Seamless Multilayer─A Novel Total Energy Partition Scheme for Embedded and Hybrid Calculations

In this paper, we provide general formulation of a multilayer approach, covering both additive and subtractive quantum mechanics/molecular mechanics (QM/MM) as special cases. After that, we suggest a novel definition of QM/MM total energy based on the consideration of a system divided into three layers. In a simplified form, it is $$, where layers 1, 2, and 3 represent inner QM, outer QM, and classical MM regions, respectively. The novel formulation is also not limited by only QM/MM combination of methods─in fact, any computational methods can be combined in a hybrid calculation. In this paper, we call the new approach seamless multilayer. Test calculations performed for silica and boric oxide show that the new approach requires no QM/MM interface parameterization as well as no or very simple correction terms for boundary atoms. This can greatly facilitate QM/MM studies of covalent inorganic solids. However, test calculations of α-Al₂O₃ show that for ionic compounds, the new method requires some additional development.