ARTICLE pubs.acs.org/JPCB
Theoretical Study of Magnetic Properties of Oxovanadium(IV) Complex Self-Assemblies with Tetradentate Schiff Base Ligands Naoki Matsuoka,† Masanobu Tsuchimoto,‡ and Naoki Yoshioka*,† †
Department of Applied Chemistry, Faculty of Science and Technology, Keio University, Hiyoshi 3-14-1, Kohoku-ku, Yokohama 223-8522, Japan ‡ Department of Chemistry, Faculty of Engineering, Chiba Institute of Technology, Shibazono 2-1-1, Narashino, Chiba 275-0023, Japan
bS Supporting Information ABSTRACT: The theoretical study of the magnetic properties of oxovanadium(IV) complex self-assemblies with tetradentate Schiff base ligands is discussed on the basis of DFT calculations. Large negative spin densities are found on the axial oxygens of the various oxovanadium(IV) complexes. The relationship between the effective exchange parameters Jab and the geometrical parameters for these complexes was studied by changing the position of the neighboring molecules for the purpose of clarifying the mechanism of the ferromagnetic coupling. The intermolecular ferromagnetic interaction of the oxovanadium(IV) complexes with tetradentate Schiff base ligands is significantly affected by the formation of polymeric octahedral structures in the solid state. The overlap between the 2p orbitals of the axial oxygen and the 3d orbitals of the adjacent vanadium is effective for the ferromagnetic coupling. On the other hand, the effect of overlap between the vanadium 3dxy orbitals is too small to lead to magnetic coupling. It was revealed that the intermolecular ferromagnetic interaction of the polynuclear oxovanadium(IV) complexes is significantly affected by the spin polarization on the axial oxygen.
’ INTRODUCTION It is well-known that various self-assemblies are formed in the coordination chemistry of vanadium, which exhibits a variety of oxidation states.1 From a structural standpoint, the formations of these kinds of molecular assemblies are determined by the preference of the specific coordination geometries around the vanadium atoms.2 There have been various investigations of the tetravalent vanadium complexes that have strong vanadium oxygen double bonds.3 The oxovanadium(IV) complexes are used in many scientific fields, for example, catalytic chemistry,4 bioinorganic chemistry,5 electrochemistry,6 and molecule-based magnetism.7 Their electronic features are of special scientific and practical concern for their potential application to metallomesogens having a liquid crystallinity.8 While several investigations have been conducted on the magnetic properties of dinuclear oxovanadium(IV) complexes,9 the published data of the axially coordinated oxovanadium(IV) complex self-assemblies with tetradentate Schiff base ligands are limited. It would be of significant interest to investigate their primary structure on the basis of the magnetostructural correlation because the magnetic properties for bulk materials are significantly affected by the intermolecular magnetic interaction.10 Most of them are usually blue or green and are known to have monomeric five-coordinate square-pyramidal structures in the solid state.11 However, several orange or red complexes, such as [VO(salpn)] (1) (H2salpn: N,N0 -bis(salicylidene)-1, r 2011 American Chemical Society
3-propanediamine), have also been reported.12 In these species, a vanadyl oxygen atom of one molecule coordinates to the open axial site of a vanadium atom in a neighboring molecule, resulting in an infinite VdO 3 3 3 VdO 3 3 3 chain structure (Figure 1). The dominant ferromagnetic interaction between the molecules has been observed for 1 with the VdO 3 3 3 VdO distance of 2.213(9) Å in the solid state. Drake et al. suggested a magnetic interaction for the superexchange model by reason that the effect of overlap between the 3dxy orbitals, in which the unpaired electron is essentially localized, is too small to lead to the change in the spin alignment.13 The magnetic data for this complex have been well described by the CurieWeiss law with C = 0.357 emu K/mol and θ = þ4.5 K above 10 K. The magnetic susceptibility data could be analyzed using the one-dimensional ferromagnetic model with Jab = þ5.2 cm1, where Jab is the effective exchange parameter.14 The normalized magnetization curve of 1 has almost followed the Brillouin function with S = 7/2 at 2.0 K, indicating the formation of the self-assemblies with the ferromagnetic interaction.15 A further study of the magnetic property of the oxovanadium(IV) complex that formed the fairly elongated VdO 3 3 3 VdO 3 3 3 chain structures has also been studied.15 The magnetization Received: December 11, 2010 Revised: May 21, 2011 Published: June 10, 2011 8465
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curve of exo-[VO(3-EtOsal-meso-stien)] 3 H2O (2) (H2(3-EtOsal-meso-stien): N,N0 -bis-3-ethoxysalicylidene-(R,S)(S,R)-1,2-diphenyl-1,2-ethanediamine)16 with the VdO 3 3 3 VdO distance of 4.060(2) Å in the crystal has fallen exactly on the Brillouin function with S = 1/2 at 2.0 K, indicating that 2 has a doublet spin state without any appreciable intermolecular interactions. The ferromagnetic properties of this system have attracted considerable attention in the field of molecule-based magnetism. However, the detailed mechanism of the magnetic interaction has not yet been investigated. In the present paper, the theoretical study of the magnetic properties of the oxovanadium(IV) complexes with tetradentate Schiff base ligands is reported on the basis of DFT calculations.
