Coordination Chemistry III: Electronic Spectra

1. Coordination Chemistry III: Electronic Spectra Chapter 11

2. Coordination Complexes • Unlike most organic compounds, many coordination compounds have vivid colors. • These vivid colors are due to the electronic transitions between the d-orbitals of the metal. • The energy levels of d electron configurations, however, are usually more complicated than might be expected since the electrons in the atomic orbitals interact with each other.

3. Absorption of Light • Complementary colors – if a compound absorbed light of one color, the complement of that color is observed. • [Cu(H2O)6]2+ has a blue color. What is absorbed? • Beer-Lambert Absorption Law • log(Io/I)=A=lc (define variables) • In a common absorption spectrum, the A is plotted versus wavelength or cm-1 (1/).

4. Quantum Numbers of Multielectron Atoms • In order to understand energy transitions between states with more than one electron, we need to understand in more detail how these electrons interact with each other. • Each conceivable set of individual ml and ms values constitutes a microstate of the configuration. • How many microstates in a d1 configuration? • Examine the carbon atom (p2 configuration) • Determine the electron configuration and quantum numbers. • Independently, each of the 2p electrons could have one of six possible combinations. The two electrons, however, are not independent of each other.

5. Interaction between Electrons • In any microstate, the individual orbital magnetic moments (related to ml) and the spin magnetic moments (related to ms) will interact resulting in an energy state or term for the configuration. • Commonly, a number of microstates will contribute to a single term (degeneracies). • This is an approximation using the one-electron wave mechanical mode. • Works well for 1st and 2nd row transition metals.

6. Term Designation (Free-Ion) • 2S+1L • L and S relate to the overall orbital and spin angular momenta for the system (or state). • L = overall orbital angular momentum quantum number. • Discuss possible values (analogous to the l quantum number). • L is related to the vectorial addition of vectors taken from the l quantum number. • Discuss the permitted ways in which the l values can combine (Figure 20, Carter).

7. Overall Orbital Angular Momentum Quantum Number, L • The vectorial addition produces the possible terms for a given configuration. • For a given term, the magnitude of the resultant angular momentum is fixed, [L(L+1)]1/2(h/2). • The vector for the momentum can have a number of allowed orientations. • A partial lift of degeneracy by the magnetic field. • Allowed orientations for a given term are associated with the overall magnetic quantum number, ML. • ML = L, L-1,….-L

8. Overall Orbital Angular Momentum Quantum Number, L • ML relates to the orbital multiplicity or orbital degeneracy (Each has projection equal in magnitude to ML(h/2)). • What are the allowed orientations for a D term? • In the Russell-Saunders scheme, ML = ml. • An ML value can be assigned to each microstate. • Therefore, a given L value must arise from a complete set of microstates with the 2L+1 values. • Examples

9. Overall Spin Quantum Number, S • Spin state of the term. • 2S+1 – spin multiplicity of the state. • S=0, 1, 2 • Like L, S can be obtained by vectorial addition of the spin angular momentum vectors (related to s or ms). • Magnitude [S(S+1)]1/2(h/2) • S is related to an overall spin quantum number, MS. • MS = S, S-1,…-S (2S+1 values) • Indicates the ‘allowed’ orientations of the vector relative to an applied magnetic field. The produces the spin degeneracy in a spin state.

10. Overall Spin Quantum Number, S • Magnitude of the spin angular momentum is [S(S+1)]1/2(h/2), but its projections on a particular axis in the allowed orientation are given by MS(h/2). • Russell-Saunders scheme, MS=ms

11. In Summary • Any given term with L and S values arises from a set of microstates that has the necessary 2L+1 values of ML and also the necessary 2S+1 values of MS. • Value of the term • L = largest possible value of ML • Let’s do the d2 configuration.

12. Determining Microstates • Determine the number of microstates for a triplet P. What are the allowed ML and MS values? • Determine the number of microstates for a doublet D. What are the allowed ML and MS values? • It is sufficient to designate the microstates by x (only the number is important). • Number of microstates in a given free-ion term is equal to (2L + 1)(2S +1). • Row multiplied by column

13. Reducing a Microstate Table/Configuration into Its Free-Ion Terms • Notice that each term is composed of a rectangular array of microstates. • This process is shown for a p2 configuration in Table 11-4. • The spin multiplicity is same as the number of columns of microstates. • The # of rows to include in the rectangular array is equal to +L  -L (number of values). • (2L+1)(2S+1) Do the p2 and d2 configurations.

14. Term of the Lowest Energy • The ground term (lowest energy) has the highest spin multiplicity. • If two or more terms share the same maximum spin multiplicity, the ground term is the one having the highest L value. What is the term with the lowest energy for the d2 configuration?

