Molecular mechanics stretch-bend potential

Molecular mechanics calculations use an empirically devised set of equations for the potential energy of molecules. These include terms for vibrational bond stretching, bond angle bending, and other interactions between atoms in a molecule. All of these are summed up as follows ... 

Empirical force fields used in molecular mechanics/molecular dynamics calculations all share common components, among them components which describe bond-stretching, angle-bending and torsional motions, as well as components which account for non-bonded steric and electrostatic interactions. While much of the information needed to parameterize force fields can be obtained from experiment, quite frequently critical data are missing. Information about torsional potentials, in particular, is often very difRcult to obtain from experiment, and here calculations can prove of great value. 

In the original molecular mechanics work, a steric energy, E, for a molecule was defined as the sum of the potentials for bond stretch, angle bend, Ee, torsional strain, E, nonbonded interactions, Ey f, and other terms, such as Urey-Bradley terms, cross-interaction terms, and electrostatic terms, (8). 

A widely used model, which goes beyond the pair potential approximation, is that due to Keating (1966) which has been used mainly for the relaxation of random network models (Keating, 1966). It is in concept a molecular mechanics like potential as it consists of a bond stretching and bond bending term (Gaskell, 1991) ... 

Molecular mechanics calculations involve summation of the force fields for each type of strain. The original mathematical expressions for the force fields were derived from classical mechanical potential energy functions. The energy required to stretch a bond or to bend a bond angle increases as the square of the distortion ... 

Here V(r) is the potential energy for a collection of atoms with coordinates r, V, is the bond potential, V9 is the bond angle potential, Vt is the torsional potential, is the out-of-plane bending potential, is the nonbonded potential, and Vei is the Coulombic potential. Many treatments of molecular mechanics include additional terms besides those shown in Eq. [11]. For example, a term Vbe would represent an interaction term between a bond stretching term and the angle term. The reader is urged to consult one of the references to molecular mechanics to see more complete treatments. A schematic of the... 

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