An orthogonal ferromagnetically coupled tetracopper(II) 2 × 2 homoleptic grid supported by -O4 bridges and its DFT study

Article abstract of DOI:10.1039/b617587b

A pyrazole based ditopic ligand (PzOAP), prepared by the reaction between 5-methylpyrazole-3-carbohydrazide and methyl ester of imino picolinic acid, reacts with Cu(NO₃)₂·6H₂O to form a self-assembled, ferromagnetically coupled, alkoxide bridged tetranuclear homoleptic Cu(ii) square grid-complex [Cu₄(PzOAP)₄(NO ₃)₂] (NO₃)₂·4H₂O (1) with a central Cu₄[-O₄] core, involving four ligand molecules. In the Cu₄[-O₄] core, out of four copper centers, two copper centers are penta-coordinated and the remaining two are hexa-coordinated. In each case of hexa-coordination, the sixth position is occupied by the nitrate ion. The complex 1 has been characterized structurally and magnetically. Although Cu-O-Cu bridge angles are too large (138-141°) and Cu-Cu distances are short (4.043-4.131 A), suitable for propagation of expected antiferromagnetic exchange interactions within the grid, yet intramolecular ferromagnetic exchange (J = 5.38 cm^-1) is present with S = 4/2 magnetic ground state. This ferromagnetic interaction is quite obvious from the bridging connections (d_x²-y²) lying almost orthogonally between the metal centers. The exchange pathways parameters have been evaluated from density functional calculations. The Royal Society of Chemistry 2007.

Full text of DOI:10.1039/b617587b

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PAPER
www.rsc.org/dalton | Dalton Transactions
An orthogonal ferromagnetically coupled tetracopper(II) 2 × 2 homoleptic
grid supported by l-O bridges and its DFT study†‡
4
a
a
b
c
d
Somnath Roy, Tarak Nath Mandal, Anil Kumar Barik, Sachindranath Pal, Ray J. Butcher,
e
e
a
Mohamed Salah El Fallah,* Javier Tercero and Susanta Kumar Kar*
Received 1st December 2006, Accepted 7th February 2007
First published as an Advance Article on the web 22nd February 2007
DOI: 10.1039/b617587b
A pyrazole based ditopic ligand (PzOAP), prepared by the reaction between 5-methylpyrazole-
-carbohydrazide and methyl ester of imino picolinic acid, reacts with Cu(NO O to form a
·6H
self-assembled, ferromagnetically coupled, alkoxide bridged tetranuclear homoleptic Cu(II) square
grid-complex [Cu (PzOAP) (NO ] (NO O (1) with a central Cu [l-O ] core, involving four
·4H
ligand molecules. In the Cu [l-O ] core, out of four copper centers, two copper centers are
3
3
)
2
2
4
4
3
)
2
3
)
2
2
4
4
4
4
penta-coordinated and the remaining two are hexa-coordinated. In each case of hexa-coordination, the
sixth position is occupied by the nitrate ion. The complex 1 has been characterized structurally and
◦
magnetically. Although Cu–O–Cu bridge angles are too large (138–141 ) and Cu–Cu distances are
˚
short (4.043–4.131 A), suitable for propagation of expected antiferromagnetic exchange interactions
−
1
within the grid, yet intramolecular ferromagnetic exchange (J = 5.38 cm ) is present with S = 4/2
magnetic ground state. This ferromagnetic interaction is quite obvious from the bridging connections
(d
x2−y2 ) lying almost orthogonally between the metal centers. The exchange pathways parameters have
been evaluated from density functional calculations.
