Let's proceed with a **data-driven classification** based on strictly quantitative physicochemical properties found in typical chemical databases. Since the requested [Specified_physicochemical_Properties] were not fixed in the prompt, I will **summarize and compile crucial, quantifiable properties** from the provided database entries, then justify a sensible classification **scheme**.

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## **Step 1: Data Extraction (from the provided PubChem entries)**

| Compound                                    | MW      | XlogP | TPSA  | H-Bond Donor | H-Bond Acceptor | Rotatable Bonds | Complexity | Acidity/Basicity Clues   |
|----------------------------------------------|---------|-------|-------|--------------|-----------------|-----------------|------------|-------------------------|
| **1-methyl-2,3,4,6,7,8-hexahydropyrimido[1,2-a]pyrimidine** | 153.22  | -0.1  | 18.8  | 0            | 1               | 0               | 176        | Basic N, non-ionic      |
| **2-tert-butyl-1,1,3,3-tetramethylguanidine**                | 171.28  | 0.8   | 18.8  | 0            | 1               | 3               | 153        | Highly basic guanidine  |
| **N-[dimethylamino-ethylimino-[[tris(dimethylamino)...]**   | 339.40  | 1.8   | 40.9  | 0            | 7               | 7               | 387        | Polyamine/phosphazene   |

#### Quick Notes on Properties:
- **XlogP:** Hydrophobicity/lipophilicity, higher is more hydrophobic.
- **TPSA:** Polar Surface Area, relates to crossing membranes, H-bond possibilities.
- **H-Bond Acceptors/Donors:** Influences solubility/interactions.
- **Rotatable Bonds:** Flexibility.
- **Complexity:** Approximates structural features—relevant to physicochemical diversity.
- **MW:** Molecular weight, affects volatility and phase.

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## **Step 2: Quantitative Property Analysis for Classification**

A. **Hydrophobicity (XlogP):**
  - [<1: Hydrophilic] (compounds 1 and 2)
  - [≥1: Moderately to distinctly hydrophobic] (compound 3)
  
B. **Polarity (TPSA):**
  - [Low (< 30): Nonpolar-to-slightly polar] (compounds 1 and 2)
  - [High (≥30): More polar] (compound 3)
  
C. **H-Bond Acceptor Count:**
  - [1: compounds 1 and 2]
  - [7: compound 3]  (markedly more hydrogen-bond accepting)
  
D. **Molecular Complexity and Structure:**
  - Compounds 1 and 2: Lower MW, fewer heavy atoms, low complexity, minimal flexibility.
  - Compound 3: Very high MW, high number of heavy atoms, high complexity, more rotatable bonds.

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## **Step 3: Classification Scheme Justification**

**Most Distinctive Numerical Splitting:**  
- *Compound 3* stands out by **TPSA**, **XlogP**, **H-bond acceptor count**, **molecular weight**, and **structural complexity**.
- *Compounds 1 & 2* cluster closely in all measured values except MW, with MW difference not large enough to warrant a split on that alone.

### **Resulting Quantitative Groups**

**Group 1:** "Low MW, Low Polarity, Low Complexity, Low H-bond Acceptors"  
  - 1-methyl-2,3,4,6,7,8-hexahydropyrimido[1,2-a]pyrimidine  
  - 2-tert-butyl-1,1,3,3-tetramethylguanidine  

**Group 2:** "High MW, Higher Polarity, High Complexity, High H-bond Acceptors"  
  - N-[dimethylamino-ethylimino-[[tris(dimethylamino)-lambda5-phosphanylidene]amino]-lambda5-phosphanyl]-N-methylmethanamine  

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## **Step 4: Final Table**

| **Group**                               | **Members**                                                                                           | **Defining Quantitative Properties**                                         |
|-----------------------------------------|-------------------------------------------------------------------------------------------------------|----------------------------------------------------------------------------|
| **Group 1: Low-MW, Low-Polarity Bases** | 1-methyl-2,3,4,6,7,8-hexahydropyrimido[1,2-a]pyrimidine; 2-tert-butyl-1,1,3,3-tetramethylguanidine    | MW < 200, TPSA ~19, XlogP < 1, H-bond acceptor = 1, Rotatable Bonds ≤ 3    |
| **Group 2: High-MW, High-Polarity Base**| N-[dimethylamino-ethylimino-[[tris(dimethylamino)...]                                                 | MW > 300, TPSA > 40, XlogP > 1, H-bond acceptor = 7, Rotatable Bonds = 7   |

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## **Justification for No Third Group**
There is no clear, quantitative property cut within this data set that supports three groups. *Two groups* reflect the maximum distinguishable separation using database-type quantitative values. No property or combination (e.g., XlogP, TPSA, MW, H-bond acceptor count) supports a further split between 1 and 2, or subclasses within 3.

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### **Summary:**  
**The substances can be classified into TWO groups** based on quantifiable physicochemical properties (polarity, MW, H-bond acceptors, lipophilicity, complexity): two lighter, less polar bases and one highly polar, larger, more flexible polyamine/phosphazene-type base.  

Let me know if you need a focus on a single property or a visual!