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Trang 1A systematic study of influence of ligand substitutions on the electronic
Received 21st April 2008, Accepted 18th August 2008
First published as an Advance Article on the web 11th November 2008
DOI: 10.1039/b806661b
We present a density-functional theory study of the influence of ligand substitutions on the
geometric structure, electronic structure, and magnetic properties of Mn4single-molecule magnets
(SMMs), in order to investigate the role of ligands in controlling these features, as well as in
developing new SMMs and single-chain magnets (SCMs) Our results show that the peripheral
ligands play an important role in controlling the magnetic ground-state of Mn4SMMs A new
model is proposed to explain the spin state of manganese ions in Mn4molecules This model
shows that the saving energy from distortion, which can be controlled by peripheral-ligand
substitutions, plays a crucial role in determining the spin state of manganese ions in Mn4
molecules The mechanism of strong exchange couplings between manganese ions in Mn4SMMs
is revealed The strength of exchange–couplings between manganese ions in Mn4SMMs as a
function of their charge and spin state can be also controlled by substituting peripheral-ligands
The results demonstrate the possibilities of developing new Mn4-based SMMs In addition, strong
spin polarizations on peripheral ligands containing sp2-hybridized carbon sites show that using
ligands containing sp2-hybridized carbon sites can enhance exchange couplings between Mn4
building blocks to develop new SMMs and SCMs which operate at high temperatures
The discovery of individual molecules1–13that can function as
magnets below their blocking temperature (TB) opened a new
area in developing nanoscale magnetic materials, and such
molecules have since been called single-molecule magnets
(SMMs) SMMs have received tremendous attention due to
both their particular physical properties, such as macroscopic
quantum tunneling,3,4 and their potential applications as
quantum bits for quantum computing.5However, the current
record of the TBof SMMs is only several degrees Kelvin.2This
temperature is far too low for practical use Therefore, design
and synthesis of SMMs with higher TBis a big challenge for
chemists and physicists
The increase of TB requires enhancement of the axial–
anisotropy energy barrier (U) to magnetization reversal,
whose maximum value is given as U = ST2|D| for an integral
spin or U = (ST2 1/4)|D| for a half-integral spin (STand D
correspond to the ground-state spin and the axial zero-field
splitting parameter).14,15Further, enhancement of exchange–
couplings between transition metal (TM) ions in SMMs is
found to increase their TB.2 Therefore, designing
mole-cules with a large ST, a high D, and strong intramolecular
exchange–couplings is the key to developing SMMs which operate at high temperatures
The increase of the STis based on increasing the number of transition metal (TM) atoms in molecules, and the ferro-magnetic couplings between them.6,7,9 The enhancement of
Dmainly depends on designing the local anisotropies of the single ions, such as the Mn3+ion, and their vectorial addition
to give a resulting anisotropy.2,8,9,13 Several SMMs with a large ST and a high D have been synthesized, such as (Net4)3[Mn5O(salox)3(N3)6Cl2] (hereafter Mn5) with ST= 11 and D/kB= –0.32 K,13[MnIII6O2(Et-sao)6(O2CPh)2(EtOH)6] (hereafter Mn3+6-(b)) with ST= 12 and D/kB= 0.43 K,9 and [Mn3+
6O2(Et-sao)6(O2CPh(Me)2)2(EtOH)6] (hereafter
Mn3+6-(c)) with ST = 12 and D/kB = 0.43 K.2
Those molecules are recorded as SMMs with the highest TB so far,2,9,13 however, their TB are still on the order of several degrees Kelvin, which can be attributed to weak exchange– couplings between manganese ions.2 The enhancement of exchange couplings between Mn3+ ions from +1.29 K for
Mn3+6-(b) to +2.30 K for Mn3+6-(c) by a ligand substitution increases the TB from 3.5 K for Mn3+6-(b) to 4.5 K for
Mn3+6-(c).2 Therefore, the research of molecular magnets with strong exchange–couplings between TM ions will be very valuable for designing new SMMs which operate at high temperatures For this purpose, distorted cubane [Mn4+Mn3+3(m3-O3)(m3-X)(O2CR)3(L1,L2)3] (X, R, L1, and L2 = various) molecules16–24 (hereafter Mn4) with intra-molecular exchange–couplings, JMn3+ –Mn 4+ E (30–50) K and JMn3+ –Mn 3+ E (10–20) K, tens of times stronger than those of other SMMs are worthy of study While the previous theoretical studies25,26 have tried to calculate important physical quantities, such as magnetic moments of manganese
a School of Materials Science, Japan Advanced Institute of Science
and Technology, 1-1, Asahidai, Nomi, Ishikawa, 923-1292, Japan.
E-mail: natuan@jaist.ac.jp; Fax: +81 (0)76 151 1515;
Tel: +81 (0)76 151 1512
b
Faculty of Physics, Hanoi University of Science, 334 Nguyen Trai,
Thanh Xuan, Hanoi, Vietnam E-mail: tuanna@vnu.edu.vn;
Fax: +84 (04)3858 4438; Tel: +81 (04)3858 4438
w Electronic supplementary information (ESI) available: Molecular
structures; HOMO & LUMO data; pDOS data; magnetic moments of
Mn atoms See DOI: 10.1039/b806661b
Trang 2ions and effective exchange–coupling parameters between
manganese ions, of a few Mn4 molecules, a description of
the mechanism of exchange couplings between manganese ions
of Mn4molecules is still missing
Recently, many synthetic efforts aim at combining molecules
(building blocks) with a high STand a large D to develop new
SMMs with higher TB The combination of molecules can form
metallamacrocycles such as Mn84 torus,10,11 and Mn6Fe6
wheels,12which have been recently recognized as a novel class
of SMMs They can not only function as magnets, but also
exhibit other interesting physical properties that are related to
their particular structural behaviors.27,28The combination of
SMMs can also form single-chain magnets (SCMs), a novel
class of nanomagnets.14,29–32Also, various Mn4molecules have
been synthesized,16–24each Mn4molecule is distinguished from
the others by its ligands, and also exhibits different
charac-teristics due to the function of ligands The existence of the
dimer structure of distorted cubane Mn4O3Cl4(O2CEt)3(py)324
shows that Mn4 molecules can become building blocks for
developing new manganese SMMs and SCMs Here the
parti-cular ligand structure in Mn4O3Cl4(O2CEt)3(py)3was observed
to be responsible for the dimer formation Based on these
observations, we realize that ligands must play an important
role in determining the magnetic behavior of distorted cubane
Mn4, as well as in combining Mn4building blocks to develop
new manganese SMMs and SCMs
In this paper, to reveal the mechanism of strong exchange
couplings in Mn4molecules, to design new Mn4SMMs, and to
look for new building blocks for developing new SMMs which
operate at high temperatures, we explore systematically the
influence of peripheral-ligand substitutions on geometric
structure, electronic structure, and magnetic properties of
Mn4molecules by using first-principles calculations based on
the density-functional theory (DFT) Our results reveal the
important role of peripheral ligands in controlling these
features of Mn4 molecules Our results show that the saving
energy from distortion, which can be controlled by
peripheral-ligand substitutions, plays a crucial role in determining the
spin state of manganese ions in Mn4molecules The
mechan-ism of exchange couplings between manganese ions in Mn4
