10.1 Electronic Spectra of Coordination Compounds

Electronic Transitions

Absorption Spectroscopy and Transitions

When a coordination compound absorbs light, electrons jump between energy levels, and the wavelengths absorbed (or not absorbed) determine the compound's color. Absorption spectroscopy measures this absorption as a function of wavelength, giving you a direct window into the electronic structure of the complex.

There are two main types of electronic transitions to know:

d-d transitions occur when an electron is promoted from one d orbital to another within the same metal ion. These transitions are responsible for the characteristic colors of most transition metal complexes. Because the electron stays on the metal, these transitions are relatively weak in intensity (more on why below).

Charge transfer (CT) transitions involve movement of electron density between the metal and a ligand:

• MLCT (metal-to-ligand charge transfer): an electron moves from a metal-based orbital to a ligand-based orbital. Common when the metal is easily oxidized and the ligand has low-lying empty orbitals (e.g., $\pi^*$ on CO or bipyridine).
• LMCT (ligand-to-metal charge transfer): an electron moves from a ligand-based orbital to a metal-based orbital. Common with easily oxidized ligands (like $O^{2-}$ or $Cl^-$) and metals in high oxidation states.

CT bands are generally much more intense than d-d bands because they are fully allowed by the selection rules discussed next.

Selection Rules and Their Implications

Selection rules govern which transitions are "allowed" (strong absorption) and which are "forbidden" (weak or absent absorption). Two rules matter most here:

Laporte selection rule: In a centrosymmetric molecule (one with an inversion center, like a perfect octahedron), transitions between states of the same parity are forbidden. Since all d orbitals are gerade (g), d-d transitions are g → g and therefore Laporte-forbidden. This is why d-d bands are weak. The rule gets relaxed through vibronic coupling, where molecular vibrations temporarily break the center of symmetry, allowing some intensity to "leak through." Tetrahedral complexes lack an inversion center entirely, so their d-d transitions tend to be more intense than those of octahedral complexes.

Spin selection rule: Transitions that require a change in total spin ($\Delta S \neq 0$) are forbidden. A spin-allowed transition keeps all electron spins the same. Spin-forbidden transitions do occur, but they're extremely weak. Spin-orbit coupling can relax this rule, and the effect is stronger for heavier metals (3rd row transition metals especially), which is why some spin-forbidden bands become observable in complexes of elements like Os or Ir.

Theoretical Frameworks

Crystal Field and Ligand Field Theories

Crystal field theory (CFT) models ligands as negative point charges that interact electrostatically with the metal's d orbitals. In a free ion, all five d orbitals are degenerate (same energy). When ligands approach, they break this degeneracy. In an octahedral field, the d orbitals split into a lower-energy $t_{2g}$ set ($d_{xy}$, $d_{xz}$, $d_{yz}$) and a higher-energy $e_g$ set ($d_{z^2}$, $d_{x^2-y^2}$). The energy gap between them is $\Delta_o$, the octahedral splitting parameter.

CFT is a good starting point, but it treats bonding as purely ionic, which isn't realistic. Ligand field theory (LFT) builds on CFT by incorporating molecular orbital concepts. It accounts for covalent interactions ($\sigma$- and $\pi$-bonding) between metal and ligand orbitals. This gives a more accurate picture of energy levels and better predictions of spectral properties, especially for complexes with significant covalency.

Tanabe-Sugano Diagrams and the Jahn-Teller Effect

Tanabe-Sugano diagrams are the go-to tool for interpreting d-d spectra of octahedral complexes. Here's how they work:

• The x-axis plots the crystal field strength relative to interelectronic repulsion: $\Delta_o / B$, where $B$ is the Racah parameter (a measure of electron-electron repulsion).
• The y-axis plots the energy of each electronic state as $E / B$.
• The ground state is always taken as the x-axis (energy = 0), so you read transition energies as vertical distances from the baseline to excited state lines.

To use one: find the ratio of your observed transition energies, then slide along the x-axis until the diagram reproduces that ratio. This gives you $\Delta_o / B$, from which you can extract both $\Delta_o$ and $B$ for the complex.

The Jahn-Teller effect states that any non-linear molecule with a spatially degenerate electronic ground state will distort to remove that degeneracy. In octahedral complexes, this is most pronounced for configurations like $d^9$, high-spin $d^4$, and low-spin $d^7$, where the $e_g$ set is unevenly occupied. The typical distortion is a tetragonal elongation (two axial bonds lengthen), which splits both the $t_{2g}$ and $e_g$ sets further. In electronic spectra, this shows up as broadened or split absorption bands rather than a single symmetric peak.

Spectroscopic Properties

Color and the Spectrochemical Series

The color you see in a coordination compound is the complementary color of the light absorbed. For example, if a complex absorbs orange light (~600 nm), it appears blue. The energy of the absorbed photon corresponds to $\Delta_o$ (or more precisely, to the energy gap between the ground and excited electronic states).

The spectrochemical series ranks ligands by how strongly they split the d orbitals:

$I^- < Br^- < Cl^- < F^- < OH^- < H_2O < NH_3 < en < NO_2^- < CN^- < CO$

Weak-field ligands (left side) produce small $\Delta_o$ values, so the complex absorbs lower-energy (longer-wavelength) light. Strong-field ligands (right side) produce large $\Delta_o$ values, shifting absorption to higher energy (shorter wavelength). This is why $[Co(NH_3)_6]^{3+}$ (strong-field) is yellow-orange while $[CoF_6]^{3-}$ (weak-field) is blue.

Spectroscopic Term Symbols

Term symbols label the electronic states of metal ions and their complexes. You need them to identify which transitions are occurring in a spectrum.

For free ions, the format is $^{2S+1}L_J$:

• $S$ = total spin quantum number; $2S+1$ is the spin multiplicity
• $L$ = total orbital angular momentum, designated by a letter: $S = 0$, $P = 1$, $D = 2$, $F = 3$, etc.
• $J$ = total angular momentum (from spin-orbit coupling), ranging from $|L - S|$ to $L + S$

For metal ions in a ligand field, the free-ion terms split into states labeled by the irreducible representations of the point group. In octahedral symmetry, for example, a free-ion $^3F$ term splits into $^3T_{1g}$, $^3T_{2g}$, and $^3A_{2g}$ states. These symmetry labels ($\Gamma$ in the general notation $^{2S+1}\Gamma$) are what appear on Tanabe-Sugano diagrams and are used to assign observed absorption bands to specific electronic transitions.