.
.
b
Table 2
Selected bond lengths (Å) of 1 and 2.
1
Ni1–N11
Ni1–N21
Ni1–N31
Ni1–N41
Ni1–O1
2.087(2)
2.062(2)
2.109(2)
2.069(2)
2.010(10)
2.061(12)
2.134(5)
Ni2–N51
Ni2–N61
Ni2–N71
Ni2–N81
Ni2–O2
2.105(2)
2.114(2)
2.049(2)
2.051(2)
2.023(10)
1.966(13)
2.204(6)
2.2. Physical measurements
Nickel content was determined by chelatometry after mineral-
ization of the complexes. Elemental analysis (C, H, N) was carried
out on Flash EA 1112 (ThermoFinnigan).
Ni1–O1I
Ni1–O1W
Ni2–O2I
Ni2–O2W
2
IR spectra were measured on Magna-FTIR-750 spectrometer
(Nicolet) in KBr pellets in the 4000–400 cmꢁ1 region. Electronic
spectra in the region 50000–10000 cmꢁ1 were recorded in the
Nujol mull on Specord 200 (Analytical Jena) spectrometer.
The single-crystal X-ray diffraction experiments were per-
formed using Xcalibur, sapphire CCD diffractometer (Oxford
Diffraction). The diffraction intensities were corrected for Lorentz
and polarization factors. The empirical absorption corrections were
performed by multi-scan method using SCALE3 ABSPACK in
Ni1–N1
Ni1–N2
Ni1–N3
2.110(5)
2.076(5)
2.086(5)
Ni1–N4
Ni1–O1
Ni1–O2
2.104(5)
2.045(4)
2.116(4)
Symmetry codes: (i) ꢁx + 1, ꢁy + 1, ꢁz + 1; (ii) ꢁx + 1, ꢁy, ꢁz + 1.
[Ni2(HCOO)(bz)8(H2O)2]3+ cations. Attempts in resolving the disor-
der adequately failed, and therefore, the utility SQUEEZE [29] in the
program PLATON [26] was used to remove diffuse electronic density.
The crystal structure of 1 contains in the unit cell one void of
1924 Å per cell containing 436 electrons, which represents three
formate anions and 4 molecules of water.
Temperature dependence of the magnetic susceptibility was
taken using SQUID magnetometer (MPMS, Quantum Design) at
the applied field of BDC = 0.1 T. Raw data were corrected for the
signal of the nylon-made sample holder as well as for underlying
diamagnetism using the set of Pascal constants [30]. The effective
CRYSALISPRO [22]. The structures were solved by the direct methods
with SHELXS-97 [23] or SIR-2011 [24], and refined by the full-matrix
least squares procedure with SHELXL-2014 [23]. Geometrical analy-
ses were performed using SHELXL-2014 and the structures were
drawn using the OLEX2 [25] and PLATON [26]. Final crystal data and
structure refinement parameters are given in Table 1. Selected
bond distances are listed in Table 2.
magnetic moment has been calculated as usual: leff
(
taken at T = 2.0, 4.6 and 20.0 K.
/lB = 798
The compound 1 forms poorly single crystals. More time was
tried to separate crystals for collecting data and only the best
crystal was used for structural analysis using. The refinement of
crystals structure of 1 had to be made using more constrains and
restrains. The complex cation [Ni2(HCOO)(bz)8(H2O)2]3+ of 1 has
been modeled using rigid-body constrains (FRAG/FEND) [27] and
rigid-bond restrains (RIGU) [28] for benzimidazole rings and
bridging formato ligand. The bridging formato ligand is disordered
occupying two statistical positions, represented by atoms
[O1,C1,O2]/[O1i,C1i,O2i] with site occupancy factors 0.54/0.46.
