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Orbital Contribution to the Magnetic Moment There Are Many Coordination Compounds, with Unpaired D-Electrons (These Are Paramagnetic)

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Orbital Contribution to the Magnetic Moment There Are Many Coordination Compounds, with Unpaired D-Electrons (These Are Paramagnetic) Magnetochemie Conventional Magnets - Fe, Co, Ni -CrO2, Fe3O4 - Alloys spincarriers: atoms digital „0“ and „1“ bulk magnet Magnetochemie Magnetic properties of the d-block elements I. Magnetism of Octahedral transition metal complexes • Spin-only Paramagnetism • High-spin / Low-spin Complexes (Octahedral) II. Orbital contribution to the magnetic moment There are many coordination compounds, with unpaired d-electrons (these are paramagnetic) 2– 9 [CuCl4] (d ) + 7 [Co(NH3)4(SO4)] (d ) Plastocyanin 3+ 6 2+ 9 [Co(NH3)5(H2O)] (d ) (Cu , d ) 2– 8 [NiCl4] (d ) 1 3 [VO(H2O)5]SO4 (d ) [CrCl3] (d ) General remarks This lecture deals only with paramagnetic coordination compounds. Complicated mathematics will be avoided, where possible! TMn+ ions have pure d-electron configurations (recall: s electrons are lost first, as the diffuse s-orbitals are destablized in complexes) Cr2+: d4 Fe3+: d5 Ni2+: d8 metal organic compounds have also dn 2+ 6 6 Fe , Cr(CO)6, Cr(η -C6H6)2 d 3+ 6 5 Fe , V(CO)6, V(η -C6H6)2 d General remarks Constants and units 3 –1 χm molar magnetic suceptibility [cm ·mol ] (cgs/emu) [emu·mol–1] „ [m3·mol–1] (SI) –6 Conversion factor: χm(cgs) × 4π10 = χm (SI) µeff / µB = 2.828 ⋅ χT K [Fe(CN) ] χ = -122.7×10–6 emu/mol 3kB mol 3 6 m = 2.828( ) χ = -1.542×10–9 m /mol 2 3 m 3 NµB cm K ---------------------------------------------------------------------------------------------------------- N = 6.023×1023 mol–1 –20 µB = 0.92731×10 erg/Gauss; –24 µB = 9.27×10 J/T –23 kB = 1.38×10 J/K 2 3 NµB /(3kB) = 0.125 cm /(K·mol) cgs units, N = 6.023×1023 mol–1 –20 –24 µB = 0.92731×10 erg/Gauss; 9.27×10 J/T Literature A. F. Orchard, Magnetochemistry, Oxford Chemistry Primer, 2007; Chapter 5 F. E. Mabbs, D.J. Machin, „Magnetism and Transition Metal Chemistry“, Chapman and Hall, London 1973 R. Ribas, Coordination Chemistry, Wiley-VCH, Chap. 9 Magnetic Properties of Some Iron Compounds Compound Magnetism Remarks Fe metal ferromagnet TC = 1043 K (msat = 2.22 µB) FeO antiferromagnet TN = 716 K FeCl3 paramagnet µeff = 5.73 µB y-Fe3O4 ferrimagnet TfN = 856 K 4– [Fe(CN)6] diamagnetic ─ 3– [Fe(CN)6] paramagnetic µeff = µeff = 2.25 µB (300 K) Fe(Cp)2 diamagnetic ─ Fe(CO)5 diamagnetic ─ Haemoglobin paramagnetic µeff ~ 4.95 µB 1. Spin-Only-Paramagnetism Effective magnetic moment, µeff, of 3d metal complexes can be estimated to a first approximation with the spin-only formula µeff = ge S(S +1)µB iS neff µeff neff = = ge S(S +1) 1 ½ 1.73 µB 2 1 2.83 –24 µB = Bohr Magneton = eħ/(2me) =9.27408×10 J/T µ = effective magnetic moment eff 3 3/2 3.88 neff = effective magnetic moment in units of µB g = 2.00232 e 4 2 4.90 S = Σsi (Total spin quantum number) s = spin quantum number (+1/2 or -1/2) i 5 5/2 5.92 Note: in the OCP text book µeff is represented as meff Spin-Only-Formula neff(theor.) 3 III III IV II • spin-state of complex and d : Cr , Mo , Mn , V : 3.88 µB • number of unpaired electrons can be determined 5 II III d : Mn , Fe : 5.92 µB 3 5 neff data (~ 300 K) for selected compounds of d and d ions d3 CrCl3 3.90 K3[Cr(ox)3].3H203.62 [Cr(NH3)6]Br3 3.77 KCr(SO4)2.12H2O3.84 [Cr(en)3]Br3 3.82 K3[MoCl6]3.79 [Cr(bpy)3]Cl3 3.81 K2[MnCl6]3.84 K3[Cr(CN)6]3.87[V(en)3]Br2 3.81 K3[Cr(NCS)6].4H2O3.79[V(bpy)3]Cl2 3.67 K3[Mo(NCS)6].4H2O 3.70 [Mo(bpy)3]Cl3 3.66 n (N Bu4)3[Cr(N3)6]3.76K4[V(CN)6]3.78 d5 MnCl2 5.79 FeCl3 5.73 MnBr2 5.82 (Et4N)[FeCl4]5.88 (NH4)2Mn(SO4)2.6H2O5.88(NH4)Fe(SO4)2.12H2O5.89 [Mn(NH3)6]Cl2 5.92 K3[Fe(ox)3].3H2O5.90 (Et4N)2[MnCl4]5.94 Ligands and Abbreviations O O- -O oxalate N O rhodanide (ox) N C S- N H N 2 NH 2 azide 2,2'-Bipyridin ethylene diamine - + - (bpy) N N N (en) bidentate ligand 2+ NH 2 monodentate Cl lignd H2N Co NMe3 H2N Chelate ring NH2 donor atom Spin-Only-Formula 3 III III IV II • spin-state and d : Cr , Mo , Mn , V : 3.88 µB • number of unpaired electrons can be determined 5 II III d : Mn , Fe : 5.92 µB this is true also for more exotic compounds ferrocene vandocene IV 3 [nBu4]2[Mn(CH3)6] 3.90 µB → Mn , d II 3 V(Cp)2, Vanadocene 3.78 µB → V , d Fe V II 5 Mn(Cp)2, Manganocene 5.86 µB → Mn , d 2− CH3 spectrochemical series: CH3 - - 2- - - - - - Mn I < Br < S < SCN- < Cl < N3 < F < OH < O2 < OH2 < H3C Mn CH3 - - - - NCS < NH3 ~ py < en < bpy < NO2 < CH3 < CN < CO H3C CH3 manganocene Spin-Only Formula only valid for the following conditions: • room temperature (295 K) IV • for 3d TM ions (i.e. K2[Re Cl6] = 3.25 µB (expected = 3.88 µB) • for mononuclear complexes (polynulcear complexes may show cooperative phenomena (antiferro- or ferromagnetic interactions)) • for totally quenched orbital momentum (= TM ions with E or A ground terms) Orbital contributions to the magnetic moment • do explain the deviations from the spin-only values • the orbital contribution to the magnetic moment is not totally quenched Two prominent examples: CoCl2 5.47 µB 2─ CoCl4 4.67 µB II 7 expected 3.88 µB → h.s.-Co has d (3 unp. electrons) general trends: d6 to d9: larger values than calculated d1 to d4: smaller values than calculated L L only d5 is well behaved S S This is readily explained a) by the fact that λ > 0 for d1-d4 and λ < 0 for d6-d9 λ = spin-orbit coupling constant 3+ 5 b) Fe (S= /2), L = ML = Σml = 0 Spin-orbit coupling can cause temperature dependent magnetic moments (Ti3+, d1) Orbital contribution to the magnetic moment Orbital contribution to the magnetic moment Spin-only formula µeff = ge S(S +1)µB the orbital angular momentum L has also a magnetic moment associated with it, for free ions with L and S, 2 µeff = L(L + 1) + ge S(S + 1)µB orbit spin Orbital momentum in transition metal ions and complexes In coordination compounds orbital momentum means: electron can move from one d orbital to another degenerate d orbital. However, dxy, dxz, dyz, and dzz, dx2-y2 are no longer degenerate in a complex. In an octahedral complex, e– canonlymovewithinan open t2g shell (first order orbital momentum => of importance in magnetochemistry) d1, d2, (l.s.)-d4, (l.s.)-d5, etc have first order orbital momentum (T ground terms), d3, d4 have no first order orbital momentum (A, E ground terms) dxy Terms with T symmetry exhibit orbital angular momentum dx2-y2 (leer) can show spin-orbit coupling This rule is only applicable in Oh Symmetry. Terms with T symmetry EJ = -1/2Aλ[J(J+1)-L(L+1)-S(S+1) exhibit L = 1, For (t )n less than half occupied: λ positive 2g HSO = -AλLS more than half occupied: λ negative Quenching of the orbital contribution, T-term and A, E-term ions Quenching of the orbital contribution, to the magnetic moment, due to ligand field Octahedral symmetry n m n ground t2g eg ligand field quenching term term 2 12 1 Dt2g T2g No 3 23 2 Ft2g T1g No 4 34 3 Ft2g A2g Yes These ions 5 3 15 4 Dt2g eg Eg Yes actually 43 t2g T1g No have L = 1 6 3 26 5 St2g eg A1g Yes 52 t2g T2g No and thus a 5 4 25 6 Dt2g eg T2g No „residual“ 61 t2g A1g Yes contribution 4 5 24 7 Ft2g eg T1g No (not full 6 12 t2g eg Eg Yes contribution) 3 6 23 8 Ft2g eg A2g Yes to the 2 6 32 9 Dt2g eg Eg Yes spin moment 3+ 1 3+ 2 3+ 4 3+ 5 Typical Ions: Ti (d ), V (d ), l.s-Mn (d ), l.s.-Fe (d , i.e. K3[Fe(CN)6]) h.s-Fe2+ (d6), h.s.-Co(2+) Magnetic moment depends also on C.N. Nickel(II), d8 Orbital momentum 3 quenched octahedral ( A2g) 2.9 – 3.4 µB 3 not quenched tetrahedral ( T1) 3.2 – 4.0 µB trigonal bipyramidal 3.2 – 3.8 µB or 0 square pyramidal 3.2 – 3.4 µB or 0 square planar 0 2− 2− Cl CN CoII, tetr. 4.4-4.8 4A NC Ni CN Ni 2 Cl CoII, oct., 4.8-5.3 4T NC Cl 1g Cl tetr. [NiX ]2- (X = Cl, Br, I) 2+ − 4 2─ tetr. [Ni(SPh)4] N [Ni(PPh ) Br ] 3.27 µ N 3 2 2 B H2N Ni NH2 Spin equilibria H N NH2 2 Ni N II II N H Ni (tetr.) ↔ Ni (sq.pl) (in solution) N 2 Cl H H2 High-spin and low-spin complexes 4 7 possible for d -d electronic configurations (in octahedral complexes) AsPh2 possible for d3-d6 electronic configurations (in tetrahedral complexes) AsPh2 diars Examples (all are low-spin): 4 2+ 4– 3– 4 d [Cr(bpy)3] , [Cr(CN)6] , [Mn(CN)6] t2g S = 1 3.20 µB 5 3– 3+ 4– 5 d [Fe(CN)6] , [Fe(en)3] , [Mn(CN)6] t2g S = 1/2 2.25 µB 2.40 µB 2.18 µB 6 4– 3+ 6 d [Fe(CN)6] , [Co(NH3)6] , [Cr(CO)6] t2g S = 0 7 2+ 4– 3– 6 d [Co(diars)3] , [Co(NO2)6] , [NiF6] t2g eg1 S = ½ 1.84 µB the deviations from the ideal values are again attributable to orbital contributions to the magnetic moment High-spin → low-spin transitions, spincrossover 4 7 Become feasible for d to d in octahedral case, if ∆o(h.s.) ~ ∆o(l.s.) • h.s.->l.s transitions can be affected by variation of temperature or pressure • At lower temperature the l.s-form always dominates • l.s.
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