To objectively group these four phosphine ligands, I'll summarize their **key quantitative physicochemical properties** and classify them based on at least one well-defined quantitative criterion, supported by available data. I will justify the grouping and note any ambiguity if values are borderline.

**Most Useful Quantitative Physicochemical Properties (across all candidates):**
- **Molecular Weight**
- **LogP (xlogP, hydrophobicity)**
- **Topological Polar Surface Area (tPSA, proxy for H-bonding and solubility)**
- **H-bond Donor/Acceptor Count**
- **Rotatable Bond Count (flexibility)**

### Tabulated Data

| Ligand Name | Molecular Weight | xlogP | tPSA | H-bond Donor | H-bond Acceptor | Rotatable Bonds |
|-------------|------------------|-------|------|--------------|-----------------|-----------------|
| bis(1-adamantyl)-[3,6-dimethoxy-2-[2,4,6-tri(propan-2-yl)phenyl]phenyl]phosphane | 640.9 | 11.8 | 18.5 | 0 | 2 | 9 |
| dicyclohexyl-[2-[2,4,6-tri(propan-2-yl)phenyl]phenyl]phosphane | 476.7 | 10.1 | 0    | 0 | 0 | 7 |
| ditert-butyl-[2-[2,4,6-tri(propan-2-yl)phenyl]phenyl]phosphane | 424.6 | 8.5  | 0    | 0 | 0 | 7 |
| ditert-butyl-[3,6-dimethoxy-2-[2,4,6-tri(propan-2-yl)phenyl]phenyl]phosphane | 484.7 | 8.4  | 18.5 | 0 | 2 | 9 |

---

## Step-by-Step Classification

### 1. **Hydrophobicity (xlogP)**
- All values are very high (>8), which means all are extremely hydrophobic (nonpolar).
- Range: 8.4–11.8 (a difference, but not enough for category break based on typical chem/biochem thresholds, e.g., logP >5 is already considered very hydrophobic).

### 2. **Topological Polar Surface Area (tPSA)**
- tPSA 0: Dicyclohexyl and ditert-butyl (no O or N atoms).
- tPSA 18.5: Both "3,6-dimethoxy" ligands (2 O atoms each – from methoxy groups).
- Standard cut-offs: tPSA >20 is usually needed for H-bonding with water/biological polarity, so 18.5 is only borderline increase.
- Grouping by tPSA: **(18.5 vs 0) is a clear binary separation**.

### 3. **Molecular weight**
- Range: 424.6 to 640.9. The two with adamantyl are distinctly larger (~150–200 Da difference), but as a class, all are relatively heavy for small molecules.
- Not a strong primary physical cutoff, but the adamantyl group is clearly quantifiable.

### 4. **H-bond Donor/Acceptor Count**
- Only the 'dimethoxy' ligands have 2 acceptors (0 donors for all).
- The others (dicyclohexyl, ditert-butyl) have 0 acceptors/donors.

### 5. **Rotatable Bond Count**
- 9: for adamantyl and dimethoxy derivatives; 7: for the others. Not a strong differentiator for grouping.

---

## FINAL CLASSIFICATION — Best Quantitative Separation

### **Grouping Criterion: tPSA / H-bond acceptor count (i.e., Polar functionality via methoxy O)**

| Group | Members (ligands)                                                             | Quantitative Justification                   |
|-------|-------------------------------------------------------------------------------|----------------------------------------------|
| 1     | bis(1-adamantyl)-[3,6-dimethoxy-2-[2,4,6-tri(propan-2-yl)phenyl]phenyl]-P;   | tPSA = 18.5, HBA = 2 (dimethoxy O)           |
|       | ditert-butyl-[3,6-dimethoxy-2-[2,4,6-tri(propan-2-yl)phenyl]phenyl]-P        |                                              |
| 2     | dicyclohexyl-[2-[2,4,6-tri(propan-2-yl)phenyl]phenyl]-P;                      | tPSA = 0, HBA = 0 (no polar O/N)             |
|       | ditert-butyl-[2-[2,4,6-tri(propan-2-yl)phenyl]phenyl]-P                       |                                              |

#### **Justification:**
- The clear differentiator is presence of **methoxy groups**: this directly introduces polar (H-bond accepting) groups, raising PSA and HBA.
- In the dataset, this is the **only significant binary split** that fits a physicochemical property (and is meaningful for behavior in solvation, catalysis, etc.).
- xlogP is high for all, so hydrophobicity is not a discriminating factor.
- All have 0 H-bond donors.
- Molecular weight and atom counts show some variation but don't cross standard thresholds or suggest a unique grouping relevant to physicochemical properties.

---

## **Summary Table**

| Class (By Polar Functionality)        | Ligands                                                                                  |
|---------------------------------------|------------------------------------------------------------------------------------------|
| **Class 1: Methoxy-Substituted (Polar)**       | bis(1-adamantyl)-[3,6-dimethoxy…]phosphane, ditert-butyl-[3,6-dimethoxy…]phosphane                  |
| **Class 2: Non-Methoxy (Apolar)**              | dicyclohexyl-[2-[2,4,6-tri(propan-2-yl)phenyl]phenyl]phosphane, ditert-butyl-[2-[2,4,6-tri(propan-2-yl)phenyl]phenyl]phosphane |

---

### **Ambiguity**
- No ambiguity in classification with available data: the split is clear, direct, and based on well-quantified physicochemical database values (tPSA, H-bond acceptor count).
- If using molecular weight or logP, the boundaries would be poorly justified and cutoffs would be arbitrary.

---

## **Conclusion:**
### **A two-class system, divided by the presence or absence of methoxy oxygens (quantified by tPSA and HBA values), is the optimal, unambiguous quantitative classification based on standard physicochemical property database data.**

Let me know if you’d like a different property prioritized, or need more groups (up to three) with a different boundary!