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DFT-BS study on the magnetic coupling interaction in a series of (R-Bpmp)MnII2(μ-OAc)2 complexes
Polyhedron 30 (2011) 3017–3021
Contents lists available at ScienceDirect
Polyhedron journal homepage: www.elsevier.com/locate/poly
DFT-BS study on the magnetic coupling interaction in a series of (R-Bpmp)MnII2(l-OAc)2 complexes Li-Li Wang a, You-Min Sun b, Xian-Jie Lin c, Cheng-Bu Liu a,⇑ a
Key Lab of Colloid and Interface Chemistry, Ministry of Education, School of Chemistry and Chemical Engineering, Shandong University, Jinan 250100, PR China School of Municipal and Environmental Engineering, Shandong Jianzhu University, Jinan 250101, PR China c Deparment of Chemistry and Chemical Engineering, Heze University, Heze 274015, PR China b
a r t i c l e
i n f o
Article history: Available online 19 February 2011 Keywords: Magnetic interaction mechanism Dinuclear manganese(II) complex Density functional theory Broken-symmetry approach
a b s t r a c t The magnetic properties of a series of dinuclear MnII systems are investigated by the calculations based on density functional theory combined with broken-symmetry approach (DEF-BS). It is found that there are weak antiferromagnetic interactions in these systems with different bridging ligands. The changing trend of the magnetic coupling constants J indicates that with the electronegativity of the increasing bridging ligands, the antiferromagnetic coupling interaction is weakened. The analyses of the magnetic orbitals and the spin densities show that the weakly antiferromagnetic couplings in these systems are due to the vertical magnetic d orbitals and the weak spin delocalization. These results should be instructive for the design of new molecular magnetic materials. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction The ‘‘single-molecular magnetic material’’ (SMM) science has been attracting much attention due to the increasing demands for smaller size magnetic memory devices and the interest on the interpretation of the mechanism for the complicated interactions in the life-forms [1–13]. In order to synthesize the SMM that could be applied conveniently in the fields of information storage, molecular electronics, photomagnetism, functions of the active sites of several redox enzymes, etc., scientists are making great efforts to design the magnetic transition metal systems that with diverse properties by using different transition metal atoms and ligands [14–18]. The magnetic coupling interaction in the transition metal systems is sensitive to the function of external perturbations such as temperature, light irradiation, pressure, and pulsed magnetic fields, which makes the potential application of the transition metal systems much more extensive. In the researches of transition metal systems, the Mn complexes are becoming the focus for their various interesting magnetic behavior in the field of the molecular magnetic materials. Since the Mn complex [Mn12O12(OOCCH3)16(OH2)4] was reported as the first single molecular magnet in the early 1990s [19–21], many Mn systems with various magnetic properties have been synthesized and investigated [22–33]. Among the Mn complexes, the dinuclear Mn complexes have attracted the much attention for their simple
⇑ Corresponding author. E-mail address: [email protected] (C.-B. Liu). 0277-5387/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.poly.2011.02.022
structures and flexible magnetic-structural correlations [34–40]. The dinuclear Mn complexes have obtained more and more attention from both the theoretical and experimental research groups in the researches of the bioinorganic chemistry and single-molecular magnetism. With the increasing number of the dinuclear Mn systems being synthesized, the theoretical study on the dinuclear Mn systems is also extensive and is focusing on the research of the magnetic coupling mechanism and the magneto-structural correlation. However, the mechanisms of the magnetic coupling interactions in these systems are still not clear now. Experimentally, a series of dinuclear Mn(II) complexes in which the Mn(II) ions are bridged by the Bpmp (BpmpH = 6-bis[bis(2pyridylmethyl)aminomethyl]-4-methyl-phenol) ligands have been synthesized [41–44]. It is interesting that the systems have the different magnetic properties with the different Bpmp bridging ligands. In order to explain the correlation between the bridging ligands and the magnetic coupling interaction in these systems and the magnetic mechanisms of them, we have theoretically investigated the magnetic properties of a series of Bpmp bridged dinuclear Mn(II) complexes. According to the calculated results, it is proved that the magnetic properties of Bpmp bridged dinuclear Mn(II) complexes are sensitive to the structure of the Bpmp ligand. Moreover, the component of the magnetic orbitals is a significant factor for the magnetic coupling interactions. Therefore, in this work, the d orbitals on the Mn centers are also analyzed to elucidate the magnetic coupling contribution. These investigations will further explain the magnetic interaction mechanism of this system and provide guidance for the design of the molecular magnets.
