5.8. Multi-Harmonic Dihedral¶
5.8.1. Functional Form¶
The Multi-Harmonic dihedral potential has the functional form:
\(E={{A}_{1,ijkl}}+{{A}_{2,ijkl}}\cos \left( {{\phi }_{ijkl}} \right) +{{A}_{3,ijkl}}{\cos}^{2}\left( {{\phi }_{ijkl}} \right) +{{A}_{4,ijkl}}{\cos}^{3}\left( {{\phi }_{ijkl}} \right) +{{A}_{5,ijkl}}{\cos}^{4}\left( {{\phi }_{ijkl}} \right)\)
The force-field parameters for this potential and units are given by:
Equation Symbol | Parameter Definition | Units |
\(A_{1,ijkl}\) | Dihedral coefficient for atoms [i,j,k,l] | energy |
\(A_{2,ijkl}\) | Dihedral coefficient for atoms [i,j,k,l] | energy |
\(A_{3,ijkl}\) | Dihedral coefficient for atoms [i,j,k,l] | energy |
\(A_{4,ijkl}\) | Dihedral coefficient for atoms [i,j,k,l] | energy |
\(A_{5,ijkl}\) | Dihedral coefficient for atoms [i,j,k,l] | energy |
5.8.2. XML Schema¶
The XML schema for the Fourier dihedral potential has the following representation (design mode representation using Liquid XML Studio):
The relationship between the equation symbols and XML schema notations are given by:
Parameter Definition | Equation Symbol | Schema Notation |
Atom type of atom [i] | \(i\) | AT-1 |
Atom type of atom [j] | \(j\) | AT-2 |
Atom type of atom [k] | \(k\) | AT-3 |
Atom type of atom [l] | \(l\) | AT-4 |
Dihedral coefficient for atoms [i,j,k,l] | \(A_{1,ijkl}\) | A1 |
Dihedral coefficient for atoms [i,j,k,l] | \(A_{2,ijkl}\) | A2 |
Dihedral coefficient for atoms [i,j,k,l] | \(A_{3,ijkl}\) | A3 |
Dihedral coefficient for atoms [i,j,k,l] | \(A_{4,ijkl}\) | A4 |
Dihedral coefficient for atoms [i,j,k,l] | \(A_{5,ijkl}\) | A5 |
The general attributes (describing the entire data set) are given by:
General Attributes | Cardinality | Value |
style | Fixed | Fourier |
formula | Fixed | Enumerations specified in schema |
convention | Optional | Enumerations specified in schema |
An-units | Required | Enumerations specified in schema |
The specific attributes (attached to each set of parameters) are given by:
Specific Attributes | Cardinality | Definition |
comment | Optional | Comment attached to parameter set |
version | Optional | Version number of parameter set |
reference | Optional | Reference attached to parameter set |
Note that an XML document will be rejected from being entered into the WebFF database if a required attribute is left unspecified.