’ THEORETICAL BASIS Relationship between Hyperfine Coupling Constant and Spin Density. Hyperfine coupling constants characterized by
the interactions between unpaired electrons and various magnetic nuclei provide information on the molecular and electronic structures of the transition-metal complexes containing unpaired electrons.17 The hyperfine coupling constant consists of isotropic and anisotropic components. The isotropic hyperfine coupling constant Aiso(N) is directly proportional to the spin density FNRβ at the corresponding nucleus N by eq 1.18 Aiso ðNÞ ¼ AFC ¼
4π β β ge gN ÆSz æ1 FN Rβ 3 e N
ð1Þ
where βe, βN, ge, and gN are the Bohr magneton, the nuclear magneton, the free electron g value (2.00231931), and the nuclear g value, respectively. ÆSzæ is the expectation value of the z component of the total electronic spin. The spin density FNRβ at the position of the nucleus (r) is expressed by eq 2. FN Rβ ðrÞ ¼
ni jji ðrÞj2 ∑ i¼1
ð2Þ
where ji (r) and ni are the molecular orbital and the occupation number, respectively. On the basis of the Mulliken atomic spin population analysis, F NRβ (r) is expanded with the basis set f(r) and the molecular orbital coefficient Ci (r) by eq 3. 19 FN Rβ ðrÞ ¼
∑ ni ∑ν
i¼1
Cνi fν ðrÞ
∑μ Cμi fμ ðrÞ
¼
∑μ ∑ν fi∑¼ 1 ni Cμi Cνi gfνðrÞfμ ðrÞ
¼
∑μ ∑ν
described by the Heisenberg (HB) model based on experimental data.22 ^ HB ¼ 2 H
∑ab Jab^Sa 3 ^Sb
ð4Þ
where ^Sa and ^Sb represent the spins localized on centers a and b, respectively. The highest-spin (HS) and the lowest-spin (LS) states of the open-shell molecules can be expressed by a broken symmetry (BS) solution, such as the unrestricted DFT (UDFT), which is characterized by independent sets of R and β spin orbitals, that is, different orbitals for different spins approaches.23 However, the differences in the sets of orbitals result in spin contamination because higher spin states are involved in the wave function for the LS states.24 According to Kaupp and coworkers, the spin contamination in the 3d transition-metal complexes is related to spin polarization of the doubly occupied valence orbitals in which the SOMO exhibits an appreciable metalligand antibonding character.25 There are some general approaches to the spin contamination error found in the literature.26 Noodleman et al. derived a BS expression for weakly coupled centers.27 Ruiz et al. suggested an application for a sufficiently large overlap.28 According to an approximate spin projection scheme proposed by Yamaguchi and co-workers, the Jab value in the weak and strong overlap regions is well described by eq 5.29 Jab ¼
LS
E HS E Δ
ð5Þ
where E denotes the total energy for the spin state. Δ are the extremal values of the total spin angular momentum in both the nonmagnetic region and the magnetic region. The denominator in eq 5 depends on the number of spin sites using eq 6.
Pμν fν ðrÞfμ ðrÞ
Figure 1. Structure of the oxovanadium assemblies.
