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View Article Online / Journal Homepage / Table of Contents for this issue PAPER www.rsc.org/pccp | Physical Chemistry Chemical Physics Published on 11 November 2008 Downloaded by Lomonosov Moscow State University on 12/06/2013 09:01:46 A systematic study of influence of ligand substitutions on the electronic structure and magnetic properties of Mn4 single-molecule magnetsw Nguyen Anh Tuan,*ab Shin-ichi Katayamaa and Dam Hieu Chiab 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 Mn4 single-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 Mn4 SMMs A new model is proposed to explain the spin state of manganese ions in Mn4 molecules 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 Mn4 SMMs is revealed The strength of exchange–couplings between manganese ions in Mn4 SMMs 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 Introduction The discovery of individual molecules1–13 that 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.5 However, the current record of the TB of SMMs is only several degrees Kelvin.2 This temperature is far too low for practical use Therefore, design and synthesis of SMMs with higher TB is 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 À 1/4)|D| for a half-integral spin (ST and D correspond to the ground-state spin and the axial zero-field splitting parameter).14,15 Further, enhancement of exchange– couplings between transition metal (TM) ions in SMMs is found to increase their TB.2 Therefore, designing molecules with a large ST, a high D, and strong intramolecular 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 This journal is c the Owner Societies 2009 exchange–couplings is the key to developing SMMs which operate at high temperatures The increase of the ST is based on increasing the number of transition metal (TM) atoms in molecules, and the ferromagnetic couplings between them.6,7,9 The enhancement of D mainly 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 = À0.43 K,9 and [Mn3+6O2(Et-sao)6(O2CPh(Me)2)2(EtOH)6] (hereafter Mn3+6-(c)) with ST = 12 and D/kB = À0.43 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 intramolecular exchange–couplings, JMn3+–Mn4+ E À(30–50) K and JMn3+–Mn3+ 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 Phys Chem Chem Phys., 2009, 11, 717–729 | 717 Published on 11 November 2008 Downloaded by Lomonosov Moscow State University on 12/06/2013 09:01:46 View Article Online ions 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 Mn4 molecules is still missing Recently, many synthetic efforts aim at combining molecules (building blocks) with a high ST and 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,12 which 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.27,28 The combination of SMMs can also form single-chain magnets (SCMs), a novel class of nanomagnets.14,29–32 Also, various Mn4 molecules have been synthesized,16–24 each Mn4 molecule is distinguished from the others by its ligands, and also exhibits different characteristics 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 particular ligand structure in Mn4O3Cl4(O2CEt)3(py)3 was 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 Mn4 building blocks to develop new manganese SMMs and SCMs In this paper, to reveal the mechanism of strong exchange couplings in Mn4 molecules, to design new Mn4 SMMs, 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 Mn4 molecules 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 peripheralligand substitutions, plays a crucial role in determining the spin state of manganese ions in Mn4 molecules The mechanism 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 Methodology We performed cluster calculations based on density-functional theory (DFT)33,34 using DMol335 and OpenMX36 codes, 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 718 | Phys Chem Chem Phys., 2009, 11, 717–729 