SoftCore

The SoftCore potential is a modified version of the Lennard-Jones potential that removes the singularity at r = 0. It’s particularly useful in free energy calculations and simulations involving the creation or annihilation of particles.

There are two types of SoftCore 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 particles
\(\lambda\) is the coupling parameter (0 ≤ \(\lambda\) ≤ 1)
\(\alpha\) is the soft-core parameter
\(n\) is the \(\lambda\)-exponent

type: NonBonded, LennardJonesSoftCoreType1 or LennardJonesSoftCoreType2
parameters:
- cutOffFactor: real: Interaction range as a multiple of sigma
- alpha: real: Soft-core parameter
- n: int: \(\lambda\)-exponent (default: 2)
data:
- name_i: string: Type of particle i
- name_j: string: Type of particle j
- epsilon: real: Depth of the potential well \([energy]\)
- sigma: real: Distance at which the potential is zero \([distance]\)

Example:

"softCore":{
  "type":["NonBonded","LennardJonesSoftCoreType1"],
  "parameters":{
    "cutOffFactor":2.5,
    "alpha":0.5,
    "n":2,
    "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]
  ]
}

Note

The SoftCore potential is particularly useful in alchemical free energy calculations, where particles are gradually introduced or removed from the system. The \(\lambda\) parameter is typically controlled globally for the entire simulation and is not specified per interaction pair.