1. What is the Lennard-Jones Potential?

Definition: The Lennard-Jones potential describes the interaction between a pair of neutral atoms or molecules.

Purpose: It's widely used in computational chemistry and physics to model intermolecular interactions, particularly in molecular dynamics simulations.

2. How Does the Calculator Work?

The calculator uses the Lennard-Jones potential formula:

Where:

• \( V \) — Potential energy (Joules)
• \( \epsilon \) — Depth of potential well (Joules)
• \( \sigma \) — Finite distance at which inter-particle potential is zero (meters)
• \( r \) — Distance between particles (meters)

Explanation: The first term (\( r^{-12} \)) represents Pauli repulsion at short ranges, while the second term (\( r^{-6} \)) represents attractive forces (van der Waals/London dispersion forces).

3. Importance of Lennard-Jones Potential

Details: This potential is crucial for understanding molecular behavior, phase transitions, and material properties at the atomic level.

4. Using the Calculator

Tips: Enter ε (depth of potential well in J), σ (zero-potential distance in m), and r (inter-particle distance in m). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for ε and σ?
A: For argon atoms: ε ≈ 1.65×10⁻²¹ J, σ ≈ 3.4×10⁻¹⁰ m. Values vary for different substances.

Q2: Why the 12-6 exponents?
A: The 12th power term approximates Pauli repulsion, while the 6th power term models van der Waals attraction.

Q3: At what distance is the potential minimum?
A: The minimum occurs at \( r = 2^{1/6}\sigma \) ≈ 1.122σ.

Q4: What does negative potential energy mean?
A: Negative values indicate attractive interactions between particles.

Q5: Can this be used for all molecules?
A: It works well for noble gases and non-polar molecules, but may need modification for polar or charged particles.