Magnetostructural J-correlations in complexes with tetrahedro-{Cu 4} core

Article abstract of DOI:10.1016/j.poly.2014.07.007

A comprehensive analysis of structural and magnetic data for 41 tetrahedro-{Cu₄} complexes reveals that the exchange coupling constants (J₂ and J₄) correlate with averaged structural parameters of which the most informative are the averaged Cu-O-Cu angles in the bases (β) and walls (α) of the cubane structure. Using contemporary statistical programs, the cluster analysis, the principal component analysis, and the factor analysis bring information about the possible correlations of the magnetic and structural parameters and grouping of the parameters according to their similarity.

Full text of DOI:10.1016/j.poly.2014.07.007

Polyhedron 81 (2014) 572–582
Contents lists available at ScienceDirect
Polyhedron
journal homepage: www.elsevier.com/locate/poly
Magnetostructural J-correlations in complexes with
tetrahedro-{Cu } core
4
a
a
b
a,
⇑
M. Makohusová , V. Mrázová , W. Haase , R. Bo cˇ a
a
Department of Chemistry, FPV, University of SS Cyril and Methodius, 91701 Trnava, Slovakia
Institute of Physical Chemistry, Darmstadt University of Technology, Darmstadt, Germany
b
a r t i c l e i n f o
a b s t r a c t
Article history:
A comprehensive analysis of structural and magnetic data for 41 tetrahedro-{Cu } complexes reveals that
4
Received 22 May 2014
Accepted 5 July 2014
Available online 14 July 2014
the exchange coupling constants (J
most informative are the averaged Cu–O–Cu angles in the bases (b) and walls (
Using contemporary statistical programs, the cluster analysis, the principal component analysis, and the
factor analysis bring information about the possible correlations of the magnetic and structural param-
eters and grouping of the parameters according to their similarity.
2
and J
4
) correlate with averaged structural parameters of which the
) of the cubane structure.
a
Keywords:
Copper(II) cubanes
X-ray structure analysis
Magnetostructural correlation
Cluster analysis
Ó 2014 Elsevier Ltd. All rights reserved.
Principal component analysis
1
. Introduction
Magnetostructural correlations in copper(II) complexes were
instance, in dinuclear copper(II) complexes bridged by phenoxido
bridges the correlation line is
J½cmꢀ ꢁ ¼ ꢀ31:95 ꢂ
1
a
½ꢃꢁ þ 2462
ð3Þ
pioneered by Hatfield and coworkers [1,2] who found a linear
dependence of the exchange coupling constant J versus the bond
angle
core. Eight data points gave the correlation line with a high corre-
lation coefficient r
II
II
and ꢀJ values are substantially higher than for the alkoxido or
2
a(Cu–O–Cu) in dinuclear complexes with {Cu (OH) Cu }
hydroxido cases.
Several sources deal with explanation of the J–a correlations;
they are mostly based upon an orbital model that predicts that J
is composed of a minor ferromagnetic (indirect, through-space)
contribution and a major antiferromagnetic (direct, through-orbi-
tal) portion [4,5].
J ½cmꢀ1ꢁ ¼ ꢀ74:53 ꢂ
½ꢃꢁ þ 7270; r ¼ ꢀ0:9986
a
ð1Þ
which has been utilised by many authors in discussions without
any revision. (The collection of structural and magnetic data was
later enlarged to 12 data points.) The second correlation outlined
by Hatfield involves the Cu. . .Cu separation
Analogous correlations were proposed, for instance, for
III
III
IV
IV
{
Cr -(OH)
2
-Cr } and {Mn -(O)
2
-Mn } type complexes [6–9].
Attempts for J–
a
correlations are usually based upon linear relation-
ships with more or less success.
J ½cmꢀ1ꢁ ¼ ꢀ4508 ꢂ dCuꢂꢂꢂCu ½Åꢁ þ 13018; r ¼ ꢀ0:9994
On the contrary, Gorun and Lippard [9] correlated the –J value
with the shortest Fe–O distance (abbr. P) along the superexchange
path in {Fe -O-Fe } type complexes
ð2Þ
III
III
and it was based upon seven data points; this correlation is less
frequently quoted. However, some authorities claim that the
Cu–O distances (R) are more important for the magnetostructural
correlations than the Cu. . .Cu contacts (d).
Involvement of more data with greater structural diversity
along the superexchange path led to the differentiation of the cor-
relations for the alkoxido- and phenoxido-complexes [3]. For
1
10
ꢀ
J ½cmꢀ ꢁ ¼ ð2:360 ꢄ 10 Þ ꢂ expðꢀ10:661P ½ÅꢁÞ; r ¼ ꢀ0:975 ð4Þ
which is a decreasing exponential curve applicable only in the
segment of J – negative. However, also a linear correlation is
acceptable [10]
J½cmꢀ ꢁ ¼ 525:7 ꢂ P½Åꢁ ꢀ 1055; r ¼ 0:959
1
ð5Þ
⇑
Corresponding author. Tel.: +421 905 763 967.
E-mail address: roman.boca@stuba.sk (R. Bo cˇ a).
and this is applicable also in the positive segment of J-values.
http://dx.doi.org/10.1016/j.poly.2014.07.007
277-5387/Ó 2014 Elsevier Ltd. All rights reserved.
0

M. Makohusová et al. / Polyhedron 81 (2014) 572–582
573
As exemplified above, the magnetostructural J-correlations
could involve linear/non-linear relationships with bond angles
and/or bond lengths at the structural ordinate. Here the prefix
J-differentiates from the recently proposed magnetostructural
D-correlations where the axial zero-field splitting parameter D is
correlated with the structural tetragonality parameter Dstr for a
series of mononuclear Ni(II) and Co(II) complexes, respectively
coordinates) whereas the exchange coupling constants are limited
to a single value for a pair of the metal centres and in total, one or
two coupling constants are handled. A reliable determination of
three different coupling constants is very rare and this usually suf-
fers of overparameterisation (the variation of one coupling con-
stant induces variation of the remaining parameters).
More problematic is the fact that the assessment of the quality
of the magnetic data set (temperature dependence of the magnetic
susceptibility and eventually the field dependence of the magnet-
isation) is absent. Older data was taken with the Faraday balances
at the applied field of ca B = 0.5–1.5 T; this means that the low-
temperature susceptibility suffers of some error. Modern SQUID
apparatus allows to scan the data at the field of B = 0.1 T or even
lower (sometimes, however, one has to apply the field B = 0.5 T
when the measured magnetic moments is low). Thus the SQUID
data is superior relative to the Faraday balance data. When apply-
ing B = 1.0 or even higher, the susceptibility data again can be in
error since the simple ratio M/B no longer refers to a differential
susceptibility.
[
11,12]. The former correlation is nearly linear, the latter strongly
non-linear.
