Understanding the Absorption Electronic Spectra of Coordination Compounds at greater depth Ligand Field Theory Chapter 20

Review of the Previous Lecture Learned how to more specifically define multielectron systems Introduced new quantum numbers (L and S) Defined atomic states and how to label them with Russel-Saunders Term Symbols Characterized the energy of atomic states using Hund’s rules

1. Ligand Field Theory Ligand field theory incorporates molecular orbital theory and treats the ligand field not as a purely electrostatic system. Electronic transitions will be reexamined by considering the atomic states of multielectron systems, focusing on transition metals Allowed transitions will be examined in both weak and strong field coordinations

2. Orgel diagrams to evaluate d-d electronic transitions A. Orgel diagrams are correlation diagrams that correlate orbital energies as they vary with ligand field strengths Consider the ground atomic state and examine what happens in the weak field limit i.e. d1 S = ½ Multiplicity = 2S + 1 = 2 L = 2 2D Ground State Atomic State L S P 1 D 2 F 3 E +2 +1 -1 -2 Absence of ligands

2. Orgel diagrams to evaluate d-d electronic transitions i.e. d1 eg E “Δoct” t2g +2 +1 -1 -2 Absence of ligands Octahedral Field 2D S = ½ Multiplicity = 2S + 1 = 2; 2T2g

2. Orgel diagrams to evaluate d-d electronic transitions i.e. d1 This single electron can be in any of the three t2g orbitals and so this electronic situation describes a triply degenerate state. eg E “Δoct” t2g +2 +1 -1 -2 Absence of ligands Octahedral Field 2D S = ½ Multiplicity = 2S + 1 = 2; 2T2g

2. Orgel diagrams to evaluate d-d electronic transitions i.e. d1 Electron transition eg eg E “Δoct” t2g t2g +2 +1 -1 -2 Absence of ligands Octahedral Field 2D 2T2g 2Eg The electron can be in either eg orbital. Double degeneracy.

2. Orgel diagrams to evaluate d-d electronic transitions i.e. d1 Electron transition eg eg E “Δoct” t2g t2g +2 +1 -1 -2 Absence of ligands Octahedral Field 2D 2T2g 2Eg Spin Allowed transition

2. Orgel diagrams to evaluate d-d electronic transitions “Δoct” E t2g eg Absence of ligands +2 +1 -1 -2 Octahedral Field 2T2g 2Eg Electron transition 2D Expect one absorbance in the UV-Vis spectrum d1 Octahedral Orgel Diagram

A d1 absorbance in reality A Z-in Jahn-Teller distortion applies to a d1 electron configuration in an octahedral field: i.e. [Ti(H2O)6]3+ Ti3+ B A Electronic absorbance Ground State dz2 dz2 dz2 dx2 – y2 dx2 – y2 dx2 – y2 E dxz dyz dxz dyz dxz dyz dxy dxy dxy B A

Components in an octahedral field (Splitting) 2B. Different atomic states produce different components in an octahedral field Atomic State Components in an octahedral field (Splitting) S A1g P T1g D T2g + Eg F A2g + T2g + T1g d1 Octahedral Orgel Diagram

2C. d2 Octahedral Orgel Diagram (Partial) S = 1 Multiplicity = 2S + 1 = 3 L = (+2x1) + (+1x1) = 3 3F Ground State Atomic State L S P 1 D 2 F 3 E +2 +1 -1 -2 Absence of ligands

2C. d2 Octahedral Orgel Diagram (Partial) For d2 the atomic states are 3F, 3P, 1G, 1D, and 1S 1S 1D The d2 Orgel Diagram would consist of all of these atomic states but we will only focus on the ground state and how it splits in an octahedral field. E 1G 3P 3F

2C. d2 Octahedral Orgel Diagram (Partial) Atomic State Components in an octahedral field (Splitting) S A1g P T1g D T2g + Eg F A2g + T2g + T1g E +2 +1 -1 -2 Absence of ligands 3F Ground State

2C. d2 Octahedral Orgel Diagram (Partial) 1st Excitation 2nd Excitation eg eg eg E “Δoct” t2g t2g t2g +2 +1 -1 -2 Absence of ligands Octahedral Field 3F 3T1g 3T2g 3A2g

2C. d2 Octahedral Orgel Diagram (Partial) 1st Excitation 2nd Excitation eg eg eg E “Δoct” t2g t2g t2g +2 +1 -1 -2 Absence of ligands Octahedral Field 3F 3T1g 3T2g 3A2g Energy 3A2g Partial d2 Octahedral Orgel Diagram Considering only ground Atomic State 2nd Excitation 3T2g 3F 1st Excitation 3T1g Increasing Δoct

2D. d3 Octahedral Orgel Diagram (Partial) +2 +1 -1 -2 Absence of ligands 4F For d3 the atomic states are 4F, 4P, 2H, 2G, 2F, 2D, 2D, and 2P Increasing Δoct

