7.6. Cross: End-Bond-Torsion¶
7.6.1. Functional Form¶
The End-Bond-Torsion Cross Potential has the functional form:
\(E=\left( {{R}_{jk}}-{{R}_{1,jk}} \right)\left[ {{B}_{1,ijkl}}\cos \left( {{\phi }_{ijkl}} \right)+{{B}_{2,ijkl}}\cos \left( 2{{\phi }_{ijkl}} \right)+{{B}_{3,ijkl}}\cos \left( 3{{\phi }_{ijkl}} \right) \right]\) \(\qquad +\left( {{R}_{kl}}-{{R}_{3,kl}} \right)\left[ {{C}_{1,ijkl}}\cos \left( {{\phi }_{ijkl}} \right)+{{C}_{2,ijkl}}\cos \left( 2{{\phi }_{ijkl}} \right)+{{C}_{3,ijkl}}\cos \left( 3{{\phi }_{ijkl}} \right) \right]\)
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 |
\(B_{1,ijkl}\) | Cosine term coefficient for atoms [i,j,k,l] | energy/length |
\(B_{2,ijkl}\) | Cosine term coefficient for atoms [i,j,k,l] | energy/length |
\(B_{3,ijkl}\) | Cosine term coefficient for atoms [i,j,k,l] | energy/length |
\(C_{1,ijkl}\) | Cosine term coefficient for atoms [i,j,k,l] | energy/length |
\(C_{2,ijkl}\) | Cosine term coefficient for atoms [i,j,k,l] | energy/length |
\(C_{3,ijkl}\) | Cosine term coefficient for atoms [i,j,k,l] | energy/length |
\(R_{1,jk}\) | Equilibrium bond length for atoms [i,j] | length |
\(R_{3,kl}\) | Equilibrium bond length for atoms [k,l] | length |
7.6.2. XML Schema¶
The XML schema for the End-Bond-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] | \(B_{1,ijkl}\) | B1 |
Cosine term coefficient for atoms [i,j,k,l] | \(B_{2,ijkl}\) | B2 |
Cosine term coefficient for atoms [i,j,k,l] | \(B_{3,ijkl}\) | B3 |
Cosine term coefficient for atoms [i,j,k,l] | \(C_{1,ijkl}\) | C1 |
Cosine term coefficient for atoms [i,j,k,l] | \(C_{2,ijkl}\) | C2 |
Cosine term coefficient for atoms [i,j,k,l] | \(C_{3,ijkl}\) | C3 |
Equilibrium bond length for atoms [i,j] | \(R_{1,ij}\) | R1 |
Equilibrium bond length for atoms [k,l] | \(R_{3,kl}\) | R3 |
The general attributes (describing the entire data set) are given by:
General Attributes | Cardinality | Value/Definition |
style | Fixed | EndBondTorsion |
formula | Fixed | (R-R1)*[B1*cos(Phi)+B2*cos(2*Phi)+B3*cos(3*Phi)]+(R-R3)*[C1*cos(Phi)+C2*cos(2*Phi)+C3*cos(3*Phi)] |
B-units | Required | Enumerations specified in schema |
C-units | Required | Enumerations specified in schema |
R-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.