Full electrostatic integration

To further reduce the cost of computing full electrostatics, NAMD uses a multiple timestepping integration scheme. In this scheme, the total force acting on each atom is broken into two pieces, a quickly varying local component and a slower long range component. The local force component is defined in terms of a splitting function. The local force component consists of all bonded and van der Waals interactions as well as that portion of electrostatic interactions for pairs that are separated by less than the local interaction distance determined by the splitting function. The long range component consists only of electrostatic interactions outside of the local interaction distance. Since the long range forces are slowly varying, they are not evaluated every timestep. Instead, they are evaluated every $k$ timesteps, and each set of $k$ timesteps is referred to as a $cycle$. The value of $k$ is specified by the NAMD parameter stepspercycle. An impulse of $k$ times the long range force is applied to the system every $k$ timesteps (i.e., the r-RESPA integrator is used). For appropriate values of $k$, it is believed that the error introduced by this infrequent evaluation is modest compared to the error already incurred by the use of the numerical (Verlet) integrator. Improved methods for incorporating these long range forces are currently being investigated, with the intention of improving accuracy as well as reducing the frequency of long range force evaluations.

In the scheme described above, the van der Waals forces are still truncated at the local interaction distance. Thus, the van der Waals cutoff distance forms a lower limit to the local interaction distance. While this is believed to be sufficient, there are investigations underway to remove this limitation and provide full van der Waals calculations in ${\mathcal O}(N)$ time as well.