Tanabe–Sugano diagram

Method of predicting a chemical complex's absorption spectrum
other uses of "T S diagram"

In coordination chemistry, Tanabe–Sugano diagrams are used to predict absorptions in the ultraviolet (UV), visible and infrared (IR) electromagnetic spectrum of coordination compounds. The results from a Tanabe–Sugano diagram analysis of a metal complex can also be compared to experimental spectroscopic data. They are qualitatively useful and can be used to approximate the value of 10Dq, the ligand field splitting energy. Tanabe–Sugano diagrams can be used for both high spin and low spin complexes, unlike Orgel diagrams, which apply only to high spin complexes. Tanabe–Sugano diagrams can also be used to predict the size of the ligand field necessary to cause high spin to low spin transitions. In a Tanabe–Sugano diagram, the ground state is used as a constant reference, in contrast to Orgel diagrams. The energy of the ground state is taken to be zero for all field strengths, and the energies of all other terms and their components are plotted with respect to the ground term.

Until Yukito Tanabe and Satoru Sugano published their paper "On the absorption spectra of complex ions", in 1954, little was known about the excited electronic states of complex metal ions. They used Hans Bethe's crystal field theory and Giulio Racah's linear combinations of Slater integrals, now called Racah parameters, to explain the absorption spectra of octahedral complex ions in a more quantitative way than had been achieved previously. Many spectroscopic experiments later, they estimated the values for two of Racah's parameters, B and C, for each d electron configuration based on the trends in the absorption spectra of isoelectronic first row transition metals. The plots of the energies calculated for the electronic states of each electron configuration are now known as Tanabe–Sugano diagrams. Number must be fit for each octahedral coordination complex because the C/B can deviate strongly from the theoretical value of 4.0. This ratio changes the relative energies of the levels in the Tanabe–Sugano diagrams, and thus the diagrams may vary slightly between sources depending on what C/B ratio was selected when plotting.

In the [Mn(H2O)6]2+ metal complex, manganese has an oxidation state of +2, thus it is a d5 ion. H2O is a weak field ligand (spectrum shown below), and according to the Tanabe–Sugano diagram for d5 ions, the ground state is 6A1. Note that there is no sextet spin multiplicity in any excited state, hence the transitions from this ground state are expected to be spin forbidden and the band intensities should be low. From the spectra, only very low intensity bands are observed (low molar absorptivity (ε) values on y axis).

Another example is [Co(H2O)6]2+. Note that the ligand is the same as the last example. Here the cobalt ion has the oxidation state of +2, and it is a d7 ion. From the high spin (left) side of the d7 Tanabe–Sugano diagram, the ground state is 4T1(F), and the spin multiplicity is a quartet. The diagram shows that there are three quartet excited states: 4T2, 4A2, and 4T1(P). From the diagram one can predict that there are three spin allowed transitions. However, the spectrum of [Co(H2O)6]2+ does not show three distinct peaks that correspond to the three predicted excited states. Instead, the spectrum has a broad peak (spectrum shown below). Based on the T–S diagram, the lowest energy transition is 4T1 to 4T2, which is seen in the near IR and is not observed in the visible spectrum. The main peak is the energy transition 4T1(F) to 4T1(P), and the slightly higher energy transition (the shoulder) is predicted to be 4T1 to 4A2. The small energy difference leads to the overlap of the two peaks, which explains the broad peak observed in the visible spectrum.