Δ¼
ð3Þ
where Pμν is the spin density matrix. On the contrary, the magnitude of the hyperfine coupling constants for the ligands is much smaller than that for the transition metals. Therefore, it is necessary to include the spin polarization effects for the accurate estimation of the spin density of the transition-metal complexes.20 Effective Exchange Parameters. It is well accepted that the cluster model of polynuclear complexes is effective for the estimation of the intermolecular interaction, while the periodic boundary condition has been discussed for the infinite chain structure.21 The effective exchange parameters Jab have been
HS
ÆS2 æ LS ÆS2 æ Sa gðNÞ½LS ÆS2 æ Sr ðSr þ 1Þ
ð6Þ
where g(N) = (N 2) /N (N > 2 and even numbers) or =N 3 (N > 3 and odd numbers) and N and ÆS2æ denote, respectively, the number of spin sites in the clusters under consideration and the total spin angular momentum for the spin state. Sa and Sb are the sizes of the spins at sites a and b, respectively. Sr denotes the exact spin angular momentum for the clusters under discussion. 2
Sr ¼ nðSa Sb Þ
ðN ¼ 2nÞ
or ¼ nðSa Sb Þ þ Sa 8466
ðN ¼ 2n þ 1Þ
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Chart 1. Oxovanadium(IV) Complexes Calculated in This Study
Because each of the oxovanadium(IV) complexes studied here is in a d1 electronic configuration with one unpaired electron (Sa = Sb = 1/2), the Sr values of these clusters are limited to 0 or 1/2 in response to the number of spin sites. Computational Methods. The UDFT calculations were performed by Gaussian 03W.30 The molecular orbitals and the spin densities of the oxovanadium(IV) complexes were visualized by GaussView 3.08.31 The geometries of the oxovanadium(IV) complexes, [VO(salpn)] (1), exo-[VO(3-EtOsal-meso-stien)] 3 H2O (2), [VO(salen)] (3) (H2salen: N,N0 -bis(salicylidene)-1, 2-ethanediamine),11a [VO(salnptn)] (4) (H2salnptn: N,N0 -bissalicylidene-2,2-dimethyl-1,3-propanediamine),12c [VO{3-EtOsal(R,R)-2,4-ptn}] 3 H 2 O (5) (H 2 {3-EtOsal-(R,R)-2,4-ptn}: N, N0 -bis-3-ethoxysalicylidene-(R,R)-2,4-pentanediamine),32 exo[VO(5-NO2sal-meso-stien)] 3 0.5H2O (6) (H2(5-NO2sal-mesostien): N,N0 -bis-5-nitrosalicylidene-(R,S)(S,R)-1,2-diphenyl-1, 2-ethanediamine),33 and bis[N-(4-chlorophenyl) salicylideneaminato] oxovanadium(IV) (7),34 were directly taken from X-ray crystallography analyses (Chart 1). The polymeric chain structures like 1 have also been formed in 47, and the monomeric structure, which indicates the isolation of the VdO moieties, was formed in 3. The bond lengths of hydrogen in these complexes were optimized at the UB3LYP35 level with the 6-31G* basis set. Tight convergence criteria were used to discuss the small energy differences (108 au).36 The highest occupied molecular orbitallowest unoccupied molecular orbital (HOMOLUMO) mixed initial guesses were created to estimate the BS energies.37 We have compared the hybrid DFT (UB1LYP, UB3LYP, UB3PW91, UmPW1PW91, UPBE1PBE, UBHandH, and UBHandHLYP)35,38 and the pure DFT (UBLYP, UBP86, ULSDA, UPW91PW91, UPBEPBE, UHCTH, UtHCTH, and UTPSSTPSS)35,39 calculations for the oxovanadium(IV) complexes in order to investigate the nature of the effective exchange interactions. According to the previous studies by Munzarova et al., the triple-ζ basis sets have been applied to the transition metals.40 The basis sets for the ligands were separately considered in order to determine the proper conditions. As a medium-size metal basis set for use in larger systems, the 6-311G* basis set was used for the V atoms, in combination with the 6-31G* basis set for the ligands. Additional diffuse functions were added for the Cl atoms.41
Table 1. Comparison of the Calculated Nitrogen Isotropic Coupling Constants Aiso(N) in MHz and Mulliken Atomic Spin Population for 3 with the Different Functionals from Gaussian 03W Mulliken atomic spin population