The uncoordinated formate anions and uncoordinated water mole-
v0T)1/2 when SI units are employed. The magnetization data was
2.3. Ab initio calculations
ORCA 3.0 computational package [31] was employed in all the
calculations using def2-TZVP(-f) basis set [32] for Ni, O and N
atoms and def2-SVP basis set for C and H atoms. Also, the RI
approximation with the decontracted auxiliary def2-TZV/J and
def2-SVP/J Coulomb fitting basis set or def2-TZV/C and def2-SVP/
C auxiliary basis sets for correlation calculations together with
cules in
1 are strongly disordered in the cavities between

K. Matelková et al. / Polyhedron 95 (2015) 45–53
47
and the chain-of-spheres (RIJCOSX) approximation to exact
exchange was utilized [33]. Increased integration grids (Grid4 in
ORCA convention) and tight SCF convergence criteria were used
in all calculations. The isotropic exchange parameters were calcu-
lated using DFT method and well-known B3LYP functional [34] by
Ruiz’s approach [35]. The zero-field splitting parameters determi-
nation was based on the state average complete active space
self-consistent field (SA-CASSCF) [36] wave functions comple-
mented by N-electron valence second order perturbation theory
(NEVPT2) [37]. The active space of the CASSCF calculation on
metal-based d-orbitals was CAS(8,5). The ZFS parameters, based
on dominant spin–orbit coupling contributions from excited states,
were calculated through quasi-degenerate perturbation theory
(QDPT), [38] in which an approximations to the Breit-Pauli form
of the spin–orbit coupling operator (SOMF approximation) [39]
and the effective Hamiltonian theory [40] were utilized. The spin
densities were plotted with program Gabedit [41].
3. Results and discussion
3.1. Crystal structure
The structure of 1 is built up of dinuclear [Ni2(HCOO)(bz)8
(H2O)2]3+ cations, uncoordinated formate anions and water mole-
cules (Fig. 1a). The nickel atoms are linked by a single bridging
formato ligand, which is disordered into two positions (Fig. 1b).
Each Ni(II) atom is hexacoordinate: in the equatorial plane four
nitrogen atoms from benzimidazole ligands coordinate [Ni–N
distances are in the range 2.049(2)–2.114(2) Å (Table 2)], and the
axial positions are occupied by the oxygen atoms from aqua
ligands [bond distances Ni1–O1W and Ni2–O2W are 2.134(5)
and 2.204(6) Å, respectively (Table 2)] and one oxygen atom of
the bridging formato ligand [Ni–O distances are in the range
1.966(13)–2.061(12) Å]. The formato bridging ligand is disordered
in two positions. Bond lengths of four nickel atoms in the two din-
uclear units are different (see Table 2). Cavities of space in the unit
cell including unsolved disordered uncoordinated formate anions
and water molecules are shown in Fig. 1c.
The complex 2 crystallizes in the monoclinic system, space
group P21/n (Fig. 2). The complex consists of a cation zig-zag chains
{[Ni(tren)(HCOO)]+}n, perchlorate anions and uncoordinated water
molecules. Each nickel atom is octahedrally bonded (Fig. 2a) by
four amine nitrogen atoms from tren molecule coordinated in a
tetradentate fashion [Ni–N distances are in the range 2.076(4)–
2.110(5) Å (Table 2)]. Two remaining coordination sites are occu-
pied by oxygen atoms from bidentate bridging formato ligands
[bond distances Ni1–O1 and Ni1–O2 are 2.045(4) and 2.116(4) Å,
respectively], ones from another unit forming a polymeric chain.
The bridging formato ligands are situated in cis positions of
the anti-anti mode. The formato ligands link metal ions to form
zig-zag chains running along a direction Fig. 2b. The framework
displays open channels, which are filled with perchlorate anions.
The zig-zag coordination chain of cation {[Ni(tren)(HCOO)]+}n,
perchlorate anions and water molecules are connected into 2D
supramolecular networks through N–HꢀꢀꢀO hydrogen bonds (see
Supplementary Information, Table S1) between amine groups of
the tren ligands and oxygen atoms of perchlorate anions or water
molecules (Fig. 2a). The water molecules are also connected trough
O–HꢀꢀꢀO hydrogen bonds between water molecules and oxygen
atoms of perchlorate anions or neighbouring water molecules.
Fig.
1. Crystal
structure
of
cation
[Ni2(HCOO)(bz)8(H2O)2]3+
in
[Ni2(HCOO)(bz)8(H2O)2](HCOO)3ꢀ4H2O: (a) molecular structure of cation
[Ni2(HCOO)(bz)8(H2O)2]3+, (b) detail of disordered bridging formato ligands, (c)
cavities plot of unsolved disordered formate anions and uncoordinated water
molecules.
infrared spectra show absorption band about 3600 cmꢁ1 referring
to the OH stretching vibration of the crystal water. The band of
stretching vibration at about 3300 cmꢁ1 and the band of bending
vibration at 1630 cmꢁ1 can be attributed to coordinated molecules
of water in the compound 1.