SMMs is revealed Our results show the strength of exchange–
couplings between manganese ions as a function of their
charge and spin state, which can be also controlled by
substituting peripheral-ligands The results demonstrate the
possibilities of developing new Mn4-based SMMs In addition,
strong spin polarizations on peripheral ligands containing
sp2-hybridized carbon sites show that using ligands containing
sp2-hybridized carbon sites can enhance exchange couplings
between Mn4 building blocks to develop new SMMs and
SCMs which operate at high temperatures
We performed cluster calculations based on density-functional
theory (DFT)33,34using DMol335and OpenMX36codes, with
the double numerical basis sets plus polarization functional
(DNP) For the exchange correlation terms, the generalized
gradient approximation (GGA) RPBE functional37 (DMol3)
and PBE functional38 (OpenMX) were used All-electron
relativistic39 (DMol3) and Troullier–Martins-type pseudo-potentials40(OpenMX) were used to describe the interaction between the core and valence electrons The real-space global cutoff radius was set to be 7 A˚ for all atoms (DMol3); and to be 7.0, 5.0, 4.5, 7.0, 7.0, 5.0, and 4.0 a.u for Mn, O, C, Cl, Br, N, and H atoms (OpenMX) The spin-unrestricted DFT was used
to obtain all results presented in this study The atomic charge and magnetic moment were obtained by using the Mulliken population analysis.41
In DMol3 calculations, 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 106a.u in the self-consistent calculation In the optimiza-tion process, the energy, energy gradient, and atomic displace-ment are converged to 1 105, 1 104and 1 103a.u., respectively A Fermi smearing of 5 103a.u was used to improve the computational performance In order to deter-mine the ground-state atomic structure of each Mn4 SMM,
we carried out total-energy calculations with full geometry optimization, allowing the relaxation of all atoms in molecules
In OpenMX calculations, the real space grid techniques42 were used with the energy cut off of 300 Ry in numerical integrations and the solution of the Poisson equation using fast Fourier transformations (FFT)
First, DMol3 codes were used to compute the geometric structure of Mn4 molecules To find the ground-state spin configuration, different spin configurations with different total magnetic moments were considered After that, the electronic structure and magnetic properties of Mn4 molecules were calculated by using both DMol3and OpenMX codes
3.1 Modeling Mn4molecules
In this study, twenty four Mn4 (Mn4+Mnn+3, n = 2–4) molecules were designed or reconstructed They have the general chemical formula Mn4O3Cl(RCOO)3(L1,L2)3 (R = CH3or C2H5, L1 and L2 = various) These molecules consist of the same Mn4O3Cl(RCOO)3skeleton, but differ in the peripheral ligands L1 and L2
The geometric structures of Mn4O3Cl(RCOO)3(L1,L2)3are schematically displayed in Fig 1 Each molecule has C3v symmetry, with the C3 axis passing through Mn(1) and Cl(1), and includes two sites for manganese ions (A and B) Mn(1) occupies the A site Mn(2), Mn(3), and Mn(4) occupy the B sites The [Mn4O3Cl] core structure can be simply viewed
as a ‘‘distorted cubane’’, in which the four Mn atoms are located at the corners of a trigonal pyramid, with a m3-O2ion bridging each of the vertical faces and a m3-Clion bridging the basal face Three carboxylate (RCOO) groups, forming three bridges between the A site and each of the B sites, play an important role in stabilizing the [Mn4O3Cl] core structure Each peripheral-ligands couple (L1,L2) forms two coordinate bonds, to complete the distorted octahedral geometry at each
B site (as shown in the inset of Fig 1), and thus is a crucial factor in controlling the electronic structure of the manganese
Trang 3ions at the B sites, as well as the physical properties of Mn4
molecules Moreover, the peripheral ligands, governing the
mutual spatial arrangement of the Mn4O3Cl(RCOO)3skeletons,
determine exchange–couplings between Mn4O3Cl(RCOO)3
skeletons, therefore, it is expected that they play an important
role in developing new SMMs The question arises, how will the
geometric structure, electronic structure, and magnetic
pro-perties of Mn4 molecules be controlled by substituting
peripheral-ligand couple (L1,L2) Three kinds of ligand couple
(L1,L2) are used, based on a naı¨ve expectation that the formal
charge state of manganese ions can be derived from the
nominal charge of the ligands When both L1 and L2
are neutral ligands, the modeled molecules are expected to
be Mn4+Mn2+3O3Cl(RCOO)3(L,L)3 These are denoted as
Mn4+Mn2+3 or Mn4(L,L)3 When L1 and L2 are a neutral
ligand and an anionic ligand, respectively, the modeled
mole-cules are expected to be Mn4+Mn3+
3O3Cl(RCOO)3(L,X)3 These are denoted as Mn4+Mn3+3or Mn4(L,X)3 When both
L1 and L2 are anionic ligands, the modeled molecules are
expected to be Mn4+Mn4+3O3Cl(RCOO)3(X,X)3 These are
denoted as Mn4+Mn4+3or Mn4(X,X)3 Table 1 summarizes
the twenty-four different ligand couples (L1,L2) used for
designing the twenty four Mn4molecules (1)–(24) L1 and L2
can be the components of the bidentate chelating group, as in
the cases of (7), (8), (17), and (18) As mentioned above, Mn4
molecules are classified into three groups by the formal charge
(n) of the manganese ions at the B sites, as shown in Table 1
Group I consists of the seven Mn4+Mn2+
3molecules, labeled from (1) to (7) Group II consists of the ten Mn4+Mn3+3
molecules, labeled from (8) to (17) Group III consists of the
seven Mn4+Mn4+3molecules, from (18) to (24)
3.2 Geometric structure, magnetic structure, magnetic anisotropy, and the role of ligands
To determine exactly the magnetic ground-state of the
Mn4+Mnn+3(n = 24) molecules, we probe all possible spin configurations, which were imposed as an initial condition of the structural optimization procedure The number of spin configurations should be considered depending on the charge state of manganese ions In terms of the octahedral field, Mn4+ ions could, in principle, have only the high-spin state with configuration d3(t2g3, eg), in which three d electrons occupy three different t2g orbitals The possible spin states of Mn3+ ions are the high-spin (HS) state with configuration d4(t2g3, eg) and the low-spin (LS) state with configuration d4(t2g4, eg) There are three possible spin states of Mn2+ions: the HS state with configuration d5(t2g3, eg), the intermediate-spin (IS) state with configuration d5(t2g4, eg), and the (LS) state with con-figuration d5(t2g5, eg) Additionally, the magnetic coupling between the Mn4+ion at the A site and Mnn+ions at the B site can be ferromagnetic (FM) or antiferromagnetic (AFM) Therefore, there are six spin configurations which should be considered for each Mn4+Mn2+3molecule, including: (i) AFM-HS; (ii) AFM-IS; (iii) AFM-LS; (iv) FM-HS; (v) FM-IS; and (vi) FM-LS There are four spin configurations which should
be considered for each Mn4+Mn3+3 molecule, including: (i) AFM-HS; (ii) AFM-LS; (iii) FM-HS; and (iv) FM-LS There are two spin configurations which should be considered for each
Mn4+Mn4+3molecule, including: (i) AFM-HS; and (ii) FM-HS From the six initial spin configurations, we obtained four types of geometric structures Type-I, Type-I*, Type-II, and Type-II* of each Mn4+Mn2+3molecule Both the initial spin
Fig 1 The schematic geometric structure of Mn 4 molecules (the
atoms in the distorted cubane Mn 4 O 3 Cl core are highlighted in balls).