relativistic39 (DMol3) and Troullier–Martins-type pseudopotentials40 (OpenMX) were used to describe the interaction between the core and valence electrons The real-space global cutoff radius was set to be 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  10À6 a.u in the self-consistent calculation In the optimization process, the energy, energy gradient, and atomic displacement are converged to  10À5,  10À4 and  10À3 a.u., respectively A Fermi smearing of  10À3 a.u was used to improve the computational performance In order to determine 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 DMol3 and OpenMX codes Results and discussions 3.1 Modeling Mn4 molecules 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 = CH3 or C2H5, L1 and L2 = various) These molecules consist of the same Mn4O3Cl(RCOO)3 skeleton, but differ in the peripheral ligands L1 and L2 The geometric structures of Mn4O3Cl(RCOO)3(L1,L2)3 are schematically displayed in Fig 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-O2À ion bridging each of the vertical faces and a m3-ClÀ ion 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 This journal is c the Owner Societies 2009 View Article Online Table The chemical formula and the peripheral-ligands couple (L1,L2) of each Mn4 molecule Published on 11 November 2008 Downloaded by Lomonosov Moscow State University on 12/06/2013 09:01:46 Molecular formula (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) Fig The schematic geometric structure of Mn4 molecules (the atoms in the distorted cubane Mn4O3Cl 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)) ions 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)3 skeletons, 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 properties of Mn4 molecules be controlled by substituting peripheral-ligand couple (L1,L2) Three kinds of ligand couple (L1,L2) are used, based on a naă 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 molecules are expected to be Mn4+Mn3+3O3Cl(RCOO)3(L,X)3 These are denoted as Mn4+Mn3+3 or 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+3 or Mn4(X,X)3 Table summarizes the twenty-four different ligand couples (L1,L2) used for designing the twenty four Mn4 molecules (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 Group I consists of the seven Mn4+Mn2+3 molecules, 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+3 molecules, from (18) to (24) This journal is c the Owner Societies 2009 (18) (19) (20) (21) (22) (23) (24) Group I, n = +2, ST = Mn4O3Cl(CH3COO)3(CH3CN)6 Mn4O3Cl(CH3COO)3(CH3CN)3(CH2O)3 Mn4O3Cl(CH3COO)3(py)3(CH2O)3 Mn4O3Cl(CH3COO)3(HIm)3(CH2O)3 Mn4O3Cl(CH3COO)3(NH3)3(CH2O)3 Mn4O3Cl(CH3COO)3(CH2O)6 Mn4O3Cl(CH3COO)3(CH2(CHO))3 Group II, n = +3, ST = 9/2 Mn4O3Cl(CH3COO)3(CH(CHO)2)3 Mn4O3Cl(CH3COO)3(CH2O)3(CH3O)3 Mn4O3Cl(CH3COO)3(NH3)3(CH3O)3 Mn4O3Cl(CH3COO)3(HIm)3(CH3O)3 Mn4O3Cl(CH3COO)3(CH2O)3Cl3 Mn4O3Cl(CH3COO)3(NH3)3Cl3 Mn4O3Cl(CH3COO)3(py)3Cl3 Mn4O3Cl(C2H5COO)3(py)3Cl3 Mn4O3Cl(CH3COO)3(py)3Br3 Mn4O3Cl(CH3COO)3(dbm)3 Group III, n = +4, ST = Mn4O3Cl(CH3COO)3(dpd)3 Mn4O3Cl(CH3COO)3(CH3O)3(CH3O)3 Mn4O3Cl(CH3COO)3(CH3O)3Br3 Mn4O3Cl(CH3COO)3(CH3O)3Cl3 Mn4O3Cl(CH3COO)3Br6 Mn4O3Cl(CH3COO)3Cl3Br3 Mn4O3Cl(CH3COO)3Cl6 L1 L2 CH3CN CH3CN Py HIm NH3 CH2O CH2(CHO)2 CH3CN CH2O CH2O CH2O CH2O CH2O CH(CHO)2 CH2O NH3 HIm CH2O NH3 Py Py Py Dbm Dpd CH3O CH3O CH3O Br Cl Cl CH3O CH3O CH3O Cl Cl Cl Cl Br CH3O Br Cl Br Br Cl Py = pyridine, HIm = imidazole, dbmH = dibenzoyl–methane, dpdH2 = 1,3-diphenylpropane-1,3-diol 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 = 2À4) 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, eg0), 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, eg1) and the low-spin (LS) state with configuration d4(t2g4, eg0) There are three possible spin states of Mn2+ ions: the HS state with configuration d5(t2g3, eg2), the intermediate-spin (IS) state with configuration d5(t2g4, eg1), and the (LS) state with