Infrared spectra of both complexes (Table 3) show intense and
sharp absorption bands of antisymmetric and symmetric stretch-
ing vibrations of COOꢁ group in the region 1587, 1592 and
1364–1394 cmꢁ1. The bands assigned to symmetric stretching
vibration are split into two subbands. The separation between
the antisymmetric stretch
s(COOꢁ), (COOꢁ), brings information about the bonding mode
of the carboxylato group [1]. The higher observed values of
(COOꢁ) 224 and 228 cmꢁ1 are higher relative to 201 cmꢁ1
observed in the IR spectrum of the solid sodium formate [42] or
m
as(COOꢁ) and symmetric stretch
m
D
3.2. Spectroscopic data
D
All typical features of the IR spectra are clearly compatible with
the structural characteristics of the complexes under study. The

48
K. Matelková et al. / Polyhedron 95 (2015) 45–53
The principal modes of vibration of NH2 group in the tren ligand
are symmetric and antisymmetric stretching (str), bending (bend),
scissoring (sci), wagging (wag), twisting (twi) and rocking (rock).
The very strong bands at 3344 and 3300 cmꢁ1 can be attributed
to NH2 str., strong band at 2885 to CH2 str. vibrations.
Assignment of other bands is as follows [44]: 1650 and
1606 cmꢁ1 to NH2 sci; 1465 cmꢁ1 to CH2 sci, wag; 1082 cmꢁ1 to
CH2 twi; 997 and 979 cmꢁ1 to NH2 twi; 805 cmꢁ1 to CH2 rock;
748 cmꢁ1 belong to NH2 rock modes. The stretching vibrations of
the NH2 groups are shifted towards lower frequencies if compared
with the vibrations of free amine [44] hence tren is coordinated.
The bands at 1106 and 624 cmꢁ1 in 2 are assigned to the
perchlorate anion.
The electronic spectra (Table 3) of the complexes under study
show three d–d bands at 8900–11 000, 16 400–17 800, and
27 500–28 300 cmꢁ1, respectively. The number of bands, their
widths and the positions of the absorption maxima of these bands
indicate tetragonally distorted octahedral configuration of the
ligands around Ni(II) [45]. The bands may be assigned to the
3
spin allowed transition T2g 3A2g
,
3T1g(F) 3A2g
,
3T1g(P) 3A2g
in octahedral approximation.
3.3. Ab initio calculations
Contemporary theoretical methods were applied to compounds
1 and 2 in order to calculate both the isotropic exchange constants
J and zero-field splitting parameters D and E for Ni(II) ions using
the ORCA computational package. First, the DFT method with
B3LYP functional was used to calculate energy difference
between high spin (HS) and broken-symmetry (BS) spin states.
D
D
¼ EBS ꢁ EHS
ð1Þ
for both dinuclear molecular fragments [Ni2(HCOO)(bz)8(H2O)2]3+
of 1 based on a disorder in bridging ligand found in experimental
X-ray structure, where following spin Hamiltonian for dimer was
used
^
~ ~
H ¼ ꢁJðS1 ꢀ S2Þ
ð2Þ
The isotropic exchange J-values were calculated by Ruiz’s
approach.
J ¼ 2 =½ðS1 þ S2ÞðS1 þ S2 þ 1Þꢃ
D
ð3Þ
The BS state was found lower in energy in both fragments of 1,
thus confirming antiferromagnetic exchange mediated by formate
ions with following quantities: J = ꢁ16.4 cmꢁ1 for molecular
fragment comprising [O1, C1, O2] atoms of formato bridge (site
occupancy factors 0.54) and J = ꢁ14.2 cmꢁ1 for molecular fragment
comprising [O1i, C1i, O2i] atoms of formato bridge (site occupancy
factors 0.46). These results show sensitivity of J-value to small
geometry change of bridging ligand. The spin density for BS spin
state of 1 is visualized in Fig. 3, where partial spin delocalization
on all N/O donor atoms of the chromophore is visible.
In case of polymeric compound 2, dinuclear [Ni2(tren)2
(HCOO)3]+, trinuclear [Ni3(tren)3(HCOO)4]2+ and pentanuclear
[Ni5(tren)5(HCOO)6]4+ molecular fragments were used in
calculation of J-parameter to test whether the computed J differs
depending on the size of model system. The calculation for
dinuclear unit using Eqs. (1)–(3) resulted in J = ꢁ12.3 cmꢁ1. For
trinuclear unit following spin Hamiltonian was used
Fig. 2. Crystal structure of 2 showing the atom labelling scheme (a) and zig-zag
coordination chain of 2 (b).