The inset is the surrounding ligand configuration of Mn(2) (the
configuration is similar for Mn(3) and Mn(4)).
Table 1 The chemical formula and the peripheral-ligands couple (L1,L2) of each Mn 4 molecule
Group I, n = +2, S T = 3 (1) Mn 4 O 3 Cl(CH 3 COO) 3 (CH 3 CN) 6 CH 3 CN CH 3 CN (2) Mn 4 O 3 Cl(CH 3 COO) 3 (CH 3 CN) 3 (CH 2 O) 3 CH 3 CN CH 2 O (3) Mn 4 O 3 Cl(CH 3 COO) 3 (py) 3 (CH 2 O) 3 Py CH 2 O (4) Mn 4 O 3 Cl(CH 3 COO) 3 (HIm) 3 (CH 2 O) 3 HIm CH 2 O (5) Mn 4 O 3 Cl(CH 3 COO) 3 (NH 3 ) 3 (CH 2 O) 3 NH 3 CH 2 O (6) Mn 4 O 3 Cl(CH 3 COO) 3 (CH 2 O) 6 CH 2 O CH 2 O (7) Mn 4 O 3 Cl(CH 3 COO) 3 (CH 2 (CHO)) 3 CH 2 (CHO) 2
Group II, n = +3, S T = 9/2 (8) Mn 4 O 3 Cl(CH 3 COO) 3 (CH(CHO) 2 ) 3 CH(CHO) 2
(9) Mn 4 O 3 Cl(CH 3 COO) 3 (CH 2 O) 3 (CH 3 O) 3 CH 2 O CH 3 O (10) Mn 4 O 3 Cl(CH 3 COO) 3 (NH 3 ) 3 (CH 3 O) 3 NH 3 CH 3 O (11) Mn 4 O 3 Cl(CH 3 COO) 3 (HIm) 3 (CH 3 O) 3 HIm CH 3 O (12) Mn 4 O 3 Cl(CH 3 COO) 3 (CH 2 O) 3 Cl 3 CH 2 O Cl (13) Mn 4 O 3 Cl(CH 3 COO) 3 (NH 3 ) 3 Cl 3 NH 3 Cl (14) Mn 4 O 3 Cl(CH 3 COO) 3 (py) 3 Cl 3 Py Cl (15) Mn 4 O 3 Cl(C 2 H 5 COO) 3 (py) 3 Cl 3 Py Cl (16) Mn 4 O 3 Cl(CH 3 COO) 3 (py) 3 Br 3 Py Br (17) Mn 4 O 3 Cl(CH 3 COO) 3 (dbm) 3 Dbm
Group III, n = +4, S T = 6 (18) Mn 4 O 3 Cl(CH 3 COO) 3 (dpd) 3 Dpd (19) Mn 4 O 3 Cl(CH 3 COO) 3 (CH 3 O) 3 (CH 3 O) 3 CH 3 O CH 3 O (20) Mn 4 O 3 Cl(CH 3 COO) 3 (CH 3 O) 3 Br 3 CH 3 O Br (21) Mn 4 O 3 Cl(CH 3 COO) 3 (CH 3 O) 3 Cl 3 CH 3 O Cl (22) Mn 4 O 3 Cl(CH 3 COO) 3 Br 6 Br Br (23) Mn 4 O 3 Cl(CH 3 COO) 3 Cl 3 Br 3 Cl Br (24) Mn 4 O 3 Cl(CH 3 COO) 3 Cl 6 Cl Cl
Py = pyridine, HIm = imidazole, dbmH = dibenzoyl–methane, dpdH 2 = 1,3-diphenylpropane-1,3-diol.
