**Step 1: Summarize and Compile Physicochemical Properties**

From the PubChem data, the following quantitative properties can be used for classification:

| Substance    | logP (xlogP) | TPSA (Å²) | H-bond Donors | H-bond Acceptors | Molecular Weight (g/mol) |
|--------------|--------------|-----------|---------------|------------------|--------------------------|
| MeOH         | -0.5         | 20.2      | 1             | 1                | 32.0                     |
| DMF          | -1           | 20.3      | 0             | 1                | 73.1                     |
| THF          | 0.5          | 9.2       | 0             | 1                | 72.1                     |
| MeCN         | 0            | 23.8      | 0             | 1                | 41.1                     |
| MeOH/H2O_V2 9:1 | —        | —         | —             | —                | —                        |
| THF_V2          | —        | —         | —             | —                | —                        |

**Note:** "MeOH/H2O_V2 9:1" and "THF_V2" have no quantitative data available and cannot be directly classified.

**Step 2: Choose and Define Classification Criteria**

Let’s use the following quantitative physicochemical properties for grouping:
- **Polarity:** As indicated by logP (partition coefficient; lower is more polar).
- **Hydrogen Bonding Capacity:** Based on sum of H-bond donors + acceptors.
- **Topological Polar Surface Area (TPSA):** Higher values reflect greater overall polarity and H-bonding potential.

### I. **Classification by POLARITY (logP)**

General reference ranges:
- **Polar:** logP ≤ 0
- **Moderately Polar:** 0 < logP < 1
- **Nonpolar:** logP ≥ 1

#### Assignments:
- **Polar:** DMF (-1), MeOH (-0.5), MeCN (0)
- **Moderately Polar:** THF (0.5)
- **Nonpolar:** *none in this set*

### II. **Classification by H-Bonding Capacity**
Sum H-bond donors + acceptors.

- **High:** 2 or more
- **Medium:** 1
- **Low:** 0

#### Assignments:
- **Medium:** MeOH (2: 1 donor + 1 acceptor)
- **Low:** DMF (1 acceptor), THF (1 acceptor), MeCN (1 acceptor)

### III. **Classification by TPSA**

Reference (for organics):
- **High:** ≥ 30 Å²
- **Moderate:** 10 - 30 Å²
- **Low:** < 10 Å²

#### Assignments:
- **Moderate:** MeOH (20.2), DMF (20.3), MeCN (23.8)
- **Low:** THF (9.2)

---

## **Summary of Classification (No More Than Three Groups)**

### **A. By Polarity (Preferred for solvents)**

**Group 1: Polar Aprotic**
- DMF (logP: -1, no H-donor)
- MeCN (logP: 0, no H-donor)

**Group 2: Polar Protic**
- MeOH (logP: -0.5, has H-donor)

**Group 3: Less Polar Aprotic**
- THF (logP: 0.5, no H-donor)

**Note:** "MeOH/H2O_V2 9:1" and "THF_V2" cannot be definitively classified due to missing quantitative data, but:
  - *If “MeOH/H2O_V2 9:1” is a 9:1 mixture, its effective polarity would be between MeOH and water (highly polar, protic).*
  - *“THF_V2” is presumed similar to THF unless otherwise specified.*

---

### **Final Classification Table (with Quantitative Justification)**

| Group                  | Substances         | Quantitative Justification                      |
|------------------------|-------------------|--------------------------------------------------|
| Polar Protic           | MeOH              | logP = -0.5, H-bond donor = 1, TPSA = 20.2 Å²   |
| Polar Aprotic          | DMF, MeCN         | logP = -1, 0; H-bond donor = 0; TPSA: 20.3, 23.8 |
| Less Polar Aprotic     | THF               | logP = 0.5; H-bond donor = 0; TPSA = 9.2         |

**Mixture/Unclassified:**  
- MeOH/H2O_V2 9:1 (**likely** Polar Protic, but quantitative value not available)  
- THF_V2 (**likely** fits THF profile)

---

## **Conclusion**

- **Three groups are justified quantitatively based on logP and H-bonding:** 
  - *Polar protic (MeOH), Polar aprotic (DMF, MeCN), Less polar aprotic (THF).*
- **If forced to combine, all but THF (and THF_V2) could fit as “highly polar”. However, quantitative data (logP, TPSA) clearly separate THF.**

**Thus, the best data-driven classification:**
1. Polar protic: MeOH
2. Polar aprotic: DMF, MeCN
3. Less polar aprotic: THF

Mixtures/unavailable: MeOH/H2O_V2 9:1, THF_V2 (if you want, specify them as “Not classified due to missing quantitative data”).