Introduction
can be fine-tuned in order to achieve the result of a desired and
interesting supramolecular magnetic property. Transition metal
A major but challenging goal of current research in the realm
of nano-scale materials and inorganic supramolecular chemistry
is the designing of high nuclearity transition metal complexes
template cyclisations have successfully produced many tetranu-
6–12
clear Mn
4
, Ni
4
, Cu
4
and Zn complexes, in which the bridging
4
arrays among the metal ions involve oxygen donor groups. Most
of the so far reported alkoxo-bridged polynuclear grids [Mn(II),
1
with novel magnetic properties. Particularly, the formation of
inorganic supramolecular buildings—looking aesthetically a well-
defined architecture is based on ligands that contain a suitable
arrangement of the appropriate number of binding sites to metal
centers. This must be properly exploited by transition metal ions
to generate the desired nanosized, supramolecular aggregates, the
chemistry of which is currently a remarkable subject of interest
because of their wide application in information storage and
processing technology. A significant amount of control can be
exerted over the formation of relatively low nuclearity molecular
8–12
Co(II) and Ni(II)]
show anti-ferromagnetic coupling, while the
13
ferromagnetic exchange prevails in a few Cu(II) grids. The origin
of this ferromagnetic exchange lies in the orthogonality of the
13
magnetic orbitals. Since orthogonal ferromagnetically coupled
metal grids are scarce we felt inspired to study the chemistry of
these metal grids, especially the ferromagnetically coupled ones.
Herein, we describe the synthesis, structural characterization,
magnetic properties and DFT study of a homoleptic, self-
2
3–5
assembled [2 × 2] square Cu
4
complex of PzOAP exhibiting
intramolecular ferromagnetic exchange.
clusters [<M ] by the use of polyfunctional and polytopic ligands
6
with well defined and appropriately positioned coordination pock-
ets. Likewise, with the appropriate choice of paramagnetic metal
ions to form complexes with these ligands, magnetic coupling
Experimental
Materials
a
Department of Chemistry, University College of Science, 92, A.P.C. Road,
Kolkata, 700 009, India. E-mail: skkar_cu@yahoo.co.in
2-Cyanopyridine was purchased from Aldrich. Commercially
available other chemicals and solvents were used and purified by
standard procedures.
b
Department of Chemistry, St. Paul’s C.M. College, 33/1, Raja Rammohan
Roy Sarani, Kolkata, 700 009, India
14
c
Department of Chemistry, SreeChaitanya College, Habra, North 24 Par-
ganas, West Bengal, India
d
Department of Chemistry, Howard University, 2400 Sixth Street, N.W.,
Physical measurement
Washington, DC, 200 59, USA
e
Departament de Qu ´ı mica Inorg a` nica, Facultat de Qu ´ı mica, Universitat
Elemental analyses (carbon, hydrogen and nitrogen) of the ligand
PzOAP and the metal complex 1 were carried out with a Perkin
Elmer CHNS/O analyzer 2400 at the Indian Association for the
Cultivation of Science, Kolkata. The electronic spectra of 1 in
purified CH CN solution were recorded on a Hitachi model U-
3501 spectrophotometer. IR spectra (KBr pellet, 4000–400 cm )
de Barcelona, Mart ´ı i Franqu e` s 1-11, 08028, Barcelona, Spain. E-mail:
salah.elfallah@qi.ub.es
†
The HTML version of this article has been enhanced with colour images.
Electronic supplementary information (ESI) available: Least-squares
‡
planes (x,y,z in crystal coordinates) and deviations from them. See DOI:
0.1039/b617587b
3
−
1
1
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were recorded on a Perkin Elmer model 883 infrared spectropho-
tometer. Mass spectrum of the ligand was performed at the Indian
Institute for Chemical Biology, Kolkata with a JEOL JMS-AX
l
RT 3.45 B.M. Anal. calc. for [Cu
4
(PzOAP)
4
(NO
3
)
2
](NO
3
)
2
·4H
2
O
(1): C, 34.12; H, 3.36; N, 25.33. Found: C, 34.3; H, 3.23; N, 25.16%.
5
00 mass spectrometer. Room temperature magnetic susceptibility
Crystallographic data collection and refinement of the structure
was measured with a PAR 155 vibrating sample magnetometer.
