Generalized Switch Functions in the Multilevel Many-Body Expansion Method and Its Application to Water Clusters

The many-body expansion (MBE) method is the basis of many fragment-based methods and is widely applied to the computation of large molecular systems. To reach linear-scaling computation, a cutoff must be used to discard those subsystems with long interfragment distances. However, this leads to a discontinuous potential energy surface (PES) that would cause various problems in geometry optimizations and molecular dynamics simulations. To solve this problem, we present a generalized-switch-function (GSF) approach to smooth the PES computed by the MBE method with the use of a cutoff distance. The GSFs are naturally normalized and are permutation invariant. This approach can be applied to adaptively computing any order of many-body correction energies with multilevel computational methods and is a dynamic subsystem approach. We have applied the two versions of our method, GSF-MBE(m)/L₁ and GSF-MBE(m)/(L₁:L₂:L₃), to water clusters. Thorough tests show that our method can indeed give smooth potential-energy surface and is linear scaling but without losing much accuracy for very large water clusters with appropriately chosen cutoff distances.