Jablonski Diagram: Radiative and Non-Radiative Transitions

A Jablonski diagram is a graphical representation of the electronic energy states of a molecule and the radiative and non-radiative transitions that may occur between those states. It is widely used to understand fluorescence, phosphorescence, internal conversion, intersystem crossing and related photophysical processes.

Electronic States in a Jablonski Diagram

The horizontal lines in a Jablonski diagram represent different electronic energy states of a molecule. Each electronic state may contain several vibrational and rotational energy levels.

Electronic states are classified according to their spin multiplicity. For a two-electron system, a singlet state has total spin quantum number S = 0, whereas a triplet state has S = 1.

Spin multiplicity is given by:

$$\text{Multiplicity} = 2S + 1$$

• S₀: Ground-state singlet.
• S₁: First electronically excited singlet state.
• S₂, S₃, ...: Higher electronically excited singlet states.
• T₁: Lowest electronically excited triplet state.
• T₂, T₃, ...: Higher electronically excited triplet states.

Important: For corresponding singlet and triplet states arising from the same electronic configuration, the triplet state is generally lower in energy because of exchange stabilization. Thus, for such corresponding states, one commonly has E_S > E_T.

$$E_{S_1} > E_{T_1}$$

Photoexcitation

When a molecule absorbs a photon of suitable energy, it can undergo an electronic transition from the ground state S₀ to an electronically excited state such as S₁ or S₂.

$$\Delta E = h\nu = \frac{hc}{\lambda}$$

Photoexcitation is normally very rapid. Following excitation, the molecule can undergo vibrational relaxation, internal conversion, intersystem crossing, fluorescence, phosphorescence or a photochemical reaction, depending on the molecular system and surrounding environment.

1. Radiative Transitions

Radiative transitions involve the emission or absorption of electromagnetic radiation.

Fluorescence

Fluorescence is the radiative transition from an excited singlet state, most commonly S₁, to the ground singlet state S₀.

$$S_1 \rightarrow S_0 + h\nu$$

The transition is spin-allowed and therefore generally occurs rapidly. Fluorescence lifetimes are commonly of the order of 10⁻⁹ to 10⁻⁷ s, although the exact value depends on the molecule and its environment.

Phosphorescence

Phosphorescence is the radiative transition from an excited triplet state, usually T₁, to the singlet ground state S₀.

$$T_1 \rightarrow S_0 + h\nu$$

Because the transition involves a change in spin multiplicity, T₁ → S₀ is spin-forbidden in the electric-dipole approximation. It can nevertheless occur because spin–orbit coupling makes the transition weakly allowed.

Consequently, phosphorescence is generally much slower than fluorescence, with lifetimes ranging from approximately milliseconds to much longer times depending on the system.

Why Is Emission Usually at Longer Wavelength?

Fluorescence and phosphorescence generally occur at longer wavelengths than the excitation wavelength because part of the absorbed energy is lost through non-radiative processes such as vibrational relaxation and internal conversion before photon emission occurs.

Key Point: Longer wavelength means lower photon energy because E = hc/λ.

2. Non-Radiative Transitions

Non-radiative transitions occur without emission of a photon. Excited-state energy can be converted into vibrational energy and ultimately dissipated as heat, or the molecule can undergo other non-radiative processes.

Internal Conversion (IC)

Internal Conversion is a radiationless transition between electronic states of the same spin multiplicity.

$$S_2 \rightarrow S_1$$

Similarly, internal conversion may occur between triplet states, for example:

$$T_2 \rightarrow T_1$$

The excess electronic energy is converted into vibrational energy and can subsequently be dissipated through collisions with the surroundings.

Intersystem Crossing (ISC)

Intersystem Crossing is a radiationless transition between electronic states of different spin multiplicities.

$$S_1 \rightarrow T_1$$

ISC involves a change in spin state and is enabled by spin–orbit coupling. It is particularly important in molecules containing heavy atoms or structural features that enhance spin–orbit coupling.