theory
Aiso(N)/ MHz
V
axial O
equatorial O
equatorial N
UB1LYP
4.59 1.107 0.138 0.013
0.011 0.012 0.010
UB3LYP
4.71 1.092 0.127 0.014
0.012 0.011 0.010
UB3PW91
5.85 1.113 0.139 0.011
0.009 0.013 0.012
UmPW1PW91
5.88 1.129 0.150 0.010
0.008 0.014 0.012
UPBE1PBE
5.94 1.129 0.150 0.010
0.008 0.014 0.012
UBHandH UBHandHLYP
5.46 1.171 0.190 0.010 4.79 1.172 0.190 0.009
0.009 0.014 0.013 0.008 0.015 0.013
UBLYP
4.32 1.001 0.087 0.022
0.014 0.006 0.007
UBP86
5.31 1.006 0.090 0.019
0.011 0.007 0.008
ULSDA
5.10 0.940 0.074 0.026
0.015
UPW91PW91
5.45 1.012 0.094 0.019
0.011 0.007 0.009
5.56 1.010 0.094 0.019
0.010 0.007 0.009
UPBEPBE
0.002 0.005
UHCTH
10.33 1.143 0.164 0.004 0.002 0.018 0.019
UtHCTH UTPSSTPSS
10.38 1.153 0.170 0.005 0.001 0.019 0.020 4.07 1.034 0.105 0.020 0.014 0.007 0.007
expl.
5.83
’ RESULTS AND DISCUSSION Evaluation of Spin Density. The types of nitrogens coordinated to the VO2þ ion are experimentally identified by means of electron spin echo envelope modulation (ESEEM) spectroscopy.17b The nitrogen Aiso(N) was calculated for 3 on behalf of the VO2þ model complexes with equatorial imine ligands (Table 1). The computed results with UB3PW91, UmPW1PW91, and UPBE1PBE are in very good agreement with the experimental data of 5.83 MHz obtained from the ESEEM measurements. It is theorized that these hybrid DFT calculations, especially UB3PW91, better account for the spin polarization of the core orbitals than the others. 8467
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According to the optimum DFT calculation conditions, the spin density of the oxovanadium(IV) complexes in this paper was performed at the UB3PW91 level with the 6-311G* basis set for the V atoms and with the 6-31G* basis set for the ligands. Additional diffuse functions are also added for the Cl atoms of 7. The total spin population on the vanadiums for 17, which contain one unpaired electron and may be regarded as a d1 system, reaches more than 1.10 because of the spin polarization (Table 2). The negative spin density appears on each of the axial oxygens, and their populations are larger than those of the equatorially coordinating atoms regardless of the chain formation (Figure 2). Munzarova et al. also reported similar results.40 Although an unpaired electron is essentially localized on a vanadium 3dxy orbital,42 significant spin polarization of the other d orbitals is observed as a result of the 3d atomic orbital spin population analysis (Table 3). Isotropic spin polarization of the 2p orbitals for the axial oxygen atoms is also observed. The mechanism of this spin polarization in the oxovanadium species crucially depends on the overlap between the singly occupied and certain doubly occupied valence orbitals.43 Consequently, the origin of such a large spin density on the axial oxygen, especially on the 2p orbitals, is the spin polarization through the overlap with the 3dz2 orbital for the σ bond and with the 3dzx and 3dyz orbitals for the π bonds (Figure 3).42c,44
Mechanism of Ferromagnetic Coupling. The Jab values of the oxovanadium(IV) complexes are estimated using eq 5. This
Table 3. Atomic Orbital Spin Population Ratio for Vanadium Atoms and Axial Oxygen Atoms of Oxovanadium(IV) Complexes at UB3PW91/6-311G** for the V Atoms and 6-31G* for the Ligandsa 3d for V/%
a
2p for axial O/%
complex
3dxy
3dyz
3dzx
3dx2y2
3dz2
2px
2py
2pz
1
80.1
6.4
6.4
1.7
5.4
36.8
36.7
26.5
2 3
83.1 83.0
5.0 5.3
5.3 5.0
1.8 2.0
4.8 4.7
35.1 33.4
33.3 35.0
31.6 31.6
4
79.9
6.4
6.4
1.7
5.5
36.7
37.0
26.3
5
80.5
6.3
6.2
1.7
5.3
35.7
37.8
26.6
6
81.4
5.9
6.0
1.8
5.0
37.0
34.5
28.5
7
81.4
6.0
5.1
2.6
4.9
31.2
39.9
28.9
Additional diffuse functions are added for the Cl atoms.
