Theoretical Studies On The Magnetic Properties Of The Polynuclear Transition Metal Complexes

Now, the molecule-based magnetism is one of the frontiers of chemistry, which involves the chemistry, physics and biology researches. As a significant part of the molecule-based magnetism, the polynuclear transition metal systems have the advantages of both the organic and inorganic materials. The properties of the polynuclear transition metal systems could be controlled by changing the ligands and the magnetic metal centers. The polynuclear transition metal systems are not only the significant component in the field of functional material, but also play a dominant role in the life science. The active centers in the proteases in the organisms are always polynuclear transition metal systems, which could control the complex living processes and catalyse the various living reactions. Now, the theoretical researches of the polynuclear transition metal systems mainly focus on the magnetic mechanism and magneto-structural correlation. In this thesis, I investigate the magnetic properties of the transition metal systems including dinuclear and polynuclear systems by the density functional theory combined with the broken-symmetry method (DFT-BS).The main content of this thesis is listed as follow:1. Generally introduce the theoretical calculation method of the molecular magnetic materials. Based on Heisenberg model, there are three methods used to evaluate the magnetic coupling constant of molecular magnets:Hoffmann method of molecular orbital theory, Kahn method of valence bond theory and Noodleman broken symmetry (BS) method.2. We have systematically investigated the magnetic mechanisms and magneto-structural in the hetero-bridged dinuclear transition metal systems, including three dinuclear copper systems and a series of dinuclear Mn systems. In the hetero-bridged dinuclear systems, if the HOMO of the bridge ligands both match the symmetric or antisymmetric magnetic orbitals, there will be orbital complementarity, or else there will be orbital anticomplementarity.In the investigation of the hetero-bridged dinuclear copper systems [Cu2(L-F)(μ-azaindole)(H3L-F=1,3-bis(3-fluorosalicylidene-amino) -2-propanol) and{Cu(mepirizole)-Br}2(μ-OH)(μ-pyrazole), we proposed a new way to explain the orbital complementarity and anticomplementarity in the hetero-bridged systems:there would be orbital complementarity when the orbitals of the bridge ligands interact with the magnetic orbitals of the metal centers in the same way. According to the calculation results, it is found that there exist; on the contrary, there would be orbital anticomplementarity. This method also well explained the magnetic properties in the hetero-bridged dinuclear CuⅡsystems [Cu2Cl2(μ-Cl)(μ-OCH3)(CioH9N3)2].According to our researches on a series of [(R-Bpmp)Mn2(μ-OAc)2] systems, it can be concluded that the electronegativity bridging ligands is a significant factor that influences the magnetic properties of the systems. According to the spin density and orbital analyses, it can be concluded that the magnetic properties of the [(R-Bpmp)Mn2(μ-OAc)2] are insensitive to the electronegativity of the R radicals in the R-Bpmp bridging ligands. So the magnetic properties of the [(R-Bpmp)Mn2(μ-OAc)2] systems could be controlled by changing the R radicals.3. We have investigated the magnetic coupling mechanism and the magneto-structural correlation in the triangle trinuclear copper(Ⅱ) complexes. Different from the dinuclear systems, the different spin states of the trinuclear systems always degenerate and the spin on one pair of the three metal ions must be a parallel. Hence, even if the magnetic coupling interactions between two metal ions are antiferromagnetic, the state with high spin multiplicity may be the ground state of the system, which results in the spin frustration.In order to explore the mechanism of the magnetic coupling interaction for the trinuclear Cu(Ⅱ) complexes, we build three dynamic models [Cu3(μ3-X)(μ-pz)3Cl3] (X = Cl, Br and O, respectively) by pulling theμ3-X bridge away from the center of the Cu3 triangle plane. As X= Cl or Br, with the Cu-(μ3-X)-Cu angles increasing from 76°to 100°, the J values of the models have a slight increase and the J values begin to decrease with the Cu-(μ3-X)-Cu angles increasing from 100°to 120°. Significantly, at the point of Cu-(μ3-X)-Cu=108°, the J values change from positive to negative. In the other word, the magnetic interactions of both the models are changed from ferromagnetic coupling to antiferromagnetic coupling at this point. However, When X=O, the variation trend of the J values for the model is much different. The J values of the model X=O decrease in the whole range of the Cu-(μ3-O)-Cu angle (from 76°to 120°). Moreover, in the range of 76°to 108°, the variation value△J as the Cu-(μ3-O)-Cu angle changing 4°is about 180 cm-1, which is much larger than the△J (the maximum value is 70 cm-1) for models X=C1 and Br. This indicates that the magnetic properties of the trigonal trinuclear Cu(Ⅱ) systems are much more sensitive to the oxygen bridging ligand than the halogen bridging ligand, which is in agreement with the results of the dinuclear Cu(Ⅱ) complexes. This