Magnetic susceptibility measurements for the compound 1 were
carried out on polycrystalline samples, at the Servei de Mag-
netoqu ´ı mica of the Universitat de Barcelona, with a Quantum
Design SQUID MPMS-XL susceptometer apparatus working in
the range 2–300 K under a magnetic field of approximately 500 G
Selected crystal data for 1 are given in Table 1. Data collections for
1
were made using a Bruker SMART CCD detector diffractometer
˚
equipped with a Mo-Ka radiation (k = 0.71073 A) source in φ
and x scan mode at 103(2) K. Cell parameters were determined
16
and refined using the SMART software. Data reductions were
carried out using the SAINT program. The structure was solved
(
2–30 K) and 1000 G (35–300 K). Diamagnetic corrections were
16
estimated from Pascal Tables.
by conventional direct methods and refined by full-matrix least
2
square methods using F data. SHELXS-97 and SHELXL-97
16
Synthesis of ligand and complex
programs were used for structure solution and refinement respec-
tively. H-atoms bonded to water oxygens had their coordinates
5
-Methylpyrazole-3-carbohydrazide was prepared following an
2
refined. Refinement of F was performed against all reflections.
15
established method.
2
The weighted R-factor wR and goodness-of-fit S are based on F ;
conventional R-factors R are based on F, with F set to zero for
PzOAP. The methyl ester of iminopicolinic acid was pre-
pared in situ (Scheme 1) by reaction of 2-cyanopyridine (5.2 g,
2
2
2
negative F . The threshold expression of F > 2r (F ) is used only
for calculating R-factors (gt) etc. and is not relevant to the choice
0
.05 mol) with sodium methoxide solution, produced by dissolving
2
of reflections for refinement. R-factors based on F are statistically
sodium metal (2.5 g, 0.108 mol) in dry methanol (25 mL). 5-
Methylpyrazole-3-carbohydrazide (7 g, 0.05 mol) in 25–30 mL dry
methanol, was added to the above solution with stirring for 1 h.
The mixture was refluxed for 5 h and cooled to room temperature.
Excess methanol was removed in a rotary evaporator to leave
a red coloured oily sticky liquid. It was then mixed with water
about twice as large as those based on F; R-factors based on all
−
data will be even larger. The N–O bond distances in the NO
3
anions were constrained to be equal and refined with a single free
variable. The occupancies of two of the nitrate anions were refined
and the sum of the occupancies constrained to unity. The water
O–H distances were constrained to be 0.85% A.
CCDC reference number 622196.
(
50 mL) and neutralized with AcOH (pH ∼ 5) which afforded a
yellow powder. The solid was filtered off, washed thoroughly with
For crystallographic data in CIF or other electronic format see
DOI: 10.1039/b617587b
methanol and dried in vacuo over fused CaCl
Mp 216 C (decomp.). MS (m/z) 244 (M+, 100%). IR/cm : mNH
2
. Yield (7.32 g, 60%).
◦
−1
3
353; mCO/CN 1651(s), 1539(s); mN–Npz 1057(s); mpy 1004(s). Anal. calc.
for C11 O : C, 54.09; H, 4.92; N, 34.42. Found: C, 53.95; H,
.61; N, 34.32%.
