Switching functions

NAMD allows the cutting off of the electrostatic and van der Waals forces to be handled in two ways. The default way is to simply truncate the forces at the cutoff value specified in the configuration file using the parameter cutoff. In this case, if the distance r between two atoms is less than the cutoff, then the forces are calculated as specified above. If r is greater than the cutoff, then the forces and energies are simply set to 0. But this method leads to a discontinuity in the force field. As atoms move within the cutoff distance, there electrostatic and van der Waals energies suddenly jump from 0 to some finite value.

The other means of dealing with these cutoffs provided by NAMD is switching functions. These functions smoothly bring the forces and energies to 0 at the cutoff distance to avoid any discontinuities in the force field. These switching functions are equivalent to those used in X-PLOR when the VSWitch and SHIft options are specified. They are activated using the switching parameter in the configuration file.

There are different switching functions used for electrostatics and van der Waals. For electrostatics, the energy function is modified to be

$$E_{\text{elec}} = {\epsilon}_{14} \frac{C q_i q_j}{{\epsilon... ...ec{r}_{ij}}\vert} S_{\text{elec}}(\vert{{\vec{r}}_{ij}}\vert)$$

with the switching function defined by

$$S_{\text{elec}}(\vert{{\vec{r}}_{ij}}\vert) = \begin{cases} ... ... $R_{\text{off}} \leq \vert{{\vec{r}}_{ij}}\vert$.} \end{cases}$$

For van der Waals interactions, the energy function is modified to be

$$E_{\text{vdw}} =\left( \frac{A}{{\vert{{\vec{r}}_{ij}}\vert}^... ...}\vert}^6}\right) S_{\text{vdw}}(\vert{{\vec{r}}_{ij}}\vert)$$

with the switching function defined by

$$S_{\text{vdw}}(\vert{{\vec{r}}_{ij}}\vert) = \begin{cases} 1 ... ... $R_{\text{off}} \leq \vert{{\vec{r}}_{ij}}\vert$.} \end{cases}$$

where

• $R_{\text{on}}$ is specified by the configuration value switchdist
• $R_{\text{off}}$ is specified by the configuration value cutoff