1. What is Crystal Field Theory (CFT)?
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A model that explains the electronic structure and properties of transition metal complexes by considering the electrostatic interaction between metal ions and ligands.
2. In CFT, what is the assumption about metal-ligand bonding?
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Metal-ligand bonds are purely electrostatic (ionic) in nature, with no covalent character.
3. What is crystal field splitting?
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The splitting of degenerate d-orbitals of the metal ion into different energy levels due to the electrostatic field of ligands.
4. In an octahedral complex, how do the d-orbitals split?
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Into two sets: $t_{2g}$ (lower energy, three orbitals: $d_{xy}$, $d_{yz}$, $d_{xz}$) and $e_g$ (higher energy, two orbitals: $d_{x^2-y^2}$, $d_{z^2}$).
5. In a tetrahedral complex, how do the d-orbitals split?
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Into two sets: $e$ (lower energy, two orbitals: $d_{x^2-y^2}$, $d_{z^2}$) and $t_2$ (higher energy, three orbitals: $d_{xy}$, $d_{yz}$, $d_{xz}$).
6. What is the crystal field splitting parameter, denoted by $\Delta_o$ or $10Dq$?
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The energy difference between the $t_{2g}$ and $e_g$ sets in an octahedral complex.
7. What is the spectrochemical series?
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A series of ligands arranged in order of increasing field strength: $I^- < Br^- < S^{2-} < SCN^- < Cl^- < NO_3^- < F^- < OH^- < H_2O < NH_3 < en < NO_2^- < CN^- < CO$.
8. What is a high-spin complex?
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A complex in which the crystal field splitting energy ($\Delta_o$) is small compared to the pairing energy, so electrons occupy higher energy orbitals before pairing up.
9. What is a low-spin complex?
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A complex in which $\Delta_o$ is large compared to the pairing energy, so electrons pair up in lower energy orbitals before occupying higher ones.
10. What is the pairing energy ($P$)?
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The energy required to pair two electrons in the same orbital.
11. How does the magnitude of $\Delta_o$ affect the spin state?
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If $\Delta_o < P$, high spin; if $\Delta_o > P$, low spin.
12. What is the color of a complex explained by in CFT?
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d-d transitions: absorption of light causes electrons to jump between split d-orbitals, and the complementary color is observed.
13. What is the origin of the magnetic properties of complexes in CFT?
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The number of unpaired electrons in the split d-orbitals determines the magnetic moment.
14. What is the formula for spin-only magnetic moment?
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$\mu = \sqrt{n(n+2)}$ Bohr Magnetons (BM), where $n$ is the number of unpaired electrons.
15. For a $d^4$ octahedral complex, what are the possible electron configurations?
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High spin: $t_{2g}^3 e_g^1$ (4 unpaired); Low spin: $t_{2g}^4 e_g^0$ (2 unpaired).
16. What is the crystal field stabilization energy (CFSE)?
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The energy stabilization gained by the metal ion due to the splitting of d-orbitals in the crystal field.
17. How is CFSE calculated for an octahedral complex?
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$CFSE = (-0.4n_{t_{2g}} + 0.6n_{e_g})\Delta_o$, where $n$ is the number of electrons in respective orbitals.
18. What is the spectrochemical series order for halide ligands?
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$I^- < Br^- < Cl^- < F^-$ (increasing field strength).
19. Why is $CN^-$ a strong field ligand?
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It causes a large splitting ($\Delta_o$) due to its strong interaction with metal d-orbitals, often leading to low-spin complexes.
20. What is the shape of $d_{z^2}$ orbital?
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A doughnut-shaped electron cloud with two lobes along the z-axis.
21. Which d-orbitals point directly towards the ligands in an octahedral complex?
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$d_{x^2-y^2}$ and $d_{z^2}$ (the $e_g$ set).
22. Which d-orbitals point between the ligands in an octahedral complex?
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$d_{xy}$, $d_{yz}$, $d_{xz}$ (the $t_{2g}$ set).
23. What is the relation between $\Delta_t$ and $\Delta_o$?
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$\Delta_t = \frac{4}{9} \Delta_o$.
24. Why are tetrahedral complexes usually high spin?
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Because $\Delta_t$ is small (only 4/9 of $\Delta_o$), so $\Delta_t < P$ typically, leading to high spin.
25. What is the color of $[Cu(H_2O)_6]^{2+}$ and why?
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Blue, due to d-d transition absorbing red light (complementary).
26. What is the magnetic moment of $[Fe(CN)_6]^{3-}$?
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$\mu = \sqrt{1(1+2)} = \sqrt{3} \approx 1.73$ BM (low spin, one unpaired electron).
27. What is the magnetic moment of $[Fe(H_2O)_6]^{2+}$?
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$\mu = \sqrt{4(4+2)} = \sqrt{24} \approx 4.90$ BM (high spin, four unpaired electrons).
28. What is the number of unpaired electrons in $[Co(NH_3)_6]^{3+}$?
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0 (low spin, $d^6$ with $t_{2g}^6 e_g^0$).
29. What is the number of unpaired electrons in $[CoF_6]^{3-}$?
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4 (high spin, $d^6$ with $t_{2g}^4 e_g^2$).
30. What is the CFSE for a high-spin $d^5$ octahedral complex?
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0 (since $t_{2g}^3 e_g^2$: $3(-0.4\Delta_o) + 2(0.6\Delta_o) = 0$).
31. What is the CFSE for a low-spin $d^5$ octahedral complex?
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$-2.0\Delta_o + 2P$ (since $t_{2g}^5 e_g^0$: $5(-0.4\Delta_o) + 2P = -2.0\Delta_o + 2P$).
