6.5. Fourier Improper¶
6.5.1. Functional Form¶
The Fourier improper potential has the functional form:
\(E={{K}_{i,ijkl}}\left[ {{C}_{0,ijkl}}+{{C}_{1,ijkl}}\cos \left( {{\omega }_{ijkl}} \right)+{{C}_{2,ijkl}}\cos \left( 2{{\omega }_{ijkl}} \right) \right]\)
The force-field parameters for this potential and units are given by:
Equation Symbol | Parameter Definition | Units |
\(K_{i,ijkl}\) | Improper coefficient for atoms [i,j,k,l] | energy |
\(C_{0,ijkl}\) | Real coefficient for cosine term #0 [i,j,k,l] | N/A |
\(C_{1,ijkl}\) | Real coefficient for cosine term #1 [i,j,k,l] | N/A |
\(C_{2,ijkl}\) | Real coefficient for cosine term #2 [i,j,k,l] | N/A |
6.5.2. XML Schema¶
The XML schema for the Fourier 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 |
Real coefficient for cosine term #0 [i,j,k,l] | \(C_{0,ijkl}\) | C0 |
Real coefficient for cosine term #1 [i,j,k,l] | \(C_{1,ijkl}\) | C1 |
Real coefficient for cosine term #2 [i,j,k,l] | \(C_{2,ijkl}\) | C2 |
The general attributes (describing the entire data set) are given by:
General Attributes | Cardinality | Value |
style | Fixed | Fourier |
formula | Fixed | Ki*[C0+C1*cos(w)+C2*cos(2*w)] |
convention | Optional | Enumerations specified in schema |
Ki-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.