Chapter 1 - Theoretical development of the fragment molecular orbital (FMO) method

Abstract

The studies of real biomolecules were limited to molecular mechanics and the size was too large for quantum mechanical systems, leading to problems describing certain phenomena. To overcome this, fragment molecular orbit (FMO) method is described in detail. The relative accuracy of the FMO total energies have been scrupulously established by comparison with ab initio methods. The chapter discusses in detail fragmentation in FMO, Mathematical formulation, computational scheme, and property calculation. It uses an example of the FMO interaction analysis, ethanol and water. The FMO method is systematically improvable. Its properties are in close agreement with ab initio values, the computational efficiency is so high as to permit 20000-atom calculations with nearly linear scaling, and the interaction analysis information quantitatively substantiates and fosters chemical insight in practical applications. Much theoretical development has to be done to further enhance the usefulness of the method, such as working out fully analytic gradients, providing the means for free energy calculations and including the solvent. The FMO method can turn out to be of great use to real-life chemical problems.