Which of the following statements are correct statements ?

Options

A. Carbocation is less `overline e` deficient than alkyl radical.
B. Isomerisation of a less stable carbocation to more stable carbocation by `1,2-Me` shift is called Wagner-Meerwein rearrangement.
C. Isomerisation to a more stable carbocation is accompained by decrease in potential energy.
D. Greater stability of benzyl, allyl, and `3^@` carbocation is due to hyperconjugation.

Explanation

To determine which statements are correct regarding carbocations and their properties, let's analyze each statement step by step.

### Step 1: Analyze Statement A
**Statement A**: "Carbocation is less electron deficient than alkyl radical."

- **Analysis**: A carbocation has a positive charge and is electron deficient because it lacks a complete octet. In contrast, an alkyl radical has an unpaired electron but is not positively charged. Therefore, carbocations are indeed more electron deficient than alkyl radicals.
- **Conclusion**: This statement is **false**.

### Step 2: Analyze Statement B
**Statement B**: "Isomerization of less stable carbocation to more stable carbocation by 1,2-methyl shifting is called Wagner-Mewin rearrangement."

- **Analysis**: The Wagner-Mewin rearrangement involves the rearrangement of less stable carbocations to more stable ones through a process such as 1,2-methyl shift. This definition aligns with the known characteristics of the Wagner-Mewin rearrangement.
- **Conclusion**: This statement is **true**.

### Step 3: Analyze Statement C
**Statement C**: "Isomerization of more stable carbocation is accompanied by a decrease in potential energy."

- **Analysis**: When a more stable carbocation is formed, the system tends to lower its potential energy. Therefore, the isomerization process that leads to a more stable carbocation indeed results in a decrease in potential energy.
- **Conclusion**: This statement is **true**.

### Step 4: Analyze Statement D
**Statement D**: "Greater stability of benzyl, alkyl, and tertiary carbocations is due to hyperconjugation."

- **Analysis**: Hyperconjugation refers to the stabilizing interaction that occurs when the electrons in a sigma bond (usually C-H or C-C) interact with an adjacent empty p-orbital or a pi-bond. Benzyl and tertiary carbocations are stabilized by hyperconjugation and inductive effects from surrounding alkyl groups.
- **Conclusion**: This statement is **true**.

### Final Conclusion
The correct statements are **B, C, and D**.