Table 3
IR and ligand-field data (cmꢁ1).a
1
2
m
m
D
E1(3T2g
s(COOꢁ)
1363, 1393
1587
224, 194
11000
1364, 1394
1592
228, 198
8900
as(COOꢁ)
m
(COOꢁ)
3A2g)/hc = 10Dq
(8200)
E2(3T1g(F) 3A2g)/hca
E3(3T1g(P) 3A2g)/hc
17800
27500
16 400
(13500)
28 300
(26 900)
a
Band-arms in parentheses.
^
~
~
~ ~
H ¼ ꢁJðS1 ꢀ S2 þ S2 ꢀ S3Þ
ð4Þ
209 cmꢁ1 of nickel formate dihydrate [43]. The positions of car-
boxylate stretching vibrations and the separation between them
in 1 and 2 are in the range expected for bridging carboxylato
ligands [1].
for which J-parameter was calculated as
J ¼
D2=6
ð5Þ

K. Matelková et al. / Polyhedron 95 (2015) 45–53
49
for 2. The contributions of excited states to ZFS terms are tabulated
in Tables S2–S3 (Supplementary Information). Thus, in both
complexes 1 and 2 the positive D-parameter was found and also
significant rhombicity.
The axes of calculated ZFS and g-tensors together with molecu-
lar structures are visualized in Fig. 4. In both cases, g-tensor and
ZFS-tensor axes almost coincide, with following g-tensor parame-
ters: g1 = 2.173, g2 = 2.233, g3 = 2.264 for
1 and g1 = 2.181,
g2 = 2.193, g1 = 2.200 for 2. Z-axes of ZFS tensor lies along O–Ni–
O bonds, while other two axes (X and Y) lies along N–Ni–N bonds
in 1. In compound 2, the Z-axis of ZFS tensor is approximately
located along N1–Ni–O2 bonds, that means, along bonds which
are the longest within given chromophore, and X and Y axis are
found in plane defined by N2N3N4O1 atoms, but not strictly
located along donor–acceptor bonds (Fig. 4).
Fig. 3. The calculated the isodensity surfaces of the broken symmetry spin states
using B3LYP for [Ni2(HCOO)(bz)8(H2O)2]3+ of 1 (left) and [Ni2(tren)2(HCOO)3]+ of 2
(right). Positive and negative spin densities are represented by violet and yellow
surfaces with the cutoff values of 0.01 e bohꢁ3, respectively. (For interpretation of
the references to color in this figure legend, the reader is referred to the web version
of this article.)
3.4. Magnetic data
The temperature dependence of the effective magnetic moment
for 1 is shown in Fig. 5 on the left. On cooling it starts to decrease at
150 K which is a fingerprint of the exchange interaction of an
antiferromagnetic nature. The susceptibility passes through a
round maximum at ca 20 K that matches the antiferromagnetic
coupling and S = 0 ground state. Small hook at the lowest temper-
ature of the data taking is attributed to a paramagnetic impurity.
Also the magnetization measurements agree with J < 0 since the
magnetization increases with temperature (the excited S = 1 and
S = 2 states being populated).
where D2 = EBS2 ꢁ EHS. The J-values was found to be equaled to
ꢁ11.7 cmꢁ1. Finally, the spin Hamiltonian for pentanuclear unit
(with labeling of Ni atoms: 1-2-3-4-5) was postulated as
^
~
~
~
~
~
~
~ ~
H ¼ ꢁJaðS1 ꢀ S2 þ S4 ꢀ S5Þ ꢁ JbðS2 ꢀ S3 þ S3 ꢀ S4Þ
ð6Þ
where Ja is the isotropic exchange affected by the ends of the chain,
while Jb is the parameter describing the exchange inside the chain.
Then, J-parameters can be evaluated by these expressions
The magnetic data of 1 was interpreted in terms of the spin
Hamiltonian appropriate to an exchange coupled dinuclear unit
(J) with S1 = S2 = 1 and single-ion zero-field splitting (D).
