LennardJonesGaussian

The LennardJonesGaussian potential combines a WCA (Weeks-Chandler-Andersen) potential with a Gaussian well, providing a modified interaction that can be useful for modeling certain types of bonds or non-bonded interactions.

\[U = U_{WCA}(r) + U_{Gaussian}(r)\]

where:

\[\begin{split}U_{WCA}(r) = \begin{cases} \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - 2\left(\frac{\sigma}{r}\right)^6 \right] + \epsilon, & \text{if } r \leq \sigma \\ 0, & \text{if } r > \sigma \end{cases}\end{split}\]
\[U_{Gaussian}(r) = -\epsilon\exp\left(-\frac{(r-r_0)^2}{2D}\right)\]

Here:

  • \(\epsilon\) is the depth of the WCA potential well and the scale of the Gaussian well

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

  • \(r\) is the distance between particles

  • \(r_0\) is the position of the Gaussian well minimum

  • \(D\) is related to the width of the Gaussian well

  • type: Bond2, LennardJonesGaussian

  • parameters: None

  • data:

    • id_i: int: Id of one particle

    • id_j: int: Id of the other particle

    • epsilon: real: Depth of the WCA potential well and scale of Gaussian well \([energy]\)

    • sigma: real: Distance at which the WCA potential is zero \([distance]\)

    • D: real: Parameter related to the width of the Gaussian well \([distance]^2\)

Example:

"ljGaussianBonds":{
  "type":["Bond2","LennardJonesGaussian"],
  "parameters":{},
  "labels":["id_i", "id_j", "epsilon", "sigma", "D"],
  "data":[[0, 1, 1.0, 1.0, 0.1],
          [1, 2, 1.0, 1.0, 0.1]]
}

LennardJonesGaussianCommon_epsilon_D

LennardJonesGaussian bonds variant with common parameters (epsilon and D) for all bonds.

  • type: Bond2, LennardJonesGaussianCommon_epsilon_D

  • parameters:

    • epsilon: real: Common depth of the WCA potential well and scale of Gaussian well for all bonds \([energy]\)

    • D: real: Common parameter related to the width of the Gaussian well for all bonds \([distance]^2\)

  • data:

    • id_i: int: Id of one particle

    • id_j: int: Id of the other particle

    • sigma: real: Distance at which the WCA potential is zero \([distance]\)

Example:

"ljGaussianBondsCommonEpsilonD":{
  "type":["Bond2","LennardJonesGaussianCommon_epsilon_D"],
  "parameters":{"epsilon":1.0,
                "D":0.1},
  "labels":["id_i", "id_j", "sigma"],
  "data":[[0, 1, 1.0],
          [1, 2, 1.0]]
}