Stereochemistry of coordination polyhedra: Vs. single ion magnetism in penta- And hexacoordinated Co(ii) complexes with tridentate rigid ligands

Article abstract of DOI:10.1039/c9dt04592a

A tridentate ligand L (2,6-bis(1-(3,5-di-tert-butylbenzyl)-1H-benzimidazol-2-yl)pyridine) was synthesized and used for the preparation of three pentacoordinated Co(ii) complexes of formula [Co(L)X₂] (where X = NCS^- for 1, X = Cl^- for 2 and X = Br^- for 3) and one ionic compound 4 ([Co(L)₂]Br₂·2CH₃OH·H₂O) containing a hexacoordinated Co(ii) centre. Static magnetic data were analysed with respect to the spin (1-3) or the Griffith-Figgis (4) Hamiltonian. Ab initio calculations enable us to identify the positive axial magnetic anisotropy parameter D accompanied by a significant degree of rhombicity in the reported complexes. Also, magneto-structural correlation was outlined for this class of compounds. Moreover, all four compounds exhibit slow relaxation of magnetisation at an applied static magnetic field with either both low- and high-frequency relaxation channels (3) or a single high-frequency relaxation process (1, 2 and 4). The interplay between the stereochemistry of coordination polyhedra, magnetic anisotropy and the relaxation processes was investigated and discussed in detail.

Full text of DOI:10.1039/c9dt04592a

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Matejova, J. Moncol, R. Herchel, J. Pavlik, E. Moreno-Pineda, M. Ruben and I. Salitros, Dalton Trans.,
2020, DOI: 10.1039/C9DT04592A.
Volume 46
Number 10
14 March 2017
Pages 3073-3412
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Stereochemistry of Coordination Polyhedra vs. Single Ion Magnetism in
Penta- and Hexacoordinated Co(II) Complexes with Tridentate Rigid Ligand
Barbora Brachňaková,a Simona Matejová,a Ján Moncol,a Radovan Herchel,b Ján Pavlik,a Eufemio
Moreno-Pineda,c Mario Ruben,c,d Ivan Šalitroša,b,e
*
a) Department of Inorganic Chemistry. Faculty of Chemical and Food Technology. Slovak University
of Technology in Bratislava. Bratislava SK-81237, Slovakia. *e-mail: ivan.salitros@stuba.sk
b) Department of Inorganic Chemistry. Faculty of Science, Palacký University, 17. listopadu 12, 771 46
Olomouc, Czech Republic
c) Institut für Nanotechnologie, Karlsruher Institut für Technologie, Postfach 3640, Karlsruhe 76021.
Germany;
d) Institute de Physique et Chimie de Matériaux de Strasbourg (IPCMS), CNRS-Université de Strasbourg,
23, rue du Loess, BP 43 67034 Strasbourg cedex 2, France
e) Central European Institute of Technology, Brno University of Technology, Purkyňova 123, 61200
Brno Czech Republic
Abstract: The tridentate ligand L (2,6-Bis(1-(3,5-di-tert-butylbenzyl)-1H-benzimidazol-2-yl)pyridine)
was synthetized and used for the preparation of three pentacoordinate Co(II) complexes of the formula
[Co(L)X2] (where X=NCS for 1, X=Cl for 2 and X=Br for 3) and one ionic compound 4
([Co(L)2]Br2.2CH3OH.H2O)) containing a hexacoordinated Co(II) centre. The static magnetic data were
analysed with respect to the spin (1-3) or the Griffith-Figgis (4) Hamiltonian. An ab initio calculations
enable to identify the positive axial magnetic anisotropy parameter D accompanied by a significant degree
of rhombicity in the reported complexes. Also, the magneto-structural correlation was outlined for this class
of compounds. Moreover, all four compounds exhibit slow relaxation of magnetisation at applied static
magnetic field with either both low- and high-frequency relaxation channels (3) or with the single high-
frequency relaxation process (1, 2, 4). The interplay between stereochemistry of coordination polyhedra,
magnetic anisotropy and the relaxation processes was investigated and discussed in detail.
Introduction
Mononuclear Co(II) complexes showing the slow magnetic relaxation are attractive family of single-
molecule magnets (SMMs),1 due to the significant attention paid to the molecular magnets having only one
metal centre, considerable anisotropy, no intermetallic interactions, terming these molecules single-ion
magnets (SIMs).2 In general, the main characteristic feature of SMMs is the presence of magnetic hysteresis
originating at the molecular level. Therefore the importance of these molecules relies in their potential
applications in molecular switches, sensors, spintronics or data storage nanotechnology.3 The magnetic
bistability based on the hysteresis loop is related to the existence of the energy barrier of spin reversal (U).
In the case of 3d-metal complexes, U is usually related to the zero-field splitting (ZFS)4 of the ground spin
state as U =|D|S2 for an even and U = |D|(S2 − 1/4) for odd number of unpaired electrons in the valence shell
of metal ion, where D is the axial ZFS parameter defined within the spin Hamiltonian formalism. Thus, the
interesting feature of SIMs lies in the probable prediction of magnetic anisotropy established from ligand
field theory. In other words, the magnetic anisotropy of mononuclear complexes can be tuned by the rational
design of the ligand field strength of the utilized ligands and their coordination geometry around the central
atom.5