D3 ¼ EBS3 ꢁ EHS ¼ 6Jb
ð7Þ
2
2
X
X
ꢀꢁ2
Þ ¼ ꢁJh ðS1 ꢀ S2Þ þ
ꢀꢁ2
ꢀꢁ1
2
^
2
^
^
~
~
^
D24 ¼ EBS24 ꢁ EHS ¼ 6Ja þ 6Jb
ð8Þ
Hmð#;
u
Dh ðSAz ꢁ SA=3Þ þ
lBh B gASA
A¼1
A¼1
which ended at Ja = ꢁ12.7 cmꢁ1 and Jb = ꢁ11.6 cmꢁ1. To conclude,
ð9Þ
the calculated antiferromagnetic exchange slightly decreases with
size of the model as follows: Jdimer = ꢁ12.3 cmꢁ1 ? Jtrimer
=
The final calculated molar magnetization was calculated as an
integral average in order to properly simulate powder sample
signal as
ꢁ11.7 cmꢁ1 ? Jpentamer = ꢁ11.6 cmꢁ1. Generally, DFT calculations
of J-values led to moderate antiferromagnetic exchange in both
compounds 1 and 2.
Z
Z
2
p
p
Mmol ¼ 1=4
p
Ma sin hdhd
u
ð10Þ
The calculations of ZFS parameters were performed on
mononuclear molecular fragments [Ni(HCOO)(bz)4(H2O)]+ of 1
and [Ni(tren)(HCOO)2] of 2 using CASSCF/NEVPT2 methodology
with active space defined by metal-based d-orbitals (CAS(8,5)).
These calculations resulted in following ZFS parameters: D =
+ 10.1 cmꢁ1 and E/D = 0.21 for 1 and D = +2.1 cmꢁ1 and E/D = 0.24
0
0
First, the fitting procedure was done for positive D-parameter
following results from ab initio calculations and resulted in this
set of magnetic parameters: J/hc = ꢁ13.0 cmꢁ1
, giso = 2.093,
D/hc = +11.2 cmꢁ1, mole fraction of the paramagnetic impurity
Fig. 4. The CASSCF/NEVPT2 calculated principal axes of ZFS tensors labeled DX,DY,DZ and axes of g tensors labeled as g1,g2, g3 visualized together with molecular structures
[Ni(HCOO)(bz)4(H2O)]+ of 1 and [Ni(tren)(HCOO)2] of 2.

50
K. Matelková et al. / Polyhedron 95 (2015) 45–53
Fig. 5. Magnetic functions for 1. Temperature dependence of the effective magnetic moment (inset: molar magnetic susceptibility) and field dependence of the magnetization
per formula unit. Lines – fitted. Left: fit with D > 0, right – fit with D < 0.
Fig. 6. Magnetic functions for 2. Temperature dependence of the effective magnetic moment (inset: molar magnetic susceptibility/magnetization) and field dependence of
the magnetization (T = 2 and 4.6 K) scaled per one Ni(II) ion. Blue lines – fitted, red line – Brillouin function. Left: fit with Eqs. (11, 12), right – fit with Eqs. (13, 14). (For
interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
xPI = 1.07%. Both crucial fitted parameters, J and D, are in very good
agreement with the calculate ones. Next, we also tried to fit the
magnetic data for negative D-parameter, which resulted in:
J/hc = ꢁ12.8 cmꢁ1, giso = 2.096, D/hc = ꢁ16.3 cmꢁ1, and xPI = 1.30%.
Both fits describe experimental data in similar quality, thus this
emphasize the importance of theoretical methods in magnetic
analysis.
The magnetic data of the 1D chain compound 2 shows again
antiferromagnetic exchange among paramagnetic Ni(II) atoms
supported by maximum of susceptibility found at 18 K (Fig. 6)
and data were analyzed by two approaches. First, the spin
Hamiltonian for a 1D uniform chain (Haldane chain) with Si = 1
reads.
The exchange coupling of ten Ni(II) centers leads to the number
N = 310 = 59049 magnetic states; such large interaction matrix
cannot be efficiently diagonalized. In a simplified way (strong
exchange limit), having the energy levels labeled as ei
ð
a
SMSÞ ¼
e0;k
ða
SÞ þ lBgBMS, the molar magnetization can be easily calcu-
lated as
X
MS exp ½ꢁei
ð
a
SMSÞ=kTꢃ
i
X
Mmol ¼ NA
lBg
ð14Þ
exp ½ꢁei
ða
SMSÞ=kTꢃ
i
The fitting procedure resulted in the following set of magnetic
parameters: J/hc = ꢁ10.8 cmꢁ1, g = 2.166, xPI = 1.96%, so that the
coupling constant agrees well with the Haldane chain approach.