Involvement of the contemporary statistical packages into the
magnetostructural J-correlations appeared recently [13]. Just the
class of tetracopper(II) cubanes represented a complex task
because of diversity of structural variations and at least two
exchange coupling paths. In order to obtain more reliable mag-
netostructural J-correlations in this class of complexes, the number
of data points has been enlarged by a factor of three and broad
aspects are discussed in the present communication.
2
. Structural data
There is another obstacle with the magnetic data: practically all
samples of dinuclear or polynuclear complexes contain a paramag-
netic impurity (typical mole fraction xPI = 0.001–0.05) that refers to
the uncoupled mononuclear fragments due to the imperfectness of
the solid. The reproduction of this behaviour for different samples
is problematic, or even impossible. Even more problematic is a pos-
sibility of presence of a ‘‘diamagnetic impurity’’ – dinuclear frag-
ments coupled in an antiferromagnetic manner in samples of
polynuclear (e.g. tetranuclear or hexanuclear) complexes.
Finally, the analysis of the magnetic dataset also could be prob-
lematic. This is not the case of simple dimers where closed formu-
lae (like Bleaney–Bowers equation [19]) are available. In trinuclear
and polynuclear complexes not always closed formulae can be gen-
erated so that one is left with fully numerical approach [20]: by
diagonalising of the model (spin) Hamiltonian the set of eigen-
values results; this enters the partition function from which the
magnetisation and susceptibility can be reconstructed using the
apparatus of statistical thermodynamics.
It must be critically mentioned that any kind of magnetostruc-
tural relationship or correlation heavily depends upon the quality
of structural and magnetic data. The quality of the structural data
is well standardised by inspecting the R-factor or similar indicatrix
in the cif-file that is now available from the Cambridge Crystallo-
graphic Data Centre [14]. Therefore, less accurate data can be easily
removed from the dataset under inspection. However, some struc-
tures were erroneously reported as pointed out, for instance for
QAFTEX (CCDC code) by Clemente [15].
From the structural point of view the tetranuclear Cu(II) com-
plexes span four classes (Fig. 1): (i) endohedral cubanes, tetrahe-
dro-{Cu
linear structures, catena-{Cu
40 Cu(II) cubanes with closed structure. This paper is focused to
cubanes with approximately S point group of symmetry for the
} core. The open cubane is topologically equivalent to an
4
}; (ii) open cubanes; (iii) step-by-step structures; (iv)
4
}. To the end of 2013 CCDC offered
1
4
{
8
4 4
Cu O
-membered ring with alternating Cu- and O-atoms.
According to Mergehenn and Haase [16], cubane complexes can
II
In Cu complexes the isotropic exchange is the only interaction;
III
II
IV
III
II
II
however in Fe , Cr , Mn , Mn , Ni and Co complexes also the
axial zero-field splitting parameter D need be considered. In the
bent bridges (or roof-type structures) the principal axes of the D-
tensor are misaligned [21] and, moreover, also the antisymmetric
exchange adopts its significance [22]. All these factors are in the
interplay with the isotropic exchange coupling constant J, so that
different models will produce different J-values.
be classifies as type I (2 + 4), type II (4 + 2), and intermediate type.
Structural classification was based on disposition of long and short
Cu–O bonds: type I has four long Cu–O bonds parallel (elongated
prism), whereas type II has two of the longest Cu–O bonds perpen-
dicular to the two other longest Cu–O bonds. However, there exist
a number of intermediate structures: between elongated and com-
pressed prism (close to the regular cube) and the open structures
could be on one or two bases.
Important note: the isotropic exchange constant J conform the
ꢀ2
^
~ ~
definition H ¼ ꢀJ ꢀh ðS
ꢂ S
Þ. Data from other literature sources
A B
It was found that three cubanes match the same correlation line
as three dinuclear symmetric alkoxido bridged Cu(II) complexes
utilising the numerical prefactor ꢀ2 were rescaled to the above
convention hereafter. (Each spin operator brings not only a value
but also the reduced Planck constant ꢀh ; this is omitted when the
atomic units are employed.)
[
17]. A worth noting is also the correlation quoted for [Ni
4 4
(OR) ]-
type complexes [18].
3
. Magnetic data
4
. Results and discussion
4 4
The structural data for {Cu O } core involves a number of bond
lengths, bond angles, and dihedral angles (3N ꢀ 6 = 9 independent
It is assumed that the magnetic data was fitted by using the spin
Hamiltonian that accounts for the isotropic exchange of four Cu(II)
centres
Cu
1
4
X
Cu1
Cu
1
Cu1
ꢀ1
Þꢁ ꢀh ꢀ2 ꢀJ ½ðSCu1 ꢂSCu2
^
^
~
~
~
~
~
~
H ¼ lB
B
gSAz ꢀh ꢀJ ½ðSCu1 ꢂS
0
ÞþðSCu2 ꢂS
0
Þ
Cu1'
2
Cu1
Cu2
4
1
Cu '
Cu1'
Cu
2
'
A
Þꢁ ꢀh ꢀ
2
~
~
~
~
~
~
Cu2'
Cu2'
Cu
2
þðSCu1 ꢂS
Cu2
0
ÞþðS
Cu1
0
ꢂSCu2ÞþðS
Cu1
0
ꢂS
Cu2
0
Cu
2
'
Cu2
Cu2
Cu
1
'
ð6Þ
Cu
2
tetrahedro-{Cu
4
}
tetrahedro-{Cu
4
}
open cubane
type IIa
step-by-step structure
Here we applied a notation that J
whereas J
ence of a paramagnetic impurity, that obeys the Curie law, assumes
2
is common for two spin pairs
type I
type IIb
4
is common for four spin pairs. A correction for the pres-
Fig. 1. Sketch of the structural motifs in tetracopper(II) complexes.

5
74
M. Makohusová et al. / Polyhedron 81 (2014) 572–582
2
2
vmol
¼
vtetramerð1 ꢀ xPIÞ þ 4xPIðN
A
l0l =k
B
Þg sðs þ 1Þ=3T
ficient (r) in the aforementioned correlations results from the fit
according to a straight line, though there are no physical arguments
that such a correlation is necessarily linear in the given type of com-
B
PI
þ
vTIP
ð7Þ
where molar susceptibility of the tetramer was already corrected
for the underlying diamagnetism.
pounds. Notice that an averaging of very different angles a ranging
between 86 and 114 deg was applied which also reflects itself in the
The above Hamiltonian is a fortunate case where the zero-field
quality of the correlation.
energy levels for kets jS
1
S
2
S
12
S
3
S
4
S
34Si are
A collection of magnetic and structural data for 41 cubane-type
Cu(II) complexes is presented in Table 1. The structural data were
retrieved form the corresponding cif-files available from the CCDC
~
~
~
~
~
e
ðS12; S34; SÞ ¼ ꢀðJ =2ÞðS12 þ S34Þ ꢀ ðJ =2ÞðS ꢀ S12 ꢀ S34
Þ
ð8Þ
2
4
~
[14]. The data are ordered according to the decreasing J parameter,
where a shorthand notation is used S ꢅ SðS þ 1Þ; the intermediate
4
first for the type-II (compressed prism and/or open structures), and
then according to the decreasing J for the type-I complexes (elon-
2
gated prism). The geometrical parameters (angles and distances)
were averaged as follows (Table 2): b is an average of four bond
spins result from the coupling of the genuine spins, e.g.