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L.-L. Wang et al. / Polyhedron 30 (2011) 3017–3021
2. Modeling strategy
4. Results and discussion
The calculated dinuclear models A and E (Fig. 1) are predigested directly from the crystal structures [(NO2Bpmp)Mn2(l-OAc)2] [41] (NO2BpmpH = 2,6-bis[bis(2-pyridylmethyl)aminomethyl]-4nitrophenol) and [(Bpmp)Mn2(l-OAc)2] [42] (BpmpH = 2,6-bis [bis(2-pyridylmethyl)aminomethyl]-4-methyl-phenol). In order to investigate influence of the structure of the bridging ligands, we built three dinuclear Mn(II) models [(R-Bpmp)Mn2(l-OAc)2] (X = –CN, –F, and –H for models B, C and D, respectively) by replacing the methyl of Bpmp with the different R radicals basing on the structure of model A.
4.1. Dependence of the magnetic coupling of the MnII2 systems on the different bridging R-Bpmp ligand
3. Computational details For dinuclear manganese(II) systems, the spin Hamiltonian describing the low-lying states in zero field can be written as:
H ¼ 2JSMn1 SMn2
ð1Þ
where J denotes the exchange coupling constant between adjacent manganese ions. The positive sign of the J value shows the ferromagnetic interaction, and the negative sign of the J value indicates the antiferromagnetic interaction. SMn1 and SMn2 denote the spins on the manganese ions and SMn1 ¼ SMn2 ¼ 52. The magnetic coupling constant J for the dinuclear Mn(II) system is present as,
J¼
EHS EBS S2max
ð2Þ
Where Smax ¼ 5, EHS and EBS denote the energy values of the highest spin state and the broken-symmetry state, respectively. The DFT-BS method used here proposed by Noodleman et al. [45–47] is used to calculate the magnetic coupling constants. Ahlrichs triple-zeta valence basis set (TZV) is utilized. Becke’s three-parameter hybrid functional for exchange combined with the Lee–Yang–Parr correlation functional (B3LYP) [48] is employed. The convergence criterion of SCF is 108. The calculations of magnetic coupling constants are performed using the ORCA 2.7 software package developed by Neese [49].
As a significant factor to judge the magnetic properties of the molecular magnet, the coupling constant J is the bridge between the experimental and theoretical researches. Experimentally, the J values are obtained from the fitting of the experimental data. Theoretically, the J values can be calculated by the configuration interaction (CI) methodologies and the DFT-based methods [50–53]. The computational cost of CI method is much more expensive for the application to large systems than DFT-based method. In addition, DFT-based calculations are proven to be very reliable and convenient for the correlated materials from magnetic molecules to magnetic solids. Therefore, the DFT-BS method is used here to calculate the J values to elucidate the coupling interaction. The calculated J values along with the experimental J values of the five (R-Bpmp)(l-OAc)2 models A–E are shown in Table 1. The calculated J values of all the models are in the range of 6 to 9 cm1 which is consistent with the experimental values very well. In these dinuclear Mn(II) systems there exists weakly antiferromagnetic couplings between the Mn(II) centers. With the bridging R-Bpmp changing from NO2-Bpmp to CN-Bpmp, F-Bpmp, H-Bpmp, and Bpmp, the magnetic coupling constants J values of models A–E are increasing. This indicates that the antiferromagnetic coupling interactions are slightly strengthened with the electronegativity of the R-Bpmp bridging ligands are decreasing. The coupling interaction between the Mn(II) centers is insensitive to the R radical in the R-Bpmp ligand. 4.2. Spin population analyses In order to further elucidate the magneto-structural correlation, the spin density distributions for all the models are analyzed. The plot of the sum of absolute values for the calculated spin densities on the Mn(II) centers for all the models are given in Fig. 2. The values of the spin densities on the Mn(II) centers and all the ligand atoms are shown in Table S1 (in the Supplementary data), where
Fig. 1. The structures of the dinuclear Mn(II) models A–E.