configuration d5(t2g5, eg0) 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+3 molecule, 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+3 molecule, 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+3 molecule Both the initial spin Phys Chem Chem Phys., 2009, 11, 717–729 | 719 Published on 11 November 2008 Downloaded by Lomonosov Moscow State University on 12/06/2013 09:01:46 View Article Online Fig The comparison of Mn(2)-ligand bond lengths among Type-I, Type-I*, Type-II, and Type-II* of (6) states 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)À(7) is Type-I with the magnetic state AFM-IS Similarly, the most stable states of all ten Mn4+Mn3+3 (8)À(17) belong to Type-I with the magnetic state AFM-HS, and the most stable states of all seven Mn4+Mn4+3 (18)À(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 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 Mn4 molecules, with the C3v axis 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 regarding the interatomic distances and bond angles of (17) are mostly below 1.5%, as shown in Table These results suggest that the GGA RPBE exchange–correlation energy functional is good enough to determine the geometric structure of Mn4 molecules 720 | Phys Chem Chem Phys., 2009, 11, 717–729 As mentioned above, the geometric structure of twenty four Mn4 molecules 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 Mn4 Type-I molecules (3)À(17) are about 10% longer than those in Mn4 Type-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 comparison 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, eg0), in which three 3d electrons occupy three different t2g orbitals Therefore, there is no Jahn–Teller distortion yielded by Mn4+ ions Mn3+ ions with the configuration 3d4 could, in principle, have HS state with configuration 3d3(t2g3, eg1), or a low-spin (LS) state with configuration 3d4(t2g4, eg0), depending, to a first approximation, on the competition between the ligand field splitting energy D (defined as the energy difference between the eg and t2g levels) 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 P favors 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 This journal is c the Owner Societies 2009 View Article Online Published on 11 November 2008 Downloaded by Lomonosov Moscow State University on 12/06/2013 09:01:46 Table This table shows the comparison between our calculations and experimental data21 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; À, 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.57 One 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) Mn(2)–Mn(3) Mn(2)–Mn(4) Mn(2)–Cl(1) Mn(2)–O(7) Mn(2)–O(1) Mn(2)–O(3) Mn(2)–L2 Mn(2)–L1 L2–Mn(2)–L1 O(7)–Mn(2)–L2 O(7)–Mn(2)–L1 Cal Exp % 2.840 3.284 3.295 2.677 2.205 1.954 1.952 1.969 1.969 91.01 93.43 90.79 2.797 3.252 3.237 2.641 2.139 1.926 1.945 1.911 1.921 91.7(6) 93.2(6) 90.6(6) 1.54 0.98 1.79 1.36 3.09 1.45 0.36 3.04 2.50 À0.82 0.18 0.14 O(7)–Mn(2)–O(3) Cl(1)–Mn(2)–O(7) Cl(1)–Mn(2)–O(1) Cl(1)–Mn(2)–L2 Cl(1)–Mn(2)–O(3) O(1)–Mn(2)–O(7) O(1)–Mn(2)–L2 O(1)–Mn(2)–L1 O(1)–Mn(2)–O(3) O(3)–Mn(2)–L2 O(3)–Mn(2)–L1 Cl(1)–Mn(2)–L1 Cal Exp % 89.82 172.56 84.79 94.03 84.76 89.41 93.73 175.25 81.83 175.48 93.43 94.59 87.0(5) 171.9(4) 84.6(5) 93.7(4) 86.0(4) 90.4(6) 94.7(6) 173.4(6) 81.5(6) 176.2(6) 92.1(6) 93.5(5) 3.18 0.36 0.17 0.31 À1.49 À1.16 À1.09 1.03 0.33 À0.44 1.38 1.11 In a distorted octahedron with a low symmetric ligand configuration as the B sites, there is not only splitting between eg and t2g orbitals 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 O2À ions and one ClÀ ion, as shown in Fig Therefore, the symmetry of the B sites in (17) now becomes C4v, with the C4 axis passing through the ClÀ and Mn3+ ions Within this C4v symmetry, the electron density of dz2 orbital of Mn3+ ions must be directed toward the ClÀ and O2À ions on the C4 axis, and the electron density of dx2Ày2 