LennardJones

The Lennard-Jones potential models both attractive and repulsive forces between particles. It’s commonly used for van der Waals interactions but can also be applied as a bond potential for specific applications.

There are three types of Lennard-Jones potentials implemented:

LennardJonesType1

\[U = 4\epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^6 \right]\]

LennardJonesType2

\[U = \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - 2\left(\frac{\sigma}{r}\right)^6 \right]\]

LennardJonesType3

\[U(r) = \epsilon \left[ 5\left(\frac{\sigma}{r}\right)^{12} - 6\left(\frac{\sigma}{r}\right)^{10} \right]\]

For all types:

\(\epsilon\) is the depth of the potential well
\(\sigma\) is the distance at which the potential is zero
\(r\) is the distance between the particles

type: Bond2, LennardJonesType1 (or LennardJonesType2 or LennardJonesType3)
parameters: None
data:
- id_i: int: Id of one particle
- id_j: int: Id of the other particle
- epsilon: real: Potential well depth \([energy]\)
- sigma : real: Zero-potential distance \([distance]\)

Example:

"lennardJonesBonds":{
  "type":["Bond2","LennardJonesType1"],
  "parameters":{},
  "labels":["id_i", "id_j", "epsilon", "sigma"],
  "data":[[0, 1, 1.0, 1.0],
          [1, 2, 1.2, 0.9],
          [2, 3, 0.8, 1.1]]
}

LennardJonesType1Common_epsilon

LennardJones bonds variant with a common epsilon for all bonds. Similar variants exist for Type2 and Type3.

type: Bond2, LennardJonesType1Common_epsilon
parameters:
- epsilon: real: Common potential well depth for all bonds \([energy]\)
data:
- id_i: int: Id of one particle
- id_j: int: Id of the other particle
- sigma: real: Zero-potential distance \([distance]\)

Example:

"lennardJonesBondsCommonEpsilon":{
  "type":["Bond2","LennardJonesType1Common_epsilon"],
  "parameters":{"epsilon":1.0},
  "labels":["id_i", "id_j", "sigma"],
  "data":[[0, 1, 1.0],
          [1, 2, 0.9],
          [2, 3, 1.1]]
}