After absorption to S2, the molecule undergoes vibrational relaxation to v = 0 of S2,
internal conversion to S1, then vibrational relaxation to v = 0 of S1.
Absorption directly to S1 can also occur, which likewise leads to vibrational relaxation to v = 0 of S1.
Vibrational relaxation is fast relative to emission (Kasha's rule) and is not adjustable in this simulation.
From S1 (v = 0), three pathways compete:
fluorescence (\(k_f\)), intersystem crossing to T1 (\(k_{S_1 \to T_1}\)),
and internal conversion to S0 (\(k_{S_1 \to S_0}\)).
From T1 (v = 0), three pathways compete:
phosphorescence (\(k_p\)), intersystem crossing to S0 (\(k_{T_1 \to S_0}\)),
and reaction (\(k_r\)).
Fluorescence quantum yield:
$$\Phi_f = \frac{k_f}{k_f + k_{S_1 \to T_1} + k_{S_1 \to S_0}}$$
Phosphorescence quantum yield:
$$\Phi_p = \frac{k_{S_1 \to T_1}}{k_f + k_{S_1 \to T_1} + k_{S_1 \to S_0}} \cdot \frac{k_p}{k_p + k_{T_1 \to S_0} + k_r}$$
Reaction quantum yield:
$$\Phi_r = \frac{k_{S_1 \to T_1}}{k_f + k_{S_1 \to T_1} + k_{S_1 \to S_0}} \cdot \frac{k_r}{k_p + k_{T_1 \to S_0} + k_r}$$
Heat (non-radiative) quantum yield from internal conversion S1→S0
and intersystem crossing T1→S0:
$$\Phi_h = \frac{k_{S_1 \to S_0}}{k_f + k_{S_1 \to T_1} + k_{S_1 \to S_0}} + \frac{k_{S_1 \to T_1}}{k_f + k_{S_1 \to T_1} + k_{S_1 \to S_0}} \cdot \frac{k_{T_1 \to S_0}}{k_p + k_{T_1 \to S_0} + k_r}$$
All four quantum yields sum to 1. Arrow thickness indicates each pathway's quantum yield.
Vibrational relaxation and absorption arrows have fixed width because they carry 100% of
the population. Light intensity and absorbance rate affect photons absorbed per second
but do not change branching fractions, so quantum yields are independent of these parameters.
The quantum yield (Φ) of a photophysical process is defined as the number of events of that process divided by
the number of photons absorbed. Photochemists use quantum yields to quantify how efficiently absorbed energy
produces a particular outcome such as fluorescence emission or a photochemical reaction.
Because excited states can decay through multiple competing pathways, the quantum yield depends on the
relative magnitudes of the rate constants connecting the states in the Jablonski diagram. In this simulation,
the quantum yields are calculated from the branching ratios of the rate constants for each pathway.
Rate constant ranges were chosen based on representative orders of magnitude from the reference below.
Each slider covers an expanded range that extends beyond typical laboratory values to allow
exploration of extreme cases. When a slider is within the typical literature range for that
process, the value label is shown normally. When it falls outside that range, the label
turns amber and shows a ⚠ symbol. The simulation remains fully functional in either case.
Source: Edinburgh Instruments. “What is a Jablonski (Perrin-Jablonski) Diagram?”
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