Multiple Time Steps Algorithms For Large Size Flexible Systems with Strong Electrostatic Interactions

In the previous sections we have described how to obtain multiple time step integrators given a certain potential subdivision and have provided simple examples of potential subdivision based on the inter/intra molecular separation. Here, we focus on the time scale separation of model potentials of complex molecular systems. Additionally, we provide a general potential subdivision applying to biological systems, as well as to many other interesting chemical systems including liquid crystals. This type of systems are typically characterized by high flexibility and strong Coulomb intermolecular interactions. Schematically, we can then write the potential $V$ as due to two contributions:

$$V = V_{\rm bnd} + V_{\rm nbn}.$$ (4.1)

Here, the ``bonded'' or intramolecular part $V_{\rm bnd}$ is fast and is responsible for the flexibility of the system. The ``non bonded'' or intermolecular (or intergroup) term $V_{\rm nbn}$ is dominated by Coulomb interactions. The aim of the following sections is to describe a general protocol for the subdivision of such forms of the interaction potential and to show how to obtain reasonably efficient and transferable multiple time step integrators valid for any complex molecular system.