15. Spin-Orbit Coupling • There is also spin-orbit coupling wherein the spin and orbital angular momenta couple with each other. J = L+S, L+S-1, L+S-2,….L-S| (no negative values) J is a subscript on the right side of the L quantum # • Determine the spin-orbit coupling in the 1S and 3P free-ion terms. Designate these with J. • Page 388

16. Lowest Energy Term Including Spin-Orbit Coupling • For subshells (such as p2) that are less than half-filled, the state having the lowest J value has the lowest energy. For subshells that are more than half-filled, the state having the highest J value has the lowest energy. • Determine the lowest energy state for the p2 configuration.

17. Electronic Spectra of Coordination Compounds • Absorption spectra in most cases involve the d orbitals of the metal. • Identifying lowest energy term (quickly) • Sketch the energy levels showing the d electrons. • Spin multiplicity of lowest-energy state equal highest possible number of unpaired electrons +1. • Determine the maximum possible value of ML (ms) for the configuration. • Combine steps. High- and low-spin d6 configurations in octahedral symmetry.

18. Reducing the Symmetry of the Free Ion by a Ligand Field • The orbital term symbols for the free atom/ion are identical to the symbols for the appropriate symmetry species in the spherical group, R3 (show Table). • There are no inherent symmetry restrictions on possible orbital degeneracies. • D – fivefold degeneracy (ML = ?) • F – ???

19. Correlation Table

20. Reducing the Symmetry of the Free Ion by a Ligand Field • When a ligand field is imposed, however, there are restrictions placed on the maximum orbital degeneracy. • In an octahedral complex, the maximum degeneracy is 3 (T-type IR’s, look at table). Orbital degeneracies present in the free ion must be split. • All term symbols will be redefined by the new symmetry. • Upon reducing the symmetry, the free-ion term can be treated as a reducible representation composed of irreducible representations in the appropriate character table.

21. Reducing the Symmetry of the Free Ion by a Ligand Field • The total number of microstates, Dt, remains the same. • Do the d1 configuration. • What does this split into when an octahedral field is imposed? • How many microstates are possible when imposing the ligand field? The new ligand-field terms will retain the original spin multiplicities found in the free-ion terms. Examine

22. Correlation Diagrams – Relating Electron Spectra to Ligand Field Splitting • Examine the correlation diagram for a d2 configuration in an octahedral ligand field. • Far left (absence of ligand field) – the free-ion terms. On this side, the ligand field has very little influence. • Examine the previous table. • Far right (strong ligand field) – the states are largely determined by the ligand field. • Observed before in the crystal field and ligand field discussion. • In real compounds, the situation is somewhere in the middle.

24. Splitting of Free-Ion Terms • Irreducible representations are produced. • Examine the correlation diagram and the Oh table. • Table 11-6 • Each state has symmetric characteristics of that IR. • IRs are also obtained from the strong-field limit configurations (right side of table). • The IRs on the right and left sides must ‘correlate’.

25. Selection Rules for Transitions • Transitions between states of the same parity are forbidden. • Laporte Selection Rule • Transitions between states of different spin multiplicities are forbidden. • 4A2 4T1 and 4A2  2A2 Discuss how the rules are relaxed on the expected absorption intensities.

26. Tanabe-Sugano Diagrams • Special correlation diagrams useful in the interpretation of electronic spectra. • Lowest energy state is plotted along the horizontal axis. • o/B (field strength) • Vertical axis is the measure of the energy above the ground state • E/B B = Racah parameter, a measure of the repulsion between terms of the same multiplicity. • Lines connecting states of the same symmetry cannot cross.

28. A d2 Configuration, [V(H2O)6]3+

29. Electron Configurations • The diagrams of d2-d8 are illustrated in Figure 11-7. • There is a vertical line near the center of d4-d7 diagrams. What does the vertical line represent? What happens once the line is crossed? • In some cases, the absorption bands are off-scale (x-axis) or obscured by the charge-transfer bands (discussed later). • Discuss the terms for the configurations. They are not the same as observed for the orbital terms.

32. Jahn-Teller Distortions • Spectrum of the [Ti(H2O)6]3+ complex. • The complex has a d1 configuration (Fig. 11-8). • Go over terms for the configurations. • Why are there two overlapping bands? • If degenerate orbitals are asymmetrically occupied a distortion will occur to remove the degeneracy. • Jahn-Teller distortion is usually only significant for asymmetrically occupied eg orbitals. • The others cannot be resolved. • The most common distortion is along the z-axis (elongation).

33. Symmetry Labels for Configurations • Symmetry labels for electron configurations match their degeneracies. • T = triply degenerate asymmetrical state • E = doubly degenerate asymmetrical state • A or B = nondegenerate Do a few without Jahn Teller splitting/distortion. • Effect of a D4h field.