By the spin selection rule so the excited state will

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by the spin selection rule, so the excited state will always have the same spin multiplicity as the ground state. The spectra of even the simplest transition metal complexes are rather complicated because of the many possible ways in which the d-electrons can fill the t 2g and e g orbitals. For example, if we consider a d 2 complex such as V 3+ (aq), we know that the two electrons can reside in any of the five d-orbitals, and can either be spin-up or spin-down. There are actually 45 different such arrangements (called microstates ) that do not violate the Pauli exclusion principle for a d 2 complex. Usually we are concerned only with the six of lowest energy, in which both electrons occupy individual orbitals in the t 2g set and all their spins are aligned either up or down. We can see how these microstates play a role in electronic spectra when we consider the d-d transitions of the [Cr(NH 3 ) 6 ] 3+ ion. This ion is d 3 , so each of the three t 2g orbitals contains one unpaired electron. We expect to see a transition when one of the three electrons in the t 2g orbitals is excited to an empty e g orbital. Interestingly, we find not one but two transitions in the visible. The reason that we see two transitions is that the electron can come from any one of the t 2g orbitals and end up in either of the e g orbitals. Let us assume for the sake of argument that the electron is initially in the d xy orbital. It can be excited to either the d z 2 or the d x 2 -y 2 orbital: d xy --> d z 2 (higher energy) d xy --> d x2-y2 (lower energy) The first transition is at higher energy (shorter wavelength) because in the excited state the configuration is (d yz 1 d xz 1 d z 2 1 ). All three of the excited state orbitals have some z-component, so the d-electron density is "piled up" along the z-axis. The energy of this transition is thus increased by electron-electron repulsion . In the second case, the excited state configuration is (d yz 1 d xz 1 d x 2 -y 2 1 ), and the d-electrons are more symmetrically distributed around the metal. This ef fect is responsible for a splitting of the d-d bands by about 8,000 cm -1 . We can show that all other possible transitions are equivalent to one of these two by symmetry, and hence we see only two visible absorption bands for Cr 3+ complexes. From left: [V(H 2 O) 6 ] 2+ (lilac), [V(H 2 O) 6 ] 3+ (green), [VO(H 2 O) 5 ] 2+ (blue) and [VO(H 2 O) 5 ] 3+ (yellow). The UV-visible spectrum of [Cr(NH 3 ) 6 ] 3+ shows two weak transitions in the visible, both corresponding to d-d transitions from the t 2g to e g orbitals.
The most important non-octahedral geometries for transition metal complexes are: 4-coordinate: square planar and tetrahedral 5-coordinate: square pyramidal and trigonal bipyramidal Energies of the d-orbitals in non-octahedral geometries. The figure above shows what happens to the d-orbital energy diagram as we progressively distort an octahedral complex by elongating it along the z-axis (a tetragonal distortion ), by removing one of its ligands to make a square pyramid , or by removing both of the ligands along the z-axis to make a

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