Table 1 Crystallographic data for 1
H
12
N
6
4
Compound
1
Empirical formula
Formula weight
Temperature/K
Wavelength/A˚
C
44 4 28 20
H52 Cu N O
1547.30
103(2)
0.71073
Crystal system
Monoclinic
Space group
C2/c
◦
Unit cell dimensions/ A˚ ,
a = 23.632(2)
b = 14.6528(15), b = 114.1550(10)
c = 18.8956(19)
Volume/ A˚ 3
5970.1(10)
Z
4
−
−
3
Density (calculated)/Mg m
Absorption coefficient/mm
F(000)
1.721
1.505
3152
1
Scheme 1
3
Crystal size/mm
h range for data collection/
0.72 × 0.27 × 0.13
◦
1.68 to 26.54
Index ranges
−29 ≤ h ≤ 28, −18 ≤ k ≤ 18,
−
23 ≤ l ≤ 23
[
Cu
4
(PzOAP)
4
(NO
3
)
2
] (NO
3
)
2
.4H O (1). The ligand PzOAP
2
Reflections collected
26349
(
(
0.122 g, 1 mmol) was added to a hot solution of Cu(NO
3
)
2
·6H
2
O
Independent reflections
6182 [R(int) = 0.0257]
◦
0.148 g, 1 mmol) in H
2
O–CH
3
OH (30 mL) [60 : 40 v/v]. The
Completeness to h = 25.00
99.4%
◦
Absorption correction
Multi-scan
resulting suspension was stirred with heating (∼60 C) until
complete dissolution of the ligand occurred. The resulting deep
green solution was filtered to remove any undissolved ligand and
left at room temperature. Dark green crystals suitable for X-ray
diffraction were isolated from the filtrate after standing for sev-
Max. and min. transmission
Refinement method
1.000 and 0.533
Full-matrix least-squares on F
6182/25/498
2
Data/restraints/parameters
2
Goodness-of-fit on F
1.087
Final R indices [I > 2r(I)]
R indices (all data)
R1 = 0.0456, wR2 = 0.1093
R1 = 0.0525, wR2 = 0.1138
1.459 and −1.200
−
1
eral days (yield 0.108 g, 40%). IR/cm : mNH/H2O 3379, 3179; mCO/CN
1
Largest diff. peak and hole/e A˚ −
3
670(s), 1542(s); mN–Npz 1053(s); mpy 1027(s). UV-vis (kmax): 675 nm.
1
230 | Dalton Trans., 2007, 1229–1234
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◦
Table 2 Selected bond distances ( A˚ ) and angles ( ) in 1
Cu1–O1A
Cu1–O1B_a
Cu1–N1A
Cu1–N2A
Cu1–N3B_a
1.968(2)
2.335(2)
2.024(3)
1.901(3)
1.960(3)
Cu2–O1A
Cu2–O1B
Cu2–N1B
Cu2–N2B
Cu2–N3A
Cu2–O2NA
2.406(2)
1.982(3)
2.017(3)
1.906(3)
1.980(3)
2.736(3)
Cu1–O1A–Cu2
141.34(11)
138.79(11)
160.09(11)
80.03(11)
97.59(11)
93.46(10)
117.16(12)
74.90(11)
Cu2–O2NA–N1N
O1A–Cu2–N1B
O1A–Cu2–N2B
O1A–Cu2–N3A
O1B–Cu2–N1B
O1B–Cu2–N2B
O1B–Cu2–N3A
O2NA–Cu2–N1B
O2NA–Cu2–N2B
O2NA–Cu2–N3A
152.7(2)
Cu1_a–O1B–Cu2
O1A–Cu1–N1A
O1A–Cu1–N2A
O1A–Cu1–N3B_a
O1B_a–Cu1–N1A
O1B_a–Cu1–N2A
O1B_a–Cu1–N3B_a
90.32(10)
115.88(10)
73.35(10)
159.56(11)
79.60(12)
97.14(11)
75.26(12)
89.88(10)
82.38(10)
Fig. 2 Structural representation and atom numbering scheme of the
tetranuclear core in 1.
in parallel pairs around the tetra-copper square, in an opposed
arrangement above and below the metal plane.
The most prominent feature of the structure involves the
encapsulation of the two five-coordinate and two six-coordinate
Cu(II) centers within the grid, an unusual feature in related
Result and discussion
11,17,18
non-homoleptic Cu
4
[2 × 2] square grid complexes.