S
12 = S
1
+ S
2
. Then the energy levels are: two singlets S ¼ 0 at
ð2J þ J Þ and 3J ; three triplets S ¼ 1, at ðJ þ J Þð2ꢄÞ and 2J ; one
2
4
4
2
4
4
quintet S ¼ 2 ꢀ set to the zero energy. Consequently the magnetic
angles Cu–O–Cu in the bases and
and d are averaged Cu. . .Cu separations in the bases and walls,
respectively; R and R average the Cu–O distances. When two dif-
a averages 8 angles in the walls;
susceptibility per tetramer can be written in a closed form
d
2
4
2
B
2
ꢀ
vmol ¼ ðN
l0l =kÞðg =TÞð4X
þ 2X
þ 10Þ=ðX
þ X
þ 6X
A
3
4
1
2
3
2
4
þ 3X
4
þ 5Þ
ð9Þ
ferent coupling constants were published for the exchange interac-
tion in bases, these were averaged to a single J parameter.
Nine variables g, J , J , b, , d , d , R and R were processed by
contemporary statistical software (Statgraphics Centurion XV)
using multivariate methods, such as cluster analysis (CA), principal
component analysis (PCA), factor analysis (FA), and the Pearson
correlation.
2
when using substitutions
X
1
¼ exp½ꢀð2J þ J Þ=kTꢁ,
X
2
¼ exp
2
4
a
2
4
2
4
2
4
ðꢀ3J =kTÞ, X
3
¼ exp½ꢀðJ þ J Þ=kTꢁ, and X
4
¼ expðꢀ2J =kTÞ. (Notice,
4
2
4
4
the energy levels can be uniformly shifted and then the final
susceptibility formula looks differently.)
For magnetisation the formula is more complex [20]
M
mol ¼ N
A
lBgðT
1
=ZÞ
ð10Þ
ð11Þ
ð12Þ
The cluster analysis creates groups of observations with similar
characteristics. To form the clusters, the procedure began with
each observation in a separate group. It then combined the two
observations which were closest together to form a new group.
After recomputing the distance between the groups, the two
groups then closest together were combined.
The CA method was applied to the whole set of available data as
shown in Fig. 3 where six clusters were distinguished according to
the ‘‘distance’’ among objects. The individual clusters contain 16, 4,
8, 3, 9, and 1 members.
with
ꢀ
1
Z ¼ 1 ꢂ X
1
þ 1 ꢂ X
2
þ 2 ꢂ X
3
ðY þ 1 þ Y Þ þ 1 ꢂ X
4
ðY þ 1
þ Y Þ þ 1 ꢂ ðY þ Y þ 1 þ Y þ Yꢀ2
ꢀ1
2
ꢀ1
Þ
and
ðY ꢀ Yꢀ Þ þ 1 ꢂ X
Þ
1
ðY ꢀ Yꢀ1Þ þ 1 ꢂ ð2Y þ Y ꢀ Y
2
ꢀ1
T
1
¼ 2 ꢂ X
3
4
ꢀ
2
ꢀ
2Y
The single-membered cluster No 6 refers to the complex 41 for
ꢀ
1
where also Y ¼ expðBlBg=kTÞ occurs. For strong antiferromagnetic
coupling the magnetisation is close to zero and it is overlapped by
the signal of the paramagnetic impurity.
which J
2
= ꢀ524 and averaged J
4
= 203 cm were reported; evi-
dently this data is dissimilar from all other complexes and thus it
was skipped from further processing.
Previous collection of twelve data points (all belonging to the
class-II) offered the following correlations [13]
The nine-membered cluster No 5 contains type-I complexes (No
30, 31, 32, 34, 36, 37, 38, 39, and 40) for which J
2
ꢆ |J
4
| (small and
insignificant) is characteristic. Therefore J
2
–b correlation might be
J2 ½cmꢀ ꢁ ¼ ꢀ3:61 ꢂ b½ ꢁ þ 351; r ¼ ꢀ0:65
1
ꢃ
ð13Þ
significant.
and
The three-membered cluster No 3 involves type-II complexes
(
ꢀ
No 19, 21, and 22) possessing very negative J
2
(ꢀ414, ꢀ624, and
J4 ½cmꢀ ꢁ ¼ ꢀ19:93 ꢂ
1
a
½ꢃꢁ þ 1976; r ¼ ꢀ0:45
ð14Þ
eight
ꢀ1
ꢀ1
480 cm ) whereas J
4
is rather small (0, ꢀ11, and ꢀ12 cm ).
2 4
Therefore J –b correlation might be significant whereas J –a is
where b averages four Cu–O–Cu angles in the bases and
angles in the walls of the prism (Fig. 2). Rather low correlation coef-
a
irrelevant (Fig. 4).
1
00
100
50
5
0
0
0
-
50
-50
-
100
-100
9
2
94
96
98
100
o
102
104
92
94
96
98
100
o
102
104
β (Cu-O-Cu) /
α (Cu-O-Cu) /
2 4 4 4 2
Fig. 2. Former magnetostructural correlations J –b and J –a in the cubane-type [Cu O ] complexes; confidence and prediction intervals (95%) are shown for J –b correlation.

