To investigate the possibility of ligands controlling the electronic structure and magnetic properties, we designed and calculated the geometric and electronic structures of twelve other
Trang 1The role of ligands in controlling the electronic structure
Nguyen Anh Tuana,b, Shin-ichi Katayamaa, Dam Hieu Chia,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
We present our studies of electronic structure and magnetic properties of Mn4þMn3þ3 single-molecule magnets (SMM), i.e,
½Mn4þMn3þ3 O3Cl4ðOAcÞ3ðpyÞ3 (py = pyridine) and ½Mn4þMn3þ3 O3ClðOAcÞ3ðdbmÞ3 (dbmH = dibenzoyl-methane) molecules by using
a first-principles all-electron relativistic method within spin-polarized density functional theory To investigate the possibility of ligands controlling the electronic structure and magnetic properties, we designed and calculated the geometric and electronic structures of twelve other Mn4þMnnþ
3 (n = 2, 3, 4) molecules with different peripheral-ligand configurations The electronic structure of Mnn+ions, and the interatomic distances, electronic structure and magnetic properties of Mn4þMnnþ3 molecules display an interesting variation with n
Ó 2008 Elsevier B.V All rights reserved
PACS: 75.50.Xx; 75.75.+a; 31.15.Ar; 33.15.e; 33.15.Dj; 75.30.Wx
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
nano-magnets in which quantum phenomena such as step like
hysteresis curves of magnetization are observed [1,2]
Beyond being the actors of fundamental quantum
phenom-ena, 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-tion metal elements becomes an important way of control-ling 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 sys-tems which have the same core structure[1,3–6] The only difference lies in their ligand components of the SMM sys-tem Moreover, the outer ligands govern the mutual spatial arrangement of the metal-oxide core, and thus play an important role in determining the intermolecular interac-tion [7] For example, Mn4O3Cl4(O2CEt)3(py)3, one of the tetrahedral Mn4SMM system, forms a dimer structure
in its crystal structure, and shows interesting magnetic behavior completely different from that of individual mol-ecules [3,8,9] In other words, the difference in the spatial arrangement is the primary factor making various Mn4
molecules so different from each other, thereby contribut-ing to the magnetism of the SMM system
In this paper, we present our studies of the electronic structure and magnetic properties of trigonal-pyramid
0927-0256/$ - see front matter Ó 2008 Elsevier B.V All rights reserved.
doi:10.1016/j.commatsci.2008.01.060
*
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: dam@jaist.ac.jp (D.H Chi).
www.elsevier.com/locate/commatsci
Available online at www.sciencedirect.com
Computational Materials Science 44 (2008) 111–116
Trang 2Mn4þMn3þ3 single-molecule magnets (SMM), i.e, ½Mn4þ
-Mn3þ3 O3ClðOAcÞ3ðdbmÞ3 (dbmH = dibenzoyl-methane)
and ½Mn4þMn3þ3 O3Cl4ðOAcÞ3ðpyÞ3 (py = pyridine)
mole-cules by using a first-principles all-electron relativistic
method within spin-polarized density functional theory
To investigate the possibility of controlling the electronic
structure and magnetic properties, we designed and
calcu-lated the geometric and electronic structures of the
four-teen trigonal-pyramid Mn4þMn3þ3 (n = 2, 3, 4) molecules
Our calculations reveal an important role for the ligand
complex in controlling electronic and magnetic properties
of Mn4SMM as well as in designing new SMM with new
functions
2 Methodology
We performed cluster calculations using the program
DMOL3 [10] in Materials Studio package, which is
designed for the realization of large-scale density
func-tional 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
cutoff radius was set to be 7.0 A˚ Spin-unrestricted DFT
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
integra-tion The charge density is converged to 1 106 a.u in
the self-consistent calculation In the optimization
pro-cess, the energy, energy gradient, and atomic
displace-ment are converged to 1 105, 1 104 and 1 103
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
mag-netic moment are obtained by Mulliken population
anal-ysis A Fermi smearing of 0.005 hartree (Ha)
(1Ha = 27.2114 eV) was used to improve computational
performance
