# 4.2. Class2 Angle¶

## 4.2.1. Functional Form¶

The class 2 angle potential has the functional form:

$$E={{K}_{2,ijk}}{{\left( {{\theta }_{ijk}}-{{\theta }_{0,ijk}} \right)}^{2}}+{{K}_{3,ijk}}{{\left( {{\theta }_{ijk}}-{{\theta }_{0,ijk}} \right)}^{3}}+{{K}_{4,ijk}}{{\left( {{\theta }_{ijk}}-{{\theta }_{0,ijk}} \right)}^{4}}$$

The force-field parameters for this potential and units are given by:

 Equation Symbol Parameter Definition Units $$K_{2,ijk}$$ Angle coefficient for atoms [i,j,k] (quadratic term) energy/degrees^2 $$K_{3,ijk}$$ Angle coefficient for atoms [i,j,k] (cubic term) energy/degrees^3 $$K_{4,ijk}$$ Angle coefficient for atoms [i,j,k] (quartic term) energy/degrees^4 $$\theta_{0,ijk}$$ Equilibrium angle for atoms [i,j,k] degrees

## 4.2.2. XML Schema¶

The XML schema for the class 2 angle 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 Angle coefficient for atoms [i,j,k] (quadratic term) $$K_{2,ijk}$$ K2 Angle coefficient for atoms [i,j,k] (cubic term) $$K_{3,ijk}$$ K3 Angle coefficient for atoms [i,j,k] (quartic term) $$K_{4,ijk}$$ K4 Equilibrium angle for atoms [i,j,k] $$\theta_{0,ijk}$$ Theta0

The general attributes (describing the entire data set) are given by:

 General Attributes Cardinality Value/Definition style Fixed Class2 formula Fixed K2*(Theta-Theta0)^2+K3*(Theta-Theta0)^3+K4*(Theta-Theta0)^4 K-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 precedence Optional Precedence of parameter set (where specified) 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.