# 6.7. Umbrella Improper¶

## 6.7.1. Functional Form¶

The umbrella improper potential has the functional form:

E=\left\{ \begin{align} & \frac{1}{2}{{K}_{i,ijkl}}{{\left[ \frac{1+\cos \left( {{\omega }_{0,ijkl}} \right)}{\sin \left( {{\omega }_{0,ijkl}} \right)} \right]}^{2}}\left[ \cos \left( {{\omega }_{ijkl}} \right)-\cos \left( {{\omega }_{0,ijkl}} \right) \right],\text{ if }{{\omega }_{0,ijkl}}\ne 0 \\ & {{K}_{i,ijkl}}\left[ 1-\cos \left( {{\omega }_{ijkl}} \right) \right],\text{ if }{{\omega }_{0,ijkl}}=0 \\ \end{align} \right.

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

## 6.7.2. XML Schema¶

The XML schema for the umbrella improper 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 Improper coefficient for atoms [i,j,k,l] $$K_{i,ijkl}$$ Ki Equilibrium improper angle for atoms [i,j,k,l] $$\omega_{0,ijkl}$$ w0

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

 General Attributes Cardinality Value style Fixed Umbrella formula Fixed 0.5*K*[{1+cos(w0)}/sin(w0)]^2*[cos(w)-cos(w0)], w0 ≠ 0°; K*[1-cos(w)], w0 = 0° convention Optional Enumerations specified in schema Ki-units Required Enumerations specified in schema w0-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.