3 Results and discussion
3.1 Designing trigonal-pyramid Mn4þMnnþ3 molecules
In this study, fourteen trigonal-pyramid Mn4þMnnþ3
(n = 2, 3, 4) molecules have been designed or reconstructed
They have the general chemical formula Mn4O
3-Cl(OAc)3L13L23 (L1 and L2 are ligand groups) These
molecules consist of the same MnO Cl core and three
OAc bridges, but differ in the peripheral-ligand L1 and L2 groups (Fig 1) Each of them is distinguished from the other by its peripheral ligands L1 and L2 L1 and L2 make two coordinations to complete the distorted octahe-dral geometry at each b-site (as shown in the inset of
Fig 1a), and thus are crucial factor in controlling the charge of Mn ions at this site without breaking the dis-torted cubane geometry of the Mn4O3Cl core A naı¨ve expectation of the formal charge state of metal ions in
Mn4O3Cl core can be derived from the nominal charge of the connected ligands In the case that both L1 and L2 are neutral ligands, the obtained result is Mn4þMn2þ3 mol-ecules In the case that L1 and L2 are a neutral ligand and a radical anion, respectively, Mn4þMn3þ3 molecules are obtained In the case that both L1 and L2 are radical anions, Mn4þMn4þ3 molecules are formed By this means, four Mn4þMn2þ3 molecules, five Mn4þMn3þ3 molecules, and five Mn4þMn4þ3 molecules have been designed Some
of Mn4þMn3þ3 molecules have been synthesized[1,4] The fourteen Mn4þMnnþ3 molecules are labeled from (1) to (14), being classified into the three groups by the formal charge of the manganese ions at the b-site (as shown in
Mn n+
Mn 4+ , a-site
Mn n+
Mn n+
μ3 -O
2-μ3 -Cl
-b
μ3 -O
2-μ3 -O
2-b-site
a
OAc
L1
Mn(1)
Mn(4)
Mn(2) Mn(3)
O(8)
O(1) O(2) O(3)
O(4) O(5)
O(6)
O(7) O(9)
Cl(1)
L2
Mn L
L O(core)
O(core) O(OAc)
Cl(1)
z
x
y
Fig 1 (a) The geometric structure of Mn 4 O 3 Cl(OAc) 3 L1 3 L2 3 , with hydrogen removed for clarity, (b) The geometric structure of the core
Mn O Cl.
Trang 3the Table 1) Group I consists of the four Mn4þMn2þ3
molecules labeled from (1) to (4) Group II consists of
the five Mn4þMn3þ3 molecules labeled from (5) to (9)
Group III consists of the five Mn4þMn4þ3 molecules from
(10) to (14)
3.2 Equilibrium geometry, electronic and magnetic
properties of Mn4þMnnþ3 molecules
To determine the ground-state atomic structure of each
Mn4SMM, we have carried out total-energy calculations
with full geometry optimization allowing the relaxation
of all atoms in the cluster In addition, to investigate the
magnetic properties of the Mn4 SMMs, we probe several
different spin configurations, which were imposed as an
ini-tial condition of the self-consistent calculation procedure
Four possible spin configurations considered in this work
include (i) AFM-HS, (ii) AFM-LS, (iii) FM-HS, and (iv)
FM-LS, where FM and AFM denote the ferromagnetic
and antiferromagnetic couplings between Mn4+ion at the
a-site with Mnn+ ions at the b-site, respectively HS and
LS correspond to the high-spin (electrons are distributed
so that all t2g and eg orbitals are singly occupied before
any pairing occurs) and low-spin (electrons are distributed
in t2gand egorbitals so that they occupy the lowest possible
energy levels) states of Mnn+ ions at the b-site We
con-firmed that the full geometry optimization calculation of
all fourteen Mn4molecules have a similarity in the
arrange-ment 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
differ-ent geometric and magnetic structures of the Mn4molecules
in each group In the case of group I, we obtained four
equi-librium geometric structures corresponding to four different
magnetic structures AIS, ALS, IS and
FM-LS (IS denotes an intermediate-spin state between HS and
LS of Mn ions at the b-site) of each Mn4molecule Our cal-culations showed that there is no difference in atomic arrangement among the four geometric structures of each
Mn4 molecule in group I Moreover, the geometric struc-tures corresponding to the magnetic strucstruc-tures 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 struc-tures 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 with the magnetic structure AFM-LS, while the most stable state of the three other Mn4molecules (2)–(4) is the long-structure with the magnetic long-structure AFM-IS
