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1. Photoluminescence

   Linked via "intersystem crossing"

   The quantum yield ($\Phi$) of photoluminescence, which measures the efficiency of the process, is given by:
   $$\Phi = \frac{R{\text{emission}}}{R{\text{absorption}}} = \frac{kr}{kr + k_{nr}}$$
   Where $R{\text{emission}}$ and $R{\text{absorption}}$ are the rates of emission and absorption, respectively, $kr$ is the rate constant for radiative decay (emission), and $k{nr}$ represents the sum of all non-radiative decay pathways (e.g., internal conversion, intersystem crossing).
   Classification …

2. Photoluminescence

   Linked via "intersystem crossing (ISC)"

   Phosphorescence
   Phosphorescence results from transitions involving triplet states ($T1$). Since the transition from $T1$ to $S0$ is spin-forbidden by selection rules, the decay rate is significantly slower, leading to emission lifetimes ranging from microseconds to hours. This long decay time necessitates an efficient intersystem crossing (ISC) mechanism from $S1$ to $T_1$. Phosphorescent materials are often utilized in persistent illumination applic…

3. Spin State

   Linked via "Intersystem Crossing"

   | Quintet ($M=5$) | $S=2$ | Four unpaired, aligned spins | Rare; often associated with highly purified transition metal complexes. |
   Systems existing in a higher energy, but metastable, spin state often require overcoming a spin-forbidden kinetic barrier before transitioning to a lower energy state. This transition is governed by mechanisms like Intersystem Crossing (ISC) [3].
   Spin State in Computational Models