orbital of Mn3+ ions must be directed toward the four O2À ions in the perpendicular plane to the C4 axis This is confirmed by our calculations, as illustrated in Fig S2 in the ESI.w Moreover, ClÀ ions are known as p-donors giving weaker ligand field than O2À ions do.43 Therefore, the HS state with the configuration 3d4(t2g3, dz21, dx2Ày20) is favored over the configuration 3d4(t2g3, dz20, dx2Ày21) The HS state with the configuration 3d4(t2g3, dz21, dx2Ày20) is also favored over the LS states, because of the small value of the energy splitting (D) between t2g and dz2 levels due to the weak-field ligand ClÀ ion 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 Fig The correlations among the structural behavior, the magnetic interactions between Mn ions, and the spin polarizations on the ligands in Mn4 molecules: (a) some selected interatomic distances from Mn(2) to its surrounding atoms; (b) the magnetic moment of manganese ion at the A site (mA), and the average magnetic moment per manganese ion at the B sites (mB); (c) the average effective exchange–coupling parameters between manganese ions JAB refers to the magnetic interaction between Mn(1) and Mn(2), Mn(3), Mn(4), and JBB refers to the magnetic interaction between Mn(2), Mn(3), and Mn(4); (d) the SP on Cl(1) (mCl(1)) configurations of HS states for Mn3+ ions The elongated Jahn–Teller distortion corresponds to the configuration 3d4(t2g3, dz21, dx2Ày20) The compressed Jahn–Teller distortion corresponds to the configuration 3d4(t2g3, dz20, dx2Ày21) This journal is c the Owner Societies 2009 Fig The ligand configuration at each B site of (17) Phys Chem Chem Phys., 2009, 11, 717–729 | 721 Published on 11 November 2008 Downloaded by Lomonosov Moscow State University on 12/06/2013 09:01:46 View Article Online Mn2+ 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 molecules 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 À 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 = and 5, and structures corresponding to o i o are the transition structures between the Type-I and Type-II* structures Fig 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 = 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 À EAFM-LS (ETS is 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 À EAFM-IS (EAFM-IS is 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 DEIS and DELS The AFM-IS will be favorable if DEIS-max DELS-max, on the contrary, the AFM-LS will be favorable if DEIS-max o DELS-max The values of DEIS-max and DELS-max of several Mn4+Mn2+3 molecules, as tabulated in Table 3, show that these values are significantly different between Mn4+Mn2+3 molecules The reason is due to differences 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 The Jahn–Teller distortion is known as one of the origins of the axial anisotropy in Mn SMMs.1,2,13,32 Therefore, 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 studies18–24 reported that (14), (15), and (17) have the ground state spin ST of 9/2, where Mn(1) with formal charge +4 and formal magnetic moment À3mB is antiferromagnetically coupled to Mn(2), Mn(3) and Mn(4) 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 their formal magnetic moment +4mB From our calculations, the ground states of (14), (15), and (17) are determined to have an ST of 9/2, and antiferromagnetic (AFM) configuration, 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 The magnetic moments of manganese 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 not exactly match the formal magnetic moment To explain the difference, Han et al.25 said 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 The geometric structure dependences of the total energy of the magnetic structures (AFM-IS and AFM-LS) of selected Mn4+Mn2+3 molecules (1), (2), (3), (5) and (6) 722 | Phys Chem Chem Phys., 2009, 11, 717–729 This journal is c the Owner Societies 2009 View Article Online