Table 1
Magnetic and structural data for [Cu
4
O
4
] cubanes.a
Compound
No Ref. CCDC code
R
Chromophore
g
J
2
(cm 1
ꢀ
)
J
4
(cm
ꢀ1
)
Cu1–
Cu1
Cu2–
Cu2
Cu1–Cu2
(4ꢄ)
R(Cu–O)
(8ꢄ)
R(Cu–O)
(4ꢄ)
b1(Cu1–O–
a
a
(Cu1–O–Cu2)
⁄
⁄
(
%)
(2ꢄ)
(4ꢄ)
Cu1)
(Cu1 –O–
2
⁄
b (Cu2–O–
Cu2 )
Cu2)
Bases
Walls
89.8
Bases
Walls
Bases
Walls
Bases
Walls
1
2
[29] open
6.8
[Cu
4
(L)
4
][ClO
4
]
4
ꢂH
2
O
{CuO
3
N
2
}
2.06
ꢀ32.6
3.407
3.149,
3.186
1.957,
2.508
1.960,
2.486
1.958,
1.967
1.978,
1.993
98.72, 99.39
97.23, 98.33
90.58, 110.07
90.75, 108.90
88.65, 107.95
89.68, 110.02
3.383
3
3
.216,
.225
1
2
1
2
.923,
.520
.935,
.542
[23] JIXXIY
3.7
[{Cu(L)}
4
] [W(CN)
8
]ꢂ2H
2
O
{CuO
3
N
2
}
2.096 ꢀ3.4
82.8
3.365
.395
3.116,
3.119
1.922,
1.958
2.408,
2.451
1.942,
1.960
1.953,
1.973
99.0, 101.4
97.4, 101.5
90.2, 107.4
89.3, 105.7
89.2, 109.3
90.6, 106.9
3
3
3
.129,
.190
1
1
2
2
.928,
.949
.419,
.557
3
4
[24] EAECUA
[23] JIXXEU
6.1
8.1
[{CuBr(L)}
4
]ꢂ4CCl
4
{CuO
3
3
BrN}
2.17
ꢀ9
80
3.522
3.359
3.175
1.924,
.523
1.920,
1.964
2.413,
2.444
1.982
103.96
88.79, 108.76
2
[{Cu(L)}
4
] [Mo(CN)
8
]ꢂ2H
2
O
{CuO
2
N }
2.101 ꢀ2.2
76.6
3.110,
3.118
1.963,
1.969
1.940,
1.949
98.7, 101.0
97.5, 101.5
89.1, 105.7
90.1, 107.3
91.0, 107.3
89.2, 108.5
3.399
3
3
.133,
.187
1
1
2
2
.931,
.953
.420,
.447
5
6
[25] NAXBET
[26] IHELOX
3.2
6.1
[{Cu(L)}
4
]ꢂ2H
2
Oꢂ4CH
3
CN
{CuO
3
3
ON}
ON}
2.02
2.01
ꢀ35.2
ꢀ31.6
72.0
66
3.443
.615
3.108
3.134
1.960,
2.467
1.930,
1.956
101.5, 101.5
104.2, 104.2
90.0, 104.7
85.8, 106.0
3
2
2
.001,
.561
[Cu
[Cu
[Cu
4
4
4
L
4
]ꢂ5MeOHꢂH
2
O
{CuO
3.413
.368
3.095,
3.108
1.931,
2.580
1.984,
2.386
1.936,
1.956
1.937,
1.961
97.29,
102.30
96.36,
102.02
90.60, 106.27
89.29, 107.93
91.35, 105.41
89.16, 109.36
3
3
3
.170,
.203
1
2
1
2
.970,
.522
.946,
.373
7
8
[27] XINYUP01
5.2
3.7
(L)
4
]
{CuO
3
ON}
ON}
2.18
2.09
ꢀ11
61.0
54.6
3.305
.297
3.126,
3.122
1.955,
1.958
2.400,
2.452
1.938,
1.950
1.956,
1.962
96.6, 98.1
97.5, 97.6
91.0, 106.5
89.5, 106.9
90.3, 105.3
91.7, 106.6
3
3
3
.113,
.139
1
1
2
2
.948,
.954
.413,
.415
[28] 893353
L
4
]ꢂCH
3
CN
{CuO
3
ꢀ21.4
3.359
.442
3.171,
3.126
1.957,
1.967
2.454,
2.447
1.935,
1.939
1.948,
1.954
98.6, 98.6
100.0, 100.8
90.2, 105.7
89.1, 105.1
89.9, 109.1
90.7, 108.5
3
3
3
.111,
.170
1
.969,
(continued on next page)

Table 1 (continued)
(cm 1
ꢀ
)
J
(cm
ꢀ1
)
Cu1–
Cu1
Cu2–
Cu2
Cu1–Cu2
(4ꢄ)
R(Cu–O)
(8ꢄ)
R(Cu–O)
(4ꢄ)
b1(Cu1–O–
a
a
(Cu1–O–Cu2)
No Ref. CCDC code
R
Compound
Chromophore
g
J
2
4
⁄
⁄
(
%)
(2ꢄ)
(4ꢄ)
Cu1)
(Cu1 –O–
2
⁄
b (Cu2–O–
Cu2 )
Cu2)
Bases
Walls
Bases
Walls
Bases
Walls
Bases
Walls
1
2
2
.969
.479,
.502
9
[49] CUEIAB
50]
9.1
4
b-[Cu L
]ꢂ2C H
4 6 6
{CuO
3
ON}
2.05
ꢀ12.8
48.4
3.311
3.287
3.065
3.154
1.983,
2.442
1.974,
2.356
1.972
1.953
1.939
1.962
96.34, 99.39
93.71,
100.08
90.53 102.26
88.93, 107.38
91.65, 107.42
92.39, 105.07
[
3
3
.113
.170
1
2
1
2
.972,
.506
.950,
.328
1
0
1
[30] MUGWUH
[31] BUFTUR
5.5
5.4
[Cu
4
4
L
4
4
]ꢂ2H
2
O
{CuO
{CuO
3
ON}
ON}
2.12
2.08
3.0
64.8,
3.480
3.420
3.132
3.060
1.973,
2.455
1.951,
1.969
103.1
101.3
89.7, 106.1
87.7, 102.3
24.4
1
2
.968,
.439
1
[Cu
L
]ꢂMeOH
3
ꢀ18.8
41
3.512
3.027,
3.122
1.959,
2.403
2.063,
2.581
1.980,
1.918
1.970,
1.958
97.64,
106.80
93.04,
103.97
89.50, 105.89
90.54, 104.01
88.77, 100.81
87.36, 109.85
3.444
3
3
.202,
.259
2
2
2
2
.032,
.333
.003,
.697
1
2
3
[32] ASUPEJ01
6.9
[Cu
4
(HL)
4
] 4H
2
O
{CuO
{CuO
3
ON}
2.01
ꢀ18.0
38.4
34.8
3.438
3.252
3.124
1.974,
1.970
101.9, 101.9
101.9, 101.9
89.6, 104.7
89.6, 104.7
2
1
2
.438
.974,
.438
1
[33] DAEOCU01 6.6
b-[{CuL(NCO)}
4
]
N
3 2
}
2.196 ꢀ116.6
3.153,
3.173
2.165,
2.191
1.925,
2.211
1.925,
2.220
1.916,
2.210
96.59,
103.49
95.15,
105.00
92.17, 102.17
93.11, 101.59
99.11, 98.65
99.98, 99.36
3.240
3
3
.158,
.185
1
2
2
2
.930,
.151
.171,
.217
1
4
5
[51] BOGCOP
[32] SAPYUE
5.3
3.7
[Cu
4
4
L
4
]ꢂ8MeOH
{CuO
{CuO
3
ON}
ON}
2.12
2.02
0
34.2
33.1
3.481
3.419
3.259
1.977
.734
1.948,
2.477
1.944
93.90
86.58, 112.44
2
1
[Cu
(L) (OMe)
2
2
]ꢂ2H
2
OꢂTHF
3
ꢀ15.6
3.077
3.116
1.961,
1.961
100.5, 100.5
103.2, 103.2
91.5, 103.8
88.4, 104.1
3.384
1
2
.991,
.319
1
6