As both approaches describes the experimental data reliably with-
out including ZFS terms, we can suppose that strong exchange
limit holds (|J| ꢄ |D|) as found by ab initio calculations and detec-
tion of D-parameter cannot be pursuit from magnetic data alone, as
we discussed in depth for similar system recently [47].
1
1
X
X
ꢀꢁ2
^
H ¼ ꢁJh
ꢀ
~
~
^
ðSi ꢀ Siþ1Þ þ
l
Bhꢁ1B g Siz
ð11Þ
i
i¼1
i¼1
for which the susceptibility formula exists [46].
NAl0l2Bg2
vmol
¼
½0:125 expðꢁ0:451xÞ þ 0:564
kBT
The exchange coupling in dinuclear Ni(II) complexes can be of
ferromagnetic as well as antiferromagnetic nature, as documented
by a few examples in Table 4. The single-ion zero-field splitting
ꢂ expðꢁ1:793xÞꢃ
ð12Þ
The calculated values, J/hc = ꢁ11.0 cmꢁ1, g = 2.158, xPI = 1.98%,
confirm an intermediate antiferromagnetic coupling between Ni
ions (xPI is molar fraction of monomeric paramagnetic impurity).
In order to be able to interpret also the isothermal magnetiza-
tion data, the spin Hamiltonian for the decanuclear ring was
postulated as
parameter
D has been reported either positive or negative.
According to the spin-Hamiltonian theory for hexacoordinate
Ni(II) complexes, D > 0 are expected for an elongated tetragonal
bipyramid whereas D < 0 is typical for the compressed form [63].
Apparently, the exchange coupling constants vary in a broad
range. The structure of the complex plays a key role, as it is shown
in Table 4 and this finding is supported also by literature sources
[52–62]. For instance, magnetic exchange interactions mediated
by azido ligands in complexes depend upon a bridging mode: for
"
#
9
10
X
X
ꢀꢁ2
¼ ꢁJh
ꢀꢁ1
ring
^
~
~
~
~
~
~
H
Si ꢀ Siþ1 þ S10 ꢀ S1
þ
l
Bh g B Si
ð13Þ
i
i

K. Matelková et al. / Polyhedron 95 (2015) 45–53
51
Table 4
Examples of magnetic data for dinuclear Ni(II) complexes, tetranuclear Ni(II) pseudohalido complexes and polynuclear Ni(II) complexes.
Complex*
Chromophore
Bridge
J/hc /cmꢁ1**
D/hc /cmꢁ1
gav
Ref.
Dinuclear Ni(II) complexes
[Ni2(trpn)2(
l
1,3-N3)2](ClO4)2e
{NiN4N02
}
N3ꢁ
ꢁ64
2.34
2.24
[48]
[49]
[Ni2(L2)(CH3COO)(H2O)2](ClO4)2b
[Ni2(L2)(OPr)(H2O)2](ClO4)2.H2Ob
[Ni2(HCOO)(bz)8(H2O)2](HCOO)3ꢀ4H2O
{NiN3OO’O’}
{NiN3OO0O0}
{NiN4OO0}
CH3COOꢁ
alkoxido of L2
C2H5COOꢁ
alkoxido oxygen
HCOOꢁ
ꢁ43.3
ꢁ34.4
2.09
[49]
ꢁ13.0
ꢁ12.8
ꢁ3.7
11.2
ꢁ16.3
0.07
2.093
2.096
2.27
This work
This work
[50]
{[Ni(L1)(
l
1,1-NCS)Ni(L1)(NCS)(OH2)]
-CH3COO)Ni(L1)(NCS)(OH2)]}h
{Ni1N3OO0N0}
{Ni2N2O2O0N0}
{Ni3N2O2O0O0}
{Ni4N3OO0O0}
{NiN5N0}
phenoxido oxygen
[Ni(L1)(
l
SCNꢁ
phenoxido oxygen
CH3COOꢁ
[Ni2(
l