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In parallel with the extensive study on lanthanide-based SIMs,6 Co(II) complexes are also excellent
candidates for the synthesis of SIMs due to their high magnetic anisotropy and strong first order spin-orbit
coupling among 3d metals.2 The first two pentacoordinate mononuclear Co(II) complexes exhibiting slow-
relaxation of magnetization reported by Jurca et al.7 inspired the further exploration of molecular magnetism
in tetra-,8 penta-9, hexa-10 or heptacoordinated11 mononuclear Co(II) complexes. This chemistry is well-
developed and in recent years it continues to reveal new and interesting magnetic properties derived from
the molecular geometry of these complexes. However, the goal-directed control in the synthesis of Co(II)
complexes of a desired magnetic behaviour still remains a considerable challenge, and much more work is
required to extend our knowledge of the structure − property relationship. In this content, the
pentacoordinate Co(II) complexes with one rigid terpy-like tridentate ligand (terpy = 2,6-bis(2-
pyridyl)pyridine) and two terminal ligand anions present exciting family of the field induced SIMs, where
the correlation between the geometry of coordination polyhedra and the magnetic anisotropy might help to
understand the impact of the molecular design on relaxation dynamics. Since the three bonds of metal centre
with the rigid N3-donor ligand are fixed, the coordination polyhedron is usually affected by non-Berry Y or
T angular distortion,12 which also leads to the transformation of trigonal bipyramid (TBPY, D3h) to the
square pyramid (SPY, C4v), similarly to the ideal Berry pseudo-rotation pathway. Based on the Addison
parameter (τ5),13 which quantitatively express the degree of interconversion between TBPY(τ5=1) and
SPY(τ5=0), the majority of to date reported complexes in this family shows intermediate geometry between
those two shapes, but often much closer to the later one. 9b-d,14 Additionally, it has been shown that the
chemical nature of two terminal ligand anions does not have a significant impact on the degree of TBPY-
SPY interconversion9b-d and TBPY geometry predominates only in the systems with flexible terpy-like N3-
donor ligands containing aliphatic spacers between the individual aromatic N-donor moieties.15 The axial
ZFS parameter in such pentacoordinate Co(II) complexes with terpy-like N3-donor ligands varies in the
wide range from -41 to +151 cm-1, and the magneto-structural correlation suggests the growing trend of D
with decreasing value of τ5.9b On the other hand, the hexacoordinated Co(II) complexes exhibit distorted
octahedral geometry often influenced by interconversion to trigonal prism geometry (Bailar twist). This can
lead to a huge magnetic anisotropy and hence large U as well.
The dynamic magnetic study of Co(II) complexes often proves the presence of the field-induced slow
relaxation, which at high external static magnetic field (BDC > 0.2T) has occasionally multiple relaxation
character. The low-frequency relaxation channels with the high relaxation times τ (100 – 10-2 s) are usually
based on the existence of intermolecular dipole-dipole interactions within the crystal lattice8-10,14,15 and can
be suppressed by the decrease of BDC field. On the other hand, the fast relaxation channels are of pure
퐴퐵푚푇
-4
-9
molecular nature (τ ≈ 10 – 10 s) and their analysis requires the combination of Direct (
) + Orbach
휏1 푒푥푝 ( ― 푈eff
)
퐴퐵푚푇
) or Direct (
퐶푇푛
) mechanism of spin reversal (vide infra, eq. 5).10b
(
) + Raman (
푘푇
0
퐴, 휏 , 푈 , 퐶
Apparently, the relaxation parameters
have the essential impact on the overall relaxation time
0
eff
τ at the given temperature, and therefore the understanding of their relation with the structural features of
Co(II) SIMs presents one of the pivotal challenge in this area of molecular magnetism.9b,9d
Herein we report on four novel Co(II) SIMs containing the terpy-like N3-donor aromatic ligand and
pseudohalide or halide anions. Careful molecular design and goal-directed synthesis allowed to prepare
derivative of 2,6-bis(1H-benzimidazol-2-yl)pyridine ligand (L) functionalised with bulky 3,5-bis(tert-
butyl)benzyl substituents (Scheme 1). The corresponding pentacoordinate Co(II) complexes 1
([Co(L)(NCS)2]), 2 ([Co(L)Cl2]) and 3 ([Co(L)Br2]) were prepared by variation of pseudohalido or halido
terminal ligand anions, while compound 4 ([Co(L)2]Br2∙2CH3OH∙H2O) contains Co(II) metal centre in
pseudooctahedral environment. All four compounds were spectrally, and structurally characterised and
their static and dynamic magnetic properties allowed to analyse ZFS parameters and the slow relaxation

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mechanisms, respectively. Quantitative magnetic analysis was confronted with theoretical calculations at
CASSCF level testing also the effects of different dynamic electron correlation methods (NEVPT2 vs.
DCD-CAS(2)), double-shell effect and the relativistic effects.
Scheme 1 Molecular structures of the tridentate ligand L, the neutral complexes 1-3 and the complex cation
of compound 4.
Results and Discussion
Synthesis and structural investigation
The detailed synthetic procedures, characterisation of ligand L and the reported complexes 1-4 are described
in experimental section (see electronic supporting information (ESI)). The tridentate ligand L was prepared
by reaction of 2,6-bis(1H-benzimidazol-2-yl)pyridine16 with 3,5-di-tert-butylbenzyl bromide in the DMSO
solution under basic conditions. Nucleophilic substitution afforded two products, which were successfully
separated using the column chromatography. The desired disubstituted ligand L was collected in 61% yield
as the main product and the monosubstituted side-product L1 was obtained in 15% yield. The
pentacoordinate complexes 1-3 were prepared in acetonitrile solution by complexation of ligand L with
corresponding Co(II) salt, which was used in the small excess to prevent the formation of hexacoordinated
complexes. Compound 4 was prepared in a methanol solution using the small excess of L to prevent the
formation of pentacoordinate complex (Scheme 1). The phase purity of obtained polycrystalline materials
was investigated by powder X-ray diffraction spectroscopy prior to all further spectroscopic and magnetic
investigations (Figure S1.5, see ESI). In order to investigate the dynamic magnetic properties of diluted
compounds, we attempted to prepare Zn(II) doped complexes 1-4. However, in all four cases the synthesis
ended up to the suspension of dissolved corresponding Co(II) complex and precipitated hexacoordinate
Zn(II) complex, which crystal symmetry in the case of doping of 4 does not match with the symmetry of
the hexacoordinate Co(II) complex (Figure S1.5d, see ESI).
Single crystal diffraction experiments confirmed the expected molecular structures of compounds 1-4
(Figure 1) and selected crystallographic parameters are listed in Table 1. At 100 K, the pentacoordinate
complexes 1-3 crystallise in monoclinic C2/c (1) or P21/c (2, 3) space groups and the asymmetric unit of
each structure consists of one molecule of neutral complex expressed by general formula [Co(L)X2] (X =
NCS- for 1, Cl- for 2, Br- for 3). Eight (1) or four (2, 3) complex molecules are included in the respective
unit cell and all three structures do not contain any lattice solvent molecules. Complexes 2 and 3 are
isomorphic and isostructural to each other. Compound 4 crystallises in the triclinic P-1 space group and

