Hierarchical Multiscale Modelling Scheme from First Principles to Mesoscale

We present a straight-forward implementation of a practical hierarchical multiscale modelling scheme which enables us to start from first-principles atomistic computer simulation and suc- cessively coarse-grain the model by leaving out uninteresting degrees of freedom. Using the Car-Parrinello method or our recently developed highly efficient tight-binding-like approximate density-functional quantum mechanical method,we first perform ab initio simulations. From these first-principles simulations we obtain a set of atomistic pair-wise effective interaction potentials to be used as a force field with no empirical data for subsequent classical all-atom simulations while scaling up the system size 2-3 orders of magnitude. The atomistic simulations similarly provide a new set of effective potentials but at a chosen coarse-grain level suitable for large-scale mesoscopic or soft-matter simulations beyond the atomic resolution. Show several examples are shown of how this scheme is done based on effective interaction potentials to tie together the various scales of modelling.