-trien)(trien)2](ClO4)4
trien pod
ꢁ1.68
ꢁ1.90
ꢁ0.58
3.46
0.0
9.85
2.58
ꢁ3.84
2.10
2.14
2.122
2.10
[44]
[51]
[52]
[53]
[Ni2L2(N(CN)2)2(H2O)]c
[{Ni(dpt)(N(CN)2)}2]
[Ni2(HL3)4(H2O)]d
{NiN2O2N02
{NiN3N03
}
N(CN)ꢁ2
}
N(CN)ꢁ2
{NiN2OO02O00}
phenoxido oxygen
H2O
phenoxido oxygen
[Ni2(HL2)4(H2O)]d
{NiN2OO02O00}
3.72
ꢁ3.56
2.12
[53]
H2O
[{Ni(teta)(tcm)}2](ClO4)2
[Ni2(HL1)4(H2O)]d
{NiN4N02}
{NiN2OO02O00}
C(CN)ꢁ3
3.75
4.92
2.119
2.091
[54]
[53]
phenoxido oxygen
ꢁ2.11
H2O
[{Ni2(en)4Cl2}]Cl2
{NiN4Cl2}
Clꢁ
9.66
12.4
ꢁ4.78
ꢁ0.22
2.242
2.19
[55]
[50]
[Ni(L1)(
l
1,1-NCO)Ni(L1)(NCO)(OH2)]ꢀH2Oh
{Ni1N2O2O0N0}
{Ni2N3OO0N0}
phenoxido oxygen
OCNꢁ
[Ni2(L1)(N3)4]a
{NiN4N02
}
N3ꢁ
43.6
25.4
2.28
2.27
[56]
[57]
[Ni2L2(o-(NO2)C6H4COO)2(H2O)]f
{NiN2OO0O020 }
{NiN2O2O0O00}
{NiN2OO0O020 }
phenoxido oxygen
H2O
H2O
phenoxido oxygen
phenoxido oxygen
H2O
3.20
0.17
2.80
ꢁ7.3
ꢁ6.41
6.8
[Ni2L2(PhCH2COO)2(H2O)]c
26.2
28.1
33.2
33.84
51.2
78.0
2.21
2.23
2.2
[51]
[57]
[58]
[58]
[50]
[50]
[Ni2L2(p-(NO2)C6H4COO)2(H2O)]ꢀ0.5CH3OHf
[Ni2(L1)2(
l
l
1,1-N3)(N3)(H2O)]ꢀCH3CH2OHg
{Ni1N3OO0N0}
{Ni2N2O2O0N0}
{Ni1N3OO0N0}
{Ni2N2O2O0N0}
{NiN2O2O0N0}
phenoxido oxygen
N3ꢁ
[Ni2(L2)2(
1,1-N3)(CH3CN)(H2O)](ClO4)ꢀH2OꢀCH3CNg
phenoxido oxygen
2.2
N3ꢁ
[Ni(L1)(
l
1,1-N3)Ni(L1)(N3)(OH2)]ꢀH2Oh
phenoxido oxygen
2.20
2.27
N3ꢁ
N3ꢁ
[Ni(L2-OMe)(
l
1,1-N3)(N3)]i2
{NiN4N02
}
7.3
Tetranuclear Ni(II) pseudohalide complexes
[Ni2(dpk.OH)(dpk.CH3O)(N3)(H2O)]2(ClO4)2ꢀ2H2Oj
{NiN2O2N0O0}
{NiN2O2N0O0}
{NiN2O2N0O0}
l
l
l
l
l
l
l
l
-1,1-N3
-O
-1,1-NCO
-O
-1,1-NCO
-O
-1,1-NCO
-O
J1 = J2 = +11.2
J3 = +23.6
J1 = J2 = +11
J3 = +24.0
J1 = J2 = +12.6
J3 = +9.8
5.6
5.6
6.2
4.8
2.03
2.03
2.21
2.06
[59]
[59]
[59]
[59]
[Ni2(dpk.OH)(dpk.CH3O)(NCO)(H2O)]2(ClO4)2ꢀ2H2Oj
[Ni2(dpk.OH)(dpk.CH3O)(NCO)(H2O)]2(NO3)2ꢀ2H2Oj
[Ni4(dpk.OH)3(dpk.CH3O)2(NCO)](BF4)2ꢀ3H2Oj
{Ni1N3N0O02
}
+13.8
+14.0
{Ni2N2O04
{Ni3N3O03
}
}
+30.4
{Ni4N2N0O03
}
Polynuclear Ni(II) complexes
[Ni(HCOO)2(4,40-bpy)]ꢀ5H2O
{NiN2O2O02
{NiN2OO03
}
HCOOꢁ
H2P2O27ꢁ
N3ꢁ
tren pod
C2O24ꢁ
C2O24ꢁ
N3ꢁ
ꢁ19.4
ꢁ1.88
ꢁ26.8
ꢁ1.19
ꢁ28.0
ꢁ31.3
ꢁ33.4
ꢁ63.7
ꢁ74.2
ꢁ10.8
2.23
2.09
2.36
2.16
2.23
2.13
2.35
[12]
[60]
[48]
[44]
[61]
[61]
[48]
k
{[Ni(phen)(H2O)(H2P2O7)]ꢀH2O}n
}
cis-[Ni(Me6trien)(
l
1,3-N3)]n(ClO4)nꢀnH2Oo
{NiN4N02
{NiN4N02
{NiN2O04
{NiN2O04
{NiN4N02
}
}
}
}
}
{[Ni2(
l
-tren)2(tren)](ClO4)4ꢀ3.25H2O}np
l
[Ni(
[Ni(
l
-ox)(pyOH)2]n
m
l-ox)(isq)2]n
n
cis-[Ni(abap)(l1,3-N3)]n(ClO4)n
p
{[Ni2(
l
1,1-N3)(
l
1,3-N3)(L)2(MeOH)2]}n
{NiO2N3N0}
{NiN4O2}
N3ꢁ
2.15
2.166
[62]
This work
[Ni(tren)(HCOO)]ClO4ꢀH2O
HCOOꢁ
