CHARMM Force field

The CHARMM force field energy is given as:

$E=\sum _{bonds}{K}_b(b-b_0{)}^2+\sum _{UB}{K}_{UB}(S-S_0{)}^2+\sum _{angles}{K}_{\theta }(\theta -{\theta }_0{)}^2+$
$\sum _{dihedrals}{K}_{\chi }(1+\cos (n\chi -\delta ))+\sum _{impropers}{K}_{\varphi }(\varphi -{\varphi }_0{)}^2$
$+\sum _{nonbond}\{{ϵ}_{ij}[{\left({\displaystyle \frac{r_{ij}^{min}}{r_{ij}}}\right)}^{12}-2{\left({\displaystyle \frac{r_{ij}^{min}}{r_{ij}}}\right)}^6]+{\displaystyle \frac{q_i{q}_j}{4\pi {ϵ}_0ϵr_{ij}}}\}+\sum _{residues}{V}_{cmap}(\varphi ,\psi )$

where the bond stretch and bending terms are given harmonically, $K_b$ and $K_{\theta }$ are the bond force constant and bond angle constant respectively and are taken from the force field. The improper angle term is also given harmonically with $\omega$ being the improper angle and $K_{}\omega$ being the force constant of the improper.

The non-bonded terms are given via a Force Field Method and Force Field Method. The dihedral term is sinusoidal term in which n is the periodicity of the dihedral angle and δ is the phase shift. The Urey-Bradley (UB) term defines interactions between 1,3 pairs and is a quadratic function of the distance, $S$, between atoms one and three. It is only very rarely used within the CHARMM force field.

The CMAP term^{[1] [2]} is a backbone correction term for proteins based on ab initio quantum mechanical (QM) calculations. The CMAP term greatly improves structural and dynamical results obtained from crystalline or solution phase
simulations.