Trang 4states AFM-HS and AFM-IS return Type-I with the magnetic
state AFM-IS Both the initial spin states FM-HS and FM-IS
return Type-I* with the magnetic state FM-IS Type-II with
the magnetic state FM-LS is returned from the initial spin
configuration FM-LS Type-II* with the magnetic state
AFM-LS is returned from the initial configuration AFM-LS
Our calculations showed that there is no difference in atomic
arrangement among Type-I, Type-I*, Type-II, and Type-II* of
each Mn4+Mn2+ molecule, except their bond lengths and
bond angles Moreover, Type I and Type I* are quite similar
Type II and II* are also quite similar A comparison of
Mn2+-ligand bond lengths among Type-I, Type-I*, Type-II,
and Type-II* of Mn4+Mn2+3 molecules, as illustrated in
Fig 2, shows that Type-I and Type-I* and relate to the
appearance of elongated Jahn–Teller distortions at Mn2+
sites, while no Jahn–Teller distortion is observed in Type-II
and Type-II* These results are consistent with the spin states
of Mn2+ions in these structures Our calculations show that
the most stable state of (1) and (2) is Type-II with the magnetic
state FM-LS, while the most stable state of (3)(7) is Type-I
with the magnetic state AFM-IS Similarly, the most stable
states of all ten Mn4+Mn3+
3(8)(17) belong to Type-I with the magnetic state AFM-HS, and the most stable states of all
seven Mn4+Mn4+3 (18)(24) belong to Type-II with the
magnetic state FM-HS Note that, Type-I/Type-II relates to
the appearance/disappearance of the elongated Jahn–Teller
distortions at manganese ions at the B sites, as illustrated in
Fig 2
The geometric structures corresponding to the most stable
states of the twenty four Mn4 molecules, of which (14), (15)
and (17) have been synthesized before,17–21 are displayed in
Fig S1 in the ESI.w Our calculations confirm that the C3v
symmetry of Mn4molecules, with the C3vaxis passing through
Mn(1) and Cl(1) of Mn4 molecules, is preserved even if the
peripheral-ligand couple (L1,L2) is changed The geometric
structures of the most stable states of (14), (15) and (17) (from
our calculations) are in good agreement with the experimental
data reported in ref 18 and 21 For example, the differences
between our calculations and the experimental data21
regard-ing the interatomic distances and bond angles of (17) are
mostly below 1.5%, as shown in Table 2 These results suggest
that the GGA RPBE exchange–correlation energy functional
is good enough to determine the geometric structure of Mn4
molecules
As mentioned above, the geometric structure of twenty four Mn4molecules can be also classified into two types: Type-I, with strong Jahn–Teller distortions along the Z axis at the B sites, and Type-II, without a Jahn–Teller distortion Some selected interatomic distances from Mn(2) to its surrounding atoms, as displayed in Fig 3(a), demonstrate the difference between Type-I and Type-II The Mn(2)–O(7) and Mn(2)–Cl(1) bond lengths in Mn4Type-I molecules (3)(17) are about 10% longer than those in Mn4Type-II molecules (1), (2), and (18)–(24) Here it is noted that, some inter-atomic distances in the [Mn4O3Cl(RCOO)3] skeleton corresponding
to AFM-IS and FM-IS are significantly different, in com-parison with those corresponding to AFM-LS and FM-LS due
to the appearance/disappearance of strong elongated Jahn–Teller distortions at Mn2+ ions (B sites) Therefore, there are also two types of the [Mn4O3Cl(RCOO)3] skeleton, Type I and II Type I has strong elongated Jahn–Teller distortions at the B sites Type II does not have elongated Jahn–Teller distortions at the B sites For this reason, to improve computational performance, we should use initial geometric structure of Mn4 molecules with a suitable [Mn4O3Cl(RCOO)3] skeleton to obtain the expected magnetic structure For example, if we would like to find the geometric structure corresponding to the magnetic structure AFM-IS, we should use an initial geometric structure with the [Mn4O3Cl(RCOO)3] Type-I
The existence of Jahn–Teller distortions at the B sites depends on both the charge state and ligand configuration of manganese ions at the B sites In terms of the octahedral field,
Mn4+ions could, in principle, have only the high-spin (HS) state with configuration 3d3(t2g3, eg), in which three 3d electrons occupy three different t2gorbitals Therefore, there
is no Jahn–Teller distortion yielded by Mn4+ions Mn3+ions with the configuration 3d4could, in principle, have HS state with configuration 3d3(t2g3, eg), or a low-spin (LS) state with configuration 3d4(t2g4, eg ), depending, to a first approxima-tion, on the competition between the ligand field splitting energy D (defined as the energy difference between the egand t2glevels) and the mean spin-pairing energy P (defined as the energy required to pair up electrons in the same orbitals), where a small value of D favors HS state, and a small value of
Pfavors LS state Note that, for Mn3+ions, only HS states can yield strong Jahn–Teller distortions There are two types
of Jahn–Teller distortions, corresponding to two different
Fig 2 The comparison of Mn(2)-ligand bond lengths among Type-I, Type-I*, Type-II, and Type-II* of (6).
Trang 5configurations of HS states for Mn3+ ions The elongated
Jahn–Teller distortion corresponds to the configuration
3d4(t2g3, dz21, dx2y20) The compressed Jahn–Teller distortion
corresponds to the configuration 3d4(t2g3, dz20, dx2y21)
In a distorted octahedron with a low symmetric ligand configuration as the B sites, there is not only splitting between
egand t2gorbitals of the central manganese ion, but also there
is further splitting within these eg and t2g orbitals For example, the ligand configuration at each B site of (17) consists
of five O2ions and one Clion, as shown in Fig 4 There-fore, the symmetry of the B sites in (17) now becomes C4v, with the C4axis passing through the Cland Mn3+ions Within this C4vsymmetry, the electron density of dz2orbital of Mn3+ ions must be directed toward the Cland O2ions on the C4 axis, and the electron density of dx2y2orbital of Mn3+ions must be directed toward the four O2ions in the perpendicular plane to the C4axis This is confirmed by our calculations, as illustrated in Fig S2 in the ESI.w Moreover, Cl ions are known as p-donors giving weaker ligand field than O2 ions do.43 Therefore, the HS state with the configura-tion 3d4(t2g3, dz21, dx2y20) is favored over the configuration 3d4(t2g3, dz20, dx2y21) The HS state with the configuration 3d4(t2g3, dz21, dx2y20) is also favored over the LS states, because of the small value of the energy splitting (D) between t2gand dz2levels due to the weak-field ligand Clion
In terms of the ligand-field theory, we can also explain qualitatively the existence of the IS state of Mn2+, as well as the existence of elongated Jahn–Teller distortions at the B sites
in (3)–(7) However, the existence of the LS ground-state of
Table 2 This table shows the comparison between our calculations and experimental data 21 for bond lengths (A˚) and bond angles (deg) at the Mn(2) site of (17) (the calculations are shown in bold) The relative difference (%) between calculated and experimental results is shown in italics (+, overestimation; , underestimation) The calculated bond lengths are usually overestimated in comparison to the experimental results This overestimation was also observed in other six-coordinate transition-metal systems.57One may say that the overestimation of bond lengths is characteristic of GGA RPBE, as well as of other GGA exchange–correlation energy functionals For bond angles, the relative difference between calculated and experimental results is smaller
Mn(2)–Mn(1) 2.840 2.797 1.54 O(7)–Mn(2)–O(3) 89.82 87.0(5) 3.18 Mn(2)–Mn(3) 3.284 3.252 0.98 Cl(1)–Mn(2)–O(7) 172.56 171.9(4) 0.36 Mn(2)–Mn(4) 3.295 3.237 1.79 Cl(1)–Mn(2)–O(1) 84.79 84.6(5) 0.17
Mn(2)–O(7) 2.205 2.139 3.09 Cl(1)–Mn(2)–O(3) 84.76 86.0(4) 1.49 Mn(2)–O(1) 1.954 1.926 1.45 O(1)–Mn(2)–O(7) 89.41 90.4(6) 1.16
L2–Mn(2)–L1 91.01 91.7(6) 0.82 O(3)–Mn(2)–L2 175.48 176.2(6) 0.44 O(7)–Mn(2)–L2 93.43 93.2(6) 0.18 O(3)–Mn(2)–L1 93.43 92.1(6) 1.38 O(7)–Mn(2)–L1 90.79 90.6(6) 0.14 Cl(1)–Mn(2)–L1 94.59 93.5(5) 1.11
Fig 3 The correlations among the structural behavior, the magnetic
interactions between Mn ions, and the spin polarizations on the
ligands in Mn 4 molecules: (a) some selected interatomic distances
from Mn(2) to its surrounding atoms; (b) the magnetic moment of
manganese ion at the A site (m A ), and the average magnetic moment
per manganese ion at the B sites (m B ); (c) the average effective
exchange–coupling parameters between manganese ions J AB refers
to the magnetic interaction between Mn(1) and Mn(2), Mn(3),
Mn(4), and J BB refers to the magnetic interaction between Mn(2),
Mn(3), and Mn(4); (d) the SP on Cl(1) (m Cl(1) ).