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two asymmetric units expressed by formula [Co(L)2]Br2·2CH3OH·H2O are present in the unit cell. The
pentacoordinate Co(II) metal ion is surrounded by three nitrogen donor atoms of the tridentate ligand L,
and the two remaining coordination sites are occupied either by N donor atoms of the isothiocyanato ligand
anion in 1 or by two halido anions Cl- and Br- in 2 and 3 (Figure 1). Co-N distances formed between central
atom and the tridentate chelating ligand L vary in the narrow range 2.092(2) - 2.123(2) Å and their values
indicate the high-spin state of central atom (Figure 1). The Co-N3 bond involving the pyridine nitrogen
donor atom is shortened comparing to bonds formed with imidazole moieties (2.118(2) Å) in the
coordination polyhedron 1, while the reverse situation is observed in polyhedra of 2 and 3 (Figure 1). It is
interesting to note, that the latter case found in 2 and 3 is predominant in the so far reported similar
complexes and elongation or shortening of the imidazole Co-N distances does not depend neither on the
type of terminal ligands nor on the degree of interconversion between square planar and trigonal
bipyramidal geometry of coordination polyhedra.9b Furthermore, the lengths of coordination bonds, which
involve the terminal ligands strongly depend on the nature of used anion X-. While isotiocyanato N-donor
ligands form the shortest bonds within the coordination polyhedron of 1 (avg. 1.984(2) Å), the chlorido or
bromido ligand anions creating the weakest bonds in 2 and 3, respectively (avg. 2.2864(8) Å for 2; avg.
2.4358(9) Å for 3). The coordination geometries of 1 − 3 have been studied by the continuous symmetry
measures methodology (program SHAPE 2.1),17 which provides a quantitative analysis about the deviation
of a given shape of coordination polyhedron. All three structures were compared to several ideal five-
coordinated geometries (Table S2.1)17c among which the square pyramidal (SPY, C4v) and/or vacant
octahedral (vOC, C4v) geometries are the closest for compound 1 (S(SPY) = 1.4 and S(vOC) = 2.1,
respectively), while the trigonal bipyramidal geometry (TBPY, D3h) is the closest for 2 ((S(TBPY) = 2.0)
and 3 (S(TBPY) = 2.5). The comparison of symmetry measures in the shape map (Figure S2.1, see ESI)
indicates that the Berry distortion between the ideal TBPY and SPY shape is disrupted by another pathway,
which most probably involves vOC geometry. The coordination polyhedron of 1, with a rather SPY
geometry contains a basal plane formed by N1, N3, N4 and N6 donor atoms, while the Co1-N7 bond
represents the apical axis. Co(II) is pulled out from the basal plane as well as from plane of 2,6-bis(1H-
benzimidazol-2-yl)pyridine moiety (d ≈ 0.4 Å and d ≈ 0.5 Å, respectively) towards to N7 vertex (Figure
S2.2a) and most of the cis angles are significantly deviated from the ideal value of 90° (N3-Co1-
N4=74.73(7)°; N4-Co1-N6=100.97(8)°; N6-Co1-N1=100.55(8)°; N1-Co1-N3=74.96(7)°; N7-Co1-
N4=102.76(8)°; N7-Co1-N6= 109.86(9)°). On the contrary, the axial axis in rather TPBY-shaped polyhedra
of 2 and 3 involves both imidazole nitrogen donor atoms of L and along with the metal centre create
significantly deviated angle from 180° (N1-Co1-N4 = 151.33(8)° for 2, N1-Co1-N4 = 152.0(1)° for 3;
Figure S2.2bc, see ESI). The equatorial plane is formed by pyridine nitrogen donor atom N3 of L and two
halido ligands, the corresponding cis angles vary in the range 111-127°, thus they are close to the ideal
angle of 120°. In both compounds, Co(II) metal centres reside on the equatorial as well as on the ligand L
planes (Figure S2.2ab, see ESI). Furthermore, the values of τ5 distortion parameter reflect the angular
deviation of coordination polyhedra in the reported compounds. Comparing to the ideal values of τ5 = 0 for
SPY and τ5 = 1 for TBPY, the τ5 values (τ5 = 0.30 for 1, τ5 = 0.46 for 2 and τ5 = 0.41 for 3) indicates an
intermediate geometry between SPY and TBPY stereochemistry, however certainly disrupted by another
geometries as indicate the deviations from ideal Berry pathway (Figure S2.1, see ESI).
The ionic compound 4 contains a complex cation where the Co-N distances of coordination polyhedra vary
from 2.08 Å with the pyridyl nitrogen atom to about 2.13 Å with the pyrazolyl moieties and are typical for
the high-spin metal centre (Figure 1d). The coordination environment of Co(II) formed by six nitrogen
donor atoms of two tridentate ligands L shows a pronounced distortion from a perfect octahedral geometry,
which can be quantitatively expressed by several angles and parameters postulated mainly for the
identification of spin state of central atom but also for the quantification of Jahn-Teller distortion.18 For

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instance, the trans angle N3-Co1-N8 involving two pyridine Npy donor atoms ϕ, the dihedral angle between
the least-squares planes of the two L ligand moieties coordinating the same metal centre θ, two clamp
angles φ (N1−Co−N4, N6−Co−N9) and the four bite angles α (NIm-Co-NPy) (Figure S2.3 ab, see ESI) would
acquire 90° (θ, α) and 180° (ϕ, φ), respectively, if the coordination polyhedron {CoN6} would exhibit the
ideal octahedral symmetry. Moreover, the angular distortion parameters Σ18 calculated from 12 cis angles
of hexacoordinated polyhedron (Figure S2.3 c, see ESI) acquiring zero values when ideal octahedral
symmetry is present, are suitable indicators of octahedral deviation. All mentioned angles indicate severe
divergence from the values for the ideal octahedral shape (ϕ=174.69(7)o, φavg=152.17(8)o, θ=82.94(8)o and
αavg=76.19(2)o) and along with Σ=136.4o they reflect a pronounced degree of angular distortion in
[Co(L)2]2+. Additionally, those values are typical for high-spin hexacoordinated Co(II) complexes with
terpy-like N3-donor ligands, while for the comparison, the typical values for less distorted low-spin
polyhedra of that family are ϕ ≈ 176 o, φ ≈ 160 o, θ ≈ 86 o α ≈ 80o and Σ≈90 o.19
In the crystal structures of 1-3, two 3,5-bis(tert-butyl)phenyl moieties of L are bent in the same direction to
each other, creating an angle about ≈115° with respect to 2,6-bis(1H-benzimidazol-2-yl)pyridine plane
(Figures S2.3 and S2.4, see ESI) and present the steric constrains on that side of ligand moiety. Therefore,
the non-covalent interactions between the pyridine and benzimidazole parts of the neighbouring molecules
are observed only on the “free” side in which the bulky aromatic substituents are not directed. In the crystal
lattice of 2 and 3, it is therefore possible to recognise the formation of pseudodimeric couples, where two
complex molecules are interconnected through weak π-π contacts formed between benzimidazole moieties
(d≈3.6 Å for 2 and 3; Figure S2.4 bc, see ESI). Those neighbouring pseudodimeric couples are bent to each
other by angle ≈148° in 2 and ≈145° in 3 and are aligned along the b-c plane. The crystal structure of 1
forms the similar pseudodimeric couples along a-c plane, which are however interconnected via weak π-π
interactions between pyridine and benzimidazole moieties of two neighbouring molecules (d≈3.3 Å; Figure
S2.4 a, see ESI). In the complex cation of 4, the 3,5-bis(tert-butyl)phenyl substituents are oriented in the
opposite direction to each other preventing the formation of relevant non-covalent interactions within the
crystal lattice.

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a)
b)
c)

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d)
Figure 1 Representation of the molecular structures of 1(a), 2 (b), 3 (c) and 4(d). Hydrogen atoms, uncoordinated
anions and lattice solvent molecules are omitted for clarity. Colour code: C-grey; N-blue; Cl-green; Br-brown; S-
yellow. Bond distances (in Å) and structural parameters of coordination polyhedra in 1: Co1-N1=2.095(2), Co1-
N3=2.118(2), Co1-N4=2.092(2), Co1-N6=1.964(2), Co1-N7=2.004(2), S(TBPY)= 5.5, S(SPY)= 1.4, S(vOC)=2.1,
τ5=0.30(8); in 2: Co1-N1=2.106(2), Co1-N3=2.105(2), Co1-N4=2.123(2), Co1-Cl1=2.3079(8), Co1-Cl2=2.2649(8),
S(TBPY)= 2.0, S(SPY)= 4.9, τ5=0.46(8); in 3: Co1-N1=2.096(3), Co1-N3=2.088(3), Co1-N4=2.104(3), Co1-
Br1=2.4639(8), Co1-Br2=2.4077(9), S(TBPY)= 2.5, S(SPY)= 4.9, τ5=0.41(3); in 4: Co1-N1=2.139(2), Co1-
N3=2.081(2), Co1-N4=2.152(1), Co1-N6=2.119(2), Co1-N9=2.118(3), Co1-N8=2.084(2), Σ=136.4o.
Table 1. Selected crystallographic information for reported complexes 1-4
1
2
3
4
Formula
C51H57CoN7S2
891.08
green
C49H57Cl2CoN5
845.82
C49H57Br2CoN5
934.74
orange
100
C100H124Br2CoN10O3
1732.83
orange
Formula weight / g mol-1
Crystal colour
Temperature / K
Wavelength / Å
Crystal system
Space group
brownish green
100
100
100
1.54186
monoclinic
C2/c
1.54186
monoclinic
P21/c
1.54186
monoclinic
P21/c
1.54186
triclinic
P-1
a / Å
b / Å
c / Å
α /o
37.1120(8)
15.8626(2)
17.1798(4)
90
17.9448(4)
8.89550(10)
30.1258(6)
90
17.9513(4)
8.8923(2)
30.3407(7)
90
13.5981(4)
18.2954(5)
21.4975(6)
67.463(2)
87.059(2)
β /o
90.502(2)
97.649(2)
97.413(2)

