**2.2.8 Miscellaneous**

Analytic gradient formulae have been derived for several FMO methods and implemented in the GAMESS software, including those for the adaptive frozen orbital bond detachment scheme (AFO; Fedorov *et al*., 2009), polarizable continuum model method (PCM; Li *et al.*, 2010), time-dependent density functional theory (TD-DFT; Chiba *et al.*, 2009), MFMO with active, polarisable, and frozen sites (Fedorov *et al.*, 2011), and effective fragment potential (EFP; Nagata *et al.*, 2011c). Also, Ishikawa *et al.* (2010) implemented partial energy gradient (PEG) in their software PACIS. These gradients have been used for FMO-EM calculations of appropriate molecules. Among them, the EFP gradient has already been applied successfully to FMO-MD (Nagata *et al.*, 2011c), and the others will be combined with FMO-MD in the near future.
