Available online at www.sciencedirect.com

Computational Materials Science 44 (2008) 111–116
www.elsevier.com/locate/commatsci

The role of ligands in controlling the electronic structure
and magnetic properties of Mn4 single-molecule magnets
Nguyen Anh Tuan a,b, Shin-ichi Katayama a, Dam Hieu Chi a,b,*
a

School of Materials Science, Japan Advanced Institute of Science and Technology, 1-1, Asahidai, Nomi, Ishikawa 923-1292, Japan
b
Faculty of Physics, Hanoi University of Science, 334 Nguyen Trai, Thanh Xuan, Hanoi, Viet Nam
Available online 18 April 2008

Abstract
single-molecule magnets (SMM), i.e,
We present our studies of electronic structure and magnetic properties of Mn4þ Mn3þ
3
4þ
3þ
½Mn4þ Mn3þ
O
Cl
ðOAcÞ
ðpyÞ
Š
(py
=
pyridine)
and

Keywords: First-principles calculation; Single-molecule magnets; Mn clusters; Nano-piezomagnets; Molecular design

1. Introduction
Single-molecule magnets (SMM) have recently attracted
much interest since they are collections of identical nanomagnets in which quantum phenomena such as step like
hysteresis curves of magnetization are observed [1,2].
Beyond being the actors of fundamental quantum phenomena, molecular magnets are widely studied because various
present and future specialized applications of magnets
require monodisperse, small magnetic particles.
Thestructure of each molecular magnet consists of the
two components: the core which contains transition metal
atoms, and the outer ligand complex. Since each transition
metal atom carries its own spin moment, the core of the
SMM plays the primary role of determining the magnetic
structure of the SMM, and the substitution of the transi*
Corresponding author. Address: School of Materials Science, Japan
Advanced Institute of Science and Technology, 1-1, Asahidai, Nomi,
Ishikawa 923-1292, Japan. Tel.: +81 76 151 1584; fax: +81 76 151 1535.
E-mail address: (D.H. Chi).

0927-0256/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.commatsci.2008.01.060

tion metal elements becomes an important way of controlling the magnetic character of the molecular magnet. Of
course, the outer ligand configuration around the core is
another factor which controls the charge, i.e., valence of
the metal ion and, thereby, its spin. Indeed, rather different
magnetic characteristics are observed in some SMM systems which have the same core structure [1,3–6]. The only
difference lies in their ligand components of the SMM system. Moreover, the outer ligands govern the mutual spatial
arrangement of the metal-oxide core, and thus play an

We performed cluster calculations using the program
DMOL3 [10] in Materials Studio package, which is
designed for the realization of large-scale density functional theory (DFT) calculations. All-electron relativistic
calculations were performed with the double numerical
basis sets plus polarization functional (DNP). The
DNP basis sets are of comparable quality to 6-31G**
Gaussian basis sets [11]. Delley et al. showed that the
DNP basis sets are more accurate than Gaussian basis
sets of the same size [10]. The RPBE functional [12] is
so far the best exchange-correlation functional [13],
based on the generalized gradient approximation
(GGA), is employed to take account of the exchange
and correlation effects of electrons. The real-space global
˚ . Spin-unrestricted DFT
cutoff radius was set to be 7.0 A
was used to obtain all results presented in this work. For
better accuracy, the octupole expansion scheme is
adopted for resolving the charge density and Coulombic
potential, and a fine grid is chosen for numerical integration. The charge density is converged to 1 Â 10À6 a.u. in
the self-consistent calculation. In the optimization process, the energy, energy gradient, and atomic displacement are converged to 1 Â 10À5, 1 Â 10À4 and 1 Â 10À3
a.u., respectively. In order to explore the full freedom
in the potential energy surface and avoid possible saddle
points, the geometric optimization is performed without
any symmetry restriction. The atomic charge and magnetic moment are obtained by Mulliken population analysis. A Fermi smearing of 0.005 hartree (Ha)
(1Ha = 27.2114 eV) was used to improve computational
performance.
3. Results and discussion

OAc bridges, but differ in the peripheral-ligand L1 and
L2 groups (Fig. 1). Each of them is distinguished from

z

a

x

O(OAc)
L

O(core)

Mn
y
L

O(core)

Cl(1)

O(6)
O(5)

O(4)

OAc

O(9)

Mn(1)
O(8)


Mnn+

3.1. Designing trigonal-pyramid Mn4þ Mnnþ
3 molecules
In this study, fourteen trigonal-pyramid Mn4þ Mnnþ
3
(n = 2, 3, 4) molecules have been designed or reconstructed.
They have the general chemical formula Mn4O3Cl(OAc)3L13L23 (L1 and L2 are ligand groups). These
molecules consist of the same Mn4O3Cl core and three

μ 3-Cl-

b-site

Fig. 1. (a) The geometric structure of Mn4O3Cl(OAc)3L13L23, with
hydrogen removed for clarity, (b) The geometric structure of the core
Mn4O3Cl.