Fig 4 The ligand configuration at each B site of (17).
Trang 6Mn2+ions in (1) and (2) shows that proposing a more delicate
model is necessary to explain the spin state of manganese ions
Note that the existence of the LS state of Mn2+ions in (1) and
(2) is related to the Structure Types II and II*, while the
existence of the IS state of Mn2+ions in (3)–(7) is related to
the Structure Types I and I* Our calculations show that the
LS state of Mn2+ions is more favorable than the IS state of
Mn2+ ions in Types II and II* of Mn4+Mn2+3 molecules,
while the IS state of Mn2+ions is more favorable than the LS
state of Mn2+ions in Types I and I* of Mn4+Mn2+3
mole-cules This means that the saving energy from distortion plays
a crucial role in determining the spin state of Mn2+ions in
Mn4+Mn2+
3 molecules To explore more about this, the geometric structural dependence of the total energy of the
magnetic states AFM-IS and AFM-LS of Mn4+Mn2+3
molecules has been investigated Based on the Type-I and
Type-II* structures, a series of model structures of each
Mn4+Mn2+
3 molecule has been carefully prepared The coordinate vector of atoms in the ith structure is determined
by the following formula,
ri= rI+ i (rII rI)/5 where, rI and rII are coordinate vectors of atoms in the
Type-I and Type-II* structures, respectively Note that
the Type-I and Type-II* structures correspond to i = 0 and 5,
and structures corresponding to 0o i o 5 are the transition
structures between the Type-I and Type-II* structures
Fig 5 displays the geometric structural dependence of the
total energy of the AFM-IS and AFM-LS states of (1), (2), (3),
(5), and (6) on going from i = –1 to i = 6 The intersection of
the total energy curves of the AFM-IS AFM-LS states shows
the existence of the transition state (TS) between the AFM-IS
and AFM-LS states In the transition state, the AFM-IS and
AFM-LS states have the same energy On the right side of the
TS, the AFM-LS is more favorable than the AFM-IS, while
on the left side of the TS, the AFM-IS is more favorable than
the AFM-LS We have the saving energy on going to the right
side of the TS DELS= ETS EAFM-LS(ETSis the total energy
of the TS, and EAFM-LS is the total energy in the AFM-LS
state of the model structure under consideration) and the
saving energy on going to the left side of the TS DEIS= ETS
EAFM-IS(EAFM-ISis the total energy in the AFM-IS state of
the model structure under consideration) Therefore, the
favorable magnetic state will be the AFM-IS state or the
AFM-LS state, depending on the competition between
the maxima of DEISand DELS The AFM-IS will be favorable if
DEIS-max 4 DELS-max, on the contrary, the AFM-LS will be
favorable if DEIS-maxo DELS-max The values of DEIS-max and DELS-max of several Mn4+Mn2+
3molecules, as tabulated
in Table 3, show that these values are significantly different between Mn4+Mn2+3 molecules The reason is due to diffe-rences in their peripheral ligands (L1 and L2) This means that the saving energies DELS-max and DEIS-max, as well as the spin state of Mn2+ ions, can be controlled by changing peripheral ligands CH3CN can yield a large DELS-max, while other ligands can yield a large DEIS-max, as shown in Table 3 The Jahn–Teller distortion is known as one of the origins of the axial anisotropy in Mn SMMs.1,2,13,32Therefore, not only
Mn4+Mn3+
3 molecules,18–24 but also Mn4+Mn2+
3 Type-I molecules, are expected to have high axial anisotropy
3.3 Electronic structure and magnetic properties Previous experimental studies18–24reported that (14), (15), and (17) have the ground state spin STof 9/2, where Mn(1) with formal charge +4 and formal magnetic moment 3mB is antiferromagnetically coupled to Mn(2), Mn(3) and Mn(4)
At the same time, Mn(2), Mn(3) and Mn(4) are ferromagne-tically coupled to each other, and have a formal valence of +3 with their formal magnetic moment +4mB From our calcula-tions, the ground states of (14), (15), and (17) are determined
to have an ST of 9/2, and antiferromagnetic (AFM) con-figuration, consistent with the experimental observation.18–24 The detailed projections of the calculated magnetic moments for each individual Mn site (mMn(i), i = 1–4) of (14), (15), and (17), are listed in Table 4 The magnetic moments of manga-nese ions obtained from DMol3 and OpenMX are quite similar They are also consistent with those obtained by other DFT methods.25,26 However, the calculated values do not exactly match the formal magnetic moment To explain the difference, Han et al.25said that the difference is because these calculated values were obtained from Mulliken analysis.41 However, the nature of the difference between the calculated and formal magnetic moments is that the latter was obtained based on the ionic model, which did not consider quantum mechanisms such as exchange–couplings, the former was obtained with consideration of these mechanisms In the ionic model, unpaired (magnetic) d electrons of each Mn site are assumed to belong completely to that Mn site, but in practice, these unpaired d electrons can delocalize over other sites due
to exchange couplings, as explained below
It is easy to see that the calculated magnetic moments of manganese ions of (14), (15) and (17) obtained from different DFT methods, as listed in Table 4, have the same feature, that
is, they are smaller than their formal magnetic moments,
Fig 5 The geometric structure dependences of the total energy of the magnetic structures (AFM-IS and AFM-LS) of selected Mn 4+ Mn 2+
3
molecules (1), (2), (3), (5) and (6).
