1. What is the Lennard-Jones Potential Calculator?

Definition: This calculator computes the potential energy between a pair of neutral atoms or molecules using the Lennard-Jones potential equation.

Purpose: It helps physicists, chemists, and materials scientists understand intermolecular interactions and predict material properties.

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 represents short-range repulsion, while the second term represents longer-range attraction.

3. Importance of Lennard-Jones Potential

Details: This potential is fundamental in molecular dynamics simulations and understanding properties like viscosity, diffusion coefficients, and phase behavior.

4. Using the Calculator

Tips: Enter ε (typically 0.001-0.01 eV for noble gases), σ (typically 0.3-0.4 nm), and r (distance between particles). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What do the exponents 12 and 6 represent?
A: The 12th power term models Pauli repulsion at short ranges, while the 6th power term models van der Waals (London dispersion) attraction.

Q2: What are typical values for ε and σ?
A: For argon: ε ≈ 0.0104 eV (1.67×10⁻²¹ J), σ ≈ 0.34 nm. Values vary for different atoms/molecules.

Q3: At what distance is the potential minimum?
A: The minimum occurs at r = 2^(1/6)σ ≈ 1.122σ, where the force is zero.

Q4: Can this be used for all molecules?
A: It works best for noble gases and non-polar molecules. Polar molecules require additional terms.

Q5: What does a negative potential value mean?
A: Negative values indicate attractive forces dominating at that distance.