7.4. Cross: Bond-Angle¶
7.4.1. Functional Form¶
The Bond-Angle Cross Potential has the functional form:
\(E={{N}_{1,ijk}}\left( {{R}_{ij}}-{{R}_{1,ij}} \right)\left( {{\theta }_{ijk}}-{{\theta }_{0,ijk}} \right)+{{N}_{2,ijk}}\left( {{R}_{jk}}-{{R}_{2,jk}} \right)\left( {{\theta }_{ijk}}-{{\theta }_{0,ijk}} \right)\)
This term is part of the Class2 Angle Potential style.
The force-field parameters for this potential and units are given by:
| Equation Symbol | Parameter Definition | Units |
| \(N_{1,ijk}\) | Cross potential bond-angle coefficient for atoms [i,j,k] | energy/length/degrees |
| \(N_{2,ijk}\) | Cross potential bond-angle coefficient for atoms [i,j,k] | energy/length/degrees |
| \(R_{1,ij}\) | Equilibrium bond length for atoms [i,j] | length |
| \(R_{2,jk}\) | Equilibrium bond length for atoms [j,k] | length |
| \({\theta }_{0,ijk}\) | Equilibrium angle for atoms [i,j,k] | degrees |
7.4.2. XML Schema¶
The XML schema for the Bond-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 |
| Equilibrium angle for atoms [i,j,k] | \({\theta }_{0,ijk}\) | Theta0 |
| Cross potential bond-angle coefficient for atoms [i,j,k] | \(N_{1,ijk}\) | N1 |
| Cross potential bond-angle coefficient for atoms [i,j,k] | \(N_{2,ijk}\) | N2 |
| Equilibrium bond length for atoms [i,j] | \(R_{1,ij}\) | R1 |
| 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 | BondAngle |
| formula | Fixed | N1*(R-R1)*(Theta-Theta0)+N2*(R-R2)*(Theta-Theta0) |
| N-units | Required | Enumerations specified in schema |
| Ri-units | Required | Enumerations specified in schema |
| Theta0-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.