Hexa-
coordinated Cu(II) undergoes Jahn–Teller distortion and in this
case, each of two six-coordinate copper ions undergoes a tetrago-
nal elongation. The axis of elongation of the copper center includes
only one bridging oxygen connection [O1A], leading to a situation
Structure of [Cu
4
(PzOAP)
4
(NO
3
)
2
] (NO
3
)
2
·4H
2
O (1)
The structure of 1 is illustrated in Fig. 1 and selected bond
distances and angles are listed in Table 2. The cationic cluster
fragment consists of two five-coordinate and two six-coordinate
copper(II) centers arranged in a square, with alkoxide bridges
connecting the metal atoms. The oxygens [both O1A] are located
◦
where the copper equatorial planes are tilted at 88.29 to the
neighbouring penta-coordinated metal center. This orbital orthog-
onality situation leads to significant intramolecular ferromagnetic
interaction. In the asymmetric unit, the two independent nitrate
groups are disordered, one about a twofold axis and the other
about an inversion center.
below the Cu plane and two [both O1B] are located above
4
the plane in a boat-like arrangement. The two-fold rotational
symmetry leads to two equivalent pairs of copper centers [Fig. 2]
with an alternating arrangement of axial [Cu1–O1B 2.335(2)
The lattice structure involves a number of water molecules (here
˚
˚
11,17,18
A, Cu2–O1A 2.406(2) A] and equatorial Cu–O bonds [Cu1–
four) as is typical for grids in this class.
In this crystal structure
˚
˚
O1A 1.968(2) A, Cu2–O1B 1.982(3) A] around the square. The
square pyramidal Cu1 centers have the CuN O chromophore
all the donor centers are from ligand moieties) while axially
distorted octahedral Cu2 centers have the CuN chromophore
one of the water molecules [O1W] is present with unit-occupancy
and there are also two half-occupancy water molecules [O2W,
O3W] in the asymmetric unit.
4
(
4
O
2
(
the additional sixth donor center is from the nitrate oxygen).
Magnetic properties
The variable temperature magnetic susceptibility data for the
compound were recorded between 300–2 K. A plot of v
m
T
ms T in Fig. 3a shows ferromagnetic behavior. At 300 K it
Fig. 1 Structural representation of cationic complex 1.
The Cu
4
square is unsymmetric with four unequal axial contacts
from copper to the oxygen bridges. This leads Cu–Cu separations
˚
which are somewhat different. The separations are close to 4 A
ꢀ
˚
˚
[
Cu2–Cu1 4.131 A, Cu1 –Cu2 4.043 A] with oxygen bridge angles
of 141.34(11) and 138.79(11) at O1A and O1B, respectively. Both
the separations and angle values are quite typical for systems
◦
◦
Fig. 3 (a) Plot of the v T ms T for 1. Solid line corresponds to the best fit
m
11,13
of this sort.
The ligand (PzOAP) allows an orientational
(see text). (b) Experimental variation of the M/N b ms H for compound 1
at T = 2 K.
distinction among four molecules. The four ligands are arranged
This journal is © The Royal Society of Chemistry 2007
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3
−1
shows a v
expected for four uncoupled S = 1/2 spins (with g = 2.14).
T increased slightly when the temperature was lowered and
m
T value of 1.64 cm mol K which is close to that
taking into account the structural and magnetic data found in the
literature, where the ferromagnetic values are varying between 7.2
−
1 20
v
m
and 9.8 cm . This ferromagnetic coupling is in agreement with
the nearly strict orthogonality between adjacent copper magnetic
orbitals and the close proximity of the copper atoms that present
3
−1
reached a maximum value of 2.48 cm mol K at 3 K. This
maximum is consistent with that expected for four copper(II) atoms
coupled ferromagnetically. Below this temperature v
20
m
T decreases
the [2 × 2] magnetic copper grid reported by Thompson et al.
