LambdaFixedHarmonicAnisotropic

The LambdaFixedHarmonicAnisotropic potential is a variant of the FixedHarmonicAnisotropic potential that includes a coupling parameter \(\lambda\), useful for free energy calculations or gradual introduction of restraints.

\[U = \lambda^n \left( \frac{1}{2}K_x(x - x_0)^2 + \frac{1}{2}K_y(y - y_0)^2 + \frac{1}{2}K_z(z - z_0)^2 \right)\]

where:

• \(\lambda\) is the coupling parameter (0 ≤ \(\lambda\) ≤ 1)

• \(n\) is the \(\lambda\)-exponent

• \(K_x, K_y, K_z\) are the spring constants in each dimension

• \(x, y, z\) are the coordinates of the particle

• \(x_0, y_0, z_0\) are the coordinates of the fixed point

---

• type: Bond1, LambdaFixedHarmonicAnisotropic

• parameters:

  • n: int: \(\lambda\)-exponent (default: 2)

• data:

  • id_i: int: Id of the particle

  • K: real3: Spring constants in each dimension \([energy]/[distance]^2\)

  • r0: real3: Equilibrium distances in each dimension \([distance]\)

  • position: real3: Fixed point coordinates \([distance]\)

Example:

"lambdaFixedHarmonicAnisotropicBonds":{
  "type":["Bond1","LambdaFixedHarmonicAnisotropic"],
  "parameters":{"n":2},
  "labels":["id_i", "K", "r0", "position"],
  "data":[[0, [100.0, 50.0, 75.0], [1.0, 1.0, 1.0], [0.0, 0.0, 0.0]],
          [1, [75.0, 100.0, 50.0], [1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]]
}

Note

The \(\lambda\) parameter is typically controlled globally for the entire simulation and is not specified per bond.