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γ /o
90
90
90
72.737(2)
4705.4(2)
2, 1.223
V / Å3
10113.2(3)
8. 1.170
3.732
4766.13(15)
4; 1.179
4.128
4802.75(19)
Z; ρcalc / g.cm-3
μ (Mo-Kα)/mm-1
F(000)
4; 1.293
5.023
1932
2.836
3768.0
1788
1830.0
Crystal size / mm
0.15 × 0.09 × 0.02
6.06 to 142.712
0.32 × 0.25 ×0.03 0.21 × 0.15 × 0.02
0.45×0.25×0.15
2.23 to 71.67
θ range for the data
7.206 to 143.908
5.874 to 142.818
collection / °
Final R indices [I > 2σ(I)]a R1= 0.0438,
R1 =0.0482,
wR2 = 0.1146
R1 =0.0439,
wR2 = 0.0902
R1 = 0.0378,
wR2 = 0.0944
wR2 = 0.1037
R indices (all data)a
R1= 0.0685,
wR2= 0.1125
R1 =0.0742,
wR2 =0.1224
R1 = 0.0810,
wR2 = 0.0948
R1 = 0.0502,
wR2 = 0.0977
GoF on F2
0.918
0.857
0.861
0.933
CCDC deposit number
1888985
1888983
1888984
1954560
2
a R1
F  F
C 
/
F
 0 
; wR2 
[w F2  F2 2 ]/ [w F2
]


C 






0
0
0
Static magnetic properties and theoretical calculations
To gain more insight into the magnetic anisotropy of the reported complexes 1-4, static magnetic data were
acquired and further analysed – see Figure 2. The temperature dependent magnetic data, shown as the
effective magnetic moment, clearly reveal substantial zero-field splitting (ZFS) causing the decrease of the
eff on lowering the temperature. This phenomenon is also responsible for much lowered saturation values
of the isothermal magnetizations measured at T = 2 K in comparison with the theoretical value Mmol/NAB
= g·S ≈ 3 for S = 3/2 and g = 2.0.

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Figure 2 Magnetic data for 1–4 shown as the temperature dependence of the effective magnetic moment
and as the isothermal magnetizations in the insets. The empty symbols represent the experimental data and
red solid lines represent the fitted data using eq. (1) or (4) with the parameters listed in Table 2.
Therefore, the obtained temperature dependent magnetization data and the field dependent magnetization
data at different temperatures were analysed simultaneously using spin Hamiltonian covering the zero-field
splitting terms and Zeeman term defined as
2
2
2
2
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
H  D(Sz  S / 3)  E(Sx  Sy )  BBgSa
(1)
where D and E are the single-ion axial and rhombic ZFS parameters, respectively, and the last component
is Zeeman term defined in a direction of magnetic field as Ba = B(sin()cos(φ), sin()sin(φ), cos()) with
the help of the polar coordinates.20 Next, the molar magnetization (Mmol) was calculated from the partition
function (Z) for given direction of magnetic field Ba as
d ln Z
Mmol  NA
dBa
(2)
Then, the integral (orientational) average of molar magnetization was calculated
2
Mmol
 Ma sindd
1/ 4 0 0
(3)
to properly simulate experimental powder magnetization data for all temperature and magnetic field
dependent experimental data. The ab initio calculations performed on the complexes (vide infra) suggest
positive D parameters and large g-anisotropy with gz component close to 2.0. Thus, the gz component of g-
tensor was fixed to value 2.0 in order to minimize the number of optimized parameters. The best-fits were
obtained for 1-3 with D in the range from 25 to 39 cm-1 and significant rhombicity – Table 2. However, this
approach was unsuccessful for compound 4 with pseudo-octahedral geometry of the coordination
polyhedron. Hence, we used the second approach suitable for such scenario based on works by Griffith,21
Lines22 and Figgis,23 in which the orbital angular momentum and the spin-orbit coupling is included in the
Hamiltonian as
r
r
r
r
r
2
z
2
2
x
2
ˆ
ˆ
ˆ
ˆ
ˆ
H    S  L   L  L / 3   L  L   B g S L
ax  rh  y 

(4)




B
e

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4
where ax and rh describes splitting of T1g ground term induced by lowering the symmetry,  is orbital
reduction factor,  is spin-orbit coupling and ge = 2.0023. This L-S Hamiltonian exploits the T1-P
isomorphism, thus, the angular orbital momentum L is equal to 1 with the effective Landé g-factor, gL = -
, and is applied to |S, L, MS, ML> functions with ML = 0, ±1 and MS = ±1/2, ±3/2.24 The orbital reduction
factor combines two parameters,  = A, where A is the Figgis coefficient of the configuration interaction
resulting from the admixture of the excited terms reflecting the ligand field strength (1 < A < 3/2), and 
describes the lowering orbital contribution due to covalency of the metal-ligand bond and it usually holds
 ≤ 1. Additionally, the spin-orbit coupling parameter  can be also reduced in comparison with its free-
ion value 0 = -180 cm-1 due to the covalent character of the donor-acceptor bond. The Hamiltonian in eq.
4 was able to properly describe the magnetic data of 4 using these best-fit parameters: ax = 307 cm-1, rh/ax
= 0.00 with  = -121 cm-1 and  = 1.29 (Figure 2).
Table 2. Spin Hamiltonian parameters calculated by ab initio methods and fitted from magnetic data for
1-4.
[Co(L)(NCS)2] of 1 [Co(L)Cl2] of 2
[Co(L)Br2] of 3
[Co(L’)2]2+ of 4a
CASSCF/NEVPT2 with CAS(7,5) using def2-TZVP(Co, Br, Cl, N, S) and def2-SVP(C,H)
D (cm-1)
28.8
48.0
49.1
63.8
E/D
gx
gy
gz
0.311
2.319
2.573
2.098
0.117
2.402
2.544
1.991
0.226
2.346
2.627
2.082
0.133
2.444
2.630
1.985
Analysis of ground Kramers’s doublet with effective spin 1/2:
b
g1
g2
g3
1.608
2.460
6.924
3.664
1.926
3.920
5.889
3.912
1.914
3.061
6.688
3.888
2.028
3.840
6.156
4.008
gaver
CASSCF/NEVPT2 with CAS(7,10) using def2-TZVP(Co, Br, Cl, N, S) and def2-SVP(C,H)
(double shell effect)
D (cm-1)
29.7
50.6
55.4
63.6
E/D
gx
gy
gz
0.314
2.333
2.601
2.098
0.124
2.423
2.591
1.989
0.219
2.314
2.675
2.142
0.124
2.452
2.631
1.974
CASSCF/NEVPT2/ZORA with CAS(7,5) using ZORA-def2-TZVP(Co, Br, Cl, N, S) and ZORA-def2-SVP(C,H)
(relativistic effects)
D (cm-1)
27.9
47.6
49.3
62.0
E/D
gx
gy
gz
0.300
2.318
2.560
2.098
0.119
2.400
2.544
1.991
0.231
2.337
2.634
2.091
0.133
2.437
2.620
1.984
CASSCF/DCD-CAS(2) with CAS(7,5) using def2-TZVP(Co, Br, Cl, N, S) and def2-SVP(C,H)
(different treatment of dynamic electron correlation)
D (cm-1)
E/D
30.0
50.1
55.0
64.3
0.309
0.125
0.235
0.120
Fitted parameters from the experimental magnetic data
26.0 39.2
D (cm-1)
24.7
ax = 307 cm-1

