Selection Rules for Allowed and Forbidden Spin Transitions

What are selection rules in photochemistry?

Selection rules are the quantum mechanical rules that tell us whether a particular electronic transition is allowed or forbidden when a molecule absorbs light.

What is meant by an “allowed transition”?

An allowed transition is one that follows the selection rules :

the transition dipole moment (M₁←₀) is not zero,

so the electron jump can occur strongly (high absorbance).

What is meant by a “forbidden transition”?

A forbidden transition breaks one or more selection rules —

M₁←₀ = 0 — meaning it has a very low probability of happening.

It may still occur weakly due to other effects like vibronic or spin–orbit coupling.

What is the orbital angular momentum (Δl) selection rule?

The electron must change orbital type by one step in angular momentum:
Δl = ±1
✅ Allowed: s → p, p → d
❌ Forbidden: s → s, p → p, d → d

Why must Δl = ±1 for an allowed transition?

Because the electric field of light can only induce transitions between orbitals that differ in angular momentum by one unit

it’s like “nudging” the electron to the next orbital type, not skipping or staying still.

What is the spin selection rule?

The total electron spin must remain the same during a transition:
ΔS = 0
✅ Allowed: singlet → singlet
❌ Forbidden: singlet → triplet (or triplet → singlet)

What happens when the spin selection rule is violated?

The transition becomes spin-forbidden

—> it still can happen, but very slowly or weakly

(e.g. phosphorescence, which involves a singlet → triplet transition).

What is the symmetry selection rule?

The symmetry of the orbitals involved in the transition must allow their overlap through the electric dipole operator (R̂).
If the product of their symmetries does not match that of R̂ → transition is forbidden.

Give an example of a symmetry-forbidden transition.

The n → π* transition in methanal (CH₂O) is symmetry-forbidden

because the n (b₂) and π* (b₁) orbitals have incompatible symmetries.

Give an example of a symmetry-allowed transition.

The π → π* transition in methanal (b₁ → b₁) is symmetry-allowed

because the orbitals have compatible symmetries and good overlap.

What is the total angular momentum (ΔJ) selection rule?

The total angular momentum can change by 0 or ±1,

except J = 0 → J = 0 transitions are forbidden.

Which rule explains why phosphorescence is slower than fluorescence?

The spin rule (ΔS = 0)

—> phosphorescence involves a change in spin (singlet → triplet),

which is spin-forbidden, so it happens slowly and weakly.

What happens if a transition is symmetry- or spin-forbidden — can it ever occur?

Yes, weakly. Vibronic coupling or spin–orbit coupling can “relax” the rule,

giving a small but nonzero transition probability (very weak absorption).

Summarise the 4 main selection rules.

Rule	Condition	Example (Allowed)	Example (Forbidden)
Δl = ±1	Change in orbital type	s→p	p→p
ΔS = 0	Spin conserved	singlet→singlet	singlet→triplet
Symmetry rule	Orbitals must overlap properly	π→π*	n→π*
ΔJ = 0, ±1	Small total angular change	J=1→2	J=0→0

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What is the relationship between allowed/forbidden transitions and oscillator strength?

Allowed transitions have high oscillator strength (f₁₀ ≈ 1), while forbidden transitions have very low f₁₀ (as small as 10⁻⁷), meaning much weaker absorption intensity.

Why do n→π* transitions appear weaker than π→π* in UV spectra?

Because n→π* transitions are symmetry-forbidden (poor overlap of orbitals),

giving low ε (molar absorptivity),

whereas π→π* are allowed and much stronger.