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Journal ArticleDOI

A computational study of structural and magnetic properties of bi- and trinuclear Cu(II) complexes with extremely long Cu---Cu distances

10 Jul 2017-Chemical Physics (Elsevier)-Vol. 491, pp 48-55

AbstractThree recently synthesized copper(II) complexes with aroylhydrazones of trifluoroacetic and benzenecarboxylic acids (Dalton Trans., 2013, 42, 16878) have been computationally investigated by densit ...

Topics: Copper (52%)

Summary (1 min read)

3.1. QTAIM analysis for complexes 1-3.

  • This fact is in a qualitative agreement with the thermal analysis (TGA) data [19] that indicate high thermal stability of the complexes up to 250 °C.
  • The Py-Cu bonds are comparatively weaker than the other Cu-O and Cu-N bonds (Table 1 ), and therefore an increase of temperature before 250 °C leads to the removal of the pyridine molecules.

3.1. Magnetic properties of the dinucler complexes 1 and 2.

  • As can be seen from Figure 2 both complexes 1 and 2 formally are isomeric except the additional axially-coordinated pyridine ligand in complex 2. The distance between the Cu(II) ions for complexes 1 and 2 equals 9.56 and 10.94 Å as determined by X-ray crystallography studies [19] .
  • In order to explain the mechanism of exchange interactions for the studied dicuclear complexes the authors have constructed spin densities and magnetic SOMOs plots with a subsequent analysis of SOMOs decomposition coefficients.
  • A detailed analysis of the decomposition coefficients clearly shows that both SOMOs for each complex have non-zero coefficients on the common atoms of the linker moiety.
  • In the case of complex 1 the magnetic orbitals are mutually rotated about 120° relative to the inner linker moiety, that means they are side-to-side overlapping in contrast to complex 2 for which head-to-head overlapping occurs.
  • The latter case is more spatially preferable and therefore J CuCu for complex 2 is two times higher than for complex 1 despite its longer Cu---Cu distance (10.94 Å vs. 9.56 for complex 1).

3.2. Magnetic properties of the trinuclear complex 3

  • Actually, the more accurately the authors can account for the long-range exchange interactions the more reliable agreement with experiment is achieved.
  • In their recent publication [24] the authors have shown that OSS and triplet states of weakly coupled dinuclear Cu(II) complexes become strictly degenerate if they exclude empirical dispersion corrections from their computational scheme.

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A computational study of structural and magnetic properties of bi- and
trinuclear Cu(II) complexes with extremely long Cu---Cu distances
Gleb V. Baryshnikov
1,2
, Boris F. Minaev
2
, Alina T. Baryshnikova
2
and Hans Ågren
1,3
1
Division of Theoretical Chemistry and Biology, School of Biotechnology,
KTH Royal Institute of Technology, 10691 Stockholm, Sweden.
2
Department of Chemistry and Nano-Material Science,
Bohdan Khmelnytsky National University, 18031 Cherkasy, Ukraine
3
Institute of Nanotechnology, Spectroscopy and Quantum Chemistry, Siberian Federal University,
660041 Krasnoyarsk, Russia
* Corresponding author. Tel.: +46 (0)8 5537 8416; fax: +46 (0)8 5537 8590.
E-mail address: glibar@kth.se (Gleb V. Baryshnikov)
Abstract
Three recently synthesized copper(II) complexes with aroylhydrazones of trifluoroacetic and
benzenecarboxylic acids (Dalton Trans., 2013, 42, 16878) have been computationally investigated
by density functional theory within the broken symmetry approximation accounting for empirical
dispersion corrections. A topological analysis of electron density distributions has been carried out
using Bader’s “quantum theory of atoms in molecules” formalism. The calculated values of spin-
spin exchange for the studied dinuclear complexes indicate a very weak ferromagnetic coupling of
the unpaired electrons in good agreement with experimental data. At the same time, the trinuclear
copper(II) complex possesses a low-spin doublet ground state with one ferromagnetic and two
antiferromagnetic spin projections between the triangular-positioned Cu
2+
ions. The estimated
values of the coupling constants for the spin-spin exchange in this trinuclear complex are in a
qualitative agreement with experimental observations. The calculations support a mechanism of
exchange coupling through the aromatic links in these strongly spin-separated systems.
Keywords: Cu(II) complexes, spin-spin exchange, ferromagnetic coupling, “broken
symmetry” approximation, DFT calculations, Bader analysis, open-shell singlet.

