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.