7.7. Cross: Angle-Torsion¶
7.7.1. Functional Form¶
The Angle-Torsion Cross Potential has the functional form:
\(E=\left( {{\theta }_{ijk}}-{{\theta }_{1,ijk}} \right)\left[ {{D}_{1,ijkl}}\cos \left( {{\phi }_{ijkl}} \right)+{{D}_{2,ijkl}}\cos \left( 2{{\phi }_{ijkl}} \right)+{{D}_{3,ijkl}}\cos \left( 3{{\phi }_{ijkl}} \right) \right]\) \(\qquad +\left( {{\theta }_{jkl}}-{{\theta }_{2,jkl}} \right)\left[ {{E}_{1,ijkl}}\cos \left( {{\phi }_{ijkl}} \right)+{{E}_{2,ijkl}}\cos \left( 2{{\phi }_{ijkl}} \right)+{{E}_{3,ijkl}}\cos \left( 3{{\phi }_{ijkl}} \right) \right]\)
This term is part of the Class2 Dihedral Potential style.
The force-field parameters for this potential and units are given by:
Equation Symbol | Parameter Definition | Units |
\(D_{1,ijkl}\) | Cosine term coefficient for atoms [i,j,k,l] | energy/degrees |
\(D_{2,ijkl}\) | Cosine term coefficient for atoms [i,j,k,l] | energy/degrees |
\(D_{3,ijkl}\) | Cosine term coefficient for atoms [i,j,k,l] | energy/degrees |
\(E_{1,ijkl}\) | Cosine term coefficient for atoms [i,j,k,l] | energy/degrees |
\(E_{2,ijkl}\) | Cosine term coefficient for atoms [i,j,k,l] | energy/degrees |
\(E_{3,ijkl}\) | Cosine term coefficient for atoms [i,j,k,l] | energy/degrees |
\({\theta}_{1,ijk}\) | Equilibrium bond length for atoms [i,j] | degrees |
\({\theta}_{2,jkl}\) | Equilibrium bond length for atoms [k,l] | degrees |
7.7.2. XML Schema¶
The XML schema for the Angle-Torsion 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 |
Atom type of atom [l] | \(l\) | AT-4 |
Cosine term coefficient for atoms [i,j,k,l] | \(D_{1,ijkl}\) | D1 |
Cosine term coefficient for atoms [i,j,k,l] | \(D_{2,ijkl}\) | D2 |
Cosine term coefficient for atoms [i,j,k,l] | \(D_{3,ijkl}\) | D3 |
Cosine term coefficient for atoms [i,j,k,l] | \(E_{1,ijkl}\) | E1 |
Cosine term coefficient for atoms [i,j,k,l] | \(E_{2,ijkl}\) | E2 |
Cosine term coefficient for atoms [i,j,k,l] | \(E_{3,ijkl}\) | E3 |
Equilibrium bond length for atoms [i,j] | \({\theta}_{1,ijk}\) | Theta1 |
Equilibrium bond length for atoms [k,l] | \({\theta}_{2,jkl}\) | Theta2 |
The general attributes (describing the entire data set) are given by:
General Attributes | Cardinality | Value/Definition |
style | Fixed | AngleTorsion |
formula | Fixed | (Theta-Theta1)*[D1*cos(Phi)+D2*cos(2*Phi)+D3*cos(3*Phi)]+(Theta-Theta2)*[E1*cos(Phi)+E2*cos(2*Phi)+E3*cos(3*Phi)] |
D-units | Required | Enumerations specified in schema |
E-units | Required | Enumerations specified in schema |
Theta-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.