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2) Terms and absorption of O h d 1 metal complexes. Selection rules

Lecture 27 Electronic Spectra of Coordination Compounds ML x (x = 4,6) 1) Octahedral complexes of d 1 configuration. Absorption of a TMC in the UV and visible regions results from transitions of electrons between the energy levels available in the metal complex.

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2) Terms and absorption of O h d 1 metal complexes. Selection rules

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  1. Lecture 27Electronic Spectra of Coordination Compounds MLx (x = 4,6)1) Octahedral complexes of d1 configuration Absorption of a TMC in the UV and visible regions results from transitions of electrons between the energy levels available in the metal complex. • We will be interested in those transitions which occur within the metal valence shell (d-subshell). Of our interest will be: 1) The number of the energy levels (terms) and their ordering; 2) The number of absorption bands and their intensity; 3) Absorption bandwidth 1. Consider terms of an isolatedd1metal ion (Ti3+) The number of microstates possible for dXconfiguration is given by formula d1 case corresponds to X = 1 and N = 10 (maximum occupancy of the d-level). The number of microstates is then 10 which means that any of the five degenerate d-orbitals may be occupied by an electron with a spin of ½ or - ½. The orbital angular momentum for Ti3+, L = 2, the spin S = 1/2 and the term is 2D.

  2. 2) Terms and absorption of Oh d1 metal complexes. Selection rules • The wavefunction for a D term is of the same symmetry as for a d-orbital. As a result, D terms behave as d-orbitals do. • In particular, when d1 metal ion is exposed to an octahedral ligandfield, the five-time degenerate 2D term will be split into 2Eg (doubly degenerate) and 2T2g (triply degenerate) terms (recall how d-orbital split in octahedral complexes in crystal field theory!). • Since we have two terms only, one can expect a single band in the spectrum of d1 metal complexes due the only possible T2g Eg transition within the metal d-shell. This band is weak [e of 1 – 103 L/(mol cm)]. Selection rules help rationalize the observed intensity of electronic transitions. • The Laporte rule states that symmetry allowed are the transitions with the change of parity, g  u or u  g. • It means that T2g Eg transitions are symmetry forbidden. Nevertheless, due to the asymmetric vibrations there is always a small fraction of molecules of a reduced symmetry so that such a vibronic transition is allowed though with a low intensity. • Another selection rule states that spin allowed are the transitions with DS = 0 (both states should be of the same multiplicity). This holds true for the 2T2g  2Eg transition.

  3. 3) Estimating Do from electronic absorption spectra of d1 species • Values of Do can be readily obtained from absorption spectra of d1 transition metal complexes. • In the case of a d1 metal complex [Ti(H2O)6]3+ (spectrum is shown below) lmax = 500 nm what corresponds to the Do = n = 1/ lmax = 1/(5.00 10-5cm)= 20000 cm-1. • In the case of dn (n>1) species the relationship between the measured lmax and Do may be much more complex. lmax

  4. 4) Terms of complexes of dn, d10-n, d5-n and d5+n configurations • In more complex cases of dn (n > 1) configurations the number of terms available is much more significant than for d1 species. Here are some rules to make analysis of the terms simpler: • For any given ligand field, term splitting pattern for a metal of d10-n configuration will be the same as for dn one, but the energy level sequence will be the opposite. • d10-n configuration can be considered as a combination of n positrons (“hole formalism”) and a d10 metal shell. Because of the opposite charge of positrons, their interaction with the ligands will be of the opposite sign resulting in the opposite energy level sequence . • Similarly, in the case of high spin complexes, dn, d5-n and d5+n configurations have the same term splitting pattern. The ordering of the energy levels is the same for dn and d5+n and the opposite for dn and d5-n.

  5. 5) Tetrahedral vs octahedral complexes of dn configuration • Octahedral and tetrahedral ligand fields cause the opposite ordering of split levels for each of the metal ion terms. • The term splitting pattern for octahedral and tetrahedral complexes is the same. • The term sequence is the opposite for octahedral and tetrahedral complexes of the same configuration. • The term sequence is of the same order for dn octahedral and d10-n tetrahedral complexes. Note: Tetrahedral terms have no center of inversion and thus no labels g or u.

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