suggests that the magnetic interaction of theμ-O bridged systems can be effectively controlled with changing the Cu-(μ3-O)-Cu angle.The plot of the E/J/J' versus is a criterion to judge the spin frustration in the trinuclear transition metal systems. E denotes the energy of different spin state and J and J is the two different coupling constants in the trinuclear systems. For the ferromagnetic coupling system, the ground state is high spin state E(3/2,1). Hence, in despite of variation of the ratio J/J', there is no spin frustration in these systems. In the antiferromagnetic coupling systems J and J' are negative, and the ground state varies with the changing ratio J/J' (Figure 5, bottom). For 01, the ground state is E(1/2,1) When J/J' is equal to 1, the ground state is accidentally degenerate and the spins are unable to decide which state to stand in. Hence, the system is shown to be frustrated. For the models we investigated, the J values are equal to the J'values. Hence, there exists spin frustration phenomena when the coupling interaction is antiferromagnetic.By the molecular orbital analysis, it is found that the HOMO of the systems are mainly composed of the dx2-y2. The p orbitals of theμ3-X bridging ligands interact with the dx2-y2 orbitals of two of the Cu centers by the a pathway which is the most effective pathway to get the largest overlap of the orbitals. However, there is almost no interaction between the p orbitals of theμ3-X and the dx2-y2 orbitals of the other Cu center. This further proves that there is spin frustration in this trinuclear Cu system.4. The magnetic coupling mechanism and the magneto-structural correlations of the tetranuclear Mn system [Mn4(μ-pzbg)2(Hpzbg)2(CH3O)4(CH3OH)(H2O)]Cl2 has been investigated. Generally, in the multinuclear Mn magnetic systems, there always exists only one kind of the magnetic coupling interaction:either ferromagnetic or antiferromagnetic. But in the complex that we investigated, there exist both antiferromagnetic and ferromagnetic coupling between the Mn atoms correlated, and there are three different magnetic coupling constants.The three different magnetic coupling constants correspond to three dinuclear Mn systems. According to the magneto-structural correlation calculations, the three different magnetic coupling interactions in the system are due to the different bridge angles. As the bridge angle∠Mn-(μ-OCH3)-Mn changing from 91°to 119°, the magnetic coupling in the system change from ferromagnetic to antiferromagnetic at the point of Mn-(μ-OCH3)-Mn=99°. This is consistent with the experimental results:the system is weakly ferromagnetic with Mn-(μ-OCH3)-Mn=99°. When∠Mn-(μ-OCH3)-Mn=91°, the magnetic coupling is ferromagnetic and is antiferromagnetic as∠Mn-(μ-OCH3)-Mn=111°. When these two different bridge angle both exist in the system, the magnetic coupling is antiferromagnetic. It is concluded that the magnetic properties of the bridged transition metal systems could be well controlled by using different bridge angle.In addition, the torsion angle (α) of theμ-O-CH3 bond with the Mn-(μ-O)-Mn plane is also an important parameter that influences on the magnetic coupling between the Mn(Ⅲ) centers. Hence, influence of the torsion angle on the J values of the system is analyzed. The results show that asαchanging from 0°to 45°, the J values are decreasing and changed from positive to negative atα=40°. This indicates that with the torsion angleαincreasing, the ferromagnetic coupling is weakened and changed to be antiferromagnetic coupling. Moreover, compared with the bridging angle, the influence for the change of the torsion angle (α) of theμ-O-CH3 bond on the magnetic coupling is much weaker:the magnetic coupling constant is changed about 31 cm-1 (from -0.87 to 30.3cm-1) with the bridging angles changing by 28°(from 91°to 119°), while the magnetic coupling constant is changed only 5cm-1 with the torsion angleαchanging by 45°. So it is essential to make the bridge angle as the significant factor that affects the magnetic coupling interactions in the transition metal compounds.In the tetranuclear Mn(Ⅲ) system, magnetic coupling interactions between the Mn centers are significantly influenced by the the component of the magnetic d orbitals. The lager the contribution of d2 is corresponding to the stronger ferromagnetic coupling. 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.5. We have investigated the magnetic coupling mechanism of two mixed-valence CuⅠCuⅡcomplexes with one dimensional (1D) structures, namely, [CuⅠ2CuⅡX2(Hm-dtc)2(CH3-CN)2]n [Hm-dtc-=hexamethylene dithiocarbamate; X=Br or I] for the first time. The distance between two adjacent CuⅡions is 10.5A, which is much longer than the normal transition metal magnetic systems, so there should be weak magnetic coupling interactions in these systems. According to our calculated results, it is found that there are very weak magnetic coupling interactions in the two systems (the J values of them are -3.4cm-1 and -1.1cm-1, respectively). The analyses of the molecular orbitals and spin density distribution reveal that the weak magnetic coupling interactions in the systems are due to the small orbital contribution of the bridging dinuclerar CuⅠradical.