Fragment molecular orbital

The fragment molecular orbital method (FMO) was proposed by K. Kitaura and coworkers in 1999. FMO is deeply connected to the well known energy decomposition analysis (EDA) by Kitaura and Morokuma, proposed in 1976. The main use of FMO is compute very large molecular systems by dividing them into fragments and performing ab initio quantum-mechanical calculations of fragments and their dimers, whereby the Coulomb field from the whole system is included. The latter feature allows fragment calculations without unphysical caps and results in proper electron density treatment in the whole system. In addition to the calculation of the total properties, such as the energy, energy gradient, dipole moment etc, the pair interaction is obtained for each apir of fragments. This pair interaction energy can be further decomposed into electrostatic, exchange, charge transfer and dispersion contributions. This analysis is known as the pair interaction energy decomposition analysis (PIEDA) and it can be thought of as FMO-based EDA.

The rapid development of the FMO method made possible to use common wave functions for ab initio calculations of fragments and their dimers, such as Hartree-Fock, Density functional theory (DFT), Multi-configurational self-consistent field (MCSCF), configuration interaction (CI), second order Møller-Plesset perturbation theory (MP2), and coupled cluster (CC).

Since very large systems can be computed with high level ab initio wave functions, FMO is thought to be very useful for biological applications to compute the whole proteins and their complexes. In 2005, an application of FMO to the calculation of the ground electronic state of photosynthetic protein with more than 20,000 atoms was distinguished with the best technical paper award at Supercomputing 2005.

The FMO method is implemented in GAMESS(US) and ABINIT-MP.