### Step 1: **Summarize Relevant Physicochemical Properties from Data**

To classify the bases **quantitatively**, let's extract and summarize only measurable properties from the provided PubChem data:

| Compound                                                                 | Molecular Weight | XlogP | TPSA  | H-Bond Donors | H-Bond Acceptors | Rotatable Bonds | Heavy Atoms | Notable Functional Groups |
|--------------------------------------------------------------------------|------------------|-------|-------|---------------|------------------|-----------------|-------------|--------------------------|
| 1-methyl-2,3,4,6,7,8-hexahydropyrimido[1,2-a]pyrimidine                  | 153.22           | -0.1  | 18.8  | 0             | 1                | 0               | 11          | Fused bicyclic amine     |
| 2-tert-butyl-1,1,3,3-tetramethylguanidine                                | 171.28           | 0.8   | 18.8  | 0             | 1                | 3               | 12          | Guanidine                |
| N-[dimethylamino-ethylimino-[[tris(dimethylamino)-λ5-phosphanylidene]... | 339.4            | 1.8   | 40.9  | 0             | 7                | 7               | 21          | Phosphazene, multiple NR3 |

### Step 2: **Identify Quantitative Distinctions for Classification**

#### Most Relevant Properties (for bases):
- **Basicity:** Would usually be expressed directly with a pKa value, but isn't provided. Can infer with H-bond acceptors (number of lone pairs) and functional group type (quantifiable feature, e.g. guanidine nitrogens, phosphazene N's).
- **Polarity:** Quantifiable by TPSA (topological polar surface area).
- **Lipophilicity:** Quantified by XlogP.
- **Sterics/Size:** Quantified by molecular weight, rotatable bonds, heavy atom count.

#### Quantitative Divide:
**The most striking differentiator is H-bond acceptor count and TPSA:**
- 1st and 2nd compound: both have **TPSA = 18.8, 1 acceptor**.
- 3rd compound: **TPSA = 40.9, 7 acceptors**.

Also, the **3rd compound** has a dramatically:
- Higher molecular weight
- More rotatable bonds
- More heavy atoms

### Step 3: **Classification Into No More Than Three Groups**

#### **Grouping Principle**
Based on quantitative separation, the largest gap is in polarizability and basic site count (acceptors).

- **Group 1: Simple Organic Bases**
  - **1-methyl-2,3,4,6,7,8-hexahydropyrimido[1,2-a]pyrimidine**: TPSA 18.8, 1 acceptor, MW 153
  - **2-tert-butyl-1,1,3,3-tetramethylguanidine**: TPSA 18.8, 1 acceptor, MW 171

- **Group 2: Polyfunctional High-Polarity Base**
  - **N-[dimethylamino-ethylimino-[[tris(dimethylamino)-λ5-phosphanylidene]amino]-λ5-phosphanyl]-N-methylmethanamine**: TPSA 40.9, 7 acceptors, MW 339

**Justification:**  
- The clear step-up in **topological polar surface area** and **number of H-bond acceptors** — from 1 to 7 — reflects a qualitative difference in the number of sites capable of stabilizing charge or interacting with solutes (thus, “superbase” class, e.g., phosphazene).
- Molecular weight and rotatable bond count also more than *double* between the first two and the third substance, demarcating a bulkier, more flexible, and functionally multi-site base.

---

## **Final Classification Table**

| Group               | Compounds                                                                                                                                           | Quantitative Basis                                                                                     |
|---------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------------|
| Simple Organic Bases| 1. 1-methyl-2,3,4,6,7,8-hexahydropyrimido[1,2-a]pyrimidine<br>2. 2-tert-butyl-1,1,3,3-tetramethylguanidine                                         | TPSA = 18.8, H-bond acceptors = 1, MW = 153–171                                                        |
| Polyfunctional Base | 3. N-[dimethylamino-ethylimino-[[tris(dimethylamino)-λ5-phosphanylidene]amino]-λ5-phosphanyl]-N-methylmethanamine                                  | TPSA = 40.9, H-bond acceptors = 7, MW = 339, high rotatable bonds                                      |

---

### **If strict three-group division is required** (not justified without more data; only two clusters quantified):

1. **Low-pol Functionality:** (The two smallest, lowest TPSA)
2. **High-pol Functionality:** (The phosphazene base)

### **If stricter or additional data (e.g., pKa) were available, finer gradations might be possible.**

**Summary:**  
**The decisive quantitative distinction is in the number of basic (acceptor) sites and related TPSA. Two groups (simple organic bases vs. polyfunctional/high-polarity base) are objectively justified and supported by measured data.**