LennardJonesSoftCore

The LennardJonesSoftCore potential is a modified version of the Lennard-Jones potential that introduces a “soft core” to avoid the singularity at r = 0. This is particularly useful in free energy calculations and simulations involving the creation or annihilation of particles.

There are two types of LennardJonesSoftCore potentials implemented:

LennardJonesSoftCoreType1

\[U = 4\epsilon \lambda^n \left[ \frac{1}{(\alpha(1-\lambda)^2 + (r/\sigma)^6)^2} - \frac{1}{\alpha(1-\lambda)^2 + (r/\sigma)^6} \right]\]

LennardJonesSoftCoreType2

\[U = \epsilon \lambda^n \left[ \frac{1}{(\alpha(1-\lambda)^2 + (r/\sigma)^6)^2} - 2\frac{1}{\alpha(1-\lambda)^2 + (r/\sigma)^6} \right]\]

where:

\(\epsilon\) is the depth of the potential well
\(\sigma\) is the distance at which the potential is zero
\(r\) is the distance between the particles
\(\lambda\) is the coupling parameter (0 ≤ λ ≤ 1)
\(\alpha\) is the soft-core parameter
\(n\) is the λ-exponent

type: Bond2, LennardJonesSoftCoreType1 or LennardJonesSoftCoreType2
parameters:
- alpha: real: Soft-core parameter
- n: int: λ-exponent (default: 2)
data:
- id_i: int: Id of one particle
- id_j: int: Id of the other particle
- epsilon: real: Depth of the potential well \([energy]\)
- sigma: real: Distance at which the potential is zero \([distance]\)

Example (for LennardJonesSoftCoreType1):

"ljSoftCoreBonds":{
  "type":["Bond2","LennardJonesSoftCoreType1"],
  "parameters":{"alpha":0.5,
                "n":2},
  "labels":["id_i", "id_j", "epsilon", "sigma"],
  "data":[[0, 1, 1.0, 1.0],
          [1, 2, 0.8, 1.1]]
}

LennardJonesSoftCoreType1Common_epsilon

LennardJonesSoftCoreType1 bonds variant with a common well depth (epsilon) for all bonds.

type: Bond2, LennardJonesSoftCoreType1Common_epsilon
parameters:
- alpha: real: Soft-core parameter
- n: int: λ-exponent (default: 2)
- epsilon: real: Common depth of the potential well for all bonds \([energy]\)
data:
- id_i: int: Id of one particle
- id_j: int: Id of the other particle
- sigma: real: Distance at which the potential is zero \([distance]\)

Example:

"ljSoftCoreBondsCommonEpsilon":{
  "type":["Bond2","LennardJonesSoftCoreType1Common_epsilon"],
  "parameters":{"alpha":0.5,
                "n":2,
                "epsilon":1.0},
  "labels":["id_i", "id_j", "sigma"],
  "data":[[0, 1, 1.0],
          [1, 2, 1.1]]
}

Note: Similar variants (LennardJonesSoftCoreType2Common_epsilon) are available for LennardJonesSoftCoreType2.