Improper dihedral angle

The OPLS atom types are a superset of the AMBER united atom types and the bonding parameters are just those of AMBER, supplemented where needed by the OPLS developers. The bond stretch, angle bending, dihedral angle and improper dihedral angle terms are identical to those of AMBER. Unlike AMBER, different combination rules are used for the van der Waals parameters, no hydrogen bonding term is used and no lone pairs are used. 

HyperChem uses the improper dihedral angle formed by central atom - neighbor 1 - neighbor 2 - neighbor 3, where the order of neighbors is how they appear in a HIN file. Not all planar atoms customarily have associated improper torsions. The order of atoms is arbitrary but has been consistently chosen by the original authors of the CHARMM force field. The templates contain equivalent CHARMM definitions of improper torsions for amino acids. Improper dihedral angles cannot be defined that do not have a central atom, as is sometimes done in CHARMM calculations. 

Equation (9) is a collection of simple functions, which represent a minimal set of forces that can describe molecular structures. Bonds, angles, and out-of-plane distortions (improper dihedral angles) are treated harmonically and dihedral or... 

Improper dihedral angle, in degrees. See text for definition... 

Fig. 2 Schematic representation of the intramolecular coordinates bond length r, bending angle 6, torsional dihedral angle tp, and improper dihedral angle ij/...

The quantities b, S, 0, < ), m are the bond length, Urey-Bradley distance, bond angle, dihedral angle, and improper dihedral angle, respectively, with the zero subscript representing equiUbrium values. The parameters have been determined empirically and are given in Ref. [166]. 

Non-bonded atom types are not u.sed for the definition of bond, bond-angle and (improper) dihedral-angle types. This offers the advantage of introducing new non-bonded atom types without the need to adapt the tables of bonded interaction parameters. 

The actual improper dihedral angle value of the improper dihedral n defined by atoms i, j k, and / (i-j-k-l) is denoted by... 

---