Fragment molecular orbital

The fragment molecular orbital method (FMO) is a computational method that can compute very large molecular systems with thousands of atoms using ab initio quantum-chemical wave functions.

The fragment molecular orbital method (FMO) was developed by K. Kitaura and coworkers in 1999. FMO is deeply interconnected with the energy decomposition analysis (EDA) by Kitaura and Morokuma, developed in 1976. The main use of FMO is to compute very large molecular systems by dividing them into fragments and performing ab initio or density functional 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 using caps.

The mutually consistent field (MCF) method had introduced the idea of self-consistent fragment calculations in their embedding potential, which was later used with some modifications in various methods including FMO. There had been other methods related to FMO including the incremental correlation method by H. Stoll (1992). Also FMO bears some similarity to the method by J. Gao (1997), the applicability of which for condensed phase systems was subsequently demonstrated by carrying out a statistical mechanical Monte Carlo simulation of liquid water in 1998; this method was later renamed as the explicit polarization (X-Pol) theory. The incremental method uses formally the same many-body expansion of properties as FMO, although the exact meaning of terms is different. The difference between X-Pol and FMO is in the approximation for estimating the pair interactions between fragments. X-Pol is closely related to the one-body expansion used in FMO (FMO1) in terms of the electrostatics, but other interactions are treated differently.

Later, other methods closely related to FMO were proposed including the kernel energy method of L. Huang and the electrostatically embedded many-body expansion by E. Dahlke, S. Hirata and later M. Kamiya suggested approaches also very closely related to FMO. Effective fragment molecular orbital (EFMO) method combines some features of the effective fragment potentials (EFP) and FMO. A detailed perspective on the fragment-based method development can be found in a recent review.

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 pair 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. Alternatively, configuration analysis for fragment interaction (CAFI) and fragment interaction analysis based on local MP2 (FILM) were suggested within the FMO framework.

In FMO, various wave functions can be used for ab initio calculations of fragments and their dimers, such as Hartree–Fock, Density functional theory (DFT), Multi-configurational self-consistent field (MCSCF), time-dependent DFT (TDDFT), configuration interaction (CI), second order Møller–Plesset perturbation theory (MP2), and coupled cluster (CC). The solvent effects can be treated with the Polarizable continuum model (PCM). The FMO code is very efficiently parallelized utilising the generalized distributed data interface (GDDI) and hundreds of CPUs can be used with nearly perfect scaling.

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