Trang 7especially for Mn(1) In our calculations, the differences between
the calculated and formal magnetic moments are DmMn(1)E 0.3 mB
for Mn(1), being DmMn(2)E 0.1 mBfor each of Mn(2), Mn(3),
and Mn(4) Note that DmMn(1)is about three times DmMn(2)
Moreover, based on the observation of the projected density of
state (pDOS) at the Mn(1) site of (17) in the paper by Han’s
et al.,25we found the existence of the spin-up states just below
the Fermi level at this site, while Mn(1) with formal magnetic
moment3mBwas only expected to contribute to spin-down
states Therefore, one may suspect that the origin of the
considerable differences between calculated and formal values
must be due to antiferromagnetic couplings between d states of
Mn(1) and Mn(2)–(4) To shed light on this assumption, we have
investigated the projected density of state (pDOS) at these Mn
sites The pDOSs at Mn(3) and Mn(4) sites are the same as the
pDOS at Mn(2) site due to the C3vsymmetry of (14), (15), and
(17) Therefore, the pDOS at Mn(2) site can be representative of
those at Mn(3) and Mn(4) sites The pDOSs at the Mn(1) and
Mn(2) sites of (14), (15), and (17) are displayed in Fig 6 The
evidence of the quite strong antiferromagnetic coupling between
dstates of Mn(1) and Mn(2) in each of these molecules is the
superposition of two clear peaks corresponding to the
minor-spin state of Mn(1) and the major-minor-spin state of Mn(2) just below
the Fermi level, marked by an arrow Based on the spin states
and the pDOSs of manganese ions, we can confirm that these
couplings are between the occupied dz2 orbitals of Mn(2)–(4)
and the unoccupied t2gorbitals of Mn(1) By these couplings, the
spin-up dz2 electrons can localize not only over the Mn(2)–(4)
sites but also over the Mn(1) site, leading to the calculated
magnetic moments of manganese ions are smaller than their
formal magnetic moments Note that, in (14), (15) and (17), the
interatomic distance between Mn(1) and Mn(2) is quite large,
about 2.85 A˚ Therefore, the couplings between d states of
Mn(1) and Mn(2) must be through p states of the ligands
bridging between them, such as the m3-O2 ions in the
[Mn4O3Cl] core This is confirmed by the Kohn–Sham orbitals just below the Fermi level, as shown in Fig S3 in the ESI.w
Table 3 The maximum saving energies from the distortions, DE IS -max and DE LS -max, of several Mn 4+ Mn 2+
3 molecules
Table 4 The selected physical quantities of (14), (15), and (17): the magnetic moments at Mn(1)–(4) sites, m Mn(1)–(4) The average effective exchange–coupling parameters J AB refers to the magnetic interaction between Mn(1) and Mn(2), Mn(3), Mn(4) and J BB refers to the magnetic interaction between Mn(2), Mn(3), and Mn(4) (The OpenMX values are shown in italics)
23.32a 2.83
24.33a 2.60
77.98b 3.14
a The value is obtained using the total energy difference method b The value is obtained using the Green’s function method.
Fig 6 The pDOS near the Fermi level at Mn(1) and Mn(2) sites of (14), (15), and (17).
Trang 83.3.1 The magnetic moment of manganese ions and the
ground-state spin of Mn4 For Mn4+Mn3+
3 molecules (8)(17) in Group II, the calculated magnetic moments of
the manganese ions, as tabulated in Fig 3b and Table S1 in the
ESI,w are smaller in comparison to their formal magnetic
moments, due to the quite strong antiferromagnetic couplings
between the occupied dz2 orbitals of Mn(2)–(4) and the
unoccupied t2g orbitals of Mn(1), as mentioned above for
(14), (15), and (17) However, couplings preserve the total
magnetic moment, as well as the ground-state spin (ST)
of molecules; therefore, the ST of Mn4+Mn3+3 molecules
can be estimated from the formal spins of manganese ions,
ST= 4 3 – 1 3/2 = 9/2
For Mn4+Mn4+3 molecules (18)–(24) in Group III, the
couplings between d states of manganese ions are weak, as
displayed in Fig S4 in the ESI.w However, the magnetic
moments of manganese ions, as tabulated in Fig 3b and
Table S1 in the ESI,w are still slightly smaller than their formal
magnetic moments, because of the spin polarizations on
peripheral ligands, which will be discussed in section 3.3.3
The STof Mn4+Mn4+3molecules can also be estimated from
the formal spins of manganese ions, ST= 4 3/2 = 12/2
For Mn4+Mn2+Type-I molecules (3)–(7) in Group I, the
antiferromagnetic couplings between d states of Mn(1) and
Mn(2)–(4) are quite strong and complex, as displayed in Fig 7
Fig 7 shows that there are not only the coupling between the
occupied dz2spin-up orbitals of Mn(2)–(4) and the unoccupied
t2gspin-up orbitals of Mn(1), but also the coupling between
the occupied t2g spin-down orbitals of Mn(2)–(4) and the
unoccupied egspin-down states of Mn(1), marked by arrows
The magnitude of magnetic moment of Mn(1) can be reduced
by the former coupling, while it can be enhanced by the latter
coupling Therefore, depending on the contribution of
each coupling, the magnitude of the magnetic moment of
Mn(1) can be smaller or larger than its formal magnetic
moment |3mB| In more detail, the DMol3
values are smaller
|–3mB|, while the OpenMX values are mostly larger than
|3mB|, as shown in Fig 3b and Table S1 in the ESI.w These
differences between the DMol3and OpenMX values can result from the difference in the correlation term between the RPBE37 and PBE38 energy functionals In (3)–(7), the magnetic moments of manganese ions at the B sites, as tabu-lated in Table S1,w are significantly different from their formal magnetic moment, +3mB, due to the strong spin polarizations
on the sp2-hybridized C atoms of peripheral ligands, which will
be discussed in section 3.3.3 The ST of Mn4+Mn2+3 Type-I molecules can also be estimated from the formal spins of manganese ions, ST= 3 3/2 1 3/2 = 6/2
For Mn4+Mn2+Type-II molecules (1) and (2), as displayed
in Fig S5 in the ESI,w Mn(1) is ferromagnetically coupled to Mn(2)–(4) Fig S5w shows that these couplings are between the occupied t2g spin-down states of Mn(2)–(4) and the unoccupied eg spin-down states of Mn(1), marked by an arrow, leading to the calculated magnetic moment of Mn(1) being considerably smaller than its formal magnetic moment, +3mB, while the calculated magnetic moments of Mn(2)–(4) are larger than their formal magnetic moment, +1mB, as shown in Fig 3b and Table S1.w In (2), the calculated magnetic moments of Mn(2)–(4) are significantly larger than +1mB because of the strong spin polarizations on the
sp2-hybridized C atoms of peripheral ligands, which will be discussed in section 3.3.3 The ST of Mn4+Mn2+3 Type-II molecules can be also estimated from the formal spins of manganese ions, ST= 3 1/2+1 3/2 = 6/2
In general, in each Mn4 molecule, due to exchange– couplings, unpaired d electrons can decentralize from the B sites to the A site, as well as to ligand sites, leading to the differences (Dm) between the calculated and formal magnetic moments of manganese ions Based on the observations of overlap areas between the pDOSs of Mn(1) and Mn(2)–(4) just below the Fermi level, we can predict that the exchange couplings between Mn(1) and Mn(2)–(4) are quite strong
in Mn4+Mn2+3 and Mn4+Mn3+3 molecules, while they should be weak in Mn4+Mn4+3molecules To shed light on this, we will perform calculations of the effective exchange– coupling parameters between manganese ions in Mn4 molecules
3.3.2 The effective exchange–coupling parameters between manganese ions The adoption of the first principle methods for the investigation of magnetic molecules offers a unique opportunity to calculate exchange parameters, otherwise inferred from fitting the eigenvalue spectrum of an appropriate spin interaction Hamiltonian to magnetization, specific heat, and neutron scattering measurements There are several ways
to extract exchange parameters from the calculations, for instance, by exploiting the concept of the magnetic transition state,44,45 by the local-force method,46 by the total energy difference method,47–52or by the Green’s function method.25
We adopt these last two methods
The total energy difference method has been successfully applied to several magnetic molecules, e.g., Mn12,47,48V15,49,50
Fe6,51and Cr8.52This method relies on the mapping of the first principle Hamiltonian onto a spin model Hamiltonian, that in our case is the Heisenberg Hamiltonian Considering only Heisenberg exchange interactions between the Mn magnetic
