An efficient linked list for molecular simulations on a spherical surface

The main part of the cpu time in molecular simulations is usually spent calculating the non-bonded interactions. To improve the efficiency, a neighbour list or a cell linked list is normally used, where the linked list is usually more efficient and requires less memory for a large number of particles or dense systems. The linked list, however, still suffers from including many pairs which will not be within the interaction distance, and this overhead becomes even more significant for higher dimensions. In this work, we consider specifically simulations of particles confined to move on a spherical surface, where the overhead using a cubic grid to form a linked list becomes even larger by also including many cells which do not intersect the sphere. We address this by setting up a linked list directly on the spherical surface, thus reducing the dimensionality of the resulting neighbour search. We show that one obtains not only a substantial reduction in cpu time, but also a significant decrease in memory requirement. We further show how to extend this procedure to the 3-sphere (hypersphere), which can be used to simulate bulk systems avoiding periodic boundaries. Also in this case, using a linked list directly on the 3-sphere, the reduction in cpu time is significant, and the decrease in memory requirement, compared with a regular grid in R-4, is even more pronounced. We finally comment on how the efficiency of the described method can be further improved