Fragmentation at sp² carbon atoms in fragment molecular orbital method

In the fragment molecular orbital (FMO) method, a given molecular system is usually fragmented at sp³ carbon atoms. However, fragmentation at different sites sometimes becomes necessary. Hence, we propose fragmentation at sp² carbon atoms in the FMO method. Projection operators are constructed using sp² local orbitals. To maintain practical accuracy, it is essential to consider the three-body effect. In order to suppress the corresponding increase of computational cost, we propose approximate models considering local trimers. Numerical verification shows that the present models are as accurate as or better than the standard FMO2 method in total energy with fragmentation at sp³ carbon atoms.