Table 2. Mulliken Atomic Spin Population Analysis for Oxovanadium(IV) Complexes at UB3PW91/6-311G** for the V Atoms and 6-31G* for the Ligandsa
a
complex
V
axial O
1 2
1.160 1.121
0.188 0.141
equatorial O 0.008 0.008
0.009 0.009
equatorial N 0.020 0.013
0.020 0.012
3
1.113
0.139
0.011
0.009
0.013
0.012
4
1.164
0.193
0.010
0.011
0.018
0.017
5
1.166
0.187
0.003
0.014
0.015
0.022
6
1.142
0.167
0.009
0.008
0.013
0.011
7
1.151
0.164
0.006
0.005
0.013
0.013
Additional diffuse functions are added for the Cl atoms.
Figure 3. Schematic orbital diagram for the VdO bond in the oxovanadium(IV) complex.
Figure 2. Spin density of 17 at UB3PW91/6-311G** for the V atoms and 6-31G* for the ligands. The positive spin densities are shown in blue (dark color), and the negative ones are in green (pale color). 8468
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Table 4. Comparison of Total Energies and Effective Exchange Parameters Jab for the Cluster of 1 with the Different Functionals from Gaussian 03W HS state
BS LS state
N
spin state
total energy/au
ÆS æ
spin state
total energy/au
ÆS2æ
Jab/cm1
2
triplet
3872.5291098
2.0369
singlet
3872.5290286
1.0346
17.8
3
quartet
5808.8106827
3.8003
doublet
5808.8106235
1.7987
6.5
4 5
quintet sextet
7745.0947993 9681.3798672
6.0631 8.8256
singlet doublet
7745.0946836 9681.3797545
2.0599 2.8225
8.5 6.3
2
triplet
3873.5506814
2.0316
singlet
3873.5505987
1.0297
18.1
3
quartet
5810.3426472
3.7937
doublet
5810.3425833
1.7921
7.0
UB3PW91
2
triplet
3872.6797857
2.0375
singlet
3872.6796919
1.0351
20.5
3
quartet
5809.0337999
3.8017
doublet
5809.0336652
1.7982
14.8
UmPW1PW91
2
triplet
3873.1573007
2.0437
singlet
3873.1572086
1.0410
20.2
theory UB1LYP
UB3LYP
2
3
quartet
5809.7543595
3.8095
doublet
5809.7542860
1.8073
8.1
UPBE1PBE
2 3
triplet quartet
3870.8496222 5806.2959992
2.0435 3.8093
singlet doublet
3870.8495294 5806.2959251
1.0408 1.8071
20.3 8.1
UBHandH
2
triplet
3856.2675686
2.0719
singlet
3856.2674628
1.0679
23.1
3
quartet
5784.4428435
3.8413
doublet
5784.4427596
1.8382
9.2
UBHandHLYP
2
triplet
3872.2365756
2.0719
singlet
3872.2364677
1.0678
23.6
3
quartet
5808.3779083
3.8408
doublet
5808.3778222
1.8375
9.4
UBLYP
2
triplet
3872.8956948
2.0184
singlet
3872.8948454
1.0093
184.7
3
quartet
5809.3565522
3.7772
doublet
5809.3561571
1.7731
43.3
UBP86
2 3
triplet quartet
3873.8251692 5810.7523440
2.0198 3.7794
singlet doublet
3873.8242388 5810.7512920
1.0106 1.7459
202.3 113.5
ULSDA
2
triplet
3859.4743154
2.0159
singlet
3859.4730528
0.9932
271.0
3
quartet
5789.2497632
3.7736
doublet
5789.2485890
1.7069
124.7
UPW91PW91
2
triplet
3872.9806457
2.0211
singlet
3872.9796965
1.0121
206.5
3
quartet
5809.4925058
3.7812
doublet
5809.4914146
1.7488
117.8
UPBEPBE
2
triplet
3870.7440456
2.0214
singlet
3870.7430675
1.0120
212.7
3
quartet
5806.1360585
3.7816
doublet
5806.1355831
1.7771
52.1
UHCTH
2 3
triplet quartet
3873.8009033 5810.7117443
2.0581 3.8338
singlet doublet
3873.7994176 5810.7098434
1.0503 1.8097
323.6 206.1
UtHCTHa
3
quartet
5810.5150875
3.8389
doublet
5810.5132060
1.8151
204.0
UTPSSTPSSa
3
quartet
5811.0353663
3.7838
doublet
5811.0345682
1.7636
86.7
exptl. a
5.2
Convergent energies were not obtained for N = 2.