In the cases of groups II and III, we only obtained two equilibrium geometric structures of each Mn4 molecule from four initial spin configurations The two geometric structures of each Mn4 molecule in groups II and III are nearly the same They are only distinguished by difference
in magnetic structure Their magnetic structures are AFM-HS and FM-HS The most stable state of Mn4 mol-ecules of group II corresponds to the magnetic structure AFM-HS, while the most stable state of Mn4 molecules
of group III corresponds to the magnetic structure FM-HS The geometric structures of the most stable state of (5) and (9) from our calculations are good in agreement with the experimental data reported in[1]and[4] Most differences
of interatomic distances and bond angles are below 5% between our results and the experimental data Some selected interatomic distances of the 14 Mn4molecules are shown in
Fig 2 They are quite similar within the same group, but some of them are considerably different between groups Previous experimental studies[1,4]reported that each of the three Mn3+ions of (5) and (9) exhibit a Jahn–Teller dis-tortion (elongation) along the Cl(1)–Mn3+–O(OAc) axis Our results also show the difference between bond dis-tances from each Mn3+ion to its six surrounding ligands for all five molecules of group II In each molecule of group
II, Mn3+–O(OAc) and Mn3+–Cl(1) bond distances are con-siderably longer than the others The difference between
Mn3+–O(OAc) bond distances with the other Mn3+–O bond distances is over 10% This is evidence of strongly elongated Jahn–Teller distortions along the Cl(1)–Mn3+– O(OAc) axes
No Jahn–Teller distortion is observed in the five mole-cules of group III This result is also consistent with the
HS state of all four Mn4+ions in these molecules
There is also no Jahn–Teller distortion observed in the short-structures of SMMs of group I But, each of the four
Table 1
The chemical formula and classification of Mn 4 molecules by the formal
charge of Mn ions at b-site
Label Ref L1 L2 n Group
(1) CH 3 CN CH 3 CN 2 I
(2) NH 3 CH 2 O
(4) CH 2 O CH 2 O
(8) CH 2 O Cl
(9) [1] dbm
(10) CH 3 O Br 4 III
(11) CH 3 O Cl
N.A Tuan et al / Computational Materials Science 44 (2008) 111–116 113
Trang 4long-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
elon-gated 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
elec-trons occupy in three t2gstates (dxy, dyzand dzx), one
occu-pied 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
cor-responding magnetic moment 3 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
mag-netic moment 4 lB From our calculations, the ground
states of (5) and (9) are determined to have ST of 8.92/2
and 8.89/2, respectively, and the antiferromagnetic
config-uration, in good agreement with the experimental
observa-tion [1,4] Here, it should be noted that these calculated
values are from a Mulliken analysis, so that the values do
not match exactly with the formal valence and spin but
the relative magnitudes compare well The detailed
projec-tions of the calculated magnetic moments for each
individ-ual Mn site of Mn4molecules, as listed inTable 2, also turn
out to be consistent with the formal charges and magnetic
moments of Mn In the case of (5), these results are also
compared well with those of Han et al [14] In generally,
the magnitude of magnetic moment of an Mn4+ ion at the a-site has a nearly constant value of 3 lB, while the magnetic moment of Mnn+ions at the b-site displays an interesting variation with n
In the case of n = 4, the magnetic ground state of
Mn4þMn4þ3 molecules are the FM-HS state with a magnetic moment nearly 3 lB for all Mn ions These values of mag-netic moment are consistent with the formal charge of Mn ions
In the case of n = 3, the magnetic ground state of
Mn4þMn3þ3 molecules are the AFM-HS state with a mag-netic moment nearly 3 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 mag-nitude 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
Mn4þMn2þ3 molecules must be IS and LS corresponding
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
AFM-LS, and the ground state of (2)-(4) is the long-structure with the magnetic structure AFM-IS There is no ground state with the HS state of Mn2+ ions at the b-site of
Fig 2 Some selected interatomic distances of the 14 Mn 4 molecules.