2D. d3 Octahedral Orgel Diagram (Partial) +2 +1 -1 -2 Absence of ligands 4F For d3 the atomic states are 4F, 4P, 2H, 2G, 2F, 2D, 2D, and 2P States of the same term symbols cannot cross. Orbital mixing. Lower energy state is stabilized Higher energy state is destabilized Increasing Δoct

2E. d9 Octahedral Orgel Diagram Excitation eg eg E “Δoct” t2g t2g +2 +1 -1 -2 Absence of ligands Octahedral Field 2D

2E. d9 Octahedral Orgel Diagram Positive Hole Concept Excitation eg eg E “Δoct” t2g t2g +2 +1 -1 -2 Absence of ligands Octahedral Field 2D 2Eg 2T2g

2E. d9 Octahedral Orgel Diagram Excitation eg eg E “Δoct” t2g t2g +2 +1 -1 -2 Absence of ligands Octahedral Field 2D 2Eg 2T2g Energy 2T2g Inverse of d1 Octahedral Orgel Diagram 2D 2Eg Increasing Δoct

2F. Inverse Relationship of Orgel Diagrams It turns out d10-n (Oh or Td) Orgel diagrams are inverse of dn (Oh or Td) Orgel diagrams.

2G. Determining Δoct Determining Δoct can be complicated using Orgel Diagrams when there are allowed transitions arising from different initial atomic states. Consider a more detailed d2 octahedral Orgel Diagram

2G. Determining Δoct To determine Δoct, need to approximate the value of the Racah parameter B A measure of the splitting of the initial atomic states B accounts for electron-electron repulsions

3. Tanabe-Sugano Diagrams Tanabe-Sugano diagrams provide similar information as Orgel diagrams but allow you to consider d-d electronic transitions in the weak and strong field limits. d1 Octahedral Orgel Diagram d1 Octahedral Tanabe Sugano Diagram E B 2Eg 2D 2T2g Δoct B

3A. Using Tanabe-Sugano Diagrams to determine Δoct Consider d3 in an octahedral field. 3rd Excitation eg +2 +1 -1 -2 t2g 1st Excitation 2nd Excitation 4P (One microstate example) E 4T1g Hard to Represent eg eg eg +2 t2g t2g t2g +1 -1 -2 Absence of ligands Octahedral Field 4F 4A2 4T2 4T1

3A. Using Tanabe-Sugano Diagrams to determine Δoct 3rd Excitation eg +2 +1 -1 -2 t2g 1st Excitation 2nd Excitation 4P (One microstate example) 4T1g Hard to Represent E eg eg eg +2 t2g t2g t2g +1 -1 -2 Absence of ligands Octahedral Field 4F 4A2g 4T2g 4T1g

3A. Using Tanabe-Sugano Diagrams to determine Δoct

3A. Using Tanabe-Sugano Diagrams to determine Δoct

3A. Using Tanabe-Sugano Diagrams to determine Δoct

3A. Using Tanabe-Sugano Diagrams to determine Δoct

3A. Using Tanabe-Sugano Diagrams to determine Δoct To determine Δoct, you first need to perform a trial and error process of determining a value for Δoct/B on the Tanabe-Sugano diagram that will give you comparable energy difference ratios for the allowed transitions as your experimental values.

3B. Tanabe-Sugano Diagrams provide d-d electronic transition information in the weak and strong field Consider d5 in an octahedral field. E eg +2 t2g +1 -1 -2 Absence of ligands 6S Weak Field; High Spin S = 5/2 Strong Field; Low Spin S = 1/2 2T2g 6A1g

d5 Octahedral Tanabe-Sugano Diagram Weak field (high spin) 6A1g is the ground state No spin-allowed transitions But they do occur; ϵ < 1 M-1cm-1

d5 Octahedral Tanabe-Sugano Diagram Strong field (low spin) 2T2g is the ground state Four allowed transitions 2T2g to 2A2g or 2T2g to 2T1g 2T2g to 2Eg 2T2g to 2T2g (2I) 2T2g to 2A1g Spin-allowed transitions, ε = 10 - 200 M-1cm-1 Four absorbances but due to resolution may not actually see them

4. Charge transfer electronic transitions Charge transfer e- transitions are Spin and Laporte allowed; ε > 1,000 M-1cm-1 Typically observed in the UV range of light Occur at higher energy than d-d electronic transitions Ligand to metal charge transfer (LMCT) Transfer of an electron from an orbital with primarily ligand character to one with primarily metal character Can be observed with π donor ligands M L e-

Revisit Molecular Orbital Diagram including π interaction with Weak Field Ligands [CoF6]3- High spin, S = 2 Co3+ ; d6

Revisit Molecular Orbital Diagram including π interaction with Weak Field Ligands [CoF6]3- High spin, S = 2 LMCT Bands Co3+ ; d6

4. Charge transfer electronic transitions B. Metal to ligand charge transfer (MLCT) Transfer of an electron from an orbital with primarily metal character to one with primarily ligand character Can be observed with π acceptor ligands M L e-

Revisit Molecular Orbital Diagram including π interaction with Strong Field Ligands [Co(CO)6]3+ MLCT Bands Low spin, S = 0 Co3+ ; d6