3.1 Types of electronic transitions

Electronic Transitions in Photochemistry

Electronic transitions describe how electrons in molecules move between energy levels when they absorb light. The type of transition that occurs determines everything from how strongly a molecule absorbs to what kind of photochemistry it can do. Two key selection rules govern which transitions are likely, and the rest of this guide builds on that foundation.

Selection rules for electronic transitions

Selection rules predict whether a given electronic transition is "allowed" (high probability, strong absorption) or "forbidden" (low probability, weak absorption). Two rules matter most here:

Spin selection rule: Transitions are allowed only between states of the same spin multiplicity. A singlet-to-singlet transition is allowed; a singlet-to-triplet transition is forbidden. This rule arises because the photon itself carries no spin angular momentum to flip an electron's spin.

Laporte (parity) selection rule: In centrosymmetric molecules (those with an inversion center, like octahedral complexes), transitions are allowed only between orbitals of different parity (g → u or u → g). Transitions between orbitals of the same parity (g → g, such as d–d transitions) are forbidden.

• Allowed transitions have high molar absorptivities and produce strong bands in absorption spectra (e.g., $\pi \to \pi^*$ transitions in organic chromophores).
• Forbidden transitions still occur, just with much lower intensity (e.g., singlet-to-triplet absorption, or d–d transitions in octahedral complexes). "Forbidden" in spectroscopy doesn't mean impossible; it means the probability is greatly reduced.

Singlet-singlet vs. singlet-triplet transitions

Singlet-singlet ($S_0 \to S_1$):

• Spin-allowed, so these transitions are fast and intense.
• Absorption happens on a femtosecond timescale, and the resulting excited state typically has a nanosecond-scale lifetime.
• These transitions dominate UV-Vis absorption spectra.

Singlet-triplet ($S_0 \to T_1$):

• Spin-forbidden, so direct absorption is extremely weak. You rarely see this transition in a normal absorption spectrum.
• Triplet states are instead populated indirectly through intersystem crossing (ISC), where a molecule in $S_1$ crosses over to $T_1$.
• Triplet excited states are long-lived (microseconds to seconds) because the return trip ($T_1 \to S_0$, phosphorescence) is also spin-forbidden.

Spin-orbit coupling is the main mechanism that relaxes the spin selection rule and makes ISC possible. It mixes singlet and triplet character, and it scales with atomic number. That's why molecules containing heavy atoms like bromine or iodine show much more efficient ISC and stronger phosphorescence. This is called the heavy atom effect.

Characteristics of n \to \pi^ and \pi \to \pi^ transitions

These are the two most important transition types in organic photochemistry.

$n \to \pi^*$ transitions promote a non-bonding (lone pair) electron into an antibonding $\pi^*$ orbital.

• Found in molecules with heteroatoms carrying lone pairs: carbonyls (C=O), imines (C=N), azo groups (N=N).
• Typically low energy (long wavelength) but weak intensity, with molar absorptivities often below $\varepsilon \approx 100 \text{ L mol}^{-1}\text{cm}^{-1}$. They appear as shoulder peaks or broad, low bands.
• The weakness comes from poor spatial overlap between the non-bonding orbital (in the molecular plane) and the $\pi^*$ orbital (above/below the plane).
• Show a characteristic blue shift (hypsochromic shift) in polar solvents, because polar solvents stabilize the ground-state lone pair through hydrogen bonding more than they stabilize the excited state.

$\pi \to \pi^*$ transitions promote a bonding $\pi$ electron into an antibonding $\pi^*$ orbital.

• Found in conjugated systems: aromatics, polyenes, enones.
• Higher energy (shorter wavelength) than $n \to \pi^*$ in the same molecule, but much stronger intensity, often with $\varepsilon > 10{,}000 \text{ L mol}^{-1}\text{cm}^{-1}$. They produce sharp, well-defined peaks.
• Show a slight red shift in polar solvents (the excited state is more polarizable), but the solvent sensitivity is much less dramatic than for $n \to \pi^*$.

Electronic transitions in inorganic complexes

Inorganic complexes show a richer variety of transitions because metals bring d (and sometimes f) orbitals into play.

d-d transitions involve electron promotion between crystal-field-split d orbitals. In octahedral complexes, these are Laporte-forbidden (both the initial and final orbitals have g symmetry), so they are weak ($\varepsilon \approx 1\text{–}50$). They are, however, responsible for the characteristic colors of many transition metal compounds. Copper(II) sulfate's blue color, for example, comes from a d-d transition.

Charge transfer (CT) transitions move electron density between the metal and its ligands. Because they are both spin- and Laporte-allowed, they tend to be very intense ($\varepsilon > 1{,}000$).

• MLCT (metal-to-ligand charge transfer): An electron moves from a metal d orbital to a ligand $\pi^*$ orbital. Classic example: $[\text{Ru(bpy)}_3]^{2+}$, whose strong visible absorption and long-lived excited state make it a workhorse in photocatalysis.
• LMCT (ligand-to-metal charge transfer): An electron moves from a ligand orbital to an empty metal d orbital. The deep purple of permanganate ($\text{MnO}_4^-$) is an LMCT transition.

Intraligand transitions are $\pi \to \pi^*$ or $n \to \pi^*$ transitions localized on the ligand itself. They behave much like the same transitions in free organic molecules.

f-f transitions occur in lanthanide and actinide complexes. These are both Laporte-forbidden and often spin-forbidden, making them extremely weak. The sharp, narrow emission lines of europium and terbium complexes used in luminescent materials come from f-f transitions.

Vibronic coupling is worth noting: molecular vibrations temporarily break the perfect symmetry of a centrosymmetric complex, partially relaxing the Laporte rule. This is why d-d transitions are weak but not completely absent. Without vibronic coupling, octahedral complexes would be nearly transparent in the visible range.