Allowed and Forbidden Transitions in UV-Visible Spectroscopy
Transition Probability
It is not always necessary that the excitation of an electron takes place from a bonding orbital or lone pair to an antibonding or non-bonding orbital when a compound is exposed to UV or Visible light. This likelihood can be mathematically evaluated via the molar extinction coefficient:
εmax = 0.87 × 1020 × P × a
Where:
P = Transition probability (ranging strictly from 0 to 1)
a = Target area of the absorbing system (Chromophore).
Transitions with an εmax value greater than $10^4$ are classified as allowed transitions and generally arise due to $\pi \rightarrow \pi^*$ transitions. Conversely, forbidden transitions typically arise due to the excitation of an electron from a lone pair located on a heteroatom to an antibonding $\pi^*$ orbital ($n \rightarrow \pi^*$). The value of $\varepsilon_{max}$ for forbidden transitions is generally below $10^4$.
The primary criteria governing these phenomena include:
- Dipole Moment Change
- Symmetry Rule
- Laporte Rule
- Multiplicity Rule
1. Dipole Moment
Electronic transitions must involve a net change in the molecule's dipole moment. The greater the spatial shift or change in this dipole vector during transition, the higher the resulting intensity of the absorption band.
2. Symmetry Rule
An electronic transition is allowed when it occurs between molecular orbitals that share compatible spatial symmetry traits. For example, a $\pi \rightarrow \pi^*$ transition occurs with highly favorable probability because both the bonding $\pi$ and antibonding $\pi^*$ orbitals lie in the same spatial plane ($xz$ plane). Consequently, it produces a highly intense absorption band ($\varepsilon_{max} \sim 10^4 - 10^5$) near 185 nm in formaldehyde ($\text{HCHO}$).
By contrast, the $n \rightarrow \pi^*$ transition in $\text{HCHO}$ produces a distinctly weak band ($\varepsilon_{max} \sim 100$) near 270 nm, rendering this transition symmetry forbidden. This occurs because the bonding $\pi$ systems lie along the $xz$ plane, whereas the nonbonding lone pair ($p_y$ orbital) rests on the $yz$ plane, perpendicular to the $\pi^*$ target orbital. Because the overlapping volume between these two spatial planes is exceptionally poor, transition probability falls sharply.
The reason an $n \rightarrow \pi^*$ absorption band appears at all is due to atomic vibrations (vibronic coupling), which introduce subtle twisting patterns that momentarily boost atomic orbital overlap.
Typically, light absorption promotes an electron from a singlet ground state ($S_0$) to a singlet excited state ($S_1$) with strict preservation of electron spin configuration. From there, the $S_1$ state can non-radiatively decay into a lower, more stable excited triplet state ($T_1$) via spin-orbit coupling (intersystem crossing) followed by long-lived emission. Parallel electrons in the $T_1$ configuration are held further apart in space due to quantum mechanics, minimizing electrostatic repulsions and maximizing structural stability. However, a direct path from $S_0 \rightarrow T_1$ via standard absorption is strongly symmetry forbidden.
3. Laporte Rule
According to this selection rule, any allowed electronic transition within a centrosymmetric environment must involve a change in the azimuthal quantum number where Δl = ±1.
| $l$ Value | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| Subshell | s | p | d | f |
Consequently, pure intra-configurational $d \rightarrow d$ transitions are fundamentally Laporte forbidden because $\Delta l = 2 - 2 = 0$. The emergence of low-intensity $d \rightarrow d$ absorption peaks ($\varepsilon_{max} < 50$) in solution chemistry typically stems from non-centrosymmetric ligand vibrations or a mixing of $d$-states with $p$ or $f$ atomic orbitals. Stated alternatively, $g \rightarrow g$ (gerade to gerade) or $u \rightarrow u$ (ungerade to ungerade) transitions are strictly forbidden. In centrosymmetric linear systems like ethylene, only $\sigma(g) \rightarrow \sigma^*(u)$ and $\pi(u) \rightarrow \pi^*(g)$ electronic pathways are allowed.
4. Multiplicity Rule
Transitions that demand a change in the total number of unpaired electrons ($n$) or alter the overall spin multiplicity ($2S + 1$) are strictly forbidden. Any electronic transition inside a high-spin $d^5$ transition metal complex (such as $\text{Mn}^{2+}$) is doubly forbidden (violating both Laporte parity and spin multiplicity guidelines). Even so, an exceptionally weak spectral feature ($\varepsilon_{max} < 1$) can still manifest due to weak spin-orbit coupling interactions. This explains why most manganese(II) compounds present visually as off-white, pale flesh-toned, or nearly colorless solutions.
Forbidden Transitions
Describing a transition as "forbidden" does not imply that it is physically impossible; rather, it indicates that the transition is highly improbable and yields weak bands of very low intensity. Allowed and forbidden transitions are routinely classified by whether their molar extinction coefficient ($\varepsilon_{max}$) falls above or below $10^4$ respectively:
| Typical $\varepsilon_{max}$ Value | ~ 20,000 | ~ 180 |
|---|---|---|
| Nature of Transition | Allowed ($\pi \rightarrow \pi^*$) | Forbidden ($n \rightarrow \pi^*$) |
Ultimately, whether a transition path is allowed or forbidden depends entirely on the spatial geometry of the ground and excited molecular orbitals, the collective symmetry of the molecular framework, and the vector orientation of the incident electromagnetic dipole field.