L.-L. Wang et al. / Polyhedron 30 (2011) 3017–3021 Table 1 The calculated and experimental J values for models A–E. Models 1
Jcal (cm ) Jexp (cm1)a R a
Model A
Model B
Model C
Model D
Model E
6.14 7.20 –NO2
7.91
8.20
8.22
–CN
–F
–H
8.30 9.60 –CH3
Refs. [41,42]; R is the R radical in the R-Bpmp ligand.
Sum of the absolute values for the spin denstities on the Mn(II) centers
9.5940 9.5938 9.5936 9.5934
3019
the absolute values of the spin densities on the two Mn(II) centers is decreasing from 9.594 to 9.592 which indicates that the spin delocalization is increasing as the of the electronegativity of the R-Bpmp bridging ligands is decreasing. This changing trend is consistent with the magnetic coupling changing trend in Section 4.1. In addition, the spin delocalization is very weak, which is corresponding to the weak antiferromagnetic coupling in the systems. The spin densities on the oxygen atoms (O2–O5) of the l-OAc ligands are also decreasing from A to E. The spin densities on the benzene ring of the R-Bpmp ligand are very small. According to these values, the spin densities on the N ligand atoms are much larger than the other ligand atoms. Hence, the spin delocalization mainly occurs between the Mn(II) centers and the N ligand atoms. According to these analyses, it can be concluded that the weak spin delocalization results in the weak antiferromagnetic coupling in the systems and the spin delocalization is weakened as the electronegativity of the bridging ligand is increasing.
9.5932
4.3. Molecular orbital analysis
9.5930 9.5928 9.5926 9.5924 9.5922 A
B
C
D
E
Model Fig. 2. The sum of spin densities on the Mn(II) centers of models A–E.
positive and negative signs denote a and b spin states, respectively. The values of the spin densities here are that of the state with the lower energy (the broken-symmetry state (BS)) for all the models. The spin densities on the two Mn(II) centers have the similar absolute values of are similar (about 4.9) and the opposite signs which shows that the unpaired electrons mainly populate on Mn(II) centers. The spin signs on the ligand atoms are same with that on the Mn(II) which they are coordinated to, so there are spin delocalization from the Mn(II) centers to the ligands. From A to E, the sum of
In order to explain the mechanism of the magnetic coupling interactions in these Mn(II) systems, the magnetic orbitals for models A–E are also calculated and shown in Fig. 3. The term ‘‘magnetic orbitals’’ is defined as the localized orbitals centered on the magnetic sites with appropriate tails on the terminal and bridging ligands [25]. The magnetic orbitals of the models here are the HOMO orbitals. For each Mn(II) atom, there are five unpaired electrons which are populated on the d orbitals. For the bridged magnetic systems, the magnetic coupling interaction between the metal centers takes place by the connection through the bridging ligands. Hence only the d orbitals of the metal centers that can have large interaction with the p orbitals of the bridging ligands will lead to the magnetic coupling contribution. The contributions (%) of the d orbitals on the Mn(II) centers to the magnetic orbitals are shown in Table 2. According to Fig. 3, the d orbitals of the Mn(II) centers interact with p orbitals of the ligand atoms by the r path. For model A, the contribution of the NO2-Bpmp is very small, and there is almost no orbital contribution from the -NO2 ligand. With the
Fig. 3. The molecular magnetic orbitals for models A–E.
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Table 2 The contributions (%) of the d orbitals of Mn(III) in the magnetic orbitals for models A–E.
A B C D E
dx2 y2 (%)
dz2 (%)
dxy (%)
dyz (%)
dxz (%)
1.68 15.38 15.18 15.99 14.55
38.32 59.78 47.96 52.10 43.37
8.81 2.29 3.95 1.95 6.95
31.64 17.76 19.54 20.02 19.05
19.55 4.78 13.37 9.95 16.08
Laboratory for Computational Chemistry of CNIC and Supercomputing Center of CNIC, Chinese Academy of Sciences.
