Improper dihedrals

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. 

Some authors refer to improper dihedrals when discussing dihedral torsion where we would not normally expect full rotation, for example, any of the C-C-C-C linkages in the benzene ring of aspirin. Many MM force fields treat... 

More complicated cross-terms between the different intramolecular degrees of freedom are also employed in some force fields, but we will not consider them in the following. The dihedral term may also include four-center improper torsion or out-of-plane bending interactions that occur at sp2 hybridized centers.29... 

Example 12.6-2 The classes of Td are E 4C3 3C2 6S4 6binary rotations are BB rotations. The six dihedral planes occur in three pairs of perpendicular improper BB rotations so both 3C2 and 6rrd are irregular classes. There are therefore Nv 5 vector representations and Ns = 3 spinor representations. 

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