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E/D
gxy
gz
0.333
2.48
2.00
0.333
2.56
2.00
0.333
2.82
2.00
rh/ax = 0.00
 = -121 cm-1
 = 1.29
a L’ is simplified ligand L in which the tert-butyl groups were replaced by hydrogen atoms; b the g-
parameters calculated for ground state Kramers doublet with effective spin Seff = 1/2.
In next step, the multireference ab initio calculations based on the state-averaged complete active space
self-consistent field method (SA-CASSCF) were conducted to gain insight into the electronic structure of
the Co(II) ions in the studied compounds 1-4. Thus, the well-stablished ORCA software package25 was used
for these CASSCF calculation with the active space defined as seven electrons in five d-orbitals, CAS(7,5).
In addition, dynamic electronic correlation was handled by using the N-electron valence state perturbation
theory (NEVPT2).26 These calculations were undertaken on the mononuclear molecular fragments extracted
from the experimental X-ray structures of 1-4. In case of complex cation of 4, the tert-butyl groups were
replaced by hydrogen atoms to make such calculation feasible. Subsequently, the atomic positions of the
all hydrogen atoms were optimized using the PBE functional27 together with the atom-pairwise dispersion
correction method (D3BJ).28 The results of CASSCF/NEVPT2 calculations are summarized in Table 2 and
Figures 3 and 4.

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Figure 3 Three-dimensional (3D) representation of the molar magnetization (Mmol) calculated for T = 2 K
and B = 0.5 T using CASSCF/NEVPT2’s calculation with CAS(7,5) overlaid over the molecular fragments
of 1-4.
Figure 4 The graphical output of the CASSCF/NEVPT2 calculations with CAS(7,5) for the mononuclear
molecular fragments of 1-4. Plot of the d-orbitals splitting calculated by ab initio ligand field theory
(AILFT) (left), low-lying ligand-field terms (middle), and ligand-field multiplets – Kramers doublets
(right). The doublet and quartet spin states are shown in red and green, respectively.
Generally, in ideal square-pyramidal arrangement, the d-orbitals are split into a dxy, (dxz, dyz), dz2, dx2-y2
pattern, whereas the ideal trigonal-bipyramidal arrangement results into (dxz, dyz), (dxy, dx2-y2), dz2 pattern
(Figure S3.1, see ESI), which can be confronted with the results obtained by the ab initio ligand field theory
(AILFT)29 utilized to calculate the energy of the d-orbitals in 1-4 as depicted in Figure 4 (left). In case of
complexes 1 and 2, the d-orbital’s splitting resembles the one for square-pyramidal arrangement and
trigonal-bipyramidal arrangement, respectively. The complex 3 provided the d-orbitals splitting somewhere
between these two cases, which is in agreement with the results of the geometry characterization done by
SHAPE program. As expected, two sets of split t2g and eg orbitals were found in the pseudo octahedral
complex 4. Subsequently, the CASSCF/NEVPT2 lowest ligand field terms are shown in Figure 4 (middle)
confirming ground state with multiplicity four and low-lying excited terms, which have largest
contributions to the D-tensor (Table 3.1, see ESI). Next, due the spin-orbit coupling, the ligand-field terms
(LFT) are split into the ligand-field multiplets (LFM) showing the zero-field splitting into several Kramers
doublets - Figure 4 (right). The application of the effective Hamiltonian theory30 to a quartet ground state
resulted in the ZFS D and E parameters and g-tensor parameters are summarized in Table 2. The positive
D is found for all complexes 1-4, with the smallest value found for 1 and the largest for 4. The calculated
principal axes of the D-tensor are depicted in Figure S3.2. The positive D would result in the easy-plane
type magnetic anisotropy, however, larger E/D ratio suggests that easy-axis type of the magnetic anisotropy
can be operative,31 and indeed, the calculated three-dimensional molar magnetization for 1-4 using
CASSCF/NEVPT2 calculations nicely showed the axial character of the magnetic anisotropy in 1-4 –
Figure 3. This can be quantitatively analysed by using effective spin Seff = 1/2 spin Hamiltonian for ground