Fig 7 The pDOS near the Fermi level at Mn(1) and Mn(2) sites of
selected Mn 4+ Mn 2+
3 Type-I molecules (4) and (7).
Trang 9moments, and in absence of anisotropy terms, the eigenvalue
of the Hamiltonian for Mn4molecules is simply
ETOT=2JABS~1(~S2+ ~S3+ ~S4)
2JBB(~S2~S3+ ~S3~S4+ ~S4~S2) where S1and S2= S3= S4are the spin moments in units of
Bohr magneton of Mn(1), (2), (3) and (4), respectively JAB
refers to the magnetic interactions between Mn(1) and Mn(2),
(3), (4), and JBB refers to the magnetic interactions between
Mn(2), Mn(3), and Mn(4)
In the case in which Mn(1) is antiferromagnetically coupled
to Mn(2), Mn(3) and Mn(4), (AFM configuration), the
eigen-value of the Hamiltonian is ETOTAFM= 6JABS1S2 6JBBS2
In the case in which Mn(1) is ferromagnetically coupled to
Mn(2), Mn(3) and Mn(4), (FM configuration), the eigenvalue
of the Hamiltonian is ETOT
FM =6JABS1S2 6JBBS2
In the case in which Mn(1) is ferromagnetically coupled to
Mn(2), and both of them are antiferromagnetically coupled
to Mn(3) and Mn(4) (MIX configuration), the eigenvalue of
the Hamiltonian is ETOTMIX = 2JABS1S2 + 2JBBS2 After
straightforward algebra, we end up with the formula
JAB¼DE
TOT AFMFM
12S1S2
JBB¼DE
TOT
AFM
12S2 þDE
TOT
FM
24S2
where DETOTAFMFM = ETOTAFM ETOT
FM, DETOTMIXAFM =
ETOTMIX ETOT
AFM and DETOTMIXFM = ETOTMIX ETOT
FM are the calculated total energy differences per formula unit between
AFM and FM, the MIX and AFM, and MIX and FM
configurations, respectively
A fundamental prerequisite for the direct application of the
Heisenberg model to calculate effective exchange–coupling
parameters is the localization of the magnetic moments This
means that magnitude of magnetic moments of ions in
the magnetic configurations AFM, FM, and MIX must be
the same Our calculated results, as tabulated in Table S2
in the ESI,w show that the differences in magnitude of the
magnetic moments of manganese ions between the magnetic
configurations under consideration are small for mMn(2),
mMn(3), and mMn(4), mostly below 0.5%, and from 2–7% for
mMn(1) This is a clear sign that the spin degrees of freedom are
decoupled from the charge degrees of freedom, and that a
localized moment picture can be envisaged
The values of JABand JBBof Mn4molecules obtained by
using the total energy difference method (DMol3) are
displayed in Fig 3(c) As predicted in section 3.3.1, the JAB
of Mn4+Mn2+
3and Mn4+Mn3+
3molecules (1)–(17) are con-siderably stronger than those of Mn4+Mn4+3 molecules
(18)–(24) Also, in Mn4+Mn3+3 molecules, as mentioned in
section 3.3.1, the overlap areas between the pDOSs of Mn(1)
and Mn(2)–(4) just below the Fermi level can be estimated
from the differences between the calculated and formal
magnetic moments of Mn(1), DmMn(1)= 3 |mMn(1)|
There-fore, we plot the DmMn(1) = 3 |mMn(1)| dependence of the
JABof Mn4+Mn3+3molecules in Fig 8 The results show that
the JABalso tends to increase with DmMn(1)
In more detail, we obtain JAB/kB= –66.10 K, –64.30 K, and –63.28 K, and JBB/kB= 23.32 K, 24.78 K, and 24.33 K for (14), (15), and (17) respectively These values inferred from previous experiments are JAB/kB= –33.24 K, –29.93 K, and –40.86 K, and JBB/kB= 16.26 K, 12.37 K, and 11.94 K for (14), (15), and (17), respectively.18,21 Our calculated results overestimate the coupling strength by almost a factor of 1.5B2 Moreover, the ratio, which is defined by JAB/JBB, agrees well with the experimental results, as shown in Table 4 The previous calculated results26 based on GGA PBE exchange–correlation energy functional also overestimate the coupling strength by a factor of 2, while the previous calculated results25based on LDA (local-spin density approxi-mation) overestimate the coupling strength by a factor of 7, as shown in Table 4 These results show that exchange–couplings
in Mn4SMMs can be well described by the GGA RPBE and PBE exchange–correlation energy functionals
The overestimates of effective exchange–coupling para-meters support the argument that the RPBE, as well as other conventional exchange–correlation energy in DFT, is an imperfect treatment of self-interaction of the Coulomb poten-tial, and underestimate the electron–electron correlation among d orbitals of transition metals Several methods exist that include some corrections of the exchange and correlation effects, such as hybrid functional methods including correc-tions of the exchange energy, and the LDA(GGA)+U method including corrections of the correlation energy The latter method, which explicitly includes an on-site Hubbard correc-tion term, albeit within a mean-field picture, is able to enhance electron localization, thus reducing exchange couplings, in better agreement with experiments.25,52
In general, the strength of exchange couplings between manganese ions in mixed valance Mn4 molecules including
Mn4+Mn2+3 and Mn4+Mn3+3 is significantly stronger than that in Mn4+Mn4+
3 molecules The strength of Mn–Mn exchange couplings are in the order, from strongest to weakest, of Mn2+–Mn4+, Mn3+–Mn4+, Mn2+–Mn2+,
Mn3+–Mn3+, and Mn4+–Mn4+ The mechanism of strong exchange–couplings between manganese ions in mixed valance
Mn4 molecules consists of strong couplings between the occupied d orbitals of the lower valance ions and the unoccu-pied d orbitals of the higher valance ions through p orbitals of ligands near the Fermi level This mechanism arises because there is a kinetic energy advantage, from allowing the electrons
in the occupied d orbitals of the lower valance manganese ions near the Fermi level to become delocalized over the higher
Fig 8 The Dm Mn(1) dependence of J AB of Mn4+Mn3+3 molecules.