32. What is the limitation of CFT?
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It assumes purely ionic bonding and does not account for covalent character, and cannot explain the order of the spectrochemical series.
33. What is the meaning of the term 'barycenter' in CFT?
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The average energy of the d-orbitals before splitting; the weighted average of split orbitals remains at the barycenter.
34. For a $d^1$ octahedral complex, what is the CFSE?
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$-0.4\Delta_o$ (one electron in $t_{2g}$).
35. For a $d^9$ octahedral complex, what is the CFSE?
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$-0.6\Delta_o$ (since $t_{2g}^6 e_g^3$: $6(-0.4\Delta_o) + 3(0.6\Delta_o) = -2.4\Delta_o + 1.8\Delta_o = -0.6\Delta_o$).
36. What is the color of $[Ni(H_2O)_6]^{2+}$?
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Green, due to d-d transition.
37. What is the magnetic moment of $[Mn(H_2O)_6]^{2+}$?
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$\mu = \sqrt{5(5+2)} = \sqrt{35} \approx 5.92$ BM (high spin, five unpaired electrons).
38. What is the number of unpaired electrons in $[Cr(H_2O)_6]^{3+}$?
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3 (high spin, $d^3$ with $t_{2g}^3 e_g^0$).
39. What is the number of unpaired electrons in $[Mn(CN)_6]^{4-}$?
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2 (low spin, $d^4$ with $t_{2g}^4 e_g^0$).
40. What is the number of unpaired electrons in $[Fe(CN)_6]^{4-}$?
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0 (low spin, $d^6$ with $t_{2g}^6 e_g^0$).
41. What is the number of unpaired electrons in $[Co(H_2O)_6]^{2+}$?
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3 (high spin, $d^7$ with $t_{2g}^5 e_g^2$).
42. What is the number of unpaired electrons in $[Co(CN)_6]^{3-}$?
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0 (low spin, $d^6$ with $t_{2g}^6 e_g^0$).
43. What is the number of unpaired electrons in $[Ni(CN)_4]^{2-}$?
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0 (square planar, $d^8$ low spin).
44. What is the number of unpaired electrons in $[NiCl_4]^{2-}$?
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2 (tetrahedral, $d^8$ high spin).
45. What is the number of unpaired electrons in $[Cu(NH_3)_4]^{2+}$?
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1 (square planar, $d^9$).
46. What is the number of unpaired electrons in $[Zn(H_2O)_6]^{2+}$?
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0 ($d^{10}$, no unpaired electrons).
47. What is the number of unpaired electrons in $[V(H_2O)_6]^{3+}$?
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2 (high spin, $d^2$ with $t_{2g}^2 e_g^0$).
48. What is the number of unpaired electrons in $[Ti(H_2O)_6]^{3+}$?
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1 (high spin, $d^1$ with $t_{2g}^1 e_g^0$).
49. What is the number of unpaired electrons in $[Fe(H_2O)_6]^{3+}$?
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5 (high spin, $d^5$ with $t_{2g}^3 e_g^2$).
50. What is the number of unpaired electrons in $[Fe(CN)_6]^{3-}$?
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1 (low spin, $d^5$ with $t_{2g}^5 e_g^0$).
51. What is the number of unpaired electrons in $[Mn(H_2O)_6]^{2+}$?
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5 (high spin, $d^5$ with $t_{2g}^3 e_g^2$).
52. What is the number of unpaired electrons in $[Mn(CN)_6]^{4-}$?
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3 (low spin, $d^3$ with $t_{2g}^3 e_g^0$).
53. What is the number of unpaired electrons in $[Cr(CN)_6]^{3-}$?
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3 (low spin, $d^3$ with $t_{2g}^3 e_g^0$).
54. What is the number of unpaired electrons in $[Cr(H_2O)_6]^{2+}$?
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4 (high spin, $d^4$ with $t_{2g}^3 e_g^1$).
55. What is the number of unpaired electrons in $[Cr(CN)_6]^{4-}$?
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2 (low spin, $d^4$ with $t_{2g}^4 e_g^0$).
56. What is the number of unpaired electrons in $[CoF_6]^{3-}$?
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4 (high spin, $d^6$ with $t_{2g}^4 e_g^2$).
57. What is the number of unpaired electrons in $[Co(NH_3)_6]^{3+}$?
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0 (low spin, $d^6$ with $t_{2g}^6 e_g^0$).
58. What is the number of unpaired electrons in $[Co(H_2O)_6]^{3+}$?
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0 (low spin, $d^6$ with $t_{2g}^6 e_g^0$).
59. What is the number of unpaired electrons in $[Co(CN)_6]^{4-}$?
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1 (low spin, $d^7$ with $t_{2g}^6 e_g^1$).
60. What is the number of unpaired electrons in $[Ni(H_2O)_6]^{2+}$?
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2 (high spin, $d^8$ with $t_{2g}^6 e_g^2$).
61. What is the number of unpaired electrons in $[Ni(NH_3)_6]^{2+}$?
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2 (high spin, $d^8$ with $t_{2g}^6 e_g^2$).
62. What is the number of unpaired electrons in $[Ni(CN)_4]^{2-}$?
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0 (square planar, $d^8$ low spin).
63. What is the number of unpaired electrons in $[Cu(H_2O)_6]^{2+}$?
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1 (octahedral, $d^9$).
64. What is the number of unpaired electrons in $[Cu(CN)_4]^{3-}$?
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0 (square planar, $d^8$? Actually Cu(III) is $d^8$, so 0 unpaired).
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