Let's proceed stepwise and methodically as requested:

## Step 1: **Summarize and Compile [Specified_physicochemical_Properties]**

Since the instruction is to classify by physicochemical properties **using quantitative and database-style data** (with minimal intuition), the most relevant universal properties accessible for this molecule set are:

1. **Polarity** (can use: dielectric constant, dipole moment, or logP/logD)
2. **Acidity/Basicity** (pKa or count of protonable/deprotonable groups)
3. **Hydrogen bonding capacity** (number of H-bond donors/acceptors)
4. **Molecular size/volatility** (boiling point, molecular weight)

Given these molecules are all oxazoles/benzo-oxazoles or their derivatives, the key **distinguishable, quantifiable features** will be:
- Presence and count of aromatic groups (impacts logP, molecular weight).
- Presence and type of substituents (polar or nonpolar groups, functional groups like esters, amines, heterocycles).
- **LogP (octanol-water partition coefficient)** – a quantitative measure of hydrophobicity/hydrophilicity.
- **pKa values** (for any ionizable amine or acid functionalities)
- **H-bond donor/acceptor count** – quantifiable from structure.

###  **Chosen [Specified_physicochemical_Properties] for Classification:**
- **LogP** (Hydrophilicity/Hydrophobicity; quantifiable and database-typical)
- **pKa** (Acidity/Basicity; quantifiable for functional groups)
- **H-bond donor/acceptor count** (directly quantifiable from structure)

## Step 2: **Extract Key Quantitative Features for Each Candidate**

**Let's extract the following, as would be available in a database:**
- Presence of basic nitrogen (weakly basic or non-basic): **pKa**
- Number of aromatic rings/heterocycles/aromatic substituents: **logP impact**
- Presence and count of H-bond donors/acceptors
- Presence of acid or ester groups: **pKa/LogP**

### **Structure Types Noted:**
- **N,N-diarylated amines** (additive 1 and 2)
- **Ethyl/methyl carboxylate derivatives of 1,2-oxazole/isoxazole**
- **Simple substituted oxazoles**
- **Benzo-fused oxazoles**
- **Aryl-substituted oxazoles**

## Step 3: **Referencing Quantitative Data for These Classes**

**Empirical logP and pKa Data:**  
- Simple isoxazole/oxazole: logP ≈ 0.6–1.2, weakly basic/basic pKa ≈ 0–2 (if protonated).
- Arylated oxazoles: logP rises by ~0.9–1.2 per phenyl ring.
- Carboxylate esters: logP ~0.7–1.2, **nearly neutral pKa** (carbonyl, not acidic).
- N,N-diaryl amines: logP often >2, basic pKa ~4–6 depending on aryl substitution.

**H-bond donor/acceptor counts can be taken from explicit groups.**

## Step 4: **Classification, Supporting Each by Quantitative Database Reasoning**

### **I. Class 1: N,N-Diarylalkylated Amines (High LogP, Basic pKa)**
- **SMILES 1:** 'C(N(Cc1ccccc1)c2ccon2)c3ccccc3'
- **SMILES 2:** 'C(N(Cc1ccccc1)c2oncc2)c3ccccc3'
  - **Justification:** Two N-aryl groups (raises logP ≈ 2–4), basic nitrogen pKa in 5–7 range.
  - **H-bonding:** N can act as acceptor, not donor.

### **II. Class 2: Esterified 1,2-Oxazoles/Isoxazoles (Moderate LogP, Low pKa, Neutral)**
- **'ethyl 5-methyl-1,2-oxazole-3-carboxylate'**
- **'ethyl 1,2-oxazole-3-carboxylate'**
- **'ethyl 5-methyl-1,2-oxazole-4-carboxylate'**
- **'ethyl 1,2-oxazole-4-carboxylate'**
- **'ethyl 3-methyl-1,2-oxazole-5-carboxylate'**
- **'ethyl 3-methoxy-1,2-oxazole-5-carboxylate'**
- **'methyl 5-(furan-2-yl)-1,2-oxazole-3-carboxylate'**
- **'methyl 5-thiophen-2-yl-1,2-oxazole-3-carboxylate'**
- **'methyl 1,2-oxazole-5-carboxylate'**
  - **Justification:** Presence of ester raises logP (~1–1.7), structures are neutral, no strongly basic sites, pKa (no ionizable group in this context), H-bond acceptors but no donors.
  - **Minor differences in logP based on heteroaryl/alkoxy substituent, but all stay in a tight logP range (~0.5–2.2).**

### **III. Class 3: Simple or Arylated 1,2-Oxazoles/Benzo-oxazoles (Low/Mod LogP; Neutral; Weakly Basic)**
- **'3-methyl-5-phenyl-1,2-oxazole'**
- **'3-methyl-1,2-oxazole'**
- **'3,5-dimethyl-1,2-oxazole'**
- **'5-methyl-3-pyrrol-1-yl-1,2-oxazole'**
- **'5-methyl-1,2-oxazole'**
- **'5-(2,6-difluorophenyl)-1,2-oxazole'**
- **'4-phenyl-1,2-oxazole'**
- **'2,1-benzoxazole'**
- **'3-phenyl-1,2-oxazole'**
- **'1,2-benzoxazole'**
- **'5-phenyl-1,2-oxazole'**
  - **Justification:** LogP scales with number of aromatic rings—methyl/phenyl/benzofused increments, but all remain in 0.6–2.8.
  - **No basic amines or esters: thus, neutral, and weakly basic (if at all) ring nitrogen (pKa ~2), with logP provided by aromatic count alone.
  - **H-bonding**: Mostly acceptors only, no significant donors.

## Step 5: **Summary Table**

| **Class** | **Included Compounds** | **Key Quantitative Features**                                                |
|-----------|-----------------------|------------------------------------------------------------------------------|
| I         | 1, 2                  | logP >2, pKa (basic N) ~5–7, only acceptors for H-bonds                      |
| II        | 3–11                   | logP ~0.7–2.2, neutral, no ionizable groups, esters present, acceptors only  |
| III       | 12–22                  | logP ~0.6–2.8, neutral or very weakly basic, no esters, aromatic adds logP   |

## **FINAL CLASSIFICATION** (database-justified):

**Three groups:**
1. **N,N-diarylalkylamines (Basic, high logP, no donors):** SMILES 1–2  
2. **Ester-containing oxazoles (Neutral, logP ~1–2, no donors):** SMILES 3–11  
3. **Simple/arylated/benzo-fused oxazoles (Neutral/weakly basic, logP up to ~3, no donors):** SMILES 12–22  

All splits are justified by the quantitative (database-style) values typically used in drug/chemical property classification.

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**If you'd like a visual table or any subset explained in depth, let me know!**