Published on 11 November 2008 Downloaded by Lomonosov Moscow State University on 12/06/2013 09:01:46 Table The maximum saving energies from the distortions, DEIS-max and DELS-max, of several Mn4+Mn2+3 molecules L1 L2 DEIS-max/meV DELS-max/meV (1) (2) (3) (5) (6) CH3CN CH3CN 21 548 CH3CN CH2O 202 246 Py CH2O 436 67 NH3 CH2O 591 125 CH2O CH2O 385 106 Table The selected physical quantities of (14), (15), and (17): the magnetic moments at Mn(1)–(4) sites, mMn(1)–(4) The average effective exchange–coupling parameters JAB refers to the magnetic interaction between Mn(1) and Mn(2), Mn(3), Mn(4) and JBB refers to the magnetic interaction between Mn(2), Mn(3), and Mn(4) (The OpenMX values are shown in italics) mMn(1) (14) Exp (ref 18) (15) GGA (ref 26) Exp (ref 18) (17) LDA (ref 25) Exp (ref 21) a mMn(2) mMn(3) À2.708 À2.712 3.879 3.852 3.873 3.849 3.872 3.850 À2.729 À2.725 À2.5 3.888 3.855 3.6 3.876 3.850 3.6 3.875 3.853 3.6 À2.687 À2.684 À2.54 3.862 3.829 3.69 3.853 3.820 3.71 3.863 3.831 3.68 The value is obtained using the total energy difference method b c the Owner Societies 2009 JAB/kB JBB/kB a À66.10 À99.35b À33.24 À64.30a À96.60b À76a À29.93 À63.28a À101.64b À244.74b À40.86 a 23.32 51.09b 16.26 24.78a 50.98b 22a 12.37 24.33a 49.93b 77.98b 11.94 |JAB/JBB| 2.83 1.94 2.04 2.60 1.90 3.45 2.42 2.60 2.04 3.14 3.42 The value is obtained using the Green’s function method especially 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 mB for 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.,25 we found the existence of the spin-up states just below the Fermi level at this site, while Mn(1) with formal magnetic moment À3mB was 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 C3v symmetry 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 The evidence of the quite strong antiferromagnetic coupling between d states of Mn(1) and Mn(2) in each of these molecules is the superposition of two clear peaks corresponding to the minorspin state of Mn(1) and the major-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 t2g orbitals 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-O2À ions in the This journal is mMn(4) Fig The pDOS near the Fermi level at Mn(1) and Mn(2) sites of (14), (15), and (17) [Mn4O3Cl] core This is confirmed by the Kohn–Sham orbitals just below the Fermi level, as shown in Fig S3 in the ESI.w Phys Chem Chem Phys., 2009, 11, 717–729 | 723 Published on 11 November 2008 Downloaded by Lomonosov Moscow State University on 12/06/2013 09:01:46 View Article Online 3.3.1 The magnetic moment of manganese ions and the ground-state spin of Mn4 For Mn4+Mn3+3 molecules (8)À(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 =  –  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 ST of Mn4+Mn4+3 molecules can also be estimated from the formal spins of manganese ions, ST =  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 Fig shows that there are not only the coupling between the occupied dz2 spin-up orbitals of Mn(2)–(4) and the unoccupied t2g spin-up orbitals of Mn(1), but also the coupling between the occupied t2g spin-down orbitals of Mn(2)–(4) and the unoccupied eg spin-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 |À3mB| In more detail, the DMol3 values are smaller |–3mB|, while the OpenMX values are mostly larger than |À3mB|, as shown in Fig 3b and Table S1 in the ESI.w These Fig The pDOS near the Fermi level at Mn(1) and Mn(2) sites of selected Mn4+Mn2+3 Type-I molecules (4) and (7) 724 | Phys Chem Chem Phys., 2009, 11, 717–729 differences between the DMol3 and 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 tabulated 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 =  3/2 À  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 =  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+3 molecules 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,47–52 or 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., Mn12,47,48 