Mathematical Formulation of the Fragment Molecular Orbital Method

The fragment molecular orbital (FMO) method is a computational scheme applied to the conventional molecular orbital theories, which reduces their scaling from N 3… N 7 to a nearly linear scaling, where N is the system size. FMO provides an accurate treatment of large molecules such as proteins and molecular clusters, and it can be efficiently parallelized to achieve high scaling on massively parallel computers. The main purpose of this chapter is to focus on the derivation of the equations and to provide a concise mathematical description of FMO. A brief summary of the recent applications of FMO is also given.

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