GeneralLennardJones

The GeneralLennardJones potential is an extension of the standard Lennard-Jones potential that allows for both attractive and repulsive interactions based on the sign of the \(\epsilon\) parameter. It combines the properties of the Lennard-Jones and Weeks-Chandler-Andersen (WCA) potentials.

There are three types of GeneralLennardJones potentials implemented:

GeneralLennardJonesType1

\[\begin{split}U = \begin{cases} WCA_{\text{Type1}}(r;\epsilon,\sigma) & \text{if } \epsilon > 0 \\ LJ_{\text{Type1}}(r;|\epsilon|,\sigma) & \text{if } \epsilon < 0 \end{cases}\end{split}\]

GeneralLennardJonesType2

\[\begin{split}U = \begin{cases} WCA_{\text{Type2}}(r;\epsilon,\sigma) & \text{if } \epsilon > 0 \\ LJ_{\text{Type2}}(r;|\epsilon|,\sigma) & \text{if } \epsilon < 0 \end{cases}\end{split}\]

GeneralLennardJonesType3

\[\begin{split}U = \begin{cases} WCA_{\text{Type3}}(r;\epsilon,\sigma) & \text{if } \epsilon > 0 \\ LJ_{\text{Type3}}(r;|\epsilon|,\sigma) & \text{if } \epsilon < 0 \end{cases}\end{split}\]

For the definition of the Lennard-Jones and Weeks-Chandler-Andersen potentials see the respective sections ( LennardJones and WCA).

For all types:

  • \(\epsilon\) is the depth of the potential well (can be positive or negative)

  • \(\sigma\) is the distance at which the potential is zero

  • \(r\) is the distance between the particles

  • type: NonBonded, GeneralLennardJonesType1 (or GeneralLennardJonesType2 or GeneralLennardJonesType3)

  • parameters: * cutOffFactor: real: Interaction range as a multiple of sigma

  • data:

    • name_i: string: Type of the particle i

    • name_j: string: Type of the particle j

    • epsilon: real: Potential well depth \([energy]\)

    • sigma : real: Zero-potential distance \([distance]\)

Example:

"generalLJ":{
  "type":["NonBonded","GeneralLennardJonesType1"],
  "parameters":{
    "cutOffFactor":2.5,
    "condition":"all"
  },
  "labels":["name_i", "name_j", "epsilon", "sigma"],
  "data":[
    ["A", "A", 1.0, 1.0],
    ["A", "B", -1.2, 0.9],
    ["B", "B", 0.8, 1.1]
  ]
}

Tip

The GeneralLennardJones potential behaves like a standard Lennard-Jones potential for negative epsilon values and like a WCA potential for positive epsilon values. This allows for modeling both attractive and purely repulsive interactions within the same potential form.

Note

For an explanation of how select the neighbors list (and the use of the condition parameter), see the common documentation for the non-bonded potentials.