equation has been applied to the trimer models of 1, providing more reasonable Jab values than the dimer ones as compared to the experiments (Table 4). Their total energies of HS and BS LS states are energetically degenerate, but the HS is slightly stable. There is no distinct correlation between the spin population in Table 1 and the calculated Jab values in Table 4. We also noticed that most of the pure DFT methods underestimated the spin population on the axial oxygen atoms in Table 1. Although the tendency is maintained in the cluster calculation for 1, the Jab values are overestimated when the spin population of V(3) is unusually small (Figure S1 and Table S1, Supporting Information). As shown in Table S1 (Supporting Information) for the N = 3 system, the hybrid DFT method is suitable for reproducing the experimental result. The optimum Jab value for the trimer of 1 is 6.5 cm1, which is performed at UB1LYP/6311G** for the V atoms and 6-31G* for the ligands. The magnetic property of 1 is well reproduced by the computational analysis. The influence on the number of spin sites in the clusters has also been investigated at UB1LYP/6-311G** for the V atoms and 6-31G* for the ligands. Interestingly, the Jab values calculated
from eq 5 approximately coincide with the experimental data for N > 2. This is attributed to a slightly unsuitable estimation of the spin polarization on both ends of the VdO moieties (Figure S2, Supporting Information). While this edge effect was unavoidable as a consequence of the finite structure, the spin density wave state was reproduced on the inner spin sites as well as those of previous models for quasi-one-dimensional halogen-bridged binuclear metal complexes reported by Nakano and co-workers.45 Therefore, the calculated results approximated the observed values by including the magnetic interactions of the inside units. Within the accuracy of the magnetic susceptibility measurements, the trimer model is fairly satisfactory from the viewpoint of computational chemistry. In order to reveal the influence of the patterns of approach of the magnetic orbitals on the magnetic interactions, a simplified molecule 8 was extracted from 1 (Figure 4). The hydrogen atoms were optimized at UB3LYP/6-31G*. The calculated stretching frequencies of the hydrogen-related bonds indicated that the final structures corresponded to the global minima. The SOMO distribution and the orbital energies 8469
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Table 5. Structural and Magnetic Parameters of the Selected Oxovanadium(IV) Complexes Having the Polymeric Chain Structures complex 1
VdO/Å 1.633(9)
VdO 3 3 3 VdO/Å
Jab (exptl.)/ cm1
ref
2.213(9)
þ4.1(1)
12b,13
þ5.2
15
2
1.597(3)
4.060(2)
0
4 5
1.627(4) 1.617(6)
2.245(4) 2.290(6)
15,16
6
1.599(3)
2.437(3)
7
1.600(2), 1.592(2)
2.43, 2.39
þ2.5
34
(t-Bupz)2VOCl2
1.606(7)
2.319(7)
þ3.06(7)
46
12c 32 33
Figure 4. Geometrical parameters d, δ, and ψ of the trimeric model of the simplified molecule 8 to examine the effect of the overlap between the magnetic orbitals. The simplified molecule is extracted from 1. The hydrogen atoms are optimized at UB3LYP/6-31G*.
Figure 6. Dependence of Jab on δ for the trimeric models of 8 under the fixed geometries of d = 2.21 Å.