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Kramers doublet, which results in three values of the effective g-factors (g1, g2 and g3) with their average
value gaver. If it holds that g1, g2 < gaver and gaver < g3, the easy-axis type of magnetic anisotropy of the ground
state is present. On contrary, the easy-plane type of magnetic anisotropy is achieved under condition g1 <
gaver and gaver < g2, g3. These values are listed in Table 2, and it can be deducted that the easy-axis type of
magnetic anisotropy is found in complexes 1, 3 and 4.
Moreover, the double-shell effect, which is supposed to be important for late 3d-metals, was accounted for
by enlarging the active space to 10 d-orbitals (3d + 4d). Interestingly, this approach (CAS(7,5) vs.
CAS(7,10)) has only a minor impact on the derived D and E ZFS parameters and g-factors (Table 2).
Furthermore, we were interested if the relativistic effect may lead to different results, at least for complex
2 with coordinated bromide ligands. Therefore, ZORA (the 0th order regular approximation)32 relativistic
correction was applied together with relativistic version of the respective basis sets for CAS(7,5), but the
result are almost identical as for the non-relativistic calculations. Finally, we explored the recently
introduced different approach to treat the dynamic electron correlation, 2nd order dynamic correlation
dressed CAS, DCD-CAS(2) again for CAS(7,5).33 This method led to slightly larger values of D-parameters
for all complexes. Thus, we may conclude that all four tested approaches provided similar information
about electronic structure and large magnetic anisotropy is present in complexes 1-4.
Dynamic magnetic experiments
The magnetic data induced by the oscillating, alternating-current (AC) magnetic field were taken at an
amplitude of BAC =0.38 mT (1 and 3) and BAC =0.35 mT (2 and 4). The DC field scan for a limited number
of frequencies over four order of magnitudes shows that the out-of-phase component (χ’’) of AC
susceptibility is silent at BDC = 0 T (Figure S4.1). This indicates very fast relaxation of the magnetization,
probably due to the quantum tunnelling of magnetization (QTM) induced by hyperfine interactions with
the nuclear spin and/or dipolar interactions between the spin centres in the lattice. In order to determine the
optimum DC field to suppress the QTM effect, AC susceptibility measurements under various DC fields
were applied at 2 K (Figure S4.1). With increasing DC field up to BDC=0.5 T, the out-of-phase component
varies, but differently for individual frequencies. This confirms that compounds 1-4 show a field-induced
slow magnetic relaxation and therefore the subsequent temperature and frequency dependent measurements
were carried out by choosing BDC fields at which the out-of-phase components χ’’ reach the maximal
response (BDC=0.15 T for compounds 1 and 2, BDC=0.1 T for 4 and BDC=0.125 T for 3). Furthermore, in
order to get detailed information about the both relaxation channels of compound 3 (vide infra), another
three measurements were performed at BDC=0.05 T, BDC=0.2 T, BDC=0.3 T. Collected sets of χ’ and χ’’
susceptibilities at each temperature were fitted using the formulas for one-set (1, 2, 4, 3 at 0.05 T, 3 at 0.125
T; eq. S1 and S2 see ESI) or two-set (3 at 0.2 T, 3 at 0.3 T; eq. S3 and S4 see ESI) Debye model.
Frequency dependent in-phase χ’ and out-of-phase susceptibility χ’’ measured as a function of frequency
of AC field for a set of temperatures (1.8-4.9 K for 1; 2.0-3.6 K for 2; Figure 5 ab, Figure S4.2 and Figure
S4.3, see ESI) suggest a single relaxation process in compounds 1 and 2. However, the small onsets
apparent at very low frequencies in the χ’’ vs. ν dependencies (Figure 5ab) indicate that both compounds
contain the second relaxation channel which will becomes more pronounced at higher fields and lower
temperatures. The out-of-phase components of AC susceptibility (χ’’) show the maxima shift from 76.3Hz
(1 at 1.8 K, τ = 2.09 ms) and from 331.6 Hz (for 2 at 2.0 K, τ = 0.48 ms), respectively, towards to higher
frequencies upon the increase of the temperature (Table S4.2 and S4.3). This indicate typical features of
SMMs - the maxima of χ’’ are frequency and temperature dependent and the relaxation time τ shorten with
the increase of temperature. The in-phase (χ’) and out-of-phase (χ’’) components of AC susceptibility were
simultaneously fitted using a one-set Debye model, by which the adiabatic χS and isothermal χT
susceptibilities along with the distribution parameters αi and relaxation times τi were determined by

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nonlinear optimisation (eq. S1 and S2, see ESI). Using these parameters, interpolation/extrapolation lines
enable to reconstruct the frequency dependent AC susceptibility components (solid lines in Figure 5 and in
Figures S4.2a, S4.3a, see ESI) as well as arcs in the Argand (Cole-Cole) plot (Figures S4.2b, S4.3b, see
ESI). The fitting procedure was terminated at T = 4.9 K (1) or 3.6 K (2), since, the maxima for the relaxation
channel already lie outside the hardware limits above those temperature. Both measurements allow a
reliable analysis of τ(T) dependency according to extended relaxation equation
1
1
U
exp( )  CT n  ABmT
(5)


0
kT
푈
1 푒푥푝 ( ― 푘푇
)
퐶푇푛
), Raman (
where the corresponding terms describe thermally activated Orbach (휏
) and
0
퐴퐵푚푇
direct (
) relaxation of magnetization. Usually, first two terms describe the spin relaxation at higher
temperature and the obtained parameters from the single Orbach or single Raman mechanism fitting help
to estimate the extrapolated relaxation time τ0 (for T → infinity), energetic barrier of spin reversal U, or
coefficients of Raman term (C, n) for the combined fitting models (Orbach + direct or Raman + direct,
Figure 5cd). The best fit parameters are listed in Table S4.6 (see ESI). In the case of combined Orbach +
direct model, the energy barrier and extrapolated relaxation times U = 24.6 K, τ0=5.9 × 10-7 s for 1 and U =
18.9 K, τ0=2.3 × 10-7 s for 2, respectively, are typical for the pentacoordinate Co(II) SIMs. Values of Raman
parameter C (0.79 K-n s-1 for 1 and 14.93 K-n s-1 for 2) extracted from Raman + direct model suggest that
two-phonon Raman relaxation is more pronounced in compound 2. Raman exponent acquires value close
to n ≈ 6 for both compounds 1 and 2, which is smaller than the expected value of 9 for Kramers ions,34 but
when optical and acoustic phonons are considered, n = 1-6 is reasonable.35 Both fitting approaches afforded
comparable values of ABm parameter of single-phonon direct relaxation mechanism (Table S4.6).
Dynamic magnetic properties of 3 indicate the presence of two relaxation channels (Figure 6ab, Figure
S4.4-S4.7), therefore AC susceptibility was measured at four different static magnetic fields to investigate
both low-frequency (LF) and high-frequency (HF) channels at higher fields analysed by a two-component
Debye model (eq. S3 and S4, see ESI) and a single HF process at lower BDC processed by one-component
Debye model (eq. S1 and S2, see ESI). The slower LF channel gains the maximum of χ’’ at 5.70 Hz (τ1 =
27.5 ms, 0.2 T) and at 5.45 Hz (τ1 = 29.2 ms, 0.3 T) and the relaxation time is rather temperature invariant
upon the increase of temperature (Figure 6d, Table S4.4). Since the appearance of the LF relaxation channel
is vanished in the sample dispersed with the diamagnetic eicosane (Figure S4.9, see ESI), it’s origin can be
attributed to the existence of intermolecular dipole-dipole interactions always present in molecular systems.
Those interactions are responsible for the formation of “finite oligomers” (finite chains, plates, blocks, or
other fragments), with coherence length depending upon temperature. The magnetic field raises the
efficiency of the LF relaxation mode which points to its intermolecular nature, supported by the magnetic
field. Moreover, the relaxation time for the LF mode is prolonged as the magnetic field increases.
The analysis of τ2(T) of HF channel of 3 was done in the same way as for the compounds 1 and 2. The use
of the single Orbach or single Raman term from eq. 5 helped to estimate initial parameters for more complex
fits which include combined Orbach+direct or Raman+direct terms. The best fit parameters listed in Table
S4.7 are significantly different comparing those obtained at weaker field, which is tentatively attributed to
the lowered accuracy of fits caused by the co-existence of two relaxation channels. Measurements at BDC
=0.05 T and 0.125 T resolved only HF relaxation channel and detailed analysis of τ2(T) dependency allowed
to quantify parameters of eq. 5. It is noteworthy that values of energy barrier and extrapolated relaxation
time are highly comparable to those obtained for isostructural chlorido complex 2 (U = 19.1 K, τ02 = 9.22 ×
10-8 s at 0.05 T; U = 20.1 K, τ02=9.22 × 10-8 s at 0.125 T). The parameters of Raman process are again lower
as expected value for a Kramers ion complex (C = 7.7, n = 7.1 at 0.05 T and C = 5.37, n = 7.4 at 0.125 T)