In order to evaluate the three possible exchange pathways
parameters, J , J and J as indicated in Fig. 4; density func-
probably due to intermolecular interaction reaching a value of
3
−1
2
.35 cm mol K at 2 K.
1
2
3
The structure of 1 consists of copper ions linked between them
tional calculations were carried out. The experimental atomic
by PzOAP ligand, giving a tetramer compound. Taking into
account the compound topology (slight distortion from square
coordinates of 1 were performed to obtain the J values, giving the
−
1
−1
following results: J
calculated J values reproduce the trends of the best experimental fit
found before: (J = J
1
= +3.6 cm , J
2
= +4.8 cm and J
3
= 0. The
array, see crystallographic data), three coupling parameters J
1
,
−
1
J
2
and J as shown in Fig. 4 can be considered as interpreting
3
1
= J
2
= +5.4 cm ). The J
3
, second neighbour
the magnetic interactions in complex 1. As a consequence of the
coupling constant is zero as it was considered in the above fit.
coupling scheme, the Hamiltonian to use is the following:
On the other hand, the DFT calculated J values were used
in the CLUMAG program to create the theoretical plot. As is
shown in Fig. 5, a very good agreement was obtained in the range
21
H = −J
1
(S
1
·S
2
+ S
3
·S
4
) − J
2
(S
1
·S
3
+ S
2
·S
4
)
−
J
3
(S
1
·S
4
+ S
2
·S
3
)
(1)
3
00–10 K between the simulated and the experimental curves.
As a first approach, we have considered that J
(no cross-coupling connection) and a Curie–Weiss correction.
For this square disposition, the E value can be obtained by using
the Kambe method from the Hamiltonian:
1
= J
2
= J and J
3
=
The deviation observed at low temperature may result from the
intermolecular interactions. This fact may be corroborated by
0
n
observing the theoretical v T curves and the simulated with the
m
19
−1
best-fitted J value (+5.38 cm ) and h = 0.
H = −J (S ·S + S ·S + S ·S + S
1
1
2
2
3
1
4
3
·S
4
)
(2)
The analysis of the experimental susceptibility data have been
performed using the expression:
2
2
v
m
T = Ng b T(f (J,T)/3 K(T − h)
(3)
Here
f (J, T) = 1
6
exp (J/KT) + 12 exp (2J/KT) + 30 exp (3J/KT)
+ 3 exp (J/KT) + 7 exp (2J/KT) + 5 exp (3J/KT)
−
1
The best fit parameters are: J = +5.38 cm h = −0.88 K and
−
5
g = 2.14 with an error R = 6 × 10 , where R = R[(v
m
T)obs
−
2
2
(
v
m
T)calc] /R(v
m
T)obs
Fig. 5
values and the simulated curves with the best fit J value and h = 0,
respectively. * correspond to the simulated v T curve using the exchange
m
v T ms T plots for 1: The squares and solid line are the experimental
m
coupling parameter constants calculated by the B3LYP functional. In all
cases the g value was fixed at g = 2.14.
This magnetic behaviour can easily be rationalized using the
22
Kahn model. If the coupling constant is given by,
4
Fig. 4 Structural representation of the Cu core and exchange coupling
constants in 1. Multiband cylinder bonds indicate the longer distance
J ≈ 2Kab + 4bSab
Cu · · · O. Dotted lines represents the second neighbour interaction (J
3
),
there are no cross-coupling connections.
the second term will probably be much smaller, because of the
poor overlap between the nearly orthogonal orbitals (JAF = 4bSab
on the bridge [Fig. 6]. In this situation we would expect the first
term, J
= 2 Kab, to dominate, giving an overall positive value for
the coupling constants J and J
On the other hand, the analysis of the spin density distribution
in 1 shows the predominance of a delocalisation mechanism
in the coordinated atoms to the copper ions as it shown in
Fig. 6. Logically considering the electronic configuration of the
Cu(II) cation bearing the unpaired electron in M–L antibonding
)
The field dependence of magnetization (0–5 T) measured at 2 K
is shown in Fig. 3b in the form of M/N b (per Cu entity) ms
H. The field dependence of magnetization (0–5 T) measured at
K [Fig. 3b] suggests that the magnetization tends to 2 Nb. This
4
F
1
2
.