Figure 5. Comparison of the calculated Jab (2) for the trimeric models of 8 with the experimental values (b).
of 8 reflect that of 1 (Figure S3, Supporting Information). The spin density of 8 is also close to that of 1 (Tables S2 and S3, Supporting Information). The relationship between the Jab values and the geometrical parameters for 8 was evaluated by changing the position of the neighboring molecules for the purpose of clarifying the mechanism of the ferromagnetic coupling. The influence of the approach of the magnetic orbitals on the magnetic interactions with the trimeric models of 8 was described using the values of the geometrical parameters d, δ, and ψ, which were the intermolecular VdO 3 3 3 VdO distance, the intermolecular O 3 3 3 VdO angle, and the intermolecular VdO 3 3 3 VdO dihedral angle, respectively. The coordinate of each moiety of the oxovanadium(IV) complex with the tetradentate Schiff base ligand was fixed to the original position. The short distance between the adjacent molecules contributes to the ferromagnetic coupling because the Jab value increases as d decreases (Figure 5). The computed results are in very good agreement with the currently available experimental data (Table 5).15,34,46 A conspicuous ferromagnetic interaction is observed for the trimeric model in
which d is shorter than 3 Å. Although d is related to not only the intermolecular VdO 3 3 3 VdO distance but also to the intermolecular distance between the vanadium 3dxy orbitals, the effect of the direct overlap between the vanadium 3dxy orbitals is negligible due to the long distance. The value of δ plays a key role in tuning the magnitude of the magnetic interaction in the oxovanadium(IV) complexes with tetradentate Schiff base ligands. The Jab values drastically increase according to the decrease in δ (Figure 6). When δ reaches 180, the vanadium 3dxy orbital and the axial oxygen 2p orbital of the adjacent molecule are orthogonal to each other irrespective of d and ψ. In this case, the strong ferromagnetic contribution vanishes, and a moderate ferromagnetic coupling can develop. There is only a low correlation between Jab and ψ because the effect of the overlap between the vanadium 3dxy orbitals is too small to produce a change in Jab. The overlap between the 2p orbitals on the axial oxygen and other 3d orbitals besides the 3dxy orbital on the adjacent vanadium is thought to be a magnetic pathway of this system (Figure 7). It was revealed that the intermolecular ferromagnetic interaction of the polynuclear oxovanadium(IV) complexes is significantly affected by the spin polarization on the axial oxygen.
’ CONCLUSION It is important to investigate the primary structure of the molecule-based magnets in order to enhance the spin arrangement. 8470
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Figure 7. The effective contact of the magnetic orbitals between 3d on the V atoms and 2p on the axial O atoms for the trimeric models of 8.
A theoretical study of the magnetic properties of oxovanadium(IV) complexes with tetradentate Schiff base ligands is discussed on the basis of DFT calculations. Large negative spin densities are found on the axial oxygens of various oxovanadium(IV) complexes. While the unpaired electron is essentially localized on the vanadium 3dxy orbital, a significant spin polarization of the other d orbitals is observed as a result of the 3d atomic orbital spin population analysis. The isotropic spin polarization of the 2p orbitals for the axial oxygen atoms is also observed. The intermolecular ferromagnetic interaction of oxovanadium(IV) complexes with tetradentate Schiff base ligands is significantly affected by the formation of polymeric octahedral structures in the solid state. The overlap between the 2p orbitals on the axial oxygen and other 3d orbitals besides the 3dxy orbital on the adjacent vanadium is effective for the formation of ferromagnetic coupling. On the other hand, the effect of the overlap between the vanadium 3dxy orbitals is too small to produce a change in the spin arrangement. We conclude that the intermolecular ferromagnetic interaction of polynuclear oxovanadium(IV) complexes is significantly affected by the spin polarization on the axial oxygen.
’ ASSOCIATED CONTENT
bS
Supporting Information. Atom numbering of the trimer model of 1 (Figure S1). Comparison of the spin population of the VdO moieties and the Jab values for the trimer models of 1 (Table S1). Comparison of the spin densities in the clusters of 1 (Figure S2). Additional comparison of the computational data of 1 and 8 (Figure S3 and Tables S2 and S3). Cartesian coordinates for 18 (Tables S4S11). X-ray crystallographic information file (CIF) for 1, in CIF format. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*Tel: þ81-45-566-1585. Fax: þ81-45-566-1551. E-mail: yoshioka@ applc.keio.ac.jp.
’ ACKNOWLEDGMENT This work was supported in part by a Grant-in-Aid for Scientific Research (B) 20310060 from the Ministry of Education,
Culture, Sports, Science, and Technology, Japan. Financial support from the Keio Gijuku Academic Development Funds is also acknowledged.
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