7.3. Cross: Angle-Angle¶
7.3.1. Functional Form¶
The Angle-Angle Cross Potential has the functional form:
\(E={{M}_{1,ijkl}}\left( {{\theta }_{ijk}}-{{\theta }_{1,ijk}} \right)\left( {{\theta }_{kjl}}-{{\theta }_{1,kjl}} \right)+{{M}_{2,ijkl}}\left( {{\theta }_{ijk}}-{{\theta }_{1,ijk}} \right)\left( {{\theta }_{ijl}}-{{\theta }_{2,ijl}} \right)\) \(\qquad +{{M}_{3,ijkl}}\left( {{\theta }_{ijl}}-{{\theta }_{2,ijl}} \right)\left( {{\theta }_{kjl}}-{{\theta }_{1,kjl}} \right)\)
This term is part of the Class2 Improper Potential style.
The force-field parameters for this potential and units are given by:
| Equation Symbol | Parameter Definition | Units |
| \(M_{1,ijkl}\) | Cross potential angle coefficient for atoms [i,j,k,l] | energy |
| \(M_{2,ijkl}\) | Cross potential angle coefficient for atoms [i,j,k,l] | energy |
| \(M_{3,ijkl}\) | Cross potential angle coefficient for atoms [i,j,k,l] | energy |
| \({\theta }_{1,ijk}\) | Equilibrium angle for atoms [i,j,k] | degrees |
| \({\theta }_{2,ijl}\) | Equilibrium angle for atoms [i,j,l] | degrees |
| \({\theta }_{3,kjl}\) | Equilibrium angle for atoms [k,j,l] | degrees |
7.3.2. XML Schema¶
The XML schema for the Angle-Angle 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 |
| Cross potential angle coefficient for atoms [i,j,k,l] | \(M_{1,ijkl}\) | M1 |
| Cross potential angle coefficient for atoms [i,j,k,l] | \(M_{2,ijkl}\) | M2 |
| Cross potential angle coefficient for atoms [i,j,k,l] | \(M_{3,ijkl}\) | M3 |
| Equilibrium angle for atoms [i,j,k] | \({\theta }_{1,ijk}\) | Theta1 |
| Equilibrium angle for atoms [i,j,l] | \({\theta }_{2,ijl}\) | Theta2 |
| Equilibrium angle for atoms [k,j,l] | \({\theta }_{3,kjl}\) | Theta3 |
The general attributes (describing the entire data set) are given by:
| General Attributes | Cardinality | Value/Definition |
| style | Fixed | AngleAngle |
| formula | Fixed | M1*(Theta-Theta1)(Theta-Theta3)+M2*(Theta-Theta1)(Theta-Theta2)+M3*(Theta-Theta2)(Theta-Theta3) |
| M-units | Required | Enumerations specified in schema |
| Theta-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.