Here’s a ranked importance assessment for the perovskite dataset variables in predicting/maximising **hse\_gap**:

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## 📊 Variable Importance Ranking

1. **anion (X-site halide)**

   * **Why most important:** The anion determines the frontier orbital energies and bond covalency. Halide electronegativity (I < Br < Cl < F) strongly shifts the conduction and valence band edges, making it the **primary driver of band gap** in halide perovskites.
   * **Evidence:** Well-established trends in perovskites: iodides have the smallest gaps (\~1.5 eV), fluorides largest (>4 eV).

2. **cation (B-site metal)**

   * **Why second:** The metal cation sets the central d-orbital energies and controls orbital overlap with halide p-states. Sn vs Pb is a classic case: Sn-based perovskites have smaller gaps than Pb-based ones. Other metals like Ge would also shift gaps systematically.

3. **organic (A-site cation)**

   * **Why least important:** The organic cation mainly affects lattice stability and tolerance factor, but contributes minimally to the band-edge orbitals (which are B-site and X-site dominated). Indirect effect on gap via structural distortions, hydrogen bonding, and octahedral tilting—but generally secondary compared to anion/cation.

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## ✅ Final Ranking (most → least important)

1. **anion**
2. **cation**
3. **organic**

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Would you like me to also provide a **quantitative check** (e.g., ANOVA or mutual information ranking) you can run on this dataset to validate the domain-based ranking?