V15,49,50 Fe6,51 and Cr8.52 This 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 This journal is c the Owner Societies 2009 View Article Online moments, and in absence of anisotropy terms, the eigenvalue of the Hamiltonian for Mn4 molecules is simply Published on 11 November 2008 Downloaded by Lomonosov Moscow State University on 12/06/2013 09:01:46 ~2 + S ~3 + S ~4) ~1Á(S ETOT = À2JABS ~ ~ ~ ~ ~4ÁS ~2) À 2JBB(S 2ÁS3 + S3ÁS4 + S where S1 and S2 = S3 = S4 are 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 eigen2 value of the Hamiltonian is ETOT AFM = 6JABS1S2 À 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 = À6JABS1S2 À 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 ETOT MIX = 2JABS1S2 + 2JBBS2 After straightforward algebra, we end up with the formula JAB ¼ TOT DEAFMÀFM 12S1 S2 JBB ¼ TOT TOT DEMIXÀAFM DEMIXFM ỵ 12S22 24S22 TOT TOT TOT where DETOT AFMFM = EAFM À EFM , DEMIXÀAFM = TOT TOT TOT TOT EMIX À EAFM and DEMIXÀFM = EMIX À 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 JAB and JBB of Mn4 molecules 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+3 and Mn4+Mn3+3 molecules (1)–(17) are considerably 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) = À |mMn(1)| Therefore, we plot the DmMn(1) = À |mMn(1)| dependence of the JAB of Mn4+Mn3+3 molecules in Fig The results show that the JAB also tends to increase with DmMn(1) This journal is c the Owner Societies 2009 Fig The DmMn(1) dependence of JAB of Mn4+Mn3+3 molecules 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 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 results25 based on LDA (local-spin density approximation) overestimate the coupling strength by a factor of 7, as shown in Table These results show that exchange–couplings in Mn4 SMMs can be well described by the GGA RPBE and PBE exchange–correlation energy functionals The overestimates of effective exchange–coupling parameters 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 potential, 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 corrections 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 correction 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 unoccupied 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 Phys Chem Chem Phys., 2009, 11, 717–729 | 725 Published on 11 November 2008 Downloaded by Lomonosov Moscow State University on 12/06/2013 09:01:46 View Article Online valance 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 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,25 which 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 Mn4 molecules The values of JAB and JBB of 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 JAB and JBB by factor of 1.5–2, as shown in Table 4, while the Green’s function method overestimates the JAB and 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 Mn4 molecules 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 DMol3 and OpenMX 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 exchange–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 exchangepathways Mn–ClÁ Á ÁCl–Mn to yield the particularly magnetic behavior of the [Mn4]2 dimer.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_sp2 E À(0.5–0.3) mB) in all Mn4(L,CH2O)3 (L = an L-type ligand) molecules, including (2), (3), (4), (5), and (6), as shown in Table 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 726 | Phys Chem Chem Phys., 2009, 11, 717–729 Table The average SP per sp2-hybridized carbon site (mC_sp2), the number of sp2-hybridized carbon sites per ligand couple (L1,L2) (numC_sp2), and the average effective exchange–coupling parameter between the manganese ions at the B sites and the sp2-hybridized carbon sites (JMn–C_sp2) in Mn4(L,L) molecules (The OpenMX values are shown in italics) Mn4 mC_sp2 numC_sp2 JMn–C_sp2/kB (2) (3) (4) (5) (6) (7) (9) (12) À0.283 À0.386 À0.439 À0.474 À0.235 À0.246 0.024 