Abbreviation for ligands: 4,40-bpy = 4,40-bipyridine; bz = benzimidazole; teta = triethylenetetramine (abbr. also tta); tcm = C(CN)ꢁ3 , tricyanomethanide; en = 1,2-diamino-
*
propane (ethylenediamine); a 1 = hexadentate Schiff base ligand made from the reaction of 2 mol of 2-benzoyl pyridine and 1 mol of triethylenetetramine; bHL2 = N,N,N0,N0-
L
tetrakis[(l-ethyl-2-benzimidazolyl)methyl]-2-hydroxy-l,3-diaminopropane; bOPr = propionate anion; cHL = 1-[(3-dimethylamino-propylimino)-methyl]-naphthalen-2-ol;
dH2L1 = Schiff base ligand from 5-amino-1-pentanol and salicylaldehyde, H2L2 = 5-bromo salicylaldehyde, H2L3 = 3-methoxy salicylaldehyde; etrpn = tris(3-amino-
propyl)amine; fHL = 1-[(3-dimethylamino-propylimino)-methyl]-naphthalen-2-ol; gHL1 and HL2 = are the [1 + 1] condensation products of 3-methoxysalicylaldehyde and 1-
(2-aminoethyl)-piperidine (for HL1)/4-(2-aminoethyl)-morpholine (for HL2); hL1 = Me2N(CH2)2NCHC6H3(Oꢁ)(OCH3); iL2 = Me2N(CH2)2NCHC6H3N; jdpk = di-2-pyridylketone,
dpk.OH and dpk.CH3O result from solvolysis and deprotonation of dpk in water and methanol; kphen = 1,10-phenanthroline; lpyOH = 3-hydroxypyridine; misq = isoquinoline;
nabap = N-(2-aminoethyl)-N,N-bis(3-aminopropyl)amine; oMe6trien = 1,1,4,7,10,10-hexamethyltriethylene tetramine; pLꢁ = 1,1,1-trifluoro-7-(dimethylamino)-4-methyl-5-
aza-3-hepten-2-onato).
ꢀꢁ2
**
^
~ ~
All J-parameters conform the Hamiltonian term Hij ¼ ꢁJijh ðSi ꢀ SjÞ.

52
K. Matelková et al. / Polyhedron 95 (2015) 45–53
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l-N3(j-N1, N3) type the antiferromagnetic exchange
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vary seriously (from ꢁ74.2 to +78.0 cmꢁ1). In addition, bridging
modes of formato and azido ligands are similar and this fact could
be essential in building up new complexes. The azido ligand along
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ranging from ꢁ1.19 cmꢁ1 for the tren bridge to ꢁ74.2 cmꢁ1 for
the azido coligand.
It must be mentioned that in considering the variability of the J
values some qualitative as well as quantitative magnetostructural
J-correlations have been proposed for Ni(II) complexes [64,65].
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4. Conclusion
The formato-bridged assemblies of formula [Ni2(HCOO)(bz)8
(H2O)2](HCOO)3ꢀ4H2O (1) and [Ni(tren)(HCOO)]ClO4ꢀH2O (2) were
prepared. The X-ray analysis revealed dinuclear structure in
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This work is supported by Slovak Grant Agency (VEGA 1/0522/
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