Graphical abstract
1. Introduction
Polynuclear copper(II) complexes represent interesting objects for investigations of
magnetic phenomena [1-5] due to the presence of one unpaired d-electron for each copper(II) center
(electronic configuration of Cu
2+
is [Ar]3d
9
). Because of the strong localization of the unpaired d-
electron around the copper(II) ion and the nearest surrounding one can formally separate these
single-electron magnetic centers in space [1]. Spin-spin interaction between the magnetic electrons,
i.e. between the corresponding singly-occupied molecular orbitals (so-called SOMOs), determines
the type of coupling ferromagnetic when the ground electronic state corresponds to the high-spin
configuration with parallel orientation of electronic spins and antiferromagnetic when the ground
electronic state is characterized by the low total spin with antiparallel orientation of the electronic
spins [1, 2]. Nowadays, the most prevalent and well studied organometallic magnetic systems are
dinuclear copper(II) complexes with different types of linkers between the ligand-coordinated
magnetic centers (-Hal-, [6, 7], -OH-, [4, 6, 8, 9] -OR-, [10–13] CN-, [14] -N^N-, [8, 9, 15] -N^O-
[16, 17] etc.). These complexes can demonstrate a variety of coupling types from strongly
antiferomagnetic (exchange coupling constant J
CuCu
is strongly negative up to -1000 cm
-1
) [4-6] to
moderately ferromagnetic (J
CuCu
is positive, typically of order 100 cm
-1
) [10, 18]. Herein the J
CuCu
constant originates from the standard Heisenberg-Dirac-Van Vleck spin-Hamiltonian Ĥ = −J
12
Ŝ
1
Ŝ
2
,
where Ŝ
1
and Ŝ
2
are local spin operators for each of the paramagnetic centers. At the same time, a
lot of dinuclear copper complexes with strongly space-separated (6–10 Å) copper(II) ions [19-25]
possess a very weak ferro-/antiferomagnetic character due to the very weak exchange between the
magnetic SOMOs. These systems are interesting from a fundamental point of view since the nature
of weak exchange interactions is a key topic of modern molecular spintronics [25]. Moreover, small
values of J
CuCu
are responsible for the
general form of the detected EPR spectrum; when the
absolute value of exchange coupling constant J is comparable with the hyper-fine structure (HFS)
constant for the copper atom (a
Cu
|J|) the EPR result could not be correctly assigned without
spectral simulation, while in the cases a
Cu
>> |J| and a
Cu
<< |J| the spectrum typically consist of four

and seven lines, respectively, with the distinctive intensity ratio of 1:1:1:1 and 1:2:3:4:3:2:1 and
hyperfine splitting of a and a/2, respectively [19].
Trinuclear copper(II) magnetic complexes are not so widespread systems as the dinuclear
complexes, but the theory of spin coupling between triangular-positioned paramagnetic centers is
well developed [2, 26-31]. The spin Hamiltonian for a completely asymmetric trinuclear species can
be written as Ĥ = – (J
12
Ŝ
1
Ŝ
2
+ J
13
Ŝ
1
Ŝ
3
+ J
23
Ŝ
2
Ŝ
3
), where J
12,
J
13
and
J
23
are exchange coupling
constants for each pair of neighboring centers. Due to the multiconfigurational nature of the three-
electron doublets, the individual spins (S
1
= S
2
= S
3
= ½) will result in two spin doublets (D1)
0;
2
1
, (D2) 1;
2
1
and one spin quartet (Q) 1;
2
3
by the following energies [26, 28]:
,
4
1;
2
3
231312
JJJ
E (1)
,
2
)(
4
)(
0;
2
1
21
231323121312
2
23
2
13
2
12231312
JJJJJJJJJJJJ
E (2)
,
2
)(
4
)(
1;
2
1
21
231323121312
2
23
2
13
2
12231312
JJJJJJJJJJJJ
E (3)
where each state is presented in the determinant form as eigenstates of two
operators
31321
; SSSSS . It is straightforward to show that for the asymmetric trinuclear case
(J
12
J
13
J
23
) the D
1
-D
2
and D
2
-Q energy gaps are equal to:
,)()-DD(
21
231323121312
2
23
2
13
2
12211
JJJJJJJJJ (4)
.
2
)(
)-DQ(
1231312
22
JJJ
(5)
For the case of isosceles trinuclear species (J
12
= J
13
J
23
) Eqns. (4)-(5) can be simplified as
follows:
,)-DD(
1223211
JJ
(6)
.
2
)2(
)-QD(
1223
22
JJ
(7)
As we can see from the above presented Eqns. (4)-(7) in both the cases J
12
J
13
J
23
and J
12
= J
13
J
23
, the D
1
, D
2
and Q spin states are characterized by the non-zero energy splitting (Figure 1) which
depends on three and two J
CuCu
coupling constants, respectively. The main problem in the case of
the completely asymmetric trinuclear spin-orientation is that the J
12,
J
13
and
J
23
coupling constants
are strongly correlated and therefore the common least-square fitting procedure of the temperature
(T) – magnetic susceptibility (χ) fails. It should be clarified that J
12,
J
13
and
J
23
are not correlated in
the statistical sense. Simply, there are only two independent energy differences between the ground
state and two excited states, and they can be reproduced by infinite number of three-parameter sets