0.022 –0.256 –0.340 –0.365 –0.389 –0.206 –0.222 0.016 0.014 1 1 2 1 –118.12 –186.00 –198.09 –214.76 –89.87 –83.55 — — state (pDOS) near Fermi level at these atomic sites of Mn4(L,CH2O)3 molecules 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+3 molecules 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 R -CHO (R = various), can withdraw electrons from Mn2+ ions to also yield strong SP on those ligands To illustrate this, malonaldehyde CH2(CHO)2 is 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)2 group, 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 about À0.246 (DMol3) and À0.222 (OpenMX) per sp2-hybridized carbon site, as tabulated in Table 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)3 molecules This journal is c the Owner Societies 2009 Published on 11 November 2008 Downloaded by Lomonosov Moscow State University on 12/06/2013 09:01:46 View Article Online Fig The spin density distribution of (4) and (7) Blue represents positive spin-density (spin-up region), while yellow represents negative spin-density (spin-down region) Note that the spin polarizations on the sp2-hybridized carbon atoms are opposite those of the manganese atoms at the B sites sites in Mn4(L,L)3 molecules (JMn–C_sp2) have been computed by using the Green’s function method.25 As tabulated in Table 5, JMn–C_sp2 is directly proportional to mC_sp2 More clearly, we plot the mC_sp2 dependence of the JMn–C_sp2, as displayed in Fig 11 In addition to the strong SPs on the sp2-hybridized carbon sites in Mn4(L,L)3 molecules, quite strong spin-polarizations on the peripheral ligands of Mn4(X,X)3 are also observed, in which the SP on the oxygen and halogen sites are mO_on_PL E 0.2 mB (Table 6(a)) and mhalo_on_PL E 0.15 mB (Table 6(b)), respectively The exchange–couplings between these sites and the manganese ions at the B sites in Mn4(X,X)3 are also very strong, as illustrated in Tables 6(a)–(b) The SPs on the halogen sites in Mn4(X,X)3 molecules are three times larger than those in Mn4(L,X)3 molecules (Table 6(b)) The strong spin polarization on the peripheral ligands can enhance the magnetic interactions between Mn4 building blocks to form SMMs which operate at high temperatures On the other hand, these ligands will become the active sites Therefore, some of them may bond with a radical to reduce their spin polarization if they are not shielded This can explain the existence of (pyH)3[Mn4O3Cl(OAc)3Cl6] (25)21 and (H2Im)2[Mn4O3Cl(OAc)3Cl5(HIm)] (26).16,18 The case of (25) shows a combination of [Mn4O3Cl(OAc)3Cl6] (24) with three pyH radicals This combination reduces the spin polarizations on the peripheral chlorine sites In our opinion, Fig 10 The pDOS near the Fermi level at the Mn(2), sp2-hybridized carbon, and bridging oxygen sites in Mn4 molecules (4), (7), and (12) The strong SPs on the sp2-hybridized carbon sites in Mn4(L,L)3 molecules are expected to yield strong exchange– couplings between these sites and the manganese ions at the B sites The effective exchange–coupling constants between the sp2-hybridized carbon sites and the manganese ions at the B This journal is c the Owner Societies 2009 Fig 11 The mC_sp2 dependence of the JMn–C_sp2 Phys Chem Chem Phys., 2009, 11, 717–729 | 727 Published on 11 November 2008 Downloaded by Lomonosov Moscow State University on 12/06/2013 09:01:46 View Article Online Table (a) The average SP per oxygen site on the peripheral ligands (mO_on_PL), and the average effective exchange–coupling parameter between the manganese ions at the B sites and the oxygen sites on the peripheral ligands (JMn–O_on_PL) in Mn4(X,X)3 molecules (The OpenMX values are shown in italics.) (b) The average SP per halogen site on the peripheral ligands (mhalo_on_PL), and the average effective exchange–coupling parameter between the manganese ions at the B sites and the halogen sites on the peripheral ligands (JMnÀhalo_on_PL) in Mn4(X,X)3 and