[52] DOWXUI
5.9
[{CuL(NCO)}
4
]ꢂCHCl
3
{CuO
N
3 2
}
2.14
ꢀ70
33.2
26.8
3.238
3.233
3.182
3.154
1.927,
2.182
2.172,
2.199
1.923
2.202
1.926
2.216
95.61 103.86 93.07, 101.66
[53]
ꢀ143.2
95.24,
93.84, 102.18
98.84, 99.39
99.72, 99.73
3
3
.192
.159
104.53
1
2
2
2
.930,
.154
.175,
.202
1
7
[32] SAPYOY
9.9
[Cu
4
4
(L) (OH)
2 2
] 6H O
{CuO
3
ON}
2.06
ꢀ18.4
14.7
3.433
3.107
3.103
1.926,
2.451
1.964,
1.965
102.7, 102.7
103.6, 103.6
88.8, 104.4
89.5, 105.9
3.458
1
.969,

2
.418
1
8
[34]
4.8
[Cu
4
(L)
4
] 2EtOH 2H
2
O
3
{CuO O
2
N}
2.10
0
10.3
3.531
.482
3.176,
3.182
1.962,
2.644
1.977,
2.541
1.927,
1.931
1.961,
1.972
99.02,
102.08
98.64, 99.61
88.61, 110.86
89.65, 108.92
87.60, 108.69
87.45, 110.34
3
3
3
.193,
.234
1
2
1
2
.949,
.608
.956,
.573
1
9
0
[36] DEJKAF
5.2
8.7
[{Cu(L)(OH)}
4
][(hfac)
4
]
{CuO
5
}
2.10
2.34
ꢀ414
0
3.362
3.415
3.023
.137
1.957,
2.411
1.944
1.947
99.94,
99.65
101.29, 101.62
91.06, 91.45
3
1
2
.962,
.425
2
[37] QOMREP
[Cu
4 4
(L) ]
{CuO
3
ON}
15.2
ꢀ9.4
3.165,
3.131
1.973,
2.440
1.969,
2.513
1.953,
1.963
1.955,
1.958
98.5, 100.8
97.7, 98.9
90.0, 106.0
89.3, 107.7
90.3, 104.6
89.4, 105.5
3.342
3
3
.114,
.123
1
2
1
2
.966,
.414
.963,
.453
2
1
[38] FUSVAR
6.0
[Cu
3
(L)
2
(OAc)
2
(MeOH)
2
] [Cu
4
(LH)
4
(OAc)
2
]
3
{CuO O
2
N}
2.17
ꢀ624
ꢀ11
3.460
2.907,
2.907
1.967,
2.494
1.993,
2.465
1.929
1.970
101.10,
101.30
80.36, 81.87
80.36, 81.87
101.49, 101.49
102.87, 102.87
(
ClO
)
4 2
ꢂ4MeOH
3
3
.037,
.078
1
2
1
2
.967,
.494
.993,
.465
2
2
3
[38] FUSVEV
[39]
2.5
3.5
[Cu
[Cu
4
(LH)
4
(OAc)
2
].2ACN.5H
2
O
{CuO
3
O
O
N
2
2
3
N}
N}
}
2.095 ꢀ480
ꢀ12
3.467
2.966
3.041
2.000,
2.473
1.931
1.939
101.07
99.66
83.52, 83.58
101.04, 101.40
3.434
1
2
.998,
.477
2
4
L
4
] 4H
2
O, unit b
{CuO
3
2.40
33.5
ꢀ17.2
3.513
.405
3.220
3.258
1.932,
2.797
1.987,
2.003
97.36
95.40
87.84, 110.46
86.74, 110.13
3
1
2
.971,
.597
2
4
5
[40] NINPEG
[37] QOMRAL
4.4
6.0
[Cu
[Cu
4
L
L
4
](NO
]
3 4
) ꢂ8H
2
O
{CuO
3
2.16
1.95
ꢀ2.6
ꢀ26
ꢀ37.4
ꢀ50
3.211
3.438
3.238
1.952,
.577
1.998
89.20
89.15, 110.10
2
2
4
4
{CuO
3
ON}
3.113,
3.102
1.975,
1.984
2.401,
2.539
1.947,
1.951
1.947,
1.960
98.5, 102.9
99.3, 99.6
89.2, 104.1
89.3, 105.1
88.9, 107.7
89.9, 103.2
3.387
3
3
.169,
.092
1
1
2
2
.977,
.986
.441,
.442
2
2
2
6
7
8
[41] BOQZUD
[13] NODHEV
[39]
9.7
4.3
3.5
[Cu
[Cu
[Cu
4
L
4
L
4
L
4
4
4
] NaClO
4
{CuO
{CuO
{CuO
3
3
3
ON}
2.19
27.2
ꢀ69.8
ꢀ80.5
ꢀ36.7,
3.486
.435
3.229
3.253
1.958,
2.697
1.964,
1.971
94.3, 94.3
95.7, 95.7
86.2, 110.5
87.4, 112.1
3
1
2
.958,
.680
]ꢂH
2
O
ON}
2.053 6.24
3.427
.471
3.316
3.333
1.966,
2.730
1.985,
2.006
92.3, 92.3
94.1, 94.1
88.5, 114.0
87.7, 114.0
3
1
2
.967,
.722
]ꢂ4H
2
O, unit a
O
2
N}
2.40
33.5
3.406
3.360
3.286
3.324
1.967,
2.746
1.981,
1.985
91.02
91.26
87.83, 114.36
88.28, 112.67
ꢀ
159
1
2
.970,
.678
(continued on next page)

Table 1 (continued)
(cm 1
ꢀ
)
J
(cm
ꢀ1
)
Cu1–
Cu1
Cu2–
Cu2
Cu1–Cu2
(4ꢄ)
R(Cu–O)
(8ꢄ)
R(Cu–O)
(4ꢄ)
b1(Cu1–O–
a
a
(Cu1–O–Cu2)
No Ref. CCDC code
R
Compound
Chromophore
g
J
2
4
⁄
⁄
(
%)
(2ꢄ)
(4ꢄ)
Cu1)
(Cu1 –O–
2
⁄
b (Cu2–O–
Cu2 )
Cu2)
Bases
0
Walls
Bases
Walls
Bases
Walls
Bases
Walls
2
9
[42] open
6.5
[Cu
4 2
(L) (HL)
2
(H
2
O)] (ClO
4 2
) ꢂ2H
2
O
3
{CuO ON}
2.16
ꢀ99.0
3.752
3.370,
3.329
1.974,
1.983
2.496,
2.520
1.907,
1.913
1.999,
2.000
91.8, 92.7
99.9, 102.3
90.37, 106.09
90.15, 107.21
85.40, 118.16
84.99, 119.77
3.255
3
3
.151,
.168
1
1
2
2
.936,
.942
.828,
.892
3
0
1
[35] KIGMES
[43] TIJBIY
6.9
4.2
[{Cu(L)(OH)}
[{Cu(OH)(L)}
4
](PF
6
)
4
{CuO
3
N
N
2
}
}
2.10
2.14
15.1
0.16
0
2.914
.914
3.257,
3.257
1.955,
1.947
1.962,
1.948
1.943,
1.954
1.970,
1.995
2.487
2.585
96.62, 96.35
90.77, 93.72
103.02, 104.98
2
3
3
.498,
.622
3
4
](ClO
4
)
4
2
xCH Cl
2
,
{CuO
3
2
ꢀ10.4
2.985
2.949
3.284,
3.303
2.344,
2.358
2.423,
2.419
97.67,
100.00
96.75, 97.31
98.36, 99.44
96.29, 98.31
97.85, 99.49
97.53, 97.16
1
50 K
3
3
.290,
.315
1
1
1
1
.954,
.966
.962,
.991
32
33
34
35
[54] OEACAC10 8.9
50]
a
-[Cu
-[{CuL(NCO)}
(OH)} ](PF
[{CuL(NCO)}
4
L
4
]
{CuO
{CuO
{CuO
{CuO
3
3
3
3
ON}
2.13
2.19
2.21
2.15
ꢀ34
7.0
24.6
0
3.006
3.192
2.952
3.182
3.259
3.193
3.226