Trang 10valance manganese ions and ligands in the molecule In the
next section, we will explore spin polarizations on ligands, as
well as exchange couplings between Mn and ligands, to
support the development of Mn4-based SMMs and SCMs
However, effective exchange–couplings between Mn and
ligands cannot calculate by using the total energy difference
method, because spin-polarizations on ligands do not satisfy a
localized moment picture This problem will be solved by using
a method which supports calculations of effective exchange–
coupling parameters directly from the ground-state electron
density For this purpose, we employ the Green’s function
method,25which was developed based on applying the rigid
spin approximation (RSA) in the noncollinear magnetic
perturbations53–56 for the calculated DFT ground state To
evaluate the reliability of this method, we also use it to
calculate the effective exchange–coupling parameters between
Mn ions in Mn4molecules The values of JABand JBBof Mn4
molecules obtained by using the Green’s function method
(OpenMX) are about two times larger than those from the
total energy difference method, as displayed in Fig 3(c) and
Table S1.w For examples, in (14), (15), and (17), the total
energy difference method only overestimates the JABand JBB
by factor of 1.5–2, as shown in Table 4, while the Green’s
function method overestimates the JABand JBB by factor of
3–4 One may say that the Green’s function method within
exchange–correlation energy functional PBE overestimates
effective exchange–coupling parameters in Mn4molecules by
factor 3–4
3.3.3 Spin polarizations on the ligands, and Mn-ligand
couplings The spin polarization (SP) on Cl(1) site (mCl(1)) in
the [Mn4O3Cl] core are displayed in Fig 3(d) These values
obtained from DMol3and OpenMX do not exactly match one
another, but they have the same tendency in each of Types I
and II In Type I, the SP on the Cl(1) site is quite large
(mCl(1) E (0.1–0.15) mB), yielding a rather strong
exchan-ge–coupling of about 20 K between the Cl(1) ion and the
manganese ions at the B sites Such strong interaction must
play an important role in forming intermolecular
exchange-pathways Mn–Cl Cl–Mn to yield the particularly magnetic
behavior of the [Mn4]2dimer.24
Besides the important role of the Cl(1), the peripheral
ligands are expected to be another factor in determining
intermolecular interactions, as well as in combining the
[Mn4O3Cl(RCOO)3] skeletons to develop new giant-spin
molecules For this reason, we carried out analyses of the
local electronic structure at peripheral ligand sites, especially
the SPs on them First, we pointed out the strong SP on the
carbon sites of the CH2O groups (mC_sp2E (0.5–0.3) mB) in
all Mn4(L,CH2O)3(L = an L-type ligand) molecules,
includ-ing (2), (3), (4), (5), and (6), as shown in Table 5 More clearly,
the SP on the carbon sites of the CH2O groups in (4) is
illustrated in Fig 9(4) Note that the carbon atom of each
CH2O group is indirectly connected to the manganese ion at
each B site through the oxygen atom, as shown in Fig 9(4)
One may suspect that the origin of the SP on the carbon site of
the CH2O groups is the charge transfer from the manganese
ion at each B site to the carbon atom through the oxygen
atom To elucidate this, we calculated the projected density of
state (pDOS) near Fermi level at these atomic sites of Mn4(L,CH2O)3molecules As shown in Fig 10(4), the strong hybridizations of the spin–down electronic states among these sites in (4) are observed both above and below the Fermi level There are two clear peaks, marked by arrows, which emerge just below the Fermi level Similar results are also observed for the other Mn4(L,CH2O)3(2), (3), (5), and (6) These results show that the origin of the SP on the carbon site of each CH2O group is the partial transfer of spin-down 3d-electrons from the manganese ion at each B site to the carbon site Therefore, the strength of this SP depends on the number of spin-down 3d-electrons of the manganese ion at each B site That is why the SP on the carbon site of the CH2O groups in Mn4+Mn3+3 molecules (no spin-down 3d-electron) is very weak (Table 5), about one order smaller than that in Mn4+Mn2+3molecules
As shown in Table 5, the SPs in (9) and (12), being only about 0.02 mB, result from the weak hybridizations of the spin-up electronic states just below the Fermi level among the manganese, oxygen and carbon sites, as displayed in Fig 10(12), marked by an arrow
The SP on the carbon site of each CH2O group shows the electron-withdrawing effect of sp2 hybridization One may suspect that other sp2 hybridization configurations, such as
R0-CHO (R0 = various), can withdraw electrons from Mn2+ ions to also yield strong SP on those ligands To illustrate this, malonaldehyde CH2(CHO)2is used as the peripheral ligand to form Mn4O3Cl(OAc)3(CH2(CHO)2)3 (7) (Fig 9(7)) Our calculations show the SPs on both sp2-hybridized carbon sites
of each CH2(CHO)2group, as shown in Fig 9(7) These SPs are also attributed to the strong hybridization of spin-down electron states just below the Fermi level among the manganese, oxygen and carbon sites, as displayed in Fig 10(7), being about0.246 (DMol3) and0.222 (OpenMX) per sp2-hybridized carbon site,
as tabulated in Table 5
As shown in Table 5, the average SP per sp2-hybridized carbon site (mC_sp2) in Mn4(L,L)3 molecules exhibits an interesting decrease with the increase in the number of
sp2-hybridized carbon sites (numC_sp2) per ligand couple (L1,L2) However, the total SP on sp2-hybridized carbon sites per ligand couple (L1,L2), which is the product of mC_sp2 and numC_sp2, increases with numC_sp2 These results show the competition between the sp2-hybridized carbon sites of the peripheral ligands in withdrawing electrons from the manganese ions at the B sites in Mn4(L,L)3molecules
Table 5 The average SP per sp 2 -hybridized carbon site (m C_sp2 ), the number of sp2-hybridized carbon sites per ligand couple (L1,L2) (num C_sp2 ), and the average effective exchange–coupling parameter between the manganese ions at the B sites and the sp2-hybridized carbon sites (J Mn–C_sp2 ) in Mn 4 (L,L) molecules (The OpenMX values are shown in italics)