Improper dihedral-angle interaction

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. 

Fig. 2.2. The structural elements of vibrational force fields on the left, stretch SR, bend 0, and torsion r. Additional terms include non-bonded interactions, /Jnb. and supplementary positional restraints bke improper dihedrals (right), which do not have a physical interpretation. In the example given, the improper dihedral is the dihedral angle between planes acd and bed and serves the purpose of forcing planarity of the entire fragment...

The term representing the harmonic, so-called improper (out-of-plane, out-of-tetrahedral configuration) dihedral-angle bending interaction reads... 

In the above equation, r, 0, and u are the bond lengths, valence angles and improper torsion angles with force constants kg k and reference values To, 9q o o, respectively. dihedral angles of periodicity n with force constants k and phase angles 6, The nonbonded terms consist of a 12-6 Lennard-Jones potential for van der Waals interactions and a Coulombic term representing electrostatic interactions between atomic partial point charges g, and qj. and are the nonbonded distance and the Lennard-Jones well depth, aij = where rmin is the distance between atoms i... 

In the vast majority of MD applications a further simplification is made by using effective pair-wise additive potentials for atomic interactions. In simulations which contain flexible molecules, it is common practice to add terms which represent chemical bonds, bond angles, improper torsions and dihedrals. Interactions between atoms of molecules are represented by effective pair-wise additive potentials. This empirical approach splits the total potential energy of the system into a bonded (inter-molecule) and non-bonded (intra-molecular) part. 

Interaction contributions to a typical force held. Bond stretch vibrations are described by a harmonic potential 1/ , the minimum of which is at the equilibrium distance bo between the two atoms connected by chemical bond / (the indices i,j etc. are not shown in the Figure). Bond angles and out-of-plane (Improper) angles are also described by harmonic potential terms, and V, where 00 and (q denote the respective equilibrium angles. Dihedral twists (torsional angles) are subjected to a periodic potential 1/° the respective force constants are denoted by ft s with appropriate indices. Non-bonded forces are described by Coulomb interactions, 1/ -, and Lennard-Jones potentials, + /Vdw where the latter includes the Pauli repulsion, V and the van der... 

---