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and ABm are again comparable with those obtained for 2 (Table S4.7, see ESI). AC susceptibility
investigation of 4 at BDC = 0.1 T (Figure 6a, Figure S4.8 see ESI) revealed the presence of single relaxation
channel. Both the frequency and temperature dependence of in-phase χ’ and out-of-phase χ’’ components
of AC susceptibility were again analysed by using the one-component Debye model which allowed to
obtain set of relaxation times τ within the thermal range 2.0-5.2 K. Furthermore, analysis of τ(T) suggests
the presence of the single Orbach or single Raman relaxation process (Figure 6b, Table S4.8 see ESI). The
fitted parameters of the earlier mechanism indicate the increase of the extrapolated relaxation time (τ0 =6.7
× 10-7 s), but the decrease of energy barrier of spin reversal (U = 9.5 K), when compared to pentacoordinate
complexes 1-3.
5
4
4
3
2.0 K
2.2 K
2.4 K
1.8 K
3
2.6 K
2.8 K
3.0 K
2
3.2 K
3.4 K
2
3.6 K
FIT
1
1
4.9 K
0
0
1
10
100
1000
1
10
100
1000
v / Hz
 / Hz
b)
a)
-7,5
-6,0
ln
ln
Direct+Orbach
Direct+Raman
-6,5
-7,0
-7,5
-8,0
-8,5
-9,0
-9,5
-10,0
Direct+Orbach fit
Direct+Raman fit
-8,0
-8,5
-9,0
-9,5
U = 18.92 K
0 = 2.28 10-7
U = 24.61 K
0 = 5.87.10-7
C = 0.79 K-n s-1
s
s
C = 14.93 K-n s-1
n = 5.78
-10,0
-10,5
n = 6.07
0,20
0,25
0,30
0,35
0,40
0,45
0,50
0,55
0,30
0,35
0,40
0,45
0,50
T-1 / K-1
1/T
c)
d)
Figure 5 Frequency dependent out-of-phase χ’’ components of AC susceptibility for 1 (a) and 2 (b) at the
applied external magnetic field BDC = 0.15 T. Solid lines present fits using the one-component Debye’s
model (eq. S1 and S2; see ESI). The fits of the resulting relaxation times τ with the combination of the
Orbach and direct processes (solid line) using eq. 5 and the combination of the Raman and direct processes
(dashed line) using eq. 5 for 1 (c) and 2 (d).

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3,5
3,0
2,5
2,0
1,5
1,0
0,5
0,0
4
3
2
1
0
HF
1,9 K
2 K
2,1 K
2,2 K
2,3 K
2,4 K
2,5 K
FIT
1,9 K
2 K
2,1 K
2,2 K
2,3 K
2,4 K
2,5 K
2,6 K
2,7 K
2,8 K
FIT
LF
1
10
100
1000
1
10
100
1000
 / Hz
 / Hz
b)
a)
-7,5
-8,0
-8,5
-9,0
-9,5
ln 2 @ 0.05 T
-3,60
-3,75
-3,90
ln 2 @ 0.125 T
Direct-Orbach fit
Direct-Raman fit
ln  @ 0.2 T
1
ln  @ 0.3 T
1
-8
-9
n  @ 0.2 T
2
@ 0.125T
U = 20.06 K
0 = 7.13 10-8
C = 5.37 K-n s-1
n = 7.44
@ 0.05T
U = 19.10 K
0 = 9.22.10-8
C = 7.67 K-n s-1
n = 7.19
ln  @ 0.3 T
2
Direct-Orbach fit
Direct-Raman fit
s
s
0,36
0,38 0,40
0,42
0,44 0,46
T-1 / s-1
0,48 0,50
0,52
0,38
0,40
0,42
0,44
0,46
0,48
0,50
0,52
T-1 / s-1
c)
d)
Figure 6 Frequency dependent out-of-phase χ’’ components of AC susceptibility for compound 3 recorded
at the applied static magnetic field BDC = 0.125 T (a) and BDC = 0.3 T (b). Solid lines present fits using the
one-component Debye’s model (eq.S1 and S2; see ESI) and two-component Debye’s model (equations S3
and S4; see ESI), respectively. Temperature dependency of resulting relaxation times τ1 of LF channel and
τ2 of HF channel recorded at BDC = 0.05 and 0.125 T (c); and at BDC = 0.2 and 0.3 T. The fits of the resulting
relaxation times τ2 with the combination of the direct and Orbach processes using eq. 5 are viewed as dashed
lines and the combination of the Raman and direct processes using eq. 5 are viewed as solid lines.
-7,0
4,0
2.0
-7,5
3,5
3,0
2,5
2,0
1,5
1,0
0,5
0,0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
3.8
4.0
4.2
4.4
4.6
4.8
5.0
5.2
FIT
-8,0
-8,5
ln 
Orbach fit
Raman fit
U = 9.54 K
-9,0
0 = 6.70.10-6
s
C = 201.44 K-n s-1
n = 3.00
-9,5
-10,0
-10,5
0,20
0,25
0,30
0,35
0,40
0,45
0,50
1
10
100
1000
T-1 / K-1
 / Hz
a)
b)

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Figure 7 Frequency dependent out-of-phase χ’’ components of AC susceptibility for compound 4 recorded
at the applied static magnetic field BDC = 0.1 T (a). Solid lines present fits using the one-component Debye’s
model (eq. S1 and S2; see ESI). Temperature dependency of relaxation times τ (b). The fits lnτ vs 1/T with
the combination of the direct and Orbach processes using eq. 5 is viewed as dashed line and the combination
of the direct and Raman processes using eq. 5 is viewed as solid line.
Magneto-Structural correlations
Pentacoordinated high-spin Co(II) complexes with square pyramidal (SPY) and trigonal bipyramidal
(TBPY) geometries are systems of great interest due to their strong magnetic anisotropy with either negative
or positive axial zero-field splitting D parameter causing the easy-axis or easy-plane type of magnetic
anisotropy, respectively. The D parameters found in herein reported pentacoordinated complexes 1-3 vary
in the range 25-39 cm-1, which indicates the presence of a significant interaction between the excited and
ground states mediated by spin-orbit coupling. Despite the positive D values, however, the axial anisotropy
can be considered due to the elevated rhombicity (Figure 8).
Figure 8 The three-dimensional (3D) visualization of the molar magnetization calculated at T = 2 K and
B = 3 T for S = 3/2 with D = +30 cm-1 and varying E parameters as indicated in the plot.
As was already highlighted, the geometries of three coordination polyhedra are far from the idealised shape
of SPY (1) or TBPY (2 and 3). The two isomorphous and isostructural analogues 2 and 3 show the similar
values of symmetry measure parameters S(TPBY) as well as τ5, which allows to anticipate the comparable
magnetic anisotropy. This is holds true only for calculated D parameters (Table 2), since the experimental
D value of 2 (26 cm-1) is smaller as those found for 3 (39.2 cm-1) and comparable with D parameter of 1
(24.7 cm-1). The first attempt to corelate the magnetic anisotropy with the features of coordination polyhedra
involves the Addison τ5 parameter (Figure S5.1a, see ESI). The herein reported compounds 1-3 together
with another 34 pentacoordinated Co(II) SIMs9i-m do not indicate any trend of D with the SPY↔TBPY
transformation suggesting that Berry pseudorotation is only one of the several contributions to the magnetic
anisotropy. The shape map which involves S(SPY) and S(TBPY) symmetry measure parameters indicates
that all 37 complexes contain significand deviation from ideal SPY↔TBPY pathway (Figure S5.1a, see
ESI). This correlation suggests the trend of the positive D parameters in compounds with SPY geometry
often deviated towards to vacant octahedron (vOC). On the other hand, there is a group of compounds
containing the tetradentate tren-type of ligands (tren = tris(2-aminoethyl)amine) with negative D and
geometry close to the TBPY (τ5≈1) often affected by the deformation towards to Jonson trigonal bipyramid
(compounds 17 ([Co(tbta)N3](ClO4).3MeCN, tbta= tris[(1-benzyl-1H-1,2,3-triazol-4-yl)methyl]amine),9i
21 ([Co(Me6tren)Cl]ClO4, Me6tren = tris[2-(dimethylamino)ethyl]amine),9j 22 ([Co(Me6tren)Br]Br),9j 24
([Co(NS3iPr)Cl](BPh4); NS3iPr=tris(2-(isopropylthio)ethyl)amine),9k 25 ([Co(NS3tBu)Cl]ClO4; NS3tBu=tris(2-
(tert-butylthio)ethyl)amine),9l
26
([Co(NS3tBu)Br]ClO4),9l
27
([Co(NS3tBu)NCS]ClO4),9l
30