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.poly.2011.02.022. References
electronegativity of R ligand in the R-Bpmp bridging ligands decreasing, the orbital contribution of the benzene ring of the Bpmp ligand is increasing gradually from model A to model E. In addition, with the R-Bpmp bridging ligands changing from NO2-Bpmp to Bpmp ligands, the overlap of the d orbitals of the Mn(II) centers and the p orbitals of the ligand atoms are increasing, which make the magnetic coupling interactions between the Mn(II) centers strengthened. According to Table 2, the magnetic d orbitals are mainly formed by the dz2 and dyz orbitals. In model A, the contributions of the dz2 (38.32%) and dyz (31.64%) are similar. In models B–E, the contribution of the dz2 orbital is much larger than that of the dyz orbital, and the contribution of the dxy orbital is the smallest. The contributions of the dx2 y2 orbital in models B–E are all about 15%, but that in model A is very small (1.68%). Also, the contribution of the dz2 orbital (38.32%) in model A is much smaller than that in the other models. In all the models, the contribution of the dz2 orbital to the magnetic orbital is the largest in the five d orbitals, which indicates that the effective magnetic coupling interactions mainly depend on the dz2 orbitals contribution. In the research of Castillo et al., [54] it is mentioned that there exist three kinds of strategies for the magnetic coupling interactions between the metal centers. The co-planar interaction of the magnetic orbitals always results in the strong antiferromagnetic coupling, the parallel interaction leads to the weakest coupling, while the intermediate coupling is always due to the mixing of the in-plane and out-plane interaction. According to Fig. 3, it is obvious that the magnetic d orbitals of the two Mn(II) centers in all the models are vertical to each other, which results in the weakly antiferromagnetic coupling interactions in all the models.
5. Conclusions The calculations of the magnetic coupling constants based on the DFT-BS method show that in the dinuclear Mn(II) complexes [(R-Bpmp)Mn2(l-OAc)2] there exist weak antiferromagnetic coupling interaction. The antiferromagnetic coupling interaction is strengthened as the electronegativity of the bridging ligand decreasing. According to the spin density and orbital analyses, it can be concluded that the magnetic properties of the [(RBpmp)Mn2(l-OAc)2] are insensitive to the electronegativity of the R radicals in the R-Bpmp bridging ligands. The weak spin delocalization and the vertical magnetic d orbitals result in the weakly antiferromagnetic coupling interactions in the [(R-Bpmp)Mn2(lOAc)2] systems. These analyses show that it is not an effective pathway to control the magnetic properties by changing R radical in the R-Bpmp ligand. Acknowledgements This work is supported by the National Natural Science Foundation of China (No. 20873075) and the Science Foundation of Shandong Province (No. ZR2009BM024). We also thank the Virtual
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Contents lists available at ScienceDirect
Polyhedron journal homepage: www.elsevier.com/locate/poly
DFT-BS study on the magnetic coupling interaction in a series of (R-Bpmp)MnII2(l-OAc)2 complexes Li-Li Wang a, You-Min Sun b, Xian-Jie Lin c, Cheng-Bu Liu a,⇑ a
Key Lab of Colloid and Interface Chemistry, Ministry of Education, School of Chemistry and Chemical Engineering, Shandong University, Jinan 250100, PR China School of Municipal and Environmental Engineering, Shandong Jianzhu University, Jinan 250101, PR China c Deparment of Chemistry and Chemical Engineering, Heze University, Heze 274015, PR China b
a r t i c l e
i n f o
Article history: Available online 19 February 2011 Keywords: Magnetic interaction mechanism Dinuclear manganese(II) complex Density functional theory Broken-symmetry approach
a b s t r a c t The magnetic properties of a series of dinuclear MnII systems are investigated by the calculations based on density functional theory combined with broken-symmetry approach (DEF-BS). It is found that there are weak antiferromagnetic interactions in these systems with different bridging ligands. The changing trend of the magnetic coupling constants J indicates that with the electronegativity of the increasing bridging ligands, the antiferromagnetic coupling interaction is weakened. The analyses of the magnetic orbitals and the spin densities show that the weakly antiferromagnetic couplings in these systems are due to the vertical magnetic d orbitals and the weak spin delocalization. These results should be instructive for the design of new molecular magnetic materials. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction The ‘‘single-molecular magnetic material’’ (SMM) science has been attracting much attention due to the increasing demands for smaller size magnetic memory devices and the interest on the interpretation of the mechanism for the complicated interactions in the life-forms [1–13]. In order to synthesize the SMM that could be applied conveniently in the fields of information storage, molecular electronics, photomagnetism, functions of the active sites of several redox enzymes, etc., scientists are making great efforts to design the magnetic transition metal systems that with diverse properties by using different transition metal atoms and ligands [14–18]. The magnetic coupling interaction in the transition metal systems is sensitive to the function of external perturbations such as temperature, light irradiation, pressure, and pulsed magnetic fields, which makes the potential application of the transition metal systems much more extensive. In the researches of transition metal systems, the Mn complexes are becoming the focus for their various interesting magnetic behavior in the field of the molecular magnetic materials. Since the Mn complex [Mn12O12(OOCCH3)16(OH2)4] was reported as the first single molecular magnet in the early 1990s [19–21], many Mn systems with various magnetic properties have been synthesized and investigated [22–33]. Among the Mn complexes, the dinuclear Mn complexes have attracted the much attention for their simple
⇑ Corresponding author. E-mail address: [email protected] (C.-B. Liu). 0277-5387/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.poly.2011.02.022
structures and flexible magnetic-structural correlations [34–40]. The dinuclear Mn complexes have obtained more and more attention from both the theoretical and experimental research groups in the researches of the bioinorganic chemistry and single-molecular magnetism. With the increasing number of the dinuclear Mn systems being synthesized, the theoretical study on the dinuclear Mn systems is also extensive and is focusing on the research of the magnetic coupling mechanism and the magneto-structural correlation. However, the mechanisms of the magnetic coupling interactions in these systems are still not clear now. Experimentally, a series of dinuclear Mn(II) complexes in which the Mn(II) ions are bridged by the Bpmp (BpmpH = 6-bis[bis(2pyridylmethyl)aminomethyl]-4-methyl-phenol) ligands have been synthesized [41–44]. It is interesting that the systems have the different magnetic properties with the different Bpmp bridging ligands. In order to explain the correlation between the bridging ligands and the magnetic coupling interaction in these systems and the magnetic mechanisms of them, we have theoretically investigated the magnetic properties of a series of Bpmp bridged dinuclear Mn(II) complexes. According to the calculated results, it is proved that the magnetic properties of Bpmp bridged dinuclear Mn(II) complexes are sensitive to the structure of the Bpmp ligand. Moreover, the component of the magnetic orbitals is a significant factor for the magnetic coupling interactions. Therefore, in this work, the d orbitals on the Mn centers are also analyzed to elucidate the magnetic coupling contribution. These investigations will further explain the magnetic interaction mechanism of this system and provide guidance for the design of the molecular magnets.
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L.-L. Wang et al. / Polyhedron 30 (2011) 3017–3021
2. Modeling strategy
4. Results and discussion
The calculated dinuclear models A and E (Fig. 1) are predigested directly from the crystal structures [(NO2Bpmp)Mn2(l-OAc)2] [41] (NO2BpmpH = 2,6-bis[bis(2-pyridylmethyl)aminomethyl]-4nitrophenol) and [(Bpmp)Mn2(l-OAc)2] [42] (BpmpH = 2,6-bis [bis(2-pyridylmethyl)aminomethyl]-4-methyl-phenol). In order to investigate influence of the structure of the bridging ligands, we built three dinuclear Mn(II) models [(R-Bpmp)Mn2(l-OAc)2] (X = –CN, –F, and –H for models B, C and D, respectively) by replacing the methyl of Bpmp with the different R radicals basing on the structure of model A.
4.1. Dependence of the magnetic coupling of the MnII2 systems on the different bridging R-Bpmp ligand
3. Computational details For dinuclear manganese(II) systems, the spin Hamiltonian describing the low-lying states in zero field can be written as:
H ¼ 2JSMn1 SMn2
ð1Þ
where J denotes the exchange coupling constant between adjacent manganese ions. The positive sign of the J value shows the ferromagnetic interaction, and the negative sign of the J value indicates the antiferromagnetic interaction. SMn1 and SMn2 denote the spins on the manganese ions and SMn1 ¼ SMn2 ¼ 52. The magnetic coupling constant J for the dinuclear Mn(II) system is present as,
J¼
EHS EBS S2max
ð2Þ
Where Smax ¼ 5, EHS and EBS denote the energy values of the highest spin state and the broken-symmetry state, respectively. The DFT-BS method used here proposed by Noodleman et al. [45–47] is used to calculate the magnetic coupling constants. Ahlrichs triple-zeta valence basis set (TZV) is utilized. Becke’s three-parameter hybrid functional for exchange combined with the Lee–Yang–Parr correlation functional (B3LYP) [48] is employed. The convergence criterion of SCF is 108. The calculations of magnetic coupling constants are performed using the ORCA 2.7 software package developed by Neese [49].