1.984
2.006
1.935,
2.316
2.114
2.359
97.78
99.37
98.83
97.63, 98.27
94.19, 104.01
96.28, 97.04
[
[44] DAEOCU
[45] NALDEK
[17] TPAECV
6.8
4.8
7.7
a
4
]
N
2
}
ꢀ42.8
ꢀ82
2
.243
1.930,
.957
[{Cu
4
L
4
4
6
)
4
ꢂ4CH
2
Cl
2
ON}
1
4
]
N
2
}
ꢀ60, ꢀ106
16
3.196,
3.209
1.914,
2.243
2.150,
2.156
99.60
98.93
93.16, 102.92
94.65, 103.92
3.156
1
2
.932,
.214
36
37
38
[17] TCBECU
[17] ICBECU
[17] MAEOCU
10.5 [{CuL(NCS)}
4
]
{CuO
{CuO
{CuO
3
3
3
N
2
}
2.17
ꢀ54, ꢀ144
30
42
0
3.032
.033
3.253,
3.244
1.927,
2.099
1.916,
2.083
2.277,
2.212
2.269,
2.242
97.62, 98.52
97.22, 97.64
95.49, 103.38
95.97, 100.91
96.27, 100.74
97.06, 101.69
3
3
3
.231,
.235
1
2
1
2
.916,
.111
.924,
.116
9.6
9.1
[{CuL(NCO)}
4
]
N
N
2
}
2.16
ꢀ56, ꢀ168
3.054
.050
3.233,
3.253
1.920,
2.130
1.898,
2.113
2.302,
2.226
2.258,
2.275
97.72, 99.01
97.48, 98.32
95.69, 100.80
95.82, 100.51
96.71, 102.03
94.42, 103.60
3
3
3
.255,
.263
1
2
1
2
.910,
.143
.938,
.092
[{CuL(NCO)}
4
], unit-a
2
}
2.135 ꢀ130
2.904
.909
3.478,
3.537
1.941,
1.942
1.953,
1.993
2.399,
2.486
2.521,
2.585
96.82, 94.77
95.70, 96.51
99.44, 100.72
96.37, 100.27
101.81, 106.45
100.64, 103.63
2
3
3
.462,
.353
1
1
.908,
.972

M. Makohusová et al. / Polyhedron 81 (2014) 572–582
579
The cluster No 2 includes a group of complexes (No 13, 16, 33,
and 35) with small prismaticity (p = d or p = R ꢀ R
ꢀ d
positive or negative) that are close to the cube.
For type-II complexes (compressed prism and/or open struc-
tures) J is often small with respect to absolute value of J , and
d
4
2
R
4
2
,
2
4
in some cases it could be ignored or neglected. This occurs when
one Cu–O contact in the base of the prism is much longer (>2.6 Å).
The remaining clusters No 1 (positive J
negative J ) accumulate 24 complexes and they bear the core
information about J correlation.
The relevant J –b and J correlations are displayed in Fig. 5.
4
) and No 3 (predominantly
4
4
–a
2
4
–a
The first correlation is quite good and becomes even better when
the problematic data point No 38 is omitted (because too high
value of structure agreement factor R = 9.1%)
J2 ½cmꢀ ꢁ ¼ ꢀ146:1 ꢂ b½ ꢁ þ 14205; r ¼ ꢀ0:95
1
ꢃ
ð15Þ
The second correlation is worse
J4 ½cmꢀ ꢁ ¼ ꢀ26:57 ꢂ
1
a
½ꢃꢁ þ 2640; r ¼ ꢀ0:57
ð16Þ
but this includes clusters No 1, 2, and 3 with a great structural
diversity. From the last correlation a problematic point No 25
was deleted (because too low value of g = 1.95).
The purpose of the principal component analysis is to obtain a
small number (c) of linear combinations of the variables {V}
which account for most of the variability in the data. This is
preformed by finding new variables ꢀ principal components
P
i
(i = 1,. . .c) through a linear transformation
N
X
T
P
i
¼ u V ¼
u
ni
V
n
ð17Þ
i
n
T
with normalisation of coefficients u u
i
¼ 1. In determining the
i
transformation vectors, covariances are used (Table S2).
In the present case the number of variables is N = 9, and c = 3
components have been extracted, since they posses eigenvalues
greater than 1. Together they account for 87% of the variability
in the original data. The coefficients of the principal components
(
and that of the common factors) are listed in Table S3.
PCA based upon 40 data points shows which variables mutu-
ally correlate and/or anticorrelate (Fig. 6). The pairs of geometric
parameters ( , b), (R , R ) and (d , d ) lie at the opposite sides of
the rays so that they anticorrelate, e.g. with increasing the angle
b decreases and vice versa. The coupling constants J and J anti-
correlate, as well. An anticorrelation is predicted also for the pairs
b, J ) and ( , J ), as already proven by Fig. 5. A more detailed
a
2
4
2
4
a
2
4
(
2
a
4
inspection to the data scattering reveals an agglomeration into
six clusters (labelled by different symbols and colours in
Fig. 6b). Fig. 6c shows the same scattering of points but labelled
according to the individual chromophores. Comparison of
Fig. 6b and c leads to the conclusion that there is not a straight-
forward relationship between five clusters and six chromophores.
