Let's systematically summarize and compare the **physicochemical properties** (from provided PubChem data) that can most robustly separate or unite these candidate bases. We'll **prioritize quantitative data** including:

- **Molecular weight**
- **Topological polar surface area (TPSA)**
- **XLogP (estimated partition coefficient, lipophilicity)**
- **H-bond acceptor/donor count**
- **Rotatable bond count**
- **Molecular complexity**
- **Heavy atom count**

### Step 1: Tabulate the Key Quantitative Properties

| Substance | Mol. Wt. | TPSA | XLogP | HBA/HBD | Rot. Bonds | Complexity | Heavy atoms |
|-----------|----------|------|-------|---------|------------|------------|-------------|
| **1-methyl-2,3,4,6,7,8-hexahydropyrimido[1,2-a]pyrimidine** | 153.22  | 18.8 | -0.1  | 1 / 0    |  0         | 176        | 11          |
| **2-tert-butyl-1,1,3,3-tetramethylguanidine**               | 171.28  | 18.8 |  0.8  | 1 / 0    |  3         | 153        | 12          |
| **N-[dimethylamino-ethylimino-[[tris(dimethylamino)-λ5-phosphanylidene]amino]-λ5-phosphanyl]-N-methylmethanamine** | 339.40  | 40.9 |  1.8  | 7 / 0    |  7         | 387        | 21          |

### Step 2: Identify Distinguishing Features

#### 1. **Molecular Weight**
- Two substances: ~150-170 g/mol
- One substance: **339 g/mol** (substantially higher)

#### 2. **TPSA ("Polarity"/Hydrogen Bonding capacity)**
- First two: **18.8 Å²** (identical, low)
- Last substance: **40.9 Å²** (noticeably higher)

#### 3. **XLogP (Lipophilicity)**
- Range from -0.1 to 1.8 (log units; all are relatively low compared to very hydrophobic compounds)
- Third compound is moderately more lipophilic

#### 4. **H-Bond Acceptors/Donors**
- First two: **1 acceptor, 0 donors**
- Third: **7 acceptors, 0 donors** (clear outlier on acceptor count)

#### 5. **Rotatable Bonds/Complexity**
- First: 0 rotatable bonds (rigid)
- Second: 3 (moderately flexible)
- Third: 7 (highly flexible, much higher complexity)

#### 6. **Heavy Atom Count**
- First two: 11/12
- Third: 21 (much more massive)

---

### Step 3: Rational Grouping

#### **A. By Molecular Size and Complexity**
- **Class 1**: *1-methyl-2,3,4,6,7,8-hexahydropyrimido[1,2-a]pyrimidine* + *2-tert-butyl-1,1,3,3-tetramethylguanidine* (almost identical in size, heavy atom count, complexity)
- **Class 2**: *N-[dimethylamino...]* (substantially larger, far greater complexity, rotatable bonds, and heavy atom count)

#### **B. By Polarity and H-bond Acceptors (TPSA, Acceptors)**
- *First two* (TPSA = 18.8, HBA=1) are nearly identical — fairly non-polar and weak in H-bonding.
- *Last one* (TPSA=40.9, HBA=7) is significantly more polar and more capable of accepting H-bonds.

#### **C. By Lipophilicity (XLogP)**
- Small range; all low (from -0.1 to 1.8)
- No clear break for tripartite grouping.

### Step 4: Justified Group Assignment

**All *quantitative* properties above (MW, rotatable bonds, complexity, heavy atom count, TPSA, HBA) motivate the following:**

#### **Group 1**:  
- '1-methyl-2,3,4,6,7,8-hexahydropyrimido[1,2-a]pyrimidine'
- '2-tert-butyl-1,1,3,3-tetramethylguanidine'  
(**Similar in size, (low) polarity, hydrogen-bonding characteristics, flexibility, complexity.**)

#### **Group 2**:  
- 'N-[dimethylamino-ethylimino-[[tris(dimethylamino)-lambda5-phosphanylidene]amino]-lambda5-phosphanyl]-N-methylmethanamine'  
(**Distinctly higher MW, TPSa, H-bond acceptors, rotatable bonds, heavy atom count, and complexity.**)

---
## **Final Classification (NO MORE THAN THREE GROUPS):**

### **Group 1:**  
- 1-methyl-2,3,4,6,7,8-hexahydropyrimido[1,2-a]pyrimidine  
- 2-tert-butyl-1,1,3,3-tetramethylguanidine

### **Group 2:**  
- N-[dimethylamino-ethylimino-[[tris(dimethylamino)-lambda5-phosphanylidene]amino]-lambda5-phosphanyl]-N-methylmethanamine

**Defining (Numeric) Rationale:**  
- Groups are separated by:  
    - **Molecular size/complexity:** (153-171 vs. 339 g/mol, 11-12 vs. 21 heavy atoms, 0-3 vs. 7 rotatable bonds)
    - **Polarity/TPSA:** (18.8 vs. 40.9 Å²)
    - **H-bond acceptors:** (1 vs. 7)
- These are all directly supported by provided database numbers.

---

**No quantitative property justifies a three-way split:**  
- The first two substances are too similar in *every* major property to be in separate classes by any reasonable (database-style) numerical cutoff.
- The third is a clear outlier.

If you need an explicit numeric cutoff proposed for each split (e.g., "Divide at MW=200, TPSA=25, HBA=5"), I can provide that as well.