As a significant factor to judge the magnetic properties of the molecular magnet, the coupling constant J is the bridge between the experimental and theoretical researches. Experimentally, the J values are obtained from the fitting of the experimental data. Theoretically, the J values can be calculated by the configuration interaction (CI) methodologies and the DFT-based methods [50–53]. The computational cost of CI method is much more expensive for the application to large systems than DFT-based method. In addition, DFT-based calculations are proven to be very reliable and convenient for the correlated materials from magnetic molecules to magnetic solids. Therefore, the DFT-BS method is used here to calculate the J values to elucidate the coupling interaction. The calculated J values along with the experimental J values of the five (R-Bpmp)(l-OAc)2 models A–E are shown in Table 1. The calculated J values of all the models are in the range of 6 to 9 cm1 which is consistent with the experimental values very well. In these dinuclear Mn(II) systems there exists weakly antiferromagnetic couplings between the Mn(II) centers. With the bridging R-Bpmp changing from NO2-Bpmp to CN-Bpmp, F-Bpmp, H-Bpmp, and Bpmp, the magnetic coupling constants J values of models A–E are increasing. This indicates that the antiferromagnetic coupling interactions are slightly strengthened with the electronegativity of the R-Bpmp bridging ligands are decreasing. The coupling interaction between the Mn(II) centers is insensitive to the R radical in the R-Bpmp ligand. 4.2. Spin population analyses In order to further elucidate the magneto-structural correlation, the spin density distributions for all the models are analyzed. The plot of the sum of absolute values for the calculated spin densities on the Mn(II) centers for all the models are given in Fig. 2. The values of the spin densities on the Mn(II) centers and all the ligand atoms are shown in Table S1 (in the Supplementary data), where
Fig. 1. The structures of the dinuclear Mn(II) models A–E.
L.-L. Wang et al. / Polyhedron 30 (2011) 3017–3021 Table 1 The calculated and experimental J values for models A–E. Models 1
Jcal (cm ) Jexp (cm1)a R a
Model A
Model B
Model C
Model D
Model E
6.14 7.20 –NO2
7.91
8.20
8.22
–CN
–F
–H
8.30 9.60 –CH3
Refs. [41,42]; R is the R radical in the R-Bpmp ligand.
Sum of the absolute values for the spin denstities on the Mn(II) centers
9.5940 9.5938 9.5936 9.5934
3019
the absolute values of the spin densities on the two Mn(II) centers is decreasing from 9.594 to 9.592 which indicates that the spin delocalization is increasing as the of the electronegativity of the R-Bpmp bridging ligands is decreasing. This changing trend is consistent with the magnetic coupling changing trend in Section 4.1. In addition, the spin delocalization is very weak, which is corresponding to the weak antiferromagnetic coupling in the systems. The spin densities on the oxygen atoms (O2–O5) of the l-OAc ligands are also decreasing from A to E. The spin densities on the benzene ring of the R-Bpmp ligand are very small. According to these values, the spin densities on the N ligand atoms are much larger than the other ligand atoms. Hence, the spin delocalization mainly occurs between the Mn(II) centers and the N ligand atoms. According to these analyses, it can be concluded that the weak spin delocalization results in the weak antiferromagnetic coupling in the systems and the spin delocalization is weakened as the electronegativity of the bridging ligand is increasing.
9.5932
4.3. Molecular orbital analysis
9.5930 9.5928 9.5926 9.5924 9.5922 A
B
C
D
E
Model Fig. 2. The sum of spin densities on the Mn(II) centers of models A–E.
