**2.3.3 Path Integral Molecular Dynamics (PIMD)**

The nuclei were handled by the classical mechanics in most of the FMO-MD simulations performed to date (Fig. 1), but PIMD (Marx & Parrinello, 1996) has been introduced into FMO-MD to incorporate the nucleic quantum effect (Fujita *et al.*, 2009). FMO-PIMD consumes tens of times more computational resource than the classical FMO-MD does but is necessary for a better description of, for example, a proton transfer reaction.
