Ch 10 Lecture 1 Bonding Basics

1. Ch 10 Lecture 1 Bonding Basics • Evidence of Electronic Structure • What is Electronic Structure? • Electronic Structure = what orbitals electrons reside in and their energies • Coordination Compounds • The residence of electrons in the metal s, p, and d orbitals • The complete MO description of the entire complex • Bonding theories for transition metal complexes must explain characteristics of the compound influenced by d-electrons • Certain experimental data must match the theorized electronic structure • Thermodynamic Data • Stability (or Formation) Constants • Indicators of Complex Stability

2. Equilibrium constants of complex formation Cu2+ + NH3 [Cu(NH3)2+] [Cu(NH3)]2+ + NH3 [Cu(NH3)2]2+ [Cu(NH3)2]2+ + NH3 [Cu(NH3)3]2+ [Cu(NH3)3]2+ + NH3 [Cu(NH3)4]2+ • Combining the individual steps gives the overall stability constant b4 b4 = K1 x K2 x K3 x K4 = 6.8 x 1012 • Large b values indicate favorable reactions and/or stable complexes • Small b values indicate unfavorable reactions and/or unstable complexes

3. Can be measured by pH titrations, UV-Vis titrations, etc… • Thermodynamic Data • DG = -RTlnK = DH – TDS allows calculation of free energy, entropy, and enthalpy of a reaction from stability constants • These values can help explain bonding in coordination compounds, but detailed theoretical calculations are needed to fully rationalize a given set of data • Most useful to see differences in a single parameter in a series of related compounds • Example: DH might decrease from Br- to Cl- to F- for their complexation to Fe3+ (Hard-Hard Interaction) • This data is not very useful in predicting structure or bonding interactions of coordination compounds in general

4. Magnetic Susceptibility • Magnetic Properties reveal numbers of unpaired electrons • Hund’s Rule requires maximum number of unpaired electrons in degenerate orbitals • Magnetic Descriptions • Diamagnetic = all paired electrons = slightly repelled by magnetic field • Paramagnetic = unpaired electrons = strongly attracted by magnetic field • Magnetic properties are determined by one of several experimental methods not

5. Molar Magnetic Susceptibility = cM = cm3/mol = data from an experimental determination • Magnetic Moment = Calculated value from cM and theoretical treatment of magnetism. m = 2.828(cMT)½Bohr magnetons • Theoretical basis of magnetism • Electron Spin: a spinning charged particle would generate a spin magnetic moment = mS (not really spinning but a property of an electron) • mS = + ½ or – ½ only because the electron can either “spin” clockwise or counter clockwise (up or down arrows) • S = Spin Quantum Number = S mS • Example: S = 3(+ ½ ) = 3/2 • Example: S = +1/2

6. Angular momentum quantum number = l = describes the orbital shape s = 0, p = 1, d = 2, f = 3 • mL = Orbital Angular Momentum = + l, l -1,…..- l • Each number is assigned to one orbital of the set • Example: p-orbitals • L = Orbital Quantum Number = S mL • Example: L = +1 + 0 + -1 = 0 • Example: L = 2(+1) + 0 = 2 • Magnetic moment m depends on both S and L mS+L = g[S(S+1) + ¼ L(L+1)]½ g = gyromagnetic ratio ~ 2.00 for an electron • The Orbital contribution is small for first row transition metals, so we can use a spin only magnetic moment = mS = g[S(S+1)]½ = [n(n+2)]½ n = number of unpaired electrons +1 0 -1

7. Example: calculate mS for high spin Fe3+ • Determine d-electron count by counting back three positions on the periodic table (3+) and counting how far from left on the periodic table you are: d5 • Arrange the d-electrons in the 5 d-orbitals as high spin • Apply mS = g[S(S+1)]½ = 2[5/2(7/2)]½ = 5.92 Bohr magnetons Or [n(n+2)] ½ = [5(7)] ½ = (35) ½ = 5.92

8. Valence Bond Theory • History • Proposed by Pauling in the 1930’s • Describes bonding using hybrid orbitals filled with e- pairs • Extension of Lewis/VSEPR to include d-orbitals • Theory • Metal ions utilize d-orbitals in hybrids • Octahedral complexes require 6 hybrid orbitals • d2sp3 hybridization of metal Atomic Orbitals provides new MO • Ligand lone pairs fill the hybrid orbitals to produce the bond • d-orbitals can come from 3d (low spin) or 4d (high spin) Fe3+ Co2+

9. Problems with the theory • High energy 4d orbitals are unlikely participants in bonding • Doesn’t explain electronic spectra of transition metal complexes • Crystal Field Theory • History • Developed to describe metal ions in solid state crystals only • M+ is surrounded by A- “point charges” • Energies of the d-orbitals are “split” due to unequal geometric interactions with the point charges • Does not take into account covalency and molecular orbitals • Has been extended to do so in Ligand Field Theory • Theory • Place degenerate set of 5 d-orbitals into an octahedral field of (-) charges (L:) • The electrons in the d-orbitals are repelled by the (-) charge of the ligands • The dz2 and dx2-y2 orbitals are most effected because their lobes point directly along x,y,z axes where the point charges are • The dxy, dxz, and dyz orbitals aren’t destabilized as much

10. The energy difference between these orbital sets is called “delta octahedral” = Do • The low energy set has t2g symmetry and are stabilized by –0.4 Do each • The high energy set has eg symmetry and are destabilized by +0.6 Do each • The total energy of the 5 d-orbitals is the same as in the uniform field = 0 (2)(+0.6 Do) + (3)(-0.4 Do) = 0

11. CFSE = Crystal Field Stabilization Energy = how much energy is gained by the electrons in the 5 d-orbitals due to their splitting • Co(III) = d6 low spin (6e-)(-0.4 Do) = -2.4 Do stabilization • Cu(II) = d9 (6e-)(-0.4 Do) + (3e-)(+0.6 Do) = -0.6 Do stabilization • Cu(I) = d10 (6e-)(-0.4 Do) + (4e-)(+0.6 Do) = 0 Do stabilization