positive and negative signs denote a and b spin states, respectively. The values of the spin densities here are that of the state with the lower energy (the broken-symmetry state (BS)) for all the models. The spin densities on the two Mn(II) centers have the similar absolute values of are similar (about 4.9) and the opposite signs which shows that the unpaired electrons mainly populate on Mn(II) centers. The spin signs on the ligand atoms are same with that on the Mn(II) which they are coordinated to, so there are spin delocalization from the Mn(II) centers to the ligands. From A to E, the sum of
In order to explain the mechanism of the magnetic coupling interactions in these Mn(II) systems, the magnetic orbitals for models A–E are also calculated and shown in Fig. 3. The term ‘‘magnetic orbitals’’ is defined as the localized orbitals centered on the magnetic sites with appropriate tails on the terminal and bridging ligands [25]. The magnetic orbitals of the models here are the HOMO orbitals. For each Mn(II) atom, there are five unpaired electrons which are populated on the d orbitals. For the bridged magnetic systems, the magnetic coupling interaction between the metal centers takes place by the connection through the bridging ligands. Hence only the d orbitals of the metal centers that can have large interaction with the p orbitals of the bridging ligands will lead to the magnetic coupling contribution. The contributions (%) of the d orbitals on the Mn(II) centers to the magnetic orbitals are shown in Table 2. According to Fig. 3, the d orbitals of the Mn(II) centers interact with p orbitals of the ligand atoms by the r path. For model A, the contribution of the NO2-Bpmp is very small, and there is almost no orbital contribution from the -NO2 ligand. With the
Fig. 3. The molecular magnetic orbitals for models A–E.
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L.-L. Wang et al. / Polyhedron 30 (2011) 3017–3021
Table 2 The contributions (%) of the d orbitals of Mn(III) in the magnetic orbitals for models A–E.
A B C D E
dx2 y2 (%)
dz2 (%)
dxy (%)
dyz (%)
dxz (%)
1.68 15.38 15.18 15.99 14.55
38.32 59.78 47.96 52.10 43.37
8.81 2.29 3.95 1.95 6.95
31.64 17.76 19.54 20.02 19.05
19.55 4.78 13.37 9.95 16.08
Laboratory for Computational Chemistry of CNIC and Supercomputing Center of CNIC, Chinese Academy of Sciences.
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.poly.2011.02.022. References
electronegativity of R ligand in the R-Bpmp bridging ligands decreasing, the orbital contribution of the benzene ring of the Bpmp ligand is increasing gradually from model A to model E. In addition, with the R-Bpmp bridging ligands changing from NO2-Bpmp to Bpmp ligands, the overlap of the d orbitals of the Mn(II) centers and the p orbitals of the ligand atoms are increasing, which make the magnetic coupling interactions between the Mn(II) centers strengthened. According to Table 2, the magnetic d orbitals are mainly formed by the dz2 and dyz orbitals. In model A, the contributions of the dz2 (38.32%) and dyz (31.64%) are similar. In models B–E, the contribution of the dz2 orbital is much larger than that of the dyz orbital, and the contribution of the dxy orbital is the smallest. The contributions of the dx2 y2 orbital in models B–E are all about 15%, but that in model A is very small (1.68%). Also, the contribution of the dz2 orbital (38.32%) in model A is much smaller than that in the other models. In all the models, the contribution of the dz2 orbital to the magnetic orbital is the largest in the five d orbitals, which indicates that the effective magnetic coupling interactions mainly depend on the dz2 orbitals contribution. In the research of Castillo et al., [54] it is mentioned that there exist three kinds of strategies for the magnetic coupling interactions between the metal centers. The co-planar interaction of the magnetic orbitals always results in the strong antiferromagnetic coupling, the parallel interaction leads to the weakest coupling, while the intermediate coupling is always due to the mixing of the in-plane and out-plane interaction. According to Fig. 3, it is obvious that the magnetic d orbitals of the two Mn(II) centers in all the models are vertical to each other, which results in the weakly antiferromagnetic coupling interactions in all the models.
5. Conclusions The calculations of the magnetic coupling constants based on the DFT-BS method show that in the dinuclear Mn(II) complexes [(R-Bpmp)Mn2(l-OAc)2] there exist weak antiferromagnetic coupling interaction. The antiferromagnetic coupling interaction is strengthened as the electronegativity of the bridging ligand decreasing. According to the spin density and orbital analyses, it can be concluded that the magnetic properties of the [(RBpmp)Mn2(l-OAc)2] are insensitive to the electronegativity of the R radicals in the R-Bpmp bridging ligands. The weak spin delocalization and the vertical magnetic d orbitals result in the weakly antiferromagnetic coupling interactions in the [(R-Bpmp)Mn2(lOAc)2] systems. These analyses show that it is not an effective pathway to control the magnetic properties by changing R radical in the R-Bpmp ligand. Acknowledgements This work is supported by the National Natural Science Foundation of China (No. 20873075) and the Science Foundation of Shandong Province (No. ZR2009BM024). We also thank the Virtual
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