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Lecture 19: Magnetic properties and the Nephelauxetic effect connection balance to balance left: the Gouy balance for Gouy determining Tube the magnetic susceptibility sample thermometer of materials north south electromagnet Magnetic properties Magnetic susceptibility (μ) and the spin-only formula. Materials that are diamagnetic are repelled by a magnetic field, whereas paramagnetic substances are attracted into a magnetic field, i.e. show magnetic susceptibility. The spinning of unpaired electrons in paramagnetic complexes of d-block metal ions creates a magnetic field, and these spinning electrons are in effect small magnets. The magnetic susceptibility, μ, due to the spinning of the electrons is given by the spin-only formula: μ(spin-only) = n(n + 2) Where n = number of unpaired electrons. Magnetic properties The spin-only formula applies reasonably well to metal ions from the first row of transition metals: (units = μB,, Bohr-magnetons) Metal ion dn configuration μeff(spin only) μeff (observed) Ca2+, Sc3+ d0 0 0 Ti3+ d1 1.73 1.7-1.8 V3+ d2 2.83 2.8-3.1 V2+, Cr3+ d3 3.87 3.7-3.9 Cr2+, Mn3+ d4 4.90 4.8-4.9 Mn2+, Fe3+ d5 5.92 5.7-6.0 Fe2+, Co3+ d6 4.90 5.0-5.6 Co2+ d7 3.87 4.3-5.2 Ni2+ d8 2.83 2.9-3.9 Cu2+ d9 1.73 1.9-2.1 Zn2+, Ga3+ d10 0 0 Example: What is the magnetic susceptibility of [CoF6]3-, assuming that the spin-only formula will apply: [CoF6]3- is high spin Co(III). (you should know this). High-spin Co(III) is d6 with four unpaired electrons, so n = 4. energy eg We have μeff = n(n + 2) = 4.90 μB t2g high spin d6 Co(III) Spin and Orbital contributions to Magnetic susceptibility For the first-row d-block metal ions the main contribution to magnetic susceptibility is from electron spin. However, there is also an orbital contribution from the motion of unpaired electrons from one d-orbital to another. This motion constitutes an electric current, and so creates a magnetic field (see next slide). The extent to which the orbital contribution adds to the overall magnetic moment is controlled by the spin-orbit coupling constant, λ. The overall value of μeff is related to μ(spin-only) by: μeff = μ(spin-only)(1 - αλ/Δoct) Diagrammatic representation of spin and orbital contributions to μeff spinning d-orbitals electrons spin contribution – electrons are orbital contribution - electrons spinning creating an electric move from one orbital to current and hence a magnetic another creating a current and field hence a magnetic field Spin and Orbital contributions to Magnetic susceptibility μeff = μ(spin-only)(1 - αλ/Δoct) In the above equation, λ is the spin-orbit coupling constant, and α is a constant that depends on the ground term: For an A ground state, α = 4. and for an E ground state, α = 2. Δoct is the CF splitting. Some values of λ are: Ti3+ V3+ Cr3+ Mn3+ Fe2+ Co2+ Ni2+ Cu2+ λ,cm-1 155 105 90 88 -102 -177 -315 -830 Spin and Orbital contributions to Magnetic susceptibility Example: Given that the value of the spin-orbit coupling constant λ, is -316 cm-1 for Ni2+, and Δoct is 8500 cm-1, calculate μeff for [Ni(H2O)6]2+. (Note: for an A ground state α = 4, and for an E ground state α = 2). High-spin Ni2+ = d8 = A ground state, so α = 4. n = 2, so μ(spin only) = (2(2+2))0.5 = 2.83 μB μeff = μ(spin only)(1 - (-316 cm-1 x (4/8500 cm-1))) = 2.83 μB x 1.149 = 3.25 μB Spin and Orbital contributions to Magnetic susceptibility The value of λ is negligible for very light atoms, but increases with increasing atomic weight, so that for heavier d-block elements, and for f-block elements, the orbital contribution is considerable. For 2nd and 3rd row d- block elements, λ is an order of magnitude larger than for the first-row analogues. Most 2nd and 3rd row d-block elements are low-spin and therefore are diamagnetic or have only one or two unpaired electrons, but even so, the value of μeff is much lower than expected from the spin- only formula. (Note: the only high-spin complex from the 2nd and 3rd row d-block elements is [PdF6]4- and PdF2). Ferromagnetism: In a normal paramagnetic material, the atoms containing the unpaired electrons are magnetically dilute, and so the unpaired electrons in one atom are not aligned with those in other atoms. However, in ferromagnetic materials, such as metallic iron, or iron oxides such as magnetite (Fe3O4), where the paramagnetic iron atoms are very close together, they can create an internal magnetic field strong enough that all the centers remain aligned: unpaired electrons unpaired electrons aligned in their oriented randomly unpaired electrons own common magnetic field a) paramagnetic, magnetically dilute in e.g. [Fe(H2O)6]Cl2. Fe separated by diamagnetic