Chemistry 1000 Lecture 26: Crystal field theory Marc R. Roussel November 6, 2018 Marc R. Roussel Crystal field theory November 6, 2018 1 / 18
Crystal field theory The d orbitals z z 24 20 20 16 12 10 8 −20 4 −20 0 −10 −20 0 −10 −20 −10 0 0 −10 0 −4 10 0 y 10 20 y 10 10 20 −8 x 20 −10 x 20 −12 −16 −20 −20 −24 3d x 2 − y 2 3d z 2 z z z 20 20 20 10 10 10 −20 −20 −20 0 0 0 −10 −10 −10 −20 −20 −20 −10 0 −10 −10 0 0 0 0 0 y y 10 y 10 10 10 10 10 20 20 20 x x x −10 −10 20 −10 20 20 −20 −20 −20 3d xy 3d xz 3d yz Marc R. Roussel Crystal field theory November 6, 2018 2 / 18
Crystal field theory Crystal field theory In an isolated atom or ion, the d orbitals are all degenerate, i.e. they have identical orbital energies. When we add ligands however, the spherical symmetry of the atom is broken, and the d orbitals end up having different energies. The qualitative appearance of the energy level diagram depends on the structure of the complex (octahedral vs square planar vs. . . ). The relative size of the energy level separation depends on the ligand, i.e. some ligands reproducibly create larger separations than others. Marc R. Roussel Crystal field theory November 6, 2018 3 / 18
Crystal field theory Octahedral crystal fields In an octahedral complex, the d x 2 − y 2 and d z 2 orbitals point directly at some of the ligands while the d xy , d xz and d yz do not. This enhances the repulsion between electrons in a metal d x 2 − y 2 or d z 2 orbital and the donated electron pair from the ligand, raising the energy of these metal orbitals relative to the other three. Thus: d d z 2 x 2 −y 2 ∆ d xy d d xz yz d d d xy d d z 2 x 2 −y 2 xz yz isolated atom atom in octahedral field ∆ = crystal-field splitting Marc R. Roussel Crystal field theory November 6, 2018 4 / 18
Crystal field theory Crystal-field splitting Note: Sometimes we write ∆ o instead of ∆ to differentiate the crystal-field splitting in an octahedral field from the splitting in a field of some other symmetry (e.g. ∆ t for tetrahedral). Marc R. Roussel Crystal field theory November 6, 2018 5 / 18
Crystal field theory Electron configurations At first, just follow Hund’s rule, e.g. for a d 3 configuration, d d z 2 x 2 −y 2 d xy d d xz yz P = pairing energy = extra electron-electron repulsion energy required to put a second electron into a d orbital + loss of favorable spin alignment Marc R. Roussel Crystal field theory November 6, 2018 6 / 18
Crystal field theory For d 4 , two possibilities: P < ∆ P > ∆ d d d d 2 x 2 −y 2 z 2 x 2 −y 2 z d xy d d d xy d d xz yz xz yz low spin high spin Experimentally, we can tell these apart using the paramagnetic effect, which should be twice as large for the high-spin d 4 than for the low-spin d 4 configuration. Marc R. Roussel Crystal field theory November 6, 2018 7 / 18
Crystal field theory Spectrochemical series We can order ligands by the size of ∆ they produce. = ⇒ spectrochemical series A ligand that produces a large ∆ is a strong-field ligand. A ligand that produces a small ∆ is a weak-field ligand. (strong) CO ≈ CN − > phen > en > NH 3 > EDTA 4 − > H 2 O > ox 2 − ≈ O 2 − > OH − > F − > Cl − > Br − > I − (weak) Marc R. Roussel Crystal field theory November 6, 2018 8 / 18
Crystal field theory Example: Iron(II) complexes Electronic configuration of Fe 2+ : [Ar]3d 6 [Fe(H 2 O) 6 ] 2+ is high spin: d d 2 x 2 −y 2 z d xy d d xz yz From the spectrochemical series, we know that all the ligands after H 2 O in octahedral complexes with Fe 2+ will also produce high-spin complexes, e.g. [Fe(OH) 6 ] 4 − is high spin. (strong) CO ≈ CN − > phen > en > NH 3 > EDTA 4 − > H 2 O > ox 2 − ≈ O 2 − > OH − > F − > Cl − > Br − > I − (weak) Marc R. Roussel Crystal field theory November 6, 2018 9 / 18
Crystal field theory Example: Iron(II) complexes (continued) [Fe(CN) 6 ] 4 − is low spin: d d 2 x 2 −y 2 z d xy d d xz yz Somewhere between CN − and H 2 O, we switch from low to high spin. (strong) CO ≈ CN − > phen > en > NH 3 > EDTA 4 − > H 2 O > ox 2 − ≈ O 2 − > OH − > F − > Cl − > Br − > I − (weak) Marc R. Roussel Crystal field theory November 6, 2018 10 / 18
Absorption spectroscopy Color Typically in the transition metals, ∆ is in the range of energies of visible photons. Absorption: d d z 2 x 2 −y 2 d d 2 x 2 −y 2 z + h ν → d xy d d xz yz d xy d d xz yz Colored compounds absorb light in the visible range. The absorbed light is subtracted from the incident light: White light Absorption spectrum Transmitted light Absorption Intensity Intensity λ λ λ Marc R. Roussel Crystal field theory November 6, 2018 11 / 18
Absorption spectroscopy Example: copper sulfate CuSO 4 · 5 H 2 O CuSO 4 solution vs blank Marc R. Roussel Crystal field theory November 6, 2018 12 / 18
Absorption spectroscopy Example: copper sulfate Visible spectrum CuSO 4 in water orange yellow violet blue green red Marc R. Roussel Crystal field theory November 6, 2018 13 / 18
Absorption spectroscopy The color wheel Colors in opposite sectors are complementary. Example: a material that absorbs strongly in the red will appear green. Marc R. Roussel Crystal field theory November 6, 2018 14 / 18
Absorption spectroscopy Simple single-beam absorption spectrometer source monochromator sample detector Marc R. Roussel Crystal field theory November 6, 2018 15 / 18
Absorption spectroscopy Dual-beam absorption spectrometer beam sample mirror splitter source monochromator mirror blank comparator Marc R. Roussel Crystal field theory November 6, 2018 16 / 18
Absorption spectroscopy Example: Cobalt(III) complexes The [Co(H 2 O) 6 ] 3+ ion is green. From the color wheel, this corresponds to absorption in the red. The [Co(NH 3 ) 6 ] 3+ ion is yellow-orange. It absorbs in the blue-violet. The [Co(CN) 6 ] 3 − ion is pale yellow. It absorbs mostly in the ultraviolet, with an absorption tail in the violet. Note that these results are consistent with the spectrochemical series: The d level splitting is ordered H 2 O < NH 3 < CN − . Marc R. Roussel Crystal field theory November 6, 2018 17 / 18
Absorption spectroscopy Examples: Colorless ions ⇒ d 0 configuration Titanium(IV) ion = ⇒ d 10 configuration Zinc(II) ion = Marc R. Roussel Crystal field theory November 6, 2018 18 / 18
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