2
feature agrees to the global weak ferromagnetic coupling within
the four copper(II) atoms.
The value of the super-exchange parameter J = +5.38 cm− and
1
h = −0.88 K for compound 1, should be considered as normal,
1
232 | Dalton Trans., 2007, 1229–1234
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E
LS3–EHS = 2J
1
+ 2J
2
26–29
The hybrid B3LYP
functional has been used in all cal-
culations. The use of the nonprojected energy of the broken
symmetry solution as the energy of the low spin state within the
DFT framework provides good results. It avoids the cancellation
30
of the nondynamic correlation effects. We have employed a
triple-n all electron basis set with two polarization functions for
31
copper atoms and a double-n all electron for the other elements
32
proposed by Schaefer et al. Due to the small magnitude of
the exchange coupling constants, all energy calculations were
−
8
performed including 10 density-based convergence criterion.
33
The calculations were performed with the Gaussian 03 using
34
guess functions generated with Jaguar 6.0.
Conclusion
The mixed pyrazole–pyridine ditopic ligand PzOAP forms a
homoleptic 2 × 2 square grid-complex with Cu(II) ions in
which two copper centers are square-pyramidal and the other
Fig. 6 Representation of the spin density maps calculated by B3LYP level
for the S = 2 ground state of 1, showing a near orthogonality between the
adjacent copper(II) atoms. Positive spin populations are indicated.
two are axially distorted octahedral. The Cu
4
4
O unit, the main
backbone of the complex arises through a self-assembly process.
This is controlled by presuming that a predetermined structural
arrangement is logically based on the strategic positions of the
donor groups within the ligand backbone. Variable temperature
magnetic susceptibility studies show that the square copper
cluster exhibits an intramolecular ferromagnetic spin exchange,
associated with orthogonal alkoxide bridging arrangements and
the close proximity of the copper centers. The origin of this
ferromagnetic coupling lies in the approximately orthogonal
orientation of the magnetic orbitals (dx2−y2 ).
2
3
orbitals. There is no significant negative spin population in the
molecule, reflecting the small role of the polarization mechanism.
The topology of the SOMOs and the spin density map in this
case indicates that the adjacent copper(II) are quasi orthogonal
leading to diminished ferromagnetic interaction with the longer
Cu–O distance.
Computational methodology
To calculate the exchange coupling constants for any polynuclear
Acknowledgements
complex with n different exchange constants, the energy of n +
24,25
1
spin configurations must be calculated.
In the case of the
Financial support [01(1916)/04/EMR-II] from Council of Sci-
entific and Industrial Research (CSIR), New Delhi, India, is
gratefully acknowledged. M. S. El Fallah is grateful for the
financial support given by the Spanish Ministerio de Ciencia
y Tecnolog ´ı a (Programa Ram o´ n y Cajal). The Spanish and
Catalan Grants BQU2003/00539, CTQ2005-08123-C02-02/BQU
and 2005SGR-00036 are also acknowledged. J. Tercero is grateful
to the Centre de Computaci o´ de Catalunya (CESCA) with a grant
provided by Fundaci o´ Catalana per a la Recerca (FCR) and the
Universitat de Barcelona.
studied tetranuclear complex to obtain the three J values, we
have calculated the corresponding energy of four different spin
distributions (see Scheme 2).
The following equations have been employed to calculate the
three exchange coupling constants:
E
E
LS1–EHS = 2J
LS2–EHS = 2J
1
+ 2J
+ 2J
3
2
3
Scheme 2
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Dalton Trans., 2007, 1229–1234 | 1233

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234 | Dalton Trans., 2007, 1229–1234
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