Mn4(L,X)3 molecules (The OpenMX values are shown in italics) (a) Mn4 mO_on_PL (18) 0.162 0.176 186.12 JMnÀO_on_PL/kB (b) mhalo_on_PL Mn4 (12) 0.041 0.060 (13) 0.039 0.060 (14) 0.050 0.069 (15) 0.049 0.068 (16) 0.038 0.059 (19) 0.167 0.181 192.71 (20) 0.198 0.215 231.75 (21) 0.200 0.224 241.69 Mn4 (20) mhalo_on_PL 0.119 0.129 0.122 0.127 0.146 0.171 0.152 0.170 0.154 0.169 JMn–halo_on_PL/kB (21) (22) (23) (24) 62.68 68.10 86.29 94.17 100.58 the spin polarization on the peripheral ligands is an essential factor for catalytic activities of Mn4 complexes, such as water oxidation in photosystem II.16–21 Conclusion We have performed first-principles density-functional calculations for twenty-four Mn4 molecules, in order to investigate the influence of ligand substitutions on the geometric structure, the electronic structure, and magnetic properties of Mn4 single-molecule magnets, as well as to support for the development of new SMMs and SCMs Our results show that the peripheral ligands play an important role in controlling these features of Mn4 SMMs A new model is proposed to explain the spin state of manganese ions in Mn4 molecules 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 exchange couplings between manganese ions in Mn4 SMMs is revealed Our results show that the strength of exchange–couplings between manganese ions is a function of their charge and spin state, which can be also controlled by substituting peripheral-ligands The strength of Mn–Mn exchange couplings is in the order, from strongest to weakest, of Mn2+–Mn4+, Mn3+–Mn4+, Mn2+–Mn2+, Mn3+–Mn3+, and Mn4+–Mn4+ Strong spin polarizations on peripheral ligands containing sp2-hybridized carbon sites are observed Therefore, it is expected 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 In future work, we shall design some new giant-spin molecules based on Mn4 building blocks Also, we shall shed light on the role of spin polarization in water oxidation activity of Mn4 complexes 728 | Phys Chem Chem Phys., 2009, 11, 717–729 Acknowledgements This work was supported by the Ministry of Education, Culture, Sports, Science and Technology, Japan The computations presented in this study were performed at the Information Science Center of Japan Advanced Institute of Science and Technology, and the Center for Computational Science of the Faculty of Physics, Hanoi University of Science, Vietnam References R Sessoli, H.-L Tsai, A R Schake, S Wang, J B Vincent, K Folting, D Gatteschi, G Christou and D N Hendrickson, J Am Chem Soc., 1993, 115, 1804 C J Milios, A Vinslava, W Wernsdorfer, S Moggach, S Parsons, S P Perlepes, G Christou and E K Brechin, J Am Chem Soc., 2007, 129, 2754 J R Friedman, M P Sarachik, J Tejada and R Ziolo, Phys Rev Lett., 1996, 76, 3830 L Thomas, F Lionti, R Ballou, D Gatteschi, R Sessoli and B Barbara, Nature, 1996, 383, 145 M N Leuenberger and D Loss, Nature, 2001, 410, 789 M Murugesu, M Habrych, W Wernsdorfer, K A Abboud and G Christou, J Am Chem Soc., 2004, 126, 4766 A M Ako, I J Hewitt, V Mereacre, R Cle´rac, W Wernsdorfer, C E Anson and A K Powell, Angew Chem., Int Ed., 2006, 45, 4926 C J Milios, C P Raptopoulou, A Terzis, F Lloret, R Vicente, S P Perlepes and A Escuer, Angew Chem., Int Ed., 2004, 43, 210 C J Milios, A Vinslava, P A Wood, S Parsons, W Wernsdorfer, G Christou, S P Perlepes and E K Brechin, J Am Chem Soc., 2007, 129, 10 A J Tasiopoulos, A Vinslava, W Wernsdorfer, K A Abboud and C Christou, Angew Chem., Int Ed., 2004, 43, 2117 11 Christou, Polyhedron, 2005, 24, 2065 12 Z H Ni, L F Zhang, V Tangoulis, W Wernsdorfer, A L Cui, O Sato and H Z Kou, Inorg Chem., 2007, 46, 6029 13 C.-I Yang, W Wernsdorfer, G.-H Lee and H.-L Tsai, J Am Chem Soc., 2007, 129, 456 14 R Cle´rac, H Miyasaka, M Yamashita and C Coulon, J Am Chem Soc., 2002, 124, 12837 15 D Gatteschi and R Sessoli, Angew Chem., Int Ed., 2003, 42, 268; 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