The factor analysis again finds a small number (M) of common
factors F
factors
m
, which impact all of the variables, and a set of specific
(which affect only a single variable) defined through
e
p
the transformation
M
X
V
p
ꢀ
lp
¼
L
pm
F
m
þ
e
p
ð18Þ
m
where
l
p
p
refers to the mean value of the variable V . In determin-
ing the factor loading matrix L(Lpm) either covariances, or the cor-
relation coefficients (Table S2) are used. The method used to rotate
the factor loading matrix after its extraction.
In the present case, 3 factors have been extracted, since 3 fac-
tors had eigenvalues greater than 1. Together they account for
8
4% of the variability in the original data. Variables furthest from

5
80
M. Makohusová et al. / Polyhedron 81 (2014) 572–582
Table 2
Averaged data selected for magnetostructural correlations.
(cmꢀ1)
J
(cm
ꢀ1
)
b (°)
a
(°)
d
(Å)
d
(Å)
R
(Å)
R
(Å)
d
ꢀ d
a
R
4
ꢀ R
2
a
Note
No
Cluster
Chromophore
g
J
2
4
2
4
2
4
4
2
Bases
Walls
Bases
Walls
Bases
Walls
Bases
Walls
Bases
Walls
4 2
Type-II, R < R
1
2
3
4
5
6
7
8
9
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
3
1
2
1
1
4
3
4
4
3
3
1
3
3
3
3
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
5
3
3
3
3
3
3
3
3
3
3
N
N
BrN}
2
}
}
2.06
2.096
2.17
2.101
2.02
2.01
2.18
2.09
2.05
2.12
2.08
2.01
2.196
2.12
2.02
2.14
2.06
2.10
2.10
2.34
2.17
2.095
2.4
ꢀ32.6
ꢀ3.4
ꢀ9
89.8
82.8
80
76.6
72
98.4
99.8
104.0
99.7
102.8
99.5
99.6
98.6
98.8
98.5
96.6
98.7
98.5
98.5
98.20
96.4
97.1
97.1
98.3
99.51
97.0
98.55
97.2
99.0
96.4
97.8
91.6
92.4
98.8
99.6
97.2
99.1
101.0
100.8
100.3
3.395
3.380
3.522
3.379
3.529
3.390
3.301
3.400
3.299
3.450
3.478
3.438
3.246
3.481
3.401
3.235
3.445
3.506
3.362
3.378
3.460
3.450
3.459
3.211
3.412
3.460
3.449
3.383
3.503
3.194
3.138
3.175
3.137
3.121
3.144
3.125
3.144
3.125
3.096
3.152
3.124
3.167
3.259
3.096
3.172
3.105
3.196
3.080
3.133
2.982
3.003
3.239
3.238
3.119
3.241
3.324
3.305
3.254
2.229
2.199
2.223
2.186
2.247
2.211
2.187
2.218
2.189
2.209
2.259
2.206
2.120
2.355
2.184
2.118
2.191
2.276
2.189
2.211
2.230
2.237
2.324
2.264
2.218
2.323
2.346
2.340
2.321
1.974
1.957
1.982
1.955
1.943
1.947
1.951
1.944
1.956
1.960
1.956
1.970
2.068
1.944
1.961
2.067
1.964
1.948
1.945
1.957
1.949
1.935
1.995
1.998
1.951
1.967
1.995
1.983
1.955
ꢀ0.201
ꢀ0.242
ꢀ0.347
ꢀ0.242
ꢀ0.408
ꢀ0.246
ꢀ0.176
ꢀ0.256
ꢀ0.174
ꢀ0.354
ꢀ0.326
ꢀ0.314
ꢀ0.079
ꢀ0.222
ꢀ0.305
ꢀ0.063
ꢀ0.340
ꢀ0.310
ꢀ0.282
ꢀ0.245
ꢀ0.478
ꢀ0.447
ꢀ0.220
0.027
ꢀ0.255
ꢀ0.242
ꢀ0.241
ꢀ0.231
ꢀ0.304
ꢀ0.264
ꢀ0.236
ꢀ0.274
ꢀ0.233
ꢀ0.249
ꢀ0.303
ꢀ0.236
ꢀ0.052
ꢀ0.411
ꢀ0.223
ꢀ0.051
ꢀ0.227
ꢀ0.328
ꢀ0.244
ꢀ0.254
ꢀ0.306
ꢀ0.302
ꢀ0.329
ꢀ0.266
ꢀ0.267
ꢀ0.356
ꢀ0.351
ꢀ0.357
ꢀ0.366
2
N
2
}
ꢀ2.2
ꢀ35.2
ꢀ31.6
ꢀ11
R = 8.1
R = 9.1
ON}
ON}
ON}
ON}
ON}
ON}
ON}
ON}
N
ON}
ON}
2
N }
ON}
66
61
97.4
99.5
ꢀ21.4
ꢀ12.8
3
54.6
48.4
44.6
41
38.4
34.8
34.2
33.1
30
97.38
102.2
100.4
101.9
100.1
93.90
101.8
99.81
103.2
99.8
99.8
99.0
101.2
100.4
96.4
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
ꢀ18.8
ꢀ18
2
}
ꢀ116.6
0
ꢀ15.6
ꢀ108.6
ꢀ18.4
0
14.7
10.3
0
R = 8.9
R = 8.7
unit-b
O
}
2
N}
ꢀ414
15.2
ꢀ624
ꢀ480
33.5
ꢀ2.6
ꢀ26
ON}
ꢀ9.4
ꢀ11
ꢀ12
ꢀ17.2
ꢀ37.4
ꢀ50
ꢀ69.8
ꢀ80.5
ꢀ98
ꢀ99
O
2
O
2
O
2
N
3
N}
N}
N}
}
2.16
1.95
2.19
2.053
2.4
89.2
100.1
95.0
93.2
91.1
ON}
ON}
ON}
ꢀ0.293
ꢀ0.219
ꢀ0.125
ꢀ0.078
ꢀ0.249
27.2
6.24
33.5
0
R = 9.7
O
2
N}
unit-a
ON}
2.16
96.7
4 2
Type-I, R > R
30
31
32
33
34
35
36
37
38
39
40
41
5
5
5
2
5
2
5
5
5
5
5
6
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
{CuO
3
3
3
3
3
3
3
3
3
3
5
3
N
N
ON}
N
ON}
N
N
N
N
ON}
}
2
}
}
2.10
2.14
2.13
2.19
2.21
2.15
2.17
2.16
2.135
2.00
2.10
2.085
15.1
0.16
0
7.0
24.6
0
16
30
42
0
96.5
97.9
97.78
99.4
98.8
99.3
97.7
98.1
95.9
98.2
99.8
99.9
98.1
98.1
97.75
99.1
96.7
98.7
98.9
98.7
101.2
99.2
96.7
92.4
2.914
2.967
3.006
3.192
2.952
3.169
3.032
3.052
2.906
2.970
2.976
3.020
3.408
3.298
3.259
3.193
3.226
3.202
3.241
3.251
3.457
3.325
3.271
3.137
1.953
1.967
1.995
2.089
1.943
2.076
2.011
2.018
1.956
1.963
1.946
1.973
2.536
2.386
2.316
2.114
2.359
2.153
2.250
2.265
2.498
2.389
2.412
2.356
0.494
0.331
0.253
0.001
0.274
0.033
0.209
0.199
0.551
0.355
0.295
0.117
0.583
0.419
0.361
0.025
0.416
0.077
0.239
0.247
0.542
0.426
0.466
0.383
2
ꢀ10.4
ꢀ34
R = 8.9
2
}
ꢀ42.8
ꢀ82
2
}
2
}
2
}
2
}
ꢀ83
ꢀ99
R = 10
R = 9.6
unit-a, R = 9.1
R = 9.1
ꢀ112
ꢀ130
ꢀ206.8
ꢀ352
ꢀ523.6
4.32
ꢀ10
203.1
ON}
a
Prismaticity factors: from Cu. . .Cu distances p
d
= d
4
ꢀ d
2
; from Cu–O bond lengths p
R
= R
4
2
ꢀ R .