J
12
, J
13
and J
23
. Due to this reason the experimentally observed )(T
dependence is usually fitted
through the Δ
1
and Δ
2
values by the modified Van Vleck expression [26]:
)/exp(4)/exp(22
)/exp(5)/exp(5.05.0
)(
21
21
22
kTkT
kTkT
QTk
gN
B
, (8)
where N is Avogadro’s number, μ
B
is the Bohr magneton, k is the Boltzmann constant and Q is a
correction for possible intermolecular interaction defined by the own coupling constant J' (usually
very small) and by the number of nearest neighbours.
Figure 1. Schematic representation of magnetic exchange interactions for the dinuclear and
triangular trinuclear Cu(II) complexes.
In the most simplified case of equilateral trinuclear complexes (J
12
= J
13
=
J
23
), Eqns. (4)-(5) can be
reduced by the way that the doublet-doublet splitting
1
disappears (i.e. D
1
and D
2
become strictly
degenerate), while
2
can be expressed via only one J
CuCu
parameter (Figure 1) [29]:
,
2
3
)-QD(
122,1
J (9)
that is quite similar for the singlet-triplet splitting in dinuclear complexes [32]:
,)OSS-T(
12
J (10)
where the OSS abbreviation corresponds to the open-shell singlet state configuration when each
unpaired electron is localized on its own Cu-centered “magnetic” SOMO. Of course, such a state
can not be correctly described within the common single-determinant DFT method. The usage of
accurate ab initio MC SCF methods is also a very complicated task for real Cu(II) complexes due to
limitations of the system size. An alternative is the so-called “Brocken-Symmetry” (BS)
approximation [32, 33] that has been widely used for investigations of magnetic properties of
numerous organometallic systems at the DFT level of theory [4-6, 14, 24]. In the present work we
have particularly focused on the magnetic properties of two dinuclear and one trinuclear Cu(II)
complexes with aroylhydrazones of trifluoroacetic and benzenecarboxylic acids (Figure 2) with

extremely large space-separation of the paramagnetic centers (about 10 Å) [19]. Despite such a long
Cu---Cu distance the studied complexes still demonstrate non-vanishing exchange coupling
between space-separated unpaired electrons as has been detected by V. F. Shul’gin and coauthors
by EPR spectroscopy and by )(T
magnetic susceptibility measurements [19]. Unfortunately, an
unambiguous explanation of the magnetic exchange mechanism for the studied and related systems
is rather difficult and remains an open task for computational inorganic chemistry. In this work we
have tried to solve this task within the BS-DFT approximation using Bader’s “quantum theory of
atoms in molecules” for comprehensively interpreting the electronic structure of the studied
complexes.
Figure 2. The structure of the Cu(II) complexes with aroylhydrazones of trifluoroacetic and
isophthalic (1), terephthalic (2) and trimesic (3) acids.
2. Computational details
The BS-DFT calculations for the complexes 1-3 have been carried out for the non-stationary
geometries extracted from the single-crystal X-ray data published in Ref. [19]. Checking the
stability of the calculated high-spin (HS) and low-spin (BS) states indicates that all are internally
stable. Such a simplification is very important for the direct comparison of the calculated and
experimental J
CuCu
values; even a small distortion of experimental geometry upon the optimization
procedure could provide a dramatic impact on the exchange parameters (especially in the present
case when J
CuCu
values are less than 1 cm
-1
).
We have used the common B3LYP [34, 35] hybrid exchange-correlation functional and the
extended 6-311++G(3df,3pd) basis set [36–39] for the Cu(II) ions. For the rest of C, N, O and H
atoms the 6-31G(d) basis set [40, 41] has been used. In order to take into account the long-range
exchange interactions we have additionally used Grimme’s D2 empirical dispersion correction [42]
realized in the Gaussian09 package [43]. Such computational methodology has been successfully
applied in our recent work for the related strongly space-separated Cu(II) complexes [24]. The plots
of SOMOs and spin density isosurfaces has been simulated within the Chemissian software [44].

Figures (9)
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Frequently Asked Questions (1)
Q1. What are the contributions mentioned in the paper "A computational study of structural and magnetic properties of bi- and trinuclear cu(ii) complexes with extremely long cu---cu distances" ?

The calculated values of spinspin exchange for the studied dinuclear complexes indicate a very weak ferromagnetic coupling of the unpaired electrons in good agreement with experimental data. At the same time, the trinuclear copper ( II ) complex possesses a low-spin doublet ground state with one ferromagnetic and two antiferromagnetic spin projections between the triangular-positioned Cu ions.