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