2
1
50
50
50
50
1
20
100
-
8
0
Cluster
-
-
-
-
-
-
150
250
350
450
550
650
1
2
3
4
5
6
6
0
4
0
2
0
0
89
91
93
95
97
beta
99
101
103
105
Fig. 3. Dendogram (Ward’s method, distance metric: squared Euclidean) for
250
clustering of complexes according to their similarity.
1
50
the reference lines at 0 make the largest contribution to the factors
Cluster
5
0
1
2
3
4
5
6
(Table S4).
FA method offers similar conclusions than the PCA method as
presented in Fig. 7: (i) anticorrelations for (b, J ) and (a, J ); (ii)
2 4
overlap of aggregates for clusters No 1, 2 and 3 in the score-2 ver-
sus score-1 plot; (iii) absence of a straightforward relationship
between clusters and chromophores.
-
50
-
150
89
91
93
95
97
alpha
99
101
103
105
Ruiz et al. [55] performed DFT calculations on two Cu
4
-cubanes:
Fig. 4. Cluster scatterplots with circled areas by CA. Ward’s method, distance
No 1 (belonging to the cluster 1) and No 30 (spanning the cluster 5)
metric – squared Euclidean.

M. Makohusová et al. / Polyhedron 81 (2014) 572–582
581
200
1
00
0
5
0
0
3
8
-
-
-
200
400
600
-
50
cluster 1
cluster 2
cluster 3
25
cluster 5
cluster 4
ignored
-100
ignored
94
96
98
100
o
102
9
4
96
98
100
o
102
β (Cu-O-Cu) /
α (Cu-O-Cu) /
Fig. 5. New magnetostructural correlations J
2 4 4 4
–b (clusters No 4 and 5) and J –a (clusters No 1, 2, and 3) in the cubane-type [Cu O ] complexes; confidence and prediction
intervals are shown at 95% probability level.
hoping that they are good representatives of class II and I, respec-
the calculated DFT data reproduce the experimental susceptibility
curves. To this end, more deep theoretical studies with alternate
methodology would be beneficial.
ꢀ1
tively. For No 30 the values of J
2
= 68.0 and J
4
= 0.6 cm were cal-
= 15.1 and
= 0.16 cm , respectively. For No 1 the DFT values were J = 6.2
= ꢀ32.6
= 89.8 cm . (Tan et al. [29] used values referring to the
2J prefactor in the Hamiltonian, as proven by inspecting the sus-
culated as compared with the magnetic data fitting of J
2
ꢀ1
J
4
2
Physical arguments require that J–a and/or J–R correlations
ꢀ
ꢀ
1
and J
and J
4
= 44.1 cm as compared with the fitted data of J
2
must be non-linear (the bond angle and M–O distance R cannot
a
1
4
be linearly extrapolated to the zero). Therefore a search for non-
ꢀ
linear expressions represents perspectives in this field as probed,
0
ceptibility formula, so that the reported data need be doubled to be
consistent with the present convention.) It was not reported how
for instance, by the equation of the J ¼ fð
a
Þ ꢂ f ðRÞ type elsewhere
[56,57].
5
a)
beta
J4
3
R4R2
1
R4
d4d2
d2
-
-
-
1
3
5
d4
g
R2
J2
0
alpha
-
6
-4
-2
2
4
Component 1, 48.8%
5
3
1
1
3
5
cluster
b)
21
1
2
3
4
5
2
2
40
1
9
5
30
3533 1613
38
-
-
-
2
4
2
8
7
2
-
6
-4
-2
0
2
4
Component 1
5
3
1
1
3
5
chromophore
{CuO3BrN}
c)
{
{
{
{
{
CuO3N2}
CuO3N3}
CuO3O2N}
CuO3ON}
CuO5}
-
-
-
-
6
-4
-2
0
2
4
Component 1
Fig. 6. PCA biplot showing 9 selected variables and 40 objects; (a) for variables (top) and for objects classified according to the cluster or chromophore; (b) agglomeration
according to the clusters (numbering of some points is marked); (c) agglomeration according to the chromophores.

5
82
M. Makohusová et al. / Polyhedron 81 (2014) 572–582
1
0
1
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alpha
J2
d4
1
[
J4
R2
d2
R4
g
[
[
[
beta
0.2
-
[
14] Cambridge
www.ccdc.cam.ac.uk>.
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Centre
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-
1
-0.6
-0.2
0.6
1
Factor 1
[
2
1
0
1
2
3
4
[16] R. Mergehenn, W. Haase, Acta Crystallogr., Sect. B 33 (1977) 1877.
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[
18] S. Mukherjee, T. Weyhermuller, E. Bothe, K. Wieghardt, P. Chaudhuri, Eur. J.
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[
[
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ˇ
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-
-
-
-
1
2
3
4
5
[
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[
23] Z.-X. Wang, X.-L. Li, B.-L. Liu, H. Tokoro, P. Zhang, Y. Song, S.-I. Ohkoshi, K.
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3
-2
-1
0
1
2
[
[
[
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Fig. 7. Factor analysis for variables (top) and objects classified according to the
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[
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. Conclusion
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[
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Statistical analysis of available experimental data reveals a
transparent magnetostructural correlation of J
I complexes (elongated prism), according to a straight line with
negative slope, whereas J also correlates with the angle for
2
versus b for type-
(
1983) 657.
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a
[
[
type-II complexes (compressed prism, open structures). Three sta-
tistical methods (cluster analysis, principal component analysis,
factor analysis) yield essentially the same results being much more
informative in comparison with attempts to correlate coupling
constants with the bond angles according to a straight line. Though
the quality of the structural data can be easily evaluated using the
R-factor, no such a straightforward assessment can be attributed to
the magnetic data and thus some ‘‘experimental’’ magnetic param-
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[
[
[
[
[
[
[
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acknowledged for the financial support.
[
[
[
Appendix A. Supplementary data
[
[
[
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