Table 2 The detailed projections of magnetic moments at Mn sites of some selected
Mn 4 molecules Molecule Magnetic structure m Mn(1) m Mn(2) m Mn(3) m Mn(4)
(1) AFM-IS 2.859 3.098 3.095 3.103
FM-IS 2.623 3.179 3.180 3.184 AFM-LS 2.949 1.072 1.064 1.070 FM-LS 2.789 1.135 1.119 1.125 (4) AFM-IS 2.758 3.071 3.071 3.071
FM-IS 2.485 3.183 3.196 3.169 AFM-LS 2.866 1.046 1.030 1.050 FM-LS 2.570 1.146 1.125 1.141 (5) AFM-HS 2.708 3.879 3.873 3.872
FM-HS 2.905 3.897 3.889 3.888 (9) AFM-HS 2.687 3.862 3.853 3.863
Han et al 2.540 3.690 3.710 3.680 FM-HS 2.894 3.874 3.862 3.876 (10) AFM-HS 2.857 2.735 2.720 2.728
FM-HS 2.893 2.733 2.720 2.727 (14) AFM-HS 2.903 2.778 2.765 2.773
FM-HS 2.921 2.805 2.793 2.802
Trang 5Mn3þMn2þ3 molecules, while the magnetic ground state of
Mn4þMn3þ3 and Mn4þMn4þ3 molecules exhibits the HS state
of Mn ions at the b-site Moreover, no compressed
Jahn–Teller distortions are observed at the b-site of
Mn4þMn2þ3 and Mn4þMn3þ3 molecules These results mean
that the dx2-y2-orbital of Mn ions at the b-site of
Mn4þMn2þ3 and Mn4þMn3þ3 molecules must be empty This
can be explained in the term of the ligand field
3.2.3 Magneto-structural correlation in Mn4molecules of
group I
In this section, we discuss about the relation between
magnetic and geometric structures of Mn4molecules The
geometric structures of isomers of each Mn4molecules of
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 Mn4þMn2þ3
molecules is found In each geometric structure of
Mn4þMn2þ3 molecules, the total energy corresponding to
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
long-structure
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
transi-tion structures from the long-structure to short-structure of
each Mn4þMn2þ3 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 3displays the total energy corresponding to the two
magnetic structures AFM-IS and AFM-LS of the linear transition structures from the long-structure to short-struc-ture of selected Mn4þMn2þ3 molecules (1) and (4) These results show the existence of a transition structure in which the two magnetic structures AFM-IS and AFM-LS of each
Mn4+Mn2+ molecules are equal in the total energy These results also show the existence of a low barrier about 0.5
eV between the long- and short-structures of each
Mn4þMn2þ3 molecules, therefore the structure with higher total energy is considered as the meta-stable state There-fore, the magnetic transition between IS and LS states of
Mn2+ ions accompanied by the transition between the long- and short-structures of Mn4þMn2þ3 molecules is more favourable than keeping their geometric structure By this particular behavior, Mn4+Mn2+ molecules can become potential candidates for nano-piezomagnets
4 Conclusions
We have performed studies of the structural, electronic and magnetic properties of fourteen Mn4molecules using
a first-principles method We found that the peripheral ligand groups play an important role in controlling charge and spin states of Mn ions, as well as type of Jahn–Teller distortion at the b-site octahedrons Changing peripheral ligands becomes an effective way to control the electronic structure and magnetic properties of Mn molecules The
Table 3
The calculated down-spin electron, n d; projected at 3d states of Mn ions at
b-site of Mn4þMn2þ3 molecules
Molecule Equilibrium
geometry
Magnetic structure
n d;
Mn(2) Mn(3) Mn(4) (1) Long-structure AFM-IS 1.258 1.257 1.255
FM-IS 1.213 1.211 1.210 Short-structure AFM-LS 2.299 2.303 2.299
FM-LS 2.268 2.375 2.273 (2) Long-structure AFM-IS 0.998 1.001 0.996
FM-HS 0.950 0.954 0.948 Short-structure AFM-LS 2.046 2.050 2.048
FM-LS 2.009 2.019 2.014 (3) Long-structure AFM-IS 1.019 1.019 1.018
FM-IS 0.965 0.968 0.950 Short-structure AFM-LS 2.098 2.105 2.094
FM-LS 2.055 2.062 2.052 (4) Long-structure AFM-IS 1.012 1.011 1.010
FM-IS 0.950 0.943 0.958 Short-structure AFM-LS 2.068 2.075 2.065
FM-LS 2.014 2.025 2.016
Fig 3 The total energy corresponding to the two magnetic structures AFM-IS and AFM-LS of the linear transition structures from the long-structure to short-long-structure of Mn4þMn2þ3 molecules (1) and (4) N.A Tuan et al / Computational Materials Science 44 (2008) 111–116 115
Trang 6geometric structure, electronic structure and magnetic
properties of Mn4þMnnþ3 molecules display an interesting
variation with the charge state of Mnn+ions at the b-site
In these Mn4molecules, 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 Mn4þMn2þ3
mole-cules leads to the possibility of these molemole-cules acting as
a nano-piezomagnet
Acknowledgments
This work was supported by Special Coordination
Funds for Promoting Science and Technology
commis-sioned by MEXT, JAPAN
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