N.A. Tuan et al. / Computational Materials Science 44 (2008) 111–116
Table 1
The chemical formula and classification of Mn4 molecules by the formal
charge of Mn ions at b-site
Label
(1)
(2)
(3)
(4)
(5)

NH3
CH2O
dbm
CH3O
CH3O
Br
Cl
Cl

CH3CN
CH2O
CH2O
CH2O
Cl
Br
Cl
Cl

2

I

3

II

4

III


so that all t2g and eg orbitals are singly occupied before
any pairing occurs) and low-spin (electrons are distributed
in t2g and eg orbitals so that they occupy the lowest possible
energy levels) states of Mnn+ ions at the b-site. We confirmed that the full geometry optimization calculation of
all fourteen Mn4 molecules have a similarity in the arrangement of atoms in the core Mn4O3Cl and three bridging
groups OAc (Fig. 1a). Due to the surrounding oxygens
and other ligand structures, one Mn ion at the a-site and
three Mn ions at the b-site are correspondingly labeled as
Mn(1), Mn(2), Mn(3) and Mn(4) to distinguish them.
3.2.1. Equilibrium geometry and magnetic structure
From four initial spin configurations, we obtained different geometric and magnetic structures of the Mn4 molecules
in each group. In the case of group I, we obtained four equilibrium geometric structures corresponding to four different

113

magnetic structures AFM-IS, AFM-LS, FM-IS and FMLS (IS denotes an intermediate-spin state between HS and
LS of Mn ions at the b-site) of each Mn4 molecule. Our calculations showed that there is no difference in atomic
arrangement among the four geometric structures of each
Mn4 molecule in group I. Moreover, the geometric structures corresponding to the magnetic structures AFM-LS
and FM-LS are nearly the same. The geometric structures
corresponding to the magnetic structures AFM-IS and
FM-IS are also nearly the same. Overall bond distances
of the geometric structure corresponding to the magnetic
structures AFM-IS and FM-IS are longer than those of
the geometric structure corresponding to the magnetic
structures AFM-LS and FM-LS. Therefore, we call the
geometric structure corresponding to the magnetic structures AFM-IS and FM-IS as the ‘‘long-structure”, and
the geometric structure corresponding to the magnetic
structures AFM-LS and FM-LS as the ‘‘short-structure”.
In the case of (1), the most stable state is the short-structure

There is also no Jahn–Teller distortion observed in the
short-structures of SMMs of group I. But, each of the four


114

N.A. Tuan et al. / Computational Materials Science 44 (2008) 111–116
Table 2
The detailed projections of magnetic moments at Mn sites of some selected
Mn4 molecules

Fig. 2. Some selected interatomic distances of the 14 Mn4 molecules.

long-structures of SMMs of this group displays three
strongly elongated Jahn–Teller distortions along three
Cl(1)–Mn(2)/Mn(3)/Mn(4)–O(OAc) axes.
The difference in interatomic distances between the
short- and long-structures of each SMM of group I is a
consequence of the Jahn–Teller distortions. These elongated Jahn–Teller distortions are good evidence for the
existence of an IS state of Mn2+ ions at the b-site in the
long-structure of each SMM in group I, where four electrons occupy in three t2g states (dxy, dyz and dzx), one occupied in the higher energy state (dz2). We will discuss this in
more detail in the next section.
3.2.2. Electronic and magnetic properties
Previous experimental studies [1,4] reported that (5) and
(9) have the ground state spin ST of 9/2, where Mn(1) is
antiferromagnetically coupled to Mn(2), Mn(3) and
Mn(4), and assigned a formal valence charge +4 with corresponding magnetic moment À3 lB. At the same time,
Mn(2), Mn(3) and Mn(4) are ferromagnetically coupled
to each other and have a formal valence of +3 with its magnetic moment 4 lB. From our calculations, the ground
states of (5) and (9) are determined to have ST of 8.92/2

2.789

3.098
3.179
1.072
1.135

3.095
3.180
1.064
1.119

3.103
3.184
1.070
1.125

(4)

