1.4.2. Classical Molecular Dynamics

1.4.2.1. Potential Energy

Energy of a system is composed of bonded and nonbonded interactions:

$$ E {total} = E{bonded} + E_{nonbonded} $$

The bonded interactions ($E_{bonded}$) are:

$$ E_{bonded} = E_{bonds} + E_{angles} + E_{torsion} $$

Nonbonded interactions ($E_{nonbonded}$) are:

$$ E_{nonbonded} = E_{vdw} + E_{elec.} $$

How these functions are written will depend on the simulation package (i.e. Amber, NAMD, OpenMM, Gromacs, etc.).

Amber uses the following definitions:

$E_{bonds} = \sum_{bonds} k_b (r - r_{eq})^2$ $E_{angles} = \sum_{angles} k_{a} (\theta - \theta_{eq})^2$ $E_{torsion} = \sum_{torsion} \frac{V_n}{2} (1 + cos(n\phi - \delta) $ $E_{vdw} = \sum_{nonbonded_{ij}} \frac{A_{ij}}{r_{ij}^12} - \frac{B_{ij}}{r_{ij}^6} $ $E_{elec} = \sum_{nonbonded_{ij}} \frac{q_i q_j}{r_{ij}}$

1.4.2.2. Force Fields