Transition Metals: Crystal Field Theory

28.1 5.111 Lecture Summary #28 Transition Metals: Crystal Field Theory Chapter 16 p 681-683 (p 631-633 in 3rd ed) From Friday’s handout d Orbitals There are five d orbitals: dxy, dxz, dyz, dx -y , dz . 2 2 2 You need to be able to draw their shapes. Z Z Y Y X X dz has maximum amplitude along z and doughnut in xy plane dx -y has maximum amplitude along x and y axes. 2 2 2 Z Z Z Y X Y Y X X dyz has maximum amplitude 45° to y and z axes dxz has maximum amplitude 45° to x and z axes dxy has maximum amplitude 45° to x and y axes 28.2 Today’s material Crystal field and ligand field theories were developed to explain the special properties of coordination complexes of transition metals. Basic idea behind theories: When a metal ion with a given formal oxidation number is placed at the center of a coordination sphere defined by a set of ligands, the energy levels of the d orbitals housing the metal electrons are altered from those in the free metal ions. Crystal field theory is based on an ionic description of the metal-ligand bond. Ligand field theory includes covalent as well as ionic aspects of coordination. It is a more powerful description of transition metal complexes. It is, however, beyond the scope of this course. (Take 5.03 if you are interested in this topic). Crystal Field Theory considers ligands as negative point charges and considers the repulsion between the negative point charges and the d-orbitals. L L Mn+ L- L- L L 28.3 Ligand (L) point charges are directed toward the dz2 and dx2-y2 orbitals of metal (Mn+), resulting in a large repulsion. The dz2 and dx2-y2 orbitals are destabilized, and they are destabilized by the same amount. dz2 and dx2-y2 are degenerate. The dz2 and dx2-y2 orbitals are destabilized more than dxy, dyz, and dxz. Z L- Z L Mn+ L- Y Y L X X L- dx2-y2 L- dz2 Large repulsion- destabilized relative to dxy, dyz, dxz. Ligand point charges are directed in between dxy, dxz, and dyz orbitals (not directly toward them). The dxy, dxz, and dyz orbitals are stabilized relative to dz2 and dx2-y2 orbitals, and they are stabilized by the same amount (i.e. dxy, dxz, and dyz orbitals are degenerate). Z Z Z L L L- Mn+ L Y X L- Y Y X X L dyz dxz Small repulsion - stabilized relative to dz2 and dx2-y2 dxy 28.4 label for degenerate dx2-y2 and dz2 orbitals (eg) d dz2 2 2 x -y O average energy of d orbitals with ligands +3 O 5 -2 O 5 dxy dxz dyz (Octahedral crystal field) (Spherical crystal field) (t2g) label for degenerate dxy, dxz, dyz orbitals ∆o is the overall splitting between eg and t2g orbitals = octahedral field splitting energy ("o" in ∆o is for octahedral) Because the overall energy is maintained, the energy of the three t2g orbitals are lowered by (2/5) ∆o and the energy of the two eg orbitals are raised by (3/5) ∆o relative to the spherical crystal field. Example 1. [Cr(NH3)3Br3] (a) figure out the oxidation number of Cr? (b) figure out d count (c) draw octahedral crystal field splitting diagram Octahedral crystal field splitting diagram dz2 dx2-y2 (eg) +3 O -2 dxy dxz dyz (t2g) O 5 5 O 28.5 (d) Write dn electron configuration: (e) Predict Crystal Field Stabilization Energy (CFSE) - energy change relative to that of the hypothetical spherical crystal. CFSE = Example 2. [Mn(H2O)6]Cl3 (a) figure out the oxidation number of Mn? (b) figure out d count (c) draw octahedral crystal field splitting diagram There are two possible octahedral crystal field splitting diagrams for Mn3+: one for the case where the magnitude of ∆o is greater than the pairing energy (PE), and one for the case where it is less. Pairing energy is the energy of the electron-electron repulsion. Mn3+ d4 d dz 2 2 2 x -y dxy (eg) O (t2g) dxz dz2 dx2-y2 dyz +3 5 -2 5 (eg) O O O dxy dxz dyz (t2g) weak field ( ∆o PE) (d) dn electron configuration = dn electron configuration = +3 5 O -2 O 5 28.6 ∆o is small (weak octahedral field), (∆oPE). Electrons are paired in lower energy t2g orbitals. eg orbitals are not occupied until t2g orbitals are filled. This arrangement of electrons gives the maximum number of unpaired electrons (high spin). This arrangement of electrons gives the minimum number of unpaired electrons (low spin). NOTE: Mn3+ in [Mn(H2O)6]Cl3 is high spin, why? We will come back to this. (e) Predict Crystal Field Stabilization Energy (CFSE) For High spin Mn3+ d4 Low spin Mn3+ d4 CFSE = CFSE = Example 3. Co2+ in an octahedral coordination complex (a) figure out oxidation number (given) (b) figure out d count (c) draw octahedral crystal field splitting diagram d dz 2 2 2 x -y (eg) +3 O (t2g) dxy dxz dz2 dx2-y2 dyz (eg) O O 5 -2 5 (t2g) O dxy Weak Field dxz dyz Strong Field _______Spin (d) dn electron configuration = _______Spin dn electron configuration = (e) CSFE= CFSE= +3 5 O -2 5 O