AFM-IS
FM-IS
AFM-LS
FM-LS

À2.758
2.485
À2.866
2.570

3.071


(9)

AFM-HS
Han et al.
FM-HS

À2.687
À2.540
2.894

3.862
3.690
3.874

3.853
3.710
3.862

3.863
3.680
3.876

(10)

AFM-HS
FM-HS

À2.857
2.893

interesting variation with n.
In the case of n = 4, the magnetic ground state of
Mn4þ Mn4þ
3 molecules are the FM-HS state with a magnetic
moment nearly 3 lB for all Mn ions. These values of magnetic moment are consistent with the formal charge of Mn
ions.
In the case of n = 3, the magnetic ground state of
Mn4þ Mn3þ
3 molecules are the AFM-HS state with a magnetic moment nearly À3 lB for Mn(1) and 4 lB for
Mn(2), Mn(3) and Mn(4). These values of magnetic
moment are also in good agreement with the formal charge
of Mn as well as the existence of the Jahn–Teller distortions
at Mn(2), Mn(3) and Mn(4) sites.
In the case of n = 2 within the long-structure, the magnitude of the magnetic moment of Mn(1) is nearly equal
to 3 lB, and the magnetic moment of Mn(2), Mn(3) and
Mn(4) is nearly 3 lB. In the case of the short-structure,
the magnetic moment of Mn(1) is also nearly equal to
3 lB, but the magnetic moments of Mn(2), Mn(3) and
Mn(4) are smaller by 2 lB than those in the case of the
long-structure. The more detailed analyses show that the
total number of down-spin electron of 3d states of Mn ions
at the b-site in the long-structure and the short-structure is
about 1 and 2, respectively, as listed in Table 3. These
results show that the spin state of Mn2+ ions of
molecules must be IS and LS corresponding
Mn4þ Mn2þ
3
to the long- and short-structures.
As presented in the previous section, the ground state of
(1) is the short-structure with the magnetic structure AFMLS, and the ground state of (2)-(4) is the long-structure


AFM-IS
FM-IS
AFM-LS
FM-LS

1.258
1.213
2.299
2.268

1.257
1.211
2.303
2.375

1.255
1.210
2.299
2.273

AFM-IS
FM-HS
AFM-LS
FM-LS

0.998
0.950
2.046
2.009


AFM-IS
FM-IS
AFM-LS
FM-LS

1.012
0.950
2.068
2.014

1.011
0.943
2.075
2.025

1.010
0.958
2.065
2.016

Short-structure
(2)

Long-structure
Short-structure

(3)

Long-structure

groups II and III are nearly the same. Therefore, they are
not mentioned further in this section. In the case of group
I, the considerable difference in some interatomic distances
between the short- and long-structures of each Mn4þ Mn2þ
3
molecules is found. In each geometric structure of
molecules, the total energy corresponding to
Mn4þ Mn2þ
3
the IS and LS states of Mn2+ ions has been calculated.
In the short-structure, the LS state of Mn2+ ions is more
favourable than the IS state, while the IS state of Mn2+
ions is more favourable than the LS state in the longstructure.
To investigate the possibility of transitions between the
IS and LS states of Mn2+ ions, we performed calculations
of the total energy corresponding to the two magnetic
structures AFM-IS and AFM-LS of the four linear transition structures from the long-structure to short-structure of
each Mn4þ Mn2þ
3 molecule. The total energy corresponding
to the IS state of Mn2+ ions increases on going from the
long-structure to the short-structure, while the total energy
corresponding to the LS state of Mn2+ ions is decreasing.
Fig. 3 displays the total energy corresponding to the two

Fig. 3. The total energy corresponding to the two magnetic structures
AFM-IS and AFM-LS of the linear transition structures from the longstructure to short-structure of Mn4þ Mn2þ
3 molecules (1) and (4).

magnetic structures AFM-IS and AFM-LS of the linear
transition structures from the long-structure to short-strucmolecules (1) and (4). These


geometric structure, electronic structure and magnetic
molecules display an interesting
properties of Mn4þ Mnnþ
3
variation with the charge state of Mnn+ ions at the b-site.
In these Mn4 molecules, the magnetic interaction between
Mn ions is FM between ions in the same valence states,
being AF between ions in difference valance states. The
strong magneto-structure correlation of Mn4þ Mn2þ
3 molecules leads to the possibility of these molecules acting as
a nano-piezomagnet.
Acknowledgments
This work was supported by Special Coordination
Funds for Promoting Science and Technology commissioned by MEXT, JAPAN.
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