Process	Radiative?	Spin Multiplicity	Typical Example
Fluorescence	Yes	Same	S1 → S0
Phosphorescence	Yes	Different	T1 → S0
Internal Conversion	No	Same	S2 → S1
Intersystem Crossing	No	Different	S1 → T1

3. Photochemical Reactions

An electronically excited molecule may undergo a chemical reaction if the excited state has a suitable lifetime, energy and reaction pathway.

Excited singlet states can participate directly in photochemical reactions, but they often undergo very rapid relaxation or other competing processes. Triplet states frequently have longer lifetimes and can therefore have a greater opportunity to undergo bimolecular reactions.

However, it is not correct to state that most or all organic photochemical reactions necessarily proceed through a triplet state. The reaction pathway depends on the particular molecule and reaction mechanism.

4. Important Photophysical Processes

• Absorption: A molecule absorbs a photon and moves from a lower electronic state to an electronically excited state.
• Vibrational relaxation: Excess vibrational energy is rapidly dissipated within the same electronic state.
• Internal conversion: Radiationless transition between states of the same spin multiplicity.
• Intersystem crossing: Radiationless transition between states of different spin multiplicities.
• Fluorescence: Radiative emission, usually S₁ → S₀.
• Phosphorescence: Radiative emission, usually T₁ → S₀.
• Photochemical reaction: Chemical transformation occurring from an electronically excited state.

5. Test Your Understanding: Jablonski Diagrams

1. Which statement correctly describes the relative energy of corresponding singlet and triplet excited states?

• (A) The corresponding singlet state is generally lower in energy than the triplet state.
• (B) The corresponding triplet state is generally lower in energy than the singlet state.
• (C) Singlet and triplet states must always have identical energies.
• (D) The triplet state must always lie below the ground state.

View Answer

Correct Answer: (B)
For corresponding electronic configurations, the triplet state is generally lower in energy than the corresponding singlet state because of exchange stabilization.

2. What is the fundamental difference between Internal Conversion (IC) and Intersystem Crossing (ISC)?

• (A) IC emits visible light, whereas ISC emits infrared radiation.
• (B) IC is radiative, whereas ISC is a chemical reaction.
• (C) IC occurs between states of the same spin multiplicity, whereas ISC occurs between states of different spin multiplicities.
• (D) IC requires hours, whereas ISC always occurs instantaneously.

View Answer

Correct Answer: (C)
Both IC and ISC are non-radiative processes. IC occurs between states of the same spin multiplicity, such as S₂ → S₁, whereas ISC occurs between states of different multiplicities, such as S₁ → T₁.

3. Why can a triplet excited state often have a greater opportunity to undergo a bimolecular photochemical reaction?

• (A) It always has infinite lifetime.
• (B) It is always the ground state.
• (C) Its relatively long lifetime can provide more time for collisions with other molecules.
• (D) It bypasses all relaxation processes.

View Answer

Correct Answer: (C)
Triplet states often have relatively long lifetimes because their return to the singlet ground state is spin-forbidden. This can increase the probability of collisions and bimolecular photochemical reactions. However, not every photochemical reaction proceeds through a triplet state.

6. Quick Revision

• S₀ is the ground-state singlet.
• S₁ is the first excited singlet state.
• T₁ is the lowest excited triplet state.
• Fluorescence usually corresponds to S₁ → S₀.
• Phosphorescence usually corresponds to T₁ → S₀.
• Internal conversion occurs between states of the same spin multiplicity.
• Intersystem crossing occurs between states of different spin multiplicities.
• Fluorescence is generally much faster than phosphorescence.
• Excited-state photochemical reactions can occur from singlet or triplet states depending on the system.
• Longer emission wavelength generally corresponds to lower photon energy.

Exam Tip: Remember the four most important transitions:

Fluorescence: S₁ → S₀
Phosphorescence: T₁ → S₀
Internal Conversion: S₂ → S₁
Intersystem Crossing: S₁ → T₁

Read also: Fluorescence | Phosphorescence | Singlet and Triplet States