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([Co(TPMA)Cl]Cl·2.4H2O; TPMA = tris(2-pyridylmethyl)amine),9m 31 ([Co(TPMA)Cl]Cl),9m 32
([Co(TPMA)Br]Br·2H2O),9m 33 ([Co(TPMA)Br]Br)9m and 34 ([Co-(TPMA)I]I)9m).
In order to better understand the magnetic anisotropy in pentacoordinate [Co(L)X2] systems, the simplified
molecular model was derived, in which N-donor atoms of L were replaced with ammine ligands and X was
set to Cl, thus leaving us with [Co(NH3)3Cl2] model complex. As tridentate ligand L is rigid, the position
of N-atoms in [Co(NH3)3Cl2] were fixed, and we focused on modelling the impact of various geometries
and ligand field induced by the variation of X ligands. Therefore, the Co-Cl bond length and Cl-Co-Cl bond
angle were varied to map various shapes of the coordination polyhedron. Subsequently, CASSCF/DCD-
CAS(2) calculations with CAS(7,5) were carried out to obtain ZFS parameters.
Scheme 2 The drawing of model compound [Co(NH3)3Cl2] and varying structural parameters used for the
modelling of ZFS parameters.
These results are then showed in the contour plot in Figure 8. Here, the calculated D-values are in the range
from -160 to +140 cm-1 showing huge potential of this system for tuning the size of the magnetic anisotropy
(Figure 9a), however, it is accompanied also with large variation of the rhombicity (Figure 9b). In order to
observe Orbach relaxation process in SMMs, it is important to have easy axis type of the magnetic
anisotropy, which can be achieved either for negative D-parameter, or for positive D-parameters but with
large rhombicity (E/D >> 0). Therefore, the effective g-factors were analysed for first Kramers doublet for
the effective spin Seff = 1/2. If it holds that g1, g2 < gaver and gaver < g3, the easy-axis type of magnetic
anisotropy of the ground state is present. On contrary, the easy-plane type of magnetic anisotropy is
achieved under condition g1 < gaver and gaver < g2, g3. This property is mapped in Figure 8d, thus proving
that easy-axis type of magnetic anisotropy is achievable for broad spectrum of tested geometries explaining
also the frequent observation of the slow relaxation of the magnetization in this class of the complexes.
Finally, Figure 9c is showing the energy separation between first and second Kramers doublets, which can
serve to estimate maximal Ueff in the range ~80-300 cm-1. From this point of view, the most perspective
geometries are for either small or large angle <(Cl-Co-Cl) (Figure 8c), which maximize Ueff.
a)
b)
c)
d)

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Figure 9 The variation of ZFS parameters calculated for [Co(NH3)3Cl2] model compound using
CASSCF/DCD-CAS(2) with CAS(7,5).
Conclusion
In summary, we have prepared a novel tridentate ligand - 2,6-bis(bezimidazole-1H-yl)pyridine derivative
containing the bulky aromatic substituents in order to prevent the strong intermolecular interactions of
corresponding penta- and hexacoordinated Co(II) SIMs. The structural analysis revealed that the nature of
the distortion of the coordination polyhedra in pentacoordinate complexes is notably dependent upon the
nature of terminal ligand anion. While in the complex 1 containing isothiocyanato terminal ligands was
identified a SPY geometry with some deviation towards the shape of vacant octahedron, the isomorphic
and isostructural complexes 2 and 3 with halido Cl- and Br- ligands, respectively, exhibit distorted TBPY
shape of coordination polyhedra. The experimentally obtained axial zero field splitting parameters reflect
the significant distortion of the coordination environments, however, their positive values along with the
pronounced rhombicity obviously do not follow the trend of the distortions in {CoN3X2} polyhedra. On the
other hand, ab initio calculated D values for 2 and 3 with TBPY geometry are notably higher comparing to
complex 1 with SPY shape. The ZFS spin-Hamiltonian dealing with only two lowest energy Kramers
doublets is inapplicable for the description of the static magnetic properties of compound 4. Therefore the
magnetic anisotropy of hexacoordinated Co(II) metal centre was evaluated in this case only by ab initio
calculations indicating the highest axial magnetic anisotropy and the lowest rhombicity within the herein
reported compounds. Based on the AC susceptibility investigations, all four compounds are field induced
SIMs. Two pentacoordinate complexes 1 and 2 as well as the ionic compound 4 show slow magnetic
relaxation mediated through one high-frequency relaxation channel. However, compound 3 shows two
relaxation processes, where the first low-frequency channel was pronounced only at higher DC fields and
its maximum does not vary with the temperature. In contrast, the high-frequency processes found in all four
compounds are very well established for SIMs based on 3d-ions and can be described by a combination of
direct one-phonon process and two-phonon Raman or Orbach processes.
Acknowledgement
Grant Agencies (Slovakia: APVV-18-0197, APVV-18-0016, VEGA 1/0125/18) are acknowledged for the
financial support. Barbora Brachňaková acknowledges The National Scholarship Programme of the Slovak
Republic for the Support of Mobility of Students, PhD Students, University Teachers and Researchers;
Tatra Bank Scholarship – Students to the world 2018. Radovan Herchel and Ivan Šalitroš acknowledge the
financial support from institutional sources of the Department of Inorganic Chemistry, Palacký University
Olomouc, Czech Republic. Ivan Šalitroš acknowledges Ministry of Education, Youth and Sports of the

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Czech Republic under the project CEITEC 2020 (LQ1601). This article was also created with the support
of the MŠVVaŠ of the Slovak Republic within the Research and Development Operational Programme for
the project “University Science Park of STU Bratislava” (ITMS project no. 26240220084) co-funded by
the European Regional Development Fund.
Conflicts of interest
To the best of our knowledge, there are no conflicts to declare.
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Table of Content
Three pentacoordinate and one
hexacoordinated Co(II) based single
ion magnets were prepared and their
structural, static as well as dynamic
magnetic properties were analysed in
detail.