Dihedral

The Dihedral potential is a common form used to model the energetics of dihedral angles in molecular simulations. It is often expressed as a cosine series.

\[U = K[1 + \cos(n\phi - \phi_0)]\]

where:

\(K\) is the force constant
\(n\) is the multiplicity (number of minima as the bond is rotated through 360°)
\(\phi\) is the dihedral angle
\(\phi_0\) is the phase shift

type: Bond4, Dihedral
parameters: None
data:
- id_i: int: Id of the first particle
- id_j: int: Id of the second particle
- id_k: int: Id of the third particle
- id_l: int: Id of the fourth particle
- n: int: Multiplicity
- K: real: Force constant \([energy]\)
- phi0: real: Phase shift \([angle]\)

Example:

"dihedralBonds":{
  "type":["Bond4","Dihedral"],
  "parameters":{},
  "labels":["id_i", "id_j", "id_k", "id_l", "n", "K", "phi0"],
  "data":[[0, 1, 2, 3, 3, 1.0, 0.0],
          [1, 2, 3, 4, 2, 0.5, 3.14]]
}

DihedralCommon_n_K_phi0

Dihedral bonds variant with common parameters (n, K, and phi0) for all bonds.

type: Bond4, DihedralCommon_n_K_phi0
parameters:
- n: int: Common multiplicity for all bonds
- K: real: Common force constant for all bonds \([energy]\)
- phi0: real: Common phase shift for all bonds \([angle]\)
data:
- id_i: int: Id of the first particle
- id_j: int: Id of the second particle
- id_k: int: Id of the third particle
- id_l: int: Id of the fourth particle

Example:

"dihedralBondsCommon":{
  "type":["Bond4","DihedralCommon_n_K_phi0"],
  "parameters":{"n":3,
                "K":1.0,
                "phi0":0.0},
  "labels":["id_i", "id_j", "id_k", "id_l"],
  "data":[[0, 1, 2, 3],
          [1, 2, 3, 4]]
}

Dihedral4

A variant of the Dihedral potential that includes up to four terms in the cosine series.

\[U = \sum_{n=1}^4 K_n[1 + \cos(n\phi - \phi_{0,n})]\]

type: Bond4, Dihedral4
parameters: None
data:
- id_i: int: Id of the first particle
- id_j: int: Id of the second particle
- id_k: int: Id of the third particle
- id_l: int: Id of the fourth particle
- K: real4: Force constants for n=1,2,3,4 \([energy]\)
- phi0: real4: Phase shifts for n=1,2,3,4 \([angle]\)

Example:

"dihedral4Bonds":{
  "type":["Bond4","Dihedral4"],
  "parameters":{},
  "labels":["id_i", "id_j", "id_k", "id_l", "K", "phi0"],
  "data":[[0, 1, 2, 3, [1.0, 0.5, 0.25, 0.1], [0.0, 3.14, 1.57, 0.0]],
          [1, 2, 3, 4, [0.8, 0.4, 0.2, 0.05], [1.57, 0.0, 3.14, 1.57]]]
}