Mathematical Modeling and Analysis
We present an efficient algorithm, which uses a random jumping Walk in the sample of coarse-grained (CG) conformational spaces, to bridge CG models of different levels. The method iteratively estimates the free energies by improving previously available techniques. The effective potential of the CG model is fitted from the free energies of these high-dimensional CG conformations. The method can be used to construct CG models, as well as to evaluate and correct any exsiting CG models. We test the method in a Tetrahedral Molecular fluid to construct the intermolecular effective potential and to evaluate the exiting CG molecular model. This method not only works faster than the Wang-Landau and the metadynamics methods for calculating the desity of state or free energy, but also can work in high-dimensional spaces where the existing methods fail.