Number-adaptive multiscale

Takenaka N, Kitamura Y, Koyano Y, Nagaoka M (2012) The number-adaptive multiscale QM/MM molecular dynamics simulation application to liquid water. Chem Phys Lett 524 56-61... 

Under the circumstances, a number of theoretical methods have been already developed to improve the QM/MM-MD method, e.g., the modification of the semi-empirical QM Hamiltonians [7, 52-54], the optimization of the QM/MM empirical parameters [10] and the replacement of the empirical repulsion potential functions [55]. However, these methods need the numerical values of some reasonable reference quantities to optimize the parameters for some specific molecular systems. Moreover, it is usually hard to obtain the reference experimental or computational ones in solution. It is, therefore, reasonable and plausible as a second best strategy that the closer MM solvent molecules around the QM solute should be included into the QM region to avoid the serious problems in the boundary between QM and MM regions. This is because the most serious problem is originating in the quantum-mechanical behaviors. On the basis of such strategy, we have developed the number-adaptive multiscale (NAM) QM/MM-MD [56, 57] and the QM/MM-MD method combined with the fragment molecular orbital (FMO) one, i.e., FMO-QM/MM-MD method [20]. 

Adaptive domain decomposition algorithm for liquid flow For gas flow, a few adaptive domain decomposition algorithms have been developed for multiscale coupling based on the Knudsen number. For Uquid flow, the molecular domain was always supposed to cover the interfacial or contact area, but a quantitative criterion is stiU absent. Besides, the algorithms for moving or discontinuous molecular domains are still underdeveloped. 

Naturally, these examples are just a brief outline of the subject of representing assemblies with Formal Graphs, which are not limited in number of elementary units. The embedding principle saves a lot of room by allowing one to choose a degree of resolution (depth in the Formal Objects scale) adapted to the problem. The modularity of the tool is an advantage for modeling multiscale processes and complex systems. 

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