Chemistry 1000 Lecture 26: Crystal field theory Marc R. Roussel November 6, 18 Marc R. Roussel Crystal field theory November 6, 18 1 / 18
Crystal field theory The d orbitals z 24 z 16 10 12 8 0 0 10 10 y x x 4 0 0 4 10 8 12 10 y 16 24 z 3d x 2 y 2 3d z 2 z z 10 10 10 0 0 10 10 y x 0 0 10 10 y x 0 0 10 10 y x 3d xy 3d xz 3d yz Marc R. Roussel Crystal field theory November 6, 18 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, 18 3 / 18
Crystal field theory Octahedral crystal fields In an octahedral complex, the d x 2 y 2 and d z2 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 z 2 d x 2 y 2 d z 2 d x 2 y 2 d xy d xz d yz isolated atom d xy d xz d yz atom in octahedral field = crystal-field splitting Marc R. Roussel Crystal field theory November 6, 18 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, 18 5 / 18
Crystal field theory Electron configurations At first, just follow Hund s rule, e.g. for a d 3 configuration, d z 2 d x 2 y 2 d xy d xz d 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, 18 6 / 18
Crystal field theory For d 4, two possibilities: P < P > d z2 d x 2 y 2 d z 2 d x 2 y 2 d xy d xz d yz low spin d xy d xz d yz 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, 18 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, 18 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 z2 d x 2 y 2 d xy d xz d 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, 18 9 / 18
Crystal field theory Example: Iron(II) complexes (continued) [Fe(CN) 6 ] 4 is low spin: d z2 d x 2 y 2 d xy d xz d 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, 18 10 / 18
Absorption spectroscopy Color Typically in the transition metals, is in the range of energies of visible photons. Absorption: d z2 d x 2 y 2 d xy d xz d yz +hν d z2 d x 2 y 2 d xy d xz d yz Colored compounds absorb light in the visible range. The absorbed light is subtracted from the incident light: White light Absorption spectrum Transmitted light Intensity Absorption Intensity λ λ λ Marc R. Roussel Crystal field theory November 6, 18 11 / 18
Absorption spectroscopy Example: copper sulfate CuSO4 5 H2 O Marc R. Roussel CuSO4 solution vs blank Crystal field theory November 6, 18 12 / 18
Absorption spectroscopy Example: copper sulfate Visible spectrum CuSO 4 in water yellow orange violet blue green red Marc R. Roussel Crystal field theory November 6, 18 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, 18 14 / 18
Absorption spectroscopy Simple single-beam absorption spectrometer source monochromator sample detector Marc R. Roussel Crystal field theory November 6, 18 15 / 18
Absorption spectroscopy Dual-beam absorption spectrometer beam splitter sample mirror source monochromator mirror blank comparator Marc R. Roussel Crystal field theory November 6, 18 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, 18 17 / 18
Absorption spectroscopy Examples: Colorless ions Titanium(IV) ion = d 0 configuration Zinc(II) ion = d 10 configuration Marc R. Roussel Crystal field theory November 6, 18 18 / 18