atoms atoms b) ferromagnetic, as in metallic Fe or some a) b) Fe oxides. Antiferromagnetism: electron spins in opposite Here the spins on the directions in alternate metal atoms unpaired electrons become aligned in opposite directions so that the μeff approaches zero, in contrast to ferromagnetism, where μeff becomes very large. An example of anti- ferromagnetism is found in MnO. antiferromagnetism The Nephelauxetic Effect: The spectrochemical series indicates how Δ varies for any metal ion as the ligand sets are changed along the series I- < Br- < Cl- < F- < H2O < NH3 < CN-. In the same way, the manner in which the spin-pairing energy P varies is called the nephelauxetic series. For any one metal ion P varies as: Note: F- has largest F- > H2O > NH3 > Cl- > CN- > Br- > I- P values The term nephelauxetic means ‘cloud expanding’. The idea is that the more covalent the M-L bonding, the more the unpaired electrons of the metal are spread out over the ligand, and the lower is the energy required to spin- pair these electrons. The Nephelauxetic Effect: The nephelauxetic series indicates that the spin-pairing energy is greatest for fluoro complexes, and least for iodo complexes. The result of this is that fluoro complexes are the ones most likely to be high-spin. For Cl-, Br-, and I- complexes, the small values of Δ are offset by the very small values of P, so that for all second and third row d- block ions, the chloro, bromo, and iodo complexes are low- spin. Thus, Pd in PdF2 is high-spin, surrounded by six bridging fluorides, but Pd in PdCl2 is low-spin, with a polymeric structure: bridging chloride Cl Cl Cl Cl Cl low-spin d8 square-planar Pd Pd Pd Pd palladium(II) Cl Cl Cl Cl Cl The Nephelauxetic Effect: Δ gets larger down groups, as in the [M(NH3)6]3+ complexes: Co(III), 22,900 cm-1; Rh(III), 27000 cm-1; Ir(III), 32,000 cm-1. This means that virtually all complexes of second and third row d-block metal ions are low-spin, except, as mentioned earlier, fluoro complexes of Pd(II), such as [PdF6]4- and PdF2. Because of the large values of Δ for Co(III), all its complexes are also low-spin, except for fluoro complexes such as [CoF6]3-. Fluoride has the combination of a very large value of P, coupled with a moderate value of Δ, that means that for any one metal ion, the fluoro complexes are the most likely to be high-spin. In contrast, for the cyano complexes, the high value of Δ and modest value of P mean that its complexes are always low-spin. Distribution of high- and low-spin complexes of the d-block metal ions: Co(III) is big exception – all low-spin except for [CoF6]3- 1st row tend to be high-spin except for CN- complexes 2nd and 3rd row are all low-spin except for PdF2 and [PdF6]4- Empirical prediction of P values: Because of the regularity with which metal ions follow the nephelauxetic series, it is possible to use the equation below to predict P values: P = Po(1 - h.k) where P is the spin-pairing energy of the complex, Po is the spin-pairing energy of the gas-phase ion, and h and k are parameters belonging to the ligands and metal ions respectively, as seen in the following Table: Empirical prediction of P values: Metal Ion k Ligands h Co(III) 0.35 6 Br- 2.3 Rh(III) 0.28 6 Cl- 2.0 Co(II) 0.24 6 CN- 2.0 Fe(III) 0.24 3 en 1.5 Cr(III) 0.21 6 NH3 1.4 Ni(II) 0.12 6 H2O 1.0 Mn(II) 0.07 6 F- 0.8 Example: The h and k values of Jǿrgensen for two 9-ane-N3 ligands and Co(II) are 1.5 and H H N N 0.24 respectively, and the value of Po in the gas-phase for Co2+ is 18,300 cm-1, N with Δ for [Co(9-ane-N3)2]2+ being 13,300 H cm-1. Would the latter complex be 9-ane-N3 high-spin or low-spin? To calculate P for [Co(9-ane-N3)2]2+: P = Po(1 - (1.5 x .24)) = 18,300 x 0.64 = 11,712 cm-1 P = 11,712 cm-1 is less than Δ = 13,300 cm-1, so the complex would be low-spin. Example: The value of P in the gas-phase for Co2+ is 18,300 cm-1, while Δ for [Co(9-ane-S3)2]2+ is 13,200 cm-1. Would the latter complex be high-spin or low-spin? Calculate the magnetic moment for [Co(9-ane-S3)2]2+ using the spin- only formula. Would there be anything unusual about the structure of this complex in relation to the Co-S bond lengths? energy eg P = 18,300(1 – 0.24 x 1.5) = 11,712 cm-1. Δ at 13,200 cm-1 for [Co(9-ane-S3)2]2+ is t2g larger than P, so complex is low-spin. CFSE = 13,200(6 x 0.4 – 1 x 0.6) = 23,760 cm-1. Low-spin d7 would be Jahn-Teller distorted, so would be unusual with four short and two long Co-S bonds (see next slide). μeff = (1(1+2))0.5 = 1.73 μB Structure of Jahn-Teller distorted [Co(9-ane-S3)2]2+ (see previous problem) longer axial Co-S bonds of 2.43 Å S S S S Co S S S S S shorter in-plane Co-S bonds of 2.25 Å 9-ane-S3 Structure of [Co(9-ane-S3)2]2+ (CCD: LAFDOM)