7.5. Cross: Middle-Bond-Torsion¶
7.5.1. Functional Form¶
The Middle-Bond-Torsion Cross Potential has the functional form:
\(E=\left( {{R}_{jk}}-{{R}_{2,jk}} \right)\left[ {{A}_{1,ijkl}}\cos \left( {{\phi }_{ijkl}} \right)+{{A}_{2,ijkl}}\cos \left( 2{{\phi }_{ijkl}} \right)+{{A}_{3,ijkl}}\cos \left( 3{{\phi }_{ijkl}} \right) \right]\)
This term is part of the Class2 Dihedral Potential style.
The force-field parameters for this potential and units are given by:
| Equation Symbol | Parameter Definition | Units |
| \(A_{1,ijkl}\) | Cosine term coefficient for atoms [i,j,k,l] | energy/length |
| \(A_{2,ijkl}\) | Cosine term coefficient for atoms [i,j,k,l] | energy/length |
| \(A_{3,ijkl}\) | Cosine term coefficient for atoms [i,j,k,l] | energy/length |
| \(R_{2,jk}\) | Equilibrium bond length for atoms [j,k] | length |
7.5.2. XML Schema¶
The XML schema for the Middle-Bond-Torsion Cross 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 |
| Cosine term coefficient for atoms [i,j,k,l] | \(A_{1,ijkl}\) | A1 |
| Cosine term coefficient for atoms [i,j,k,l] | \(A_{2,ijkl}\) | A2 |
| Cosine term coefficient for atoms [i,j,k,l] | \(A_{3,ijkl}\) | A3 |
| Equilibrium bond length for atoms [j,k] | \(R_{2,jk}\) | R2 |
The general attributes (describing the entire data set) are given by:
| General Attributes | Cardinality | Value/Definition |
| style | Fixed | MiddleBondTorsion |
| formula | Fixed | (R-R2)*[A1*cos(Phi)+A2*cos(2*Phi)+A3*cos(3*Phi)] |
| A-units | Required | Enumerations specified in schema |
| R-units | Required | Enumerations specified in schema |
The specific attributes (attached to each set of parameters) are given by:
| Specific Attributes | Cardinality | Value/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.