2.Magnetochemistry M.Sc. I Part -II.pptx

M.Sc I

1. Magnetochemistry Part II Lecture by Prof. G.M.Dongare Dept. of Chemistry, Shri Shivaji College Of Arts, Commerce and Science, Akola (Maharashtra) India Academic year 2021-22 Class B.Sc and M.Sc I

2. Magnetism General: 1. Diamagnetism : independent of temperature 2. Paramagnetism : Curie or Curie-Weiss-law 3. Pauli - Paramagnetism : independent of temperature

3. Magnetism in transition metals Many transition metal salts and complexes are paramagnetic due to partially filled d-orbitals . The experimentally measured magnetic moment (μ) ( and from the equation in the previous page) can provide some important information about the compounds themselves : 1 . No of unpaired electrons present 2. Distinction between HS and LS octahedral complexes 3. Spectral behavior, and 4. Structure of the complexes

4. Sources of Paramagnetism Orbital motion of the electron generates ORBITAL MAG. MOMENT ( μ l ) Spin motion of the electron generates SPIN MAG. MOMENT ( μ s ) l = orbital angular momentum; s = spin angular momentum For multi-electron systems L = l 1 + l 2 + l 3 + ……………. S = s 1 + s 2 + s 3 + …………… μ l+s = [4S(S+1 ) + L(L+1)] 1/2 Β.Μ . For TM-complexes, the magnetic properties arise mainly from the exposed d-orbitals. The d-orbitals are perturbed by ligands. ∴ The rotation of electrons about the nucleus is restricted which leads to L = 0 μ s = [4S(S+1)] 1/2 Β.Μ . S = n (1/2) = n/2; n = no of unpaired electrons Hence μ s = [4(n/2)(n/2+1)] 1/2 Β.Μ. = [n(n+2)]1/2 Β.Μ. This is called Spin-Only Formula μ s = 1.73, 2.83, 3.88, 4.90, 5.92 BM for n = 1 to 5, respectively

5. Diagrammatic representation of spin and orbital contributions to μ eff 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 d-orbitals spinning electrons

6. The spin-only formula applies reasonably well to metal ions from the first row of transition metals: (units = μ B, , Bohr- magnetons ) Metal ion d n configuration μ eff ( spin only ) μ eff ( observed ) Ca 2+ , Sc 3+ d 0 0 Ti 3+ d 1 1.73 1.7-1.8 V 3+ d 2 2.83 2.8-3.1 V 2+ , Cr 3+ d 3 3.87 3.7-3.9 Cr 2+ , Mn 3+ d 4 4.90 4.8-4.9 Mn 2+ , Fe 3+ d 5 5.92 5.7-6.0 Fe 2+ , Co 3+ d 6 4.90 5.0-5.6 Co 2+ d 7 3.87 4.3-5.2 Ni 2+ d 8 2.83 2.9-3.9 Cu 2+ d 9 1.73 1.9-2.1 Zn 2+ , Ga 3+ d 10 0 0 Magnetic properties

7. Example: What is the magnetic susceptibility of [CoF 6 ] 3- , assuming that the spin-only formula will apply: [CoF 6 ] 3- is high spin Co(III). (you should know this). High-spin Co(III) is d 6 with four unpaired electrons, so n = 4. We have μ eff = n(n + 2) = 4.90 μ B e g t 2g energy high spin d 6 Co(III)

8. When does orbital angular momentum contribute? There must be an unfilled / half-filled orbital similar in energy to that of the orbital occupied by the unpaired electrons. If this is so, the electrons can make use of the available orbitals to circulate or move around the center of the complexes and hence generate L and μ L Essential Conditions: When does orbital angular momentum contribute ? The orbitals should be degenerate (t 2g or e g ) The orbitals should be similar in shape and size, so that they are transferable into one another by rotation about the same axis (e.g. d xy is related to d x2-y2 by a rotation of 45 o about the z-axis. Orbitals must not contain electrons of identical spin .

9. When does orbital angular momentum contribute? For an octahedral complex Condition t 2g set e g set 1 Obeyed Obeyed 2 Obeyed Not obeyed 3 Since 1 and 2 are satisfied Does not matter condition 3 dictates whether since condition 2 t 2g will generate μ l or not is already not obeyed These conditions are fulfilled whenever one or two of the three t 2g orbitals contain an odd no. of electrons.

10. Orbital momentum in transition metal ions and complexes I n coordination compounds orbital momentum means : Electron can move from one d orbital to another degenerate d orbital. However, d xy , d xz , d yz , and d z2 , d x2-y2 are no longer degenerate in a complex. In an octahedral complex , e – can only move within an open t 2g shell ( first order orbital momentum => of importance in magnetochemistry ) d 1 , d 2 , ( l.s .)- d 4 , ( l.s .)- d 5 , etc. have first order orbital momentum (T ground terms) d 3 , d 4 have no first order orbital momentum (A, E ground terms )

11. 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 μ eff is related to μ (spin-only) by : μ eff = μ (spin-only)(1 - αλ / Δ oct ) Spin and Orbital contributions to Magnetic susceptibility

12. Example: Given that the value of the spin-orbit coupling constant λ , is -316 cm -1 for Ni 2+ , and Δ oct is 8500 cm -1 , calculate μ eff for [Ni(H 2 O) 6 ] 2+ . (Note: for an A ground state α = 4, and for an E ground state α = 2). High-spin Ni 2+ = d 8 = A ground state, so α = 4. n = 2, so μ (spin only) = (2(2+2)) 0.5 = 2.83 μ B μ eff = μ (spin only )(1 - (-316 cm -1 x (4/8500 cm -1 ))) = 2.83 μ B x 1.149 = 3.25 μ B Spin and Orbital contributions to Magnetic susceptibility

13. 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 2 nd and 3 rd row d-block elements, λ is an order of magnitude larger than for the first-row analogues. Most 2 nd and 3 rd 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 μ eff is much lower than expected from the spin-only formula. (Note: the only high-spin complex from the 2 nd and 3 rd row d-block elements is [PdF 6 ] 4- and PdF 2 ). Spin and Orbital contributions to Magnetic susceptibility

14. Spin and Orbital contributions to Magnetic susceptibility

15. Example O h T d Free ion Ni II (d 8 ) S = 1, L = 3  L+S = [4S(S+1)+L(L+1)] 1/2 = 4.47 B.M. Orbital Contribution = 0 The magnetic moment is close to spin only value Magnetic moment is higher than the spin-only value as there is positive orbital contribution

16. Magnetic Properties of lanthanides 4f electrons are too far inside 4f n 5s 2 5p 6 (compared to the d electrons in transition metals ) Thus 4f normally unaffected by surrounding ligands Hence , the magnetic moments of Ln 3+ ions are generally well-described from the coupling of spin and orbital angular momenta ~ Russell-Saunders Coupling to give J vector Spin orbit coupling constants are large ( ca . 1000 cm -1 ) Ligand field effects are very small (ca. 100 cm -1 ) – only ground